إنشاءات خرسانية by المهندس فؤاد النصيري

 ‫א‬‫א‬

‫א‬ ٢٥١

 

 ٢٥١

 ‫א‬

 ‫א‬

 

 

   W،،‫א‬‫א‬،‫א‬  

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬

 K ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬    ‫א‬        ،‫א‬ ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،

‫א‬         ‫א‬   ،‫א‬ ‫א‬‫א‬  

 ‫א‬ ‫א‬ ‫א‬‫א‬  ‫א‬ ‫א‬ ‫א‬   ‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬‫א‬‫א‬،‫א‬

 K‫א‬‫א‬،‫א‬

‫א‬‫א‬?‫א‬‫א‬??‫א‬?‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬     ،‫א‬ ‫א‬ ‫א‬‫א‬        K‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫؛‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 

 

 ٢٥١

 ‫א‬

 ‫א‬

 

  ‫א‬‫א‬ ،‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬  ‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬

   ‫א‬  (Working Stress Design Method)    ‫א‬ ‫א‬  

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  (Theory of Elasticity)‫א‬  K‫א‬‫א‬‫א‬

 W‫א‬‫א‬

‫א‬  (Ultimate Strength Design Method (U.S.D.M.)) ‫א‬ ‫א‬   ‫א‬    ‫א‬ K‫א‬ ‫א‬  ‫א‬   

KCP. 110Bs 8110‫א‬‫א‬‫א‬١٩٧٢EF‫א‬

‫א‬ ‫א‬ ‫א‬  ‫א‬  ‫א‬  ‫א‬ ‫א‬ ‫א‬   K‫א‬

   E‫א‬‫א‬ F ‫א‬ ‫א‬ ‫א‬‫א‬   ‫א‬  ‫א‬‫א‬K‫א‬‫א‬‫א‬

 WK‫א‬‫א‬‫א‬‫א‬‫א‬

 K١٠ZK ٢L١٠Z٢L

 KK١٠ZKKKZKK

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

 

 ٢٥١

 ‫א‬

 ‫א‬

 

 ‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬  ‫א‬  ‫א‬    K‫א‬‫א‬‫א‬

 ‫א‬ ‫א‬  ‫א‬  ‫א‬ ‫א‬   ‫א‬ 

‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 

 W‫א‬‫א‬‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬   ‫א‬ ‫א‬ 

،‫א‬،‫א‬ ‫א‬ ،‫א‬  ‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬

‫א‬

‫א‬ ‫ א‬‫א‬

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬ ‫א‬‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬‫א‬‫א‬ ‫א‬ ‫א‬  ‫א‬  K‫א‬    ‫א‬ ‫א‬‫א‬ ‫א‬

 K‫א‬  

 W‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢

  ‫א‬ ‫א‬ ‫א‬   ‫א‬ ‫א‬‫א‬  ‫א‬  E٣ K‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٤ K‫א‬‫א‬‫א‬‫א‬E٥

W‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬

E١

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

E٢

‫א‬    ‫א‬ ‫א‬   ‫א‬  

E٤

K‫א‬‫א‬‫א‬

E٣

K‫א‬

W‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬

-١-

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

‫א‬‫א‬‫א‬ Principals of Structural Design   ‫א‬    ‫א‬  ‫א‬ ‫א‬  

‫א‬  ‫א‬ ‫א‬،  ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬KKKKKKKK     K‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 (Economy)‫א‬‫א‬ J١

 (Safety)‫א‬‫א‬ J٢

 (Deflection) ‫א‬‫א‬ ‫א‬    (Serviceability)  ‫א‬   J٣  K‫א‬‫א‬(Cracks)‫א‬

 K‫א‬‫א‬‫א‬‫א‬ J٤

‫א‬ ‫א‬   ‫א‬  ‫א‬ ‫א‬   ‫א‬   

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬          ‫א‬  ‫א‬       W

‫א‬   ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬   W‫א‬ ‫א‬

 K‫א‬‫א‬‫א‬

   K‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬ ‫א‬   W‫א‬ ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  

 K‫א‬‫א‬‫א‬‫א‬‫א‬

 

-٢-

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬‫א‬‫א‬١{١

(Different  ‫א‬‫א‬‫ א‬‫א‬

‫א‬ WK‫א‬‫א‬‫א‬ ‫א‬ Structural Elements)  E١ J١F

 (Beams)‫א‬ (Solid Slab)‫א‬ ‫א‬‫א‬E١

‫א‬  ‫א‬    ‫א‬ ‫א‬  (Slab Spans) ‫א‬  

‫א‬   ‫א‬ ‫א‬ ‫א‬ F ‫א‬  ‫א‬    K (Columns) KE(Spread Footings)

‫א‬K(Joist-Slab) ‫א‬ ‫א‬‫א‬E٢

 (Beams)‫א‬‫א‬ ‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬     Spandrel beam Door lintel

joist slab

Beam 2nd floor

column

Supported slab

Column Joist

Beam Foundation wall Slab on grade

1st floor

Landing Stairs

Basement Wall footing Spreed footing

 

Column

 E١ J١F -٣-

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬‫א‬

 K(Joists)‫א‬‫א‬‫א‬W‫א‬

 ‫א‬‫א‬ (Flange)W‫א‬

 K‫א‬‫א‬(beams)‫א‬‫א‬‫א‬‫א‬T

  (Soil)‫א‬ ‫א‬‫א‬‫א‬

 K‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬ ‫א‬  K     ‫א‬  ‫א‬ ‫א‬  W‫א‬

 K‫א‬‫א‬‫א‬ J١

 K‫א‬‫א‬‫א‬ J٢  K‫א‬‫א‬‫א‬ J٣

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ J٤  K‫א‬

 

 ‫א‬٢{١

 W‫א‬‫א‬‫א‬

 

 W‫א‬‫ א‬١{٢{١

 W‫א‬‫א‬  ‫א‬-

‫א‬-

K‫א‬‫א‬‫א‬ W‫א‬‫ א‬٢{٢{١

 K‫א‬‫א‬‫א‬‫א‬‫א‬

 

-٤-

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬٣{١

،‫א‬‫א‬،‫א‬F ‫א‬ ‫א‬     ‫א‬ ‫א‬ ‫א‬ 

 W‫א‬‫א‬‫א‬‫א‬E‫א‬،‫א‬

‫א‬ ‫א‬ ‫א‬  W‫א‬‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬ ‫א‬  •  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬E‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬ •

 ‫א‬  ‫א‬ ‫א‬   W‫א‬   ‫א‬  ‫א‬ ‫א‬  •  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •  

 

 K‫א‬‫א‬‫א‬‫א‬٤{١  

 W‫א‬١{٤{١ ٢٨‫א‬   (fcu)‫א‬ 

‫א‬‫א‬ ‫א‬‫א‬‫א‬K‫א‬‫א‬  K

‫א‬ ٢٨K ٣٠‫א‬ ١٥‫א‬‫א‬‫א‬K ١٥×١٥  K٪١٠٠‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

E١ J١F‫א‬٢٨‫א‬‫א‬

١٥ ×١٥×١٥‫א‬E (f cu)‫א‬‫א‬F‫א‬  K‫א‬‫א‬‫א‬‫א‬K٢٨  

 E٢Lf cu‫א‬‫א‬F‫א‬WE١ J١F ٤٥٠ ٤٠٠ ٣٥٠ ٣٠٠ ٢٧٥ ٢٥٠ ٢٢٥ ٢٠٠ ١٧٥ ١٥٠ ١٠٠ ‫א‬  

-٥-

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬E‫א‬F‫א‬‫א‬٢{٤{١  

 ‫א‬E‫א‬‫א‬F‫א‬‫א‬E٢ J١F‫א‬

‫א‬٢٨‫א‬‫א‬‫א‬E‫א‬‫א‬FE‫א‬F  W‫א‬‫א‬‫א‬E٣‫א‬F

 

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬E KEf cu‫א‬‫א‬F‫א‬‫א‬E٪٥٠FE٪٣٣F‫א‬

 

‫א‬  K ‫א‬ ‫א‬   ٪٥٠ ‫א‬  ‫א‬  ‫א‬      E  K‫א‬‫א‬‫א‬‫א‬

F‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E  ٠{٠٠٢‫א‬E‫א‬

 

‫א‬ ‫א‬     ‫א‬ ‫א‬   ‫א‬‫א‬    ‫א‬  E

‫א‬‫א‬‫א‬‫א‬E‫א‬F

‫א‬ ‫א‬   ‫א‬ ‫א‬  ‫א‬  ‫א‬ ‫א‬   KE٣ J١F‫א‬E‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬

    ،   ‫א‬ ‫א‬ ‫א‬ ‫א‬    E

E‫א‬F‫א‬KEF‫א‬‫א‬‫א‬  K‫א‬‫א‬

-٦-

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

Stress 6 5 4 3 2 1 0.000

0.001

0.002

0.003

0.004 Strain

 ‫א‬‫א‬E٢ J١F‫א‬

Typical concrete stress-strain curve, with short-term loading.

 

 E٣ J١F  

-٧-

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬٣{٤{١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬  WK‫א‬

 K ٢L ٣٧٠٠ ‫א‬‫א‬ E .ø٤٥L٢٨٣٥L٢٤

 W‫א‬‫א‬،‫א‬،‫א‬،‫א‬‫א‬ E  .(ØFKKKKKKKKKKKKKKKKKKKKKKK٥٢L٣٦

.(ФFKKKKKKKKKKKKKKKKKKKKKKK٦٠L٤٠

‫א‬ K K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E E‫א‬ F ٥٢L ٤٥‫א‬  ٤٥L ٢٨ ٣٥L٢٤

E٣ J١F‫א‬K‫א‬‫א‬E٤ J١F‫א‬KEΦF  K‫א‬‫א‬‫א‬‫א‬‫א‬

   ‫א‬‫א‬E٤ J١F‫א‬

-٨-

 

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 ‫א‬‫א‬E٣ J١F Φ Weight mm Kg/m 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38

0.222 0.395 0.617 0.888 1.21 1.58 2.00 2.47 2.98 3.55 4.17 4.83 5.55 6.31 7.13 7.99 8.90

1 .283 .503 .785 1.13 1.54 2.01 2.54 3.14 3.80 4.52 5.31 6.16 7.07 8.04 9.08 10.2 11.3

2 .566 1.01 1.57 2.26 3.08 4.02 5.09 6.28 7.60 9.04 10.6 12.3 14.1 16.1 18.2 20.4 22.6

Area of Cross-Section 3 4 5 6 .848 1.13 1.41 1.70 1.51 2.01 2.51 3.02 2.36 3.14 3.93 4.71 3.39 4.52 5.65 6.79 4.62 6.16 7.70 9.24 6.03 8.04 10.1 12.1 7.63 10.2 12.7 15.3 9.42 12.6 15.7 19.8 11.4 15.2 19.0 22.8 13.6 18.1 22.5 27.1 15.9 21.2 25.5 31.9 18.5 24.6 30.8 37.5 21.2 28.3 35.3 42.4 24.1 32.2 40.2 48.3 27.2 36.3 45.4 54.5 30.6 40.9 50.7 61.2 33.9 45.2 56.5 67.8

in cm2 7 8 1.98 2.26 3.52 4.02 5.50 6.28 7.92 9.05 10.8 12.3 14.1 16.1 17.8 20.4 22.0 25.1 26.6 30.4 31.7 36.2 37.2 42.5 43.1 49.3 49.5 56.6 56.3 64.3 53.6 72.6 71.4 81.6 79.1 90.4

9 2.54 4.52 7.07 10.2 13.9 18.1 22.9 28.3 34.2 40.7 47.0 55.4 63.6 72.4 81.7 91.8 102

10 2.83 5.03 7.85 11.3 15.4 20.1 25.4 31.4 38.0 45.2 53.1 61.6 70.7 80.4 90.8 102 113

 

 W‫א‬‫א‬‫א‬‫א‬٤{٤{١

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬E

‫א‬     ‫א‬ ‫א‬  ‫א‬ ‫א‬   K ‫א‬   ‫א‬‫א‬‫א‬ –‫א‬‫א‬ –‫א‬

 K٪٠{٢‫א‬

 K‫א‬E

 K‫א‬‫א‬‫א‬E

‫א‬E٥F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 KE٤ J١F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

-٩-

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 EF‫א‬‫א‬‫א‬‫א‬‫א‬E٤ J١F  

‫א‬‫א‬    EF

‫א‬ ‫א‬

F٢L

٪٠{٢ ‫א‬

‫א‬

 ‫א‬



F٢L

 E

 ٢٠

 ٣٥

 ٢٤

 ١٨

 ٤٥

 ٢٨

 ١٢

 ٥٢

 ٣٦

 ١٠

 ٥٢

 ٤٠

 

 ١٠

 ٥٢

 ٤٥

 

٣٥L٢٤  ٤٥L٢٨

 ‫א‬ ‫א‬  

٥٢L٣٦

 

٦٠L٤٠

 ‫א‬

 

 

٥٢L٤٥

   ‫א‬

 

 W‫א‬‫א‬‫א‬٥{١  

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬   ‫א‬ ‫א‬  ‫א‬ ‫א‬     ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬  K‫א‬‫א‬

 

 W‫א‬١{٥{١

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬  

 W‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬E - ١٠ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 ‫א‬   ‫א‬   ‫א‬  ‫א‬  ‫א‬ ‫א‬ E  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ ‫א‬ ،‫א‬ ‫א‬‫א‬E

 K‫א‬

 ‫א‬ ،‫א‬‫א‬ E

K‫א‬‫א‬

 WE‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬٢{٥{١

   ‫א‬‫א‬    ‫א‬  ‫א‬‫א‬  ‫א‬  

E٥١F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

       ‫א‬     

 K

- ١١ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

   

 ‫א‬‫א‬‫א‬E٥ J١F ‫א‬‫א‬‫א‬‫א‬‫א‬  E٢LF٢٨‫א‬

 ٣٠٠  ٢٧٥  ٢٥٠  ٢٢٥  ٢٠٠  ١٧٥  ١٥٠  ٧٠

 ٦٥

 ٦٠

 ٥٥

 ٥٠

 ٤٥

 ٤٠

 ١٠٥  ١٠٠

 ٩٥

 ٩٠

 ٨٠

 ٧٠

 ٦٥

‫א‬

 ‫א‬‫א‬‫א‬

f cu f co** f c*

 ‫א‬‫א‬ (e=e min)‫א‬‫א‬ ‫א‬‫א‬  ‫א‬

 ٩

  ٨

 ٨

 ٧

F‫א‬‫א‬  E‫א‬

 ٧

 ٦

 ٥

 ١٥

‫א‬E

 ٢١

 ٢٠

 ١٩

 ١٨

 ١٧

 ١٥

q ct

‫א‬E

١٠  

 ٩

 ٨

 ٧

 

q ct

 ‫א‬  ‫א‬‫א‬  ‫א‬

١٤٠٠

 

 ٣٥L٢٤E١

١٦٠٠

 

 ٤٥L٢٨E٢

٢٠٠٠

 

 ٥٢L٣٦E٣  ٦٠L٤٠E٤

٢٢٠٠   ١٦٠٠ ٢٢٠٠

٢٢٠٠

 

 

 

‫א‬E٥

 

 E

 

 ‫א‬E

١٦٠٠ ٢٢٠٠

 ٥٢L٤٥

‫א‬‫א‬   ٢٠    ‫א‬ ‫א‬ ‫א‬‫א‬   ‫א‬‫א‬  G

‫א‬‫א‬ ٢L ٢٠، ١٥، ١٠، ٥‫א‬‫א‬‫א‬‫א‬‫א‬

 K٨،١٠،١٢،٢٠‫א‬

 K‫א‬‫א‬‫א‬GG

- ١٢ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬ ٣{٥{١

    ‫א‬ ‫א‬  ‫א‬‫א‬    ‫א‬ ‫א‬  

‫א‬ ‫א‬‫א‬  ١٩١٠KE ٥ J١F‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬KE J٥ J١F‫א‬‫א‬ ،

،E J٥ J١F‫א‬‫א‬،‫א‬‫א‬‫א‬ ‫א‬   ‫א‬ ‫א‬  ‫א‬ E ‫א‬ ‫א‬ ‫א‬ ‫א‬‫א‬F ‫א‬ 

 K‫א‬

‫א‬‫א‬ ‫א‬       E ٤ ،٣  F ‫א‬   ١٩٣٢   ‫א‬  ،        ‫א‬ ‫א‬ ‫א‬ 

   ‫א‬ ‫א‬  ‫א‬ E‫א‬ ‫א‬  F J E J٥ J١F‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ١٩٥٦

 K‫א‬‫א‬‫א‬‫א‬١٩٦٣،‫א‬  

‫א‬        ١٩٧١    ‫א‬ ‫א‬ ‫א‬ 

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬E J٥ J١F،E J٥ J١F‫א‬   ‫א‬ ‫א‬ ‫א‬ ‫א‬‫א‬ ‫א‬ ‫א‬  ‫א‬    K‫א‬‫א‬‫א‬‫א‬

- ١٣ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

0.85

 ‫א‬‫א‬‫א‬‫א‬‫א‬E٥ J١F‫א‬  ‫א‬‫א‬‫א‬

 E‫א‬‫א‬F E

E‫א‬‫א‬F‫א‬‫א‬E 

E‫א‬‫א‬F‫א‬‫א‬E

E‫א‬‫א‬F‫א‬‫א‬E KE‫א‬‫א‬FE

- ١٤ -

‫א‬ ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬ ‫ א‬‫א‬

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬  

  ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬   ‫א‬ ‫א‬ 

 K‫א‬‫א‬‫א‬‫א‬‫א‬  

 W‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E١

       ‫א‬ ‫א‬  ‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬

E٢

W‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬  K‫א‬‫א‬‫א‬

E١

E٢

E٣

E٤  

W‫א‬‫א‬‫א‬‫א‬  ‫א‬ • W‫א‬‫א‬  K‫א‬‫א‬

- ١٥ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

‫א‬‫א‬ ‫א‬‫א‬W،‫א‬‫א‬‫א‬ ‫א‬

 ،‫א‬،‫א‬‫א‬،‫א‬‫א‬،‫א‬‫א‬F‫א‬

‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬E‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬

K

K‫א‬‫א‬

K‫א‬‫א‬  EDead LoadsF‫א‬‫א‬١{٢

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬

‫א‬‫א‬ ‫א‬    ‫א‬ ‫א‬ ‫א‬  ‫א‬‫א‬ ‫א‬‫א‬ ‫א‬

 KKKKKKKKK  

 (Slab Dead load)‫א‬‫א‬١{١{٢

 ‫א‬‫א‬‫א‬‫א‬‫א‬  Z(Own Weight of slab - O.W of slab)‫א‬‫א‬

E

 K(γ c)‫א‬‫א‬×(t)‫א‬×(A)‫א‬

 (γ c =2.5 t/m3)٣L٢{٥Z‫א‬‫א‬‫א‬ i.e. O.W of slab = A × t × γ c

 K‫א‬١{٠(A)‫א‬  O.W of slab = 1.0 × t × 2.5

- ١٦ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١ J٢F‫א‬  K‫א‬‫א‬

 

 E١ J٢F  E٢LF‫א‬‫א‬

EF‫א‬

 ٢٠٠

 ٨

 ٢٥٠

 ١٠

 ٣٠٠

 ١٢

 ٣٥٠

 ١٤

 ٤٠٠

 ١٦

 ٤٥٠

 ١٨

 ٥٠٠

 ٢٠  

 W‫א‬W

 ‫א‬ ‫א‬K‫א‬‫א‬‫א‬  ‫א‬

٥ J٣HE‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬F  ٢L١٥٠Z‫א‬E١ J٢F

Tiles Mortar 3-5cm sand isolated sheets

R.C slab

(plaster)

 E١ J٢F ‫א‬ ٢L ٢٥٠ J٢٠٠‫א‬‫א‬‫א‬‫א‬

 K٥‫א‬‫א‬‫א‬‫א‬

- ١٧ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 ٢L٦٠Z‫א‬‫א‬‫א‬ •

 ٢L١٠٠Z‫א‬‫א‬‫א‬ •

٢L٦٠Z‫א‬‫א‬ •

 ٢L٢٠٠Z‫א‬‫א‬ •

 

 W‫א‬‫א‬‫א‬‫א‬٢{١{٢

 W‫א‬‫א‬‫א‬‫א‬

 (Own weight of Beam)‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

E

E 

‫א‬F(O.W of slab)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E KE١ J١ J٢‫א‬

W‫א‬‫א‬‫א‬‫א‬

E

K  ‫א‬   ‫א‬    ‫א‬‫א‬ ‫א‬‫א‬    W‫א‬‫א‬‫א‬‫א‬

 Thickness of beam (t) = span / 8-10

  For simple beams choose t = span / 8

 For continuous beams ,, t = span / 10

١٠ J٨L‫א‬ZtZ‫א‬ ‫א‬‫א‬

‫א‬‫א‬

 W٠{٦Z(t) ٠{٢Z(b) K٦{٠Z‫א‬

 W‫א‬x‫א‬xx (L0) Z‫א‬‫א‬‫א‬ O.W of beam = L0 x b x (t - ts) x γc 

Where;  γc = 2.5 t/ m3 , ts = ‫ = ﺳﻤﻚ اﻟﺒﻼﻃﺔ‬10 cm = 0.1 m L0 = length of beam = 1.0 m (١{٠‫א‬)

i.e. O.w. of beam = 1.0 x 0.2 x (0.6 – 0.1) x2.5 = 0.25 t/m  L٠{٢٥Z‫א‬‫א‬‫א‬  W‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ - ١٨ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

   

 γ wall = 0.75:1.0 t/m3  

‫א‬‫א‬‫א‬‫א‬E١

t/m3 ‫א‬‫א‬‫א‬‫א‬E٢

 γ wall = 1.20

 γ wall = 0.75:1.2 t/m3 ‫א‬‫א‬‫א‬E٣

 γ wall = 0.6 :0.8 t/m3 ‫א‬‫א‬‫א‬E٤ t/m3 E‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬E٥

γ wall = 1.8

 γ wall = 1.5:1.9 t/m3‫א‬‫א‬‫א‬‫א‬E٦

 

،K ٢٠‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬  K٢٥،١٢W،‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬،‫א‬‫א‬    W wall = γ wall × t wall

 W‫א‬

( t/m)

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ W

 K‫א‬‫א‬‫א‬‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

٢L١٢٥ J٧٥‫א‬‫א‬‫א‬‫א‬‫א‬  K٢L١٥٠ J١٠٠‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬  ٢L ٥٠٠‫א‬‫א‬‫א‬‫א‬‫א‬W  K‫א‬E‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬

 

 W(Live Loads)‫א‬‫א‬٢{٢

 W‫א‬‫א‬

‫א‬‫א‬‫א‬ ‫א‬E١  K‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬، ‫א‬    ‫א‬     K‫א‬  E‫א‬F   E٢  ‫א‬  ‫א‬     ، E  F ‫א‬  K‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٣ - ١٩ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬E٢ J٢F‫א‬‫א‬

 KKKKKK‫א‬‫א‬  

 ‫א‬‫א‬WE٢ J٢F  

‫א‬‫א‬

 ٢L

 ‫א‬

   ٥٠  ١٠٠  ٢٠٠  ٤٠٠  

 W‫א‬‫ א‬ ١

 EFE

 EFE  E

E

 W  ٢

 ٢٠٠

 ‫א‬‫א‬E

 ٣٠٠

E‫א‬F‫א‬‫א‬E

 

 W‫א‬‫א‬‫ א‬ ٣

 ٣٠٠

 ‫א‬E

 ٤٠٠

 E‫א‬F‫א‬‫א‬E

 ١٠٠٠ J٥٠٠

E‫א‬F‫א‬E

 

 W‫א‬‫ א‬ ٤

 ٣٠٠

 E‫א‬F‫א‬‫א‬E

 ٤٠٠

 ‫א‬‫א‬‫א‬E

 ٥٠٠

 ‫א‬‫א‬E

 

 W‫ א‬ ٥

 ٣٠٠  ٤٠٠  ٥٠٠ J٣٠٠



 E‫א‬F‫א‬‫א‬E  ‫א‬‫א‬‫א‬‫א‬‫א‬E

 ‫א‬‫א‬‫א‬E

 ٨٠٠ J٥٠٠

‫א‬E

 W‫א‬‫ א‬ ٦

   ٥٠٠

 ‫א‬‫א‬‫א‬‫א‬E - ٢٠ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 ٦٠٠    ٥٠٠  ١٠٠٠

 ‫א‬‫א‬E

 E‫א‬F‫א‬‫ א‬ ٧

 E‫א‬F‫א‬‫א‬E

‫א‬‫א‬E‫א‬‫א‬F‫א‬‫א‬E

K‫א‬‫א‬

 

 W‫ א‬ ٨

 ٢٠٠  ٤٠٠  

 ‫א‬E

 ‫א‬‫א‬‫א‬‫א‬‫א‬E

 W‫ א‬ ٩

 ٤٠٠

 ‫א‬E

 ١٠٠٠

 ‫א‬E

   ٣٠٠  ٤٠٠

 W‫א‬‫ א‬ ١٠

 ٢{٤‫א‬‫א‬F‫א‬‫א‬‫א‬E

 ‫א‬‫א‬‫א‬E  ‫א‬‫א‬E

 ٥٠٠

 W‫א‬‫א‬‫א‬٣{٢  

 W‫א‬‫א‬ ‫א‬١{٣{٢

‫א‬  ‫א‬ ‫א‬    ‫א‬ ‫א‬  ‫א‬   ‫א‬K ٪٥ ‫א‬

KEKK‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬

(Working Stress Design K‫א‬ ‫א‬  ‫א‬    ‫א‬  ‫א‬

 W‫א‬Method)

 ,,D,,(Dead Load)‫א‬‫א‬ ,,L,,(live loads)‫א‬‫א‬ D + LZ‫א‬‫א‬

- ٢١ -

E

E 

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 (Ultimate loads)‫א‬‫א‬٢{٣{٢

 J٣ J٢F‫א‬‫א‬F‫א‬‫א‬ ‫א‬ ‫א‬

 W‫א‬EE١

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

WE ASCI‫א‬F‫א‬

U = 1.4 D + 1.7 L

(2-1)

E١  

 Dead Loads ‫א‬‫א‬‫א‬ZD

 Live loads‫א‬‫א‬ZL

‫א‬‫א‬‫א‬٠{٧٥‫א‬‫א‬‫א‬E٢  W‫א‬‫א‬

U = 1.5 (D +L)

(2-2)

 

‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬E٣  W‫א‬‫א‬‫א‬‫א‬

U = 1.4 D + 1.7 (E + L)

(2-3)

   

 (Lateral Load)‫א‬‫א‬ZE

 (2-1)‫א‬‫א‬U

   

- ٢٢ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 W٤{٢

 

 ‫א‬ B2  B1‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬W ١ 

Z‫א‬K‫א‬‫א‬E٢ J٢F K٥H‫א‬K١٠  

W‫א‬

Own weight of slab = Ws =1×1× t ×γ c = t × γ c 

 ‫א‬‫א‬E

= 0.1× 2.5 = 0.25 t/m2 = 2.5 kN / m2 Flooring (‫א‬) = 0.15 t / m2 = 1.5 kN / m2 Live Loads (L.L.) (‫א‬‫ = )א‬0.20 t/m2 = 2.0 kN / m2 Total Loads (wt) (‫ = )اﻟﺤﻤﻞ اﻟﻜﻠﻲ‬0.25+ 0.15+ 0.20 = 0.60 t/m2 = 6.0 kN/m2

W = 6.0 x (3.5/2) = 10.5 kN/m

   

B1‫א‬‫א‬E B2‫א‬‫א‬E

W = 6.0 x 3.5 = 21 kN/m

 

- ٢٣ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

‫ﺑﻼﻃﺔ‬

L=8,0 m

B2 ‫آﻤﺮة‬

B1 ‫آﻤﺮة‬

 

L=3,5 m

 E٢{٢F

 

  ‫א‬ B2  B1 ‫א‬  S1 ‫א‬ ‫א‬  ‫א‬ ‫א‬  ‫א‬ W ٢  ١٢Z‫א‬ K ‫א‬ ‫א‬  ‫א‬ E٣ J٢F

 K‫א‬‫א‬K

W‫א‬

Own weight of slab = Ws =1×1× t ×γ c = t × γ c 

 ‫א‬‫א‬E

= 0.12× 2.5 = 0.30 t/m2 = 3.0 kN / m2 Flooring (‫א‬) = 0.20 t / m2 = 2.0 kN / m2 Live Loads (L.L.) (‫א‬‫ = )א‬0.30 t/m2 = 3.0 kN / m2 Total Loads (wt) (‫ = )اﻟﺤﻤﻞ اﻟﻜﻠﻲ‬0.30+ 0.20+ 0.30 = 0.80 t/m2 = 8.0 kN/m2

W = 8.0 x (4.0/2) = 16.0 kN/m - ٢٤ -

B1‫א‬‫א‬E

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 

B2‫א‬‫א‬E

W = 8.0 x(4+3)/2 = 28 kN/m     1

4.5 m

3.0 m

S1 4.0 m

 

B1 9m

 E٣{٢F

- ٢٥ -

‫א‬ ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬ ‫א‬‫א‬

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬ ‫א‬  ‫א‬ ‫א‬‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬  

K‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬،‫א‬   ‫א‬ ‫א‬  ‫א‬ ‫א‬   ‫א‬     ‫א‬

 K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 

 W‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬ E١

‫א‬   ‫א‬   ‫א‬     ‫א‬   E٢  K‫א‬‫א‬‫א‬‫א‬

‫א‬   ‫א‬  ‫א‬  ‫א‬ ‫א‬  ‫א‬   E٣

‫א‬‫א‬  

W‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬E١

K‫א‬‫א‬‫א‬E٢

K‫א‬‫א‬‫א‬E٣

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٤  W‫א‬‫א‬‫א‬‫א‬  •   W‫א‬‫א‬  K‫א‬‫א‬ - ٢٦ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

‫א‬‫א‬‫א‬‫א‬  Structural Analysisfor Slabs and Beams

 

 W‫א‬‫א‬W١ J٣  W‫א‬‫א‬‫א‬‫א‬‫א‬  

 ‫א‬‫א‬: ‫א‬‫א‬ J١

‫א‬ ‫א‬  (Beams) ‫א‬‫א‬  (slabs) ‫א‬    

 W‫א‬‫א‬K(Footings)‫א‬(Columns)  

Slabs‫א‬

 Beams‫א‬‫ א‬

 Girders‫א‬‫ א‬ Columns‫ א‬

 Footings‫ א‬

 

 K‫א‬‫א‬‫א‬‫א‬E١ J٣F‫א‬

Over hanging beam

Simple slab or beam

continous slab or beam

(Column)

Simple frame

(Column)

 ‫א‬‫א‬‫א‬E١ J٣F - ٢٧ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 ‫א‬‫א‬W‫א‬‫א‬ J٢

‫א‬‫א‬ ‫א‬‫א‬     ‫א‬ ‫א‬، ‫א‬ ‫א‬‫א‬WK‫א‬‫א‬‫א‬

 KK‫א‬‫א‬‫א‬‫א‬

T،،،W‫א‬

 K‫א‬‫א‬‫א‬E٢ J٣F‫א‬KUL،

U - section

L - section

T circular sec

T - section square sec

Rectangular sec

 K‫א‬‫א‬‫א‬E٢ J٣F  

 W‫א‬‫א‬‫א‬‫א‬W٢ J٣ ‫א‬ Statically System ‫א‬ ‫א‬ ‫א‬      ‫א‬    ‫א‬ ‫א‬     K‫א‬    ‫א‬ ‫א‬ 

 K‫א‬‫א‬‫א‬

 

E‫א‬‫א‬F‫א‬‫א‬  W W١ J٢ J٣ E٣ J٣F (Knife Edge Support) ‫א‬       ‫א‬       ‫א‬ ‫א‬  

 K 

- ٢٨ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

Knife edge support

 

 E٣ J٣F

 W‫א‬‫א‬W٢ J٢ J٣

‫א‬‫א‬ ‫א‬‫א‬ (Linear Elastic Theory)‫א‬‫א‬  ‫א‬  ‫א‬ ‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬ K‫א‬‫א‬ ‫א‬ 

 W

 Three Moment Equation‫א‬‫א‬E

 Virtual Work Method‫א‬‫א‬‫א‬E  Moment Distribution‫א‬E

 ‫א‬  ‫א‬      E‫א‬  ‫א‬F ‫א‬ ‫א‬  ‫א‬‫א‬٠{٤،‫א‬‫א‬٠{٨(lo)‫א‬‫א‬(d)‫א‬ i.e

d / l0 < 0.8 for simple beams. d / l0 < 0.4 for continues beams.  (Deep Beam)‫א‬‫א‬ ‫א‬‫א‬‫א‬



 K‫א‬‫א‬‫א‬(Plastic Analysis)‫א‬

 

 W(Effective Span l0)‫א‬‫א‬‫א‬‫א‬W٣ J٣  W‫א‬‫א‬‫א‬E

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  l01‫א‬‫א‬‫א‬

 l02 = l0 × 1.05 ‫א‬‫א‬١{٠٥ - ٢٩ -

• •

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

  l03 = l0 + d

•

 E٤ J٣F‫א‬‫א‬‫א‬‫א‬Zd

 

L L

L 2 = 1.05 L

C L

 

C L

 ‫א‬‫א‬‫א‬E٤ J٣F 

 

W‫א‬‫א‬‫א‬E

‫א‬F‫א‬E‫א‬F‫א‬‫א‬‫א‬‫א‬E١  W‫א‬‫א‬‫א‬‫א‬‫א‬E(Rigid Connections)

  l01 = Centerline to Centerline of Supports‫א‬‫• א‬  l02 = 1.05 × l0‫א‬‫א‬١{٠٥ •

‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬E٢

‫א‬‫א‬‫א‬‫א‬‫א‬ KE‫א‬‫א‬–  K‫א‬‫א‬‫א‬‫א‬

 

L03 = Distance from Centerline to Centerline L03 =l0 +d

 W‫א‬‫א‬‫א‬E

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  (l01)‫א‬‫א‬ - ٣٠ -

•

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬

•

L02 = l0 + d2

 E٥ J٣F‫א‬‫א‬

 

d1 d2

L L 1

 

E٥ J٣F

 :(Straining Actions)‫א‬‫א‬W٤ J٣ (Normal Forces) ‫א‬‫א‬(Straining Actions)‫א‬‫א‬ ‫א‬‫א‬(Bending Moments)‫א‬(Shear Forces)‫א‬ ‫א‬ K‫א‬ ‫א‬‫א‬‫א‬‫א‬ 

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 (N)‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ (M) ‫א‬   (Q)‫א‬

 K‫א‬‫א‬‫א‬

 W‫א‬‫א‬(D.L + L.L )‫א‬‫א‬

 Z(N)‫א‬‫א‬    

  :Simple Slab or Simple BeamE‫א‬‫א‬FE١ - ٣١ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

•

 W‫א‬‫א‬(Q)‫א‬ Q = K q × wt × L

 

(3-1)

 E J٦ J٣F‫א‬‫א‬٠{٥Z (shear factor) ‫א‬ZK q

 Uniformly Distributed Load (D.L +L.L) ‫א‬‫א‬Zwt

 Span of Slab or beam ‫א‬‫א‬ZL

 

 W‫א‬‫א‬(M)‫א‬‫א‬ • 2

 

M = w × L / Km

 

(3-2)

 E J٦ J٣F‫א‬‫א‬

٨Z(moment factor)‫א‬ZKm



w t/m Loads L

wL 2 K q = 0.5

S.F.D

Q B.M.D

K m= 8 2

 

wL M= 8

E٦ J٣F  WOver Hanging Slab or Beam‫א‬‫א‬E٢

  W‫א‬‫א‬(D.L + L.L )‫א‬‫א‬  W(Q)‫א‬ - ٣٢ -

 

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

(D.L+L.L) ‫א‬‫א‬  ‫א‬  ‫א‬  ‫א‬          ‫א‬    KKKK (D.L only)  ‫א‬‫א‬  E‫א‬ ‫א‬‫א‬F ‫א‬‫א‬  KE J٧ J٣F‫א‬‫א‬(D.L + L.L)‫א‬‫א‬‫א‬‫א‬‫א‬ i.e.

Q = K q × wt × L

 

(3-3)

 

 ،E‫א‬F٠{٥Z (shear factor) ‫א‬ZK q W

 Uniformly Distributed Load  Span of Slab or beam 

(D.L +L.L) ‫א‬‫א‬ZW t

‫א‬‫א‬ZL W(M)‫א‬‫א‬

‫א‬  ‫א‬  ‫א‬    ‫א‬       E ‫א‬ ‫א‬  (D.L)  ‫א‬‫א‬  E‫א‬‫א‬F ‫א‬‫א‬    (D.L+L.L)

KE J٧ J٣F

- ٣٣ -

 

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

w1 = D.L + L.L (t/m)

D.L

Loads L

w1L 2

wL1 S.F.D

Kq = 0.5 wL1 w1L 2

M -v e

B.M.D

Case of max +ve M w1L2 8 w t/m (D.L)

w1 t/m

w1(D.L + L.L) Loads

M -ve =

w1L21 2 B.M.D

Case of max -ve M 2

wL 8

 

 E٧ J٣F

  W

Max. M +ve. = wt×L /8 – w × L1 /2

(3-4)

 

 (D.L+L.L)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ZwtW  (D.L. only)‫א‬‫א‬‫א‬‫א‬Zw

 ‫א‬‫א‬ZL1 ‫א‬‫א‬ZL  

- ٣٤ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 ‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬       E E J٧ J٣F ‫א‬‫א‬ (D.L+L.L.)‫א‬E‫א‬‫א‬F‫א‬‫א‬ (D.L.)



Max. M-ve = w × L12/2

   

 

(3-5)

 

 Continues Slab or Beam

E٢

 ‫א‬   ‫א‬ ‫א‬ ‫א‬  ‫א‬ ‫א‬‫א‬  ‫א‬   K‫א‬‫א‬‫א‬‫א‬٪٢٠‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬W W(M)‫א‬‫א‬ •

M = w×L / Km

(3-7)

 



 E٨ J٣F‫א‬‫א‬(moment factor)‫א‬ZKm

 ‫א‬‫א‬‫א‬ZL (Q)‫א‬ •

Q = K q × wt × L

 



(3-6)  



 E٩ J٣F‫א‬‫א‬ (shear factor) ‫א‬ZK q

 (D.L+L.L)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬Zwt

 ‫א‬‫א‬‫א‬ZL

L1‫א‬L،٪٢٠‫א‬،‫א‬‫א‬

Where,

L = (L1 + L2) / 2 L1 < 1.2 L2

and, wt = (wt1 + wt2) / 2 or, L2 < 1.2 L1 - ٣٥ -

 WL2

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

w t/m or w1

w t/m or w2 Loads

L or L

-9

-24

+11 wL 24

( Moment factor)

+11 w L2 9

w L2 24 B.M.D

w L2 11

 

w L2 11

 ‫א‬E٨ J٣F  

0.4

0.6

0.4 K q ( Shear factor)

0.6 wL 0.4 wL S.F.D 0.4 wL 0.6 wL

 ‫א‬E٩ J٣F

 

 W‫א‬‫א‬‫א‬‫א‬W (Q)‫א‬

Q = K q × wt × L

(3-8)

•

 

 E١٠ J٣F‫א‬‫א‬٠ (shear factor) ‫א‬ZK q - ٣٦ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 (D.L+L.L)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬Zw t 

 Effective Span of Slab or beam ‫א‬‫א‬‫א‬ZL   W(M)‫א‬‫א‬ • 2

M = w×L / Km

 

(3-9)

 E١٢ J٣FE١١ J٣F‫א‬‫א‬(moment factor)‫א‬ZKm  EffectiveSpan of Slab or beam ‫א‬‫א‬‫א‬ZL

 L ،٪٢٠  ‫א‬    ،‫א‬ ‫א‬  W

Where,

 WL2L1‫א‬

L = (L1 + L2) / 2 L1 < 1.2 L2

0.45

and, wt = (wt1 + wt2) / 2 or, L2 < 1.2 L1

0.6

0.5

 ‫א‬‫א‬‫א‬‫א‬‫א‬E١٠ J٣F -24

-10 +10

-12 +12

Km ( Moment factor)

‫א‬‫א‬E١١ J٣F

- ٣٧ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

-24

-10 +12

-12 +16

Km ( Moment factor)

‫א‬‫א‬‫א‬‫א‬E١٢ J٣F  

 W‫א‬‫א‬‫א‬W٥ J٣ ‫א‬‫א‬‫א‬‫א‬E١ J٣F‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬K‫א‬‫א‬

W‫א‬E‫א‬FE‫א‬‫א‬F E  EE٦ J٣F‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬

W‫א‬‫א‬ E 

 F ‫א‬   ‫א‬   ‫א‬ ‫א‬ ‫א‬   E٧ J٣‫א‬‫א‬FE‫א‬

 ‫א‬‫א‬‫א‬

 WE‫א‬FE

 E١٠ J٣F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬ E١٢ J٣FE١١ J٣F‫א‬

- ٣٨ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 W٦{٣  

KE٢ J٢F‫א‬‫א‬‫א‬‫א‬W١

 W‫א‬

W = 0.6 t/m2 Loads m 3.0

wL2 24

m 3.0

wL2 24

--v M e

+v e M

B.M.d

+v e M

loads & B.M at section s-s

 

Bending Moments: 2 × 0 .6 × 3 .5 2 w l 1 t M +ve = 11 = 11 = 0.668mt / m

    ‫א‬‫א‬

    M −ve

× = w l t

2 1

0 .6 × 3 .5 2 = = 0 .816 mt / m ‫א‬‫א‬ 9

  - ٣٩ -

:٢ ‫ﻣﺜﺎل‬

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

.‫أوﺟﺪ ﻋﺰوم اﻻﻧﺤﻨﺎء ﻋﻠﻰ اﻟﻜﻤﺮة اﻟﺘﺎﻟﻴﺔ ذات ﺑﺤﺮﻳﻦ و ﻳﺆﺛﺮ ﻋﻠىﻬﺎ ﺣﻤﻞ ﻣﻮزع ﺑﺎﻧﺘﻀﺎم‬ 3.5 t/m C

B 6m

 

 W‫א‬  

  M + ve   M −ve

× =w l t

× = w l t

3.5 × 6 2 = 11 .45 mt / m 11

 ‫א‬‫א‬

3 .5 × 6 2 = = 14 .0 mt / m 9

 ‫א‬‫א‬

2 1

    Q A = 0 .4 × wt × l1 = 0 .4 × 3 .5 × 6 = 8 .4 mt / m

 

  Q A = 0 .6 × wt × l1 = 0 .6 × 3 .5 × 6 = 12 .6 mt / m

 

 C ‫ و‬A‫א‬‫א‬  B‫א‬‫א‬ :٣ ‫ﻣﺜﺎل‬

.‫أوﺟﺪ ﻋﺰم اﻻﻧﺤﻨﺎء ﻋﻠﻰ اﻟﻜﻤﺮة اﻟﺘﺎﻟﻴﺔ ذات ﺑﺤﺮ واﺣﺪ و ﻳﺆﺛﺮ ﻋﻠىﻬﺎ ﺣﻤﻞ ﻣﻮزع ﺑﺎﻧﺘﻀﺎم‬ 1.8 t/m B

A 7m

 

  - ٤٠ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬   M + ve

× =w l t

2 1

 

 ‫א‬‫א‬

1 .8 × 7 2 = = 11 .025 mt / m 8

   Q A = + 0 .5 × wt × l1 = 0 .5 × 1 .8 × 7 = + 6 .3mt / m    Q B = − 0 .5 × wt × l1 = −0 .5 × 1 .8 × 7 = − 6 .3mt / m

 

  A‫א‬‫א‬  B‫א‬‫א‬

     W١ E٢ J٢F   ‫א‬ B2  B1 ‫א‬ ‫א‬ ‫א‬  ‫א‬   ‫א‬ KE٢‫א‬F  

 W٢ E٣ J٢F‫א‬ B2  B1‫א‬ S1 ‫א‬‫א‬ ‫א‬‫א‬ KE٢‫א‬F    

- ٤١ -

‫א‬

‫א‬‫א‬

‫א‬‫ א‬ 

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬   ‫א‬‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬ E‫א‬F ‫א‬  ‫א‬   ‫א‬‫א‬ ‫א‬ ،‫א‬‫א‬‫א‬ ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬

W‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬ E١

 KE‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬E٢

  ‫א‬ ‫א‬ ‫א‬   ‫א‬ ‫א‬‫א‬  ‫א‬   E٢ K‫א‬‫א‬

 ‫א‬‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬ ‫א‬  ‫א‬   E٣ K‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٤ K‫א‬

W‫א‬‫א‬  ٪١٠٠‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ W‫א‬‫א‬‫א‬‫א‬  • W‫א‬‫א‬  K‫א‬‫א‬

- ٤٢ -

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬W١ J٤

 

 W‫א‬‫א‬‫א‬ J‫א‬ J‫א‬  Solid Slabs‫א‬‫א‬E١ ‫א‬‫א‬W(Hollow Block Slabs)‫א‬‫א‬E٢ KE١{٤ F‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬W(Flat Slabs)‫א‬‫א‬E٣ F ‫א‬‫א‬  KE٢{٤  Waffle Slabs‫א‬‫א‬‫א‬‫א‬E٤  Lift Slabs‫א‬‫א‬E٥  Pre-Slabs‫א‬‫א‬E٦

- ٤٣ -

 

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 ‫א‬‫א‬ WE١ J٤F  

   ‫א‬‫א‬ WE٢ J٤F

- ٤٤ -

 

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 ‫א‬‫א‬ WE٣ J٤F ‫א‬ ‫א‬  (Solid Slabs) ‫א‬ ‫א‬     ‫א‬    K‫א‬‫א‬‫א‬‫א‬‫א‬

 

‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬  ‫א‬(Beams)‫א‬‫א‬‫א‬‫א‬‫א‬KEKKKKK‫א‬

 K‫א‬(girders)  W‫א‬‫א‬‫א‬  .‫א‬‫א‬‫א‬

 

K‫א‬

E

E 

 W

 

  W‫א‬‫א‬‫א‬‫א‬‫א‬٢{٤  W

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  

i.e. r = L / B ≥ 2

 E٤ J٤‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬

the slab is one way slab ‫א‬‫א‬B،‫א‬‫א‬L،‫א‬rW

- ٤٥ -

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

d/2 B d/2

 

 E٤ J٤F

 

‫א‬F‫א‬‫א‬ ‫א‬ ‫א‬‫א‬E٤ J٤F‫א‬

F ‫א‬‫א‬ KE‫א‬‫א‬‫א‬  ‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E

‫א‬  ‫א‬   ‫א‬   ‫א‬‫א‬ ‫א‬ ‫א‬ ‫א‬    ‫א‬  K‫א‬‫א‬‫א‬‫א‬

    F ‫א‬  ‫א‬‫א‬ ‫א‬ ‫א‬  ‫א‬ ‫א‬    

 WE‫א‬(Deflection)  

 t min.. =B/30

‫א‬ E١

t min.. =B/40

‫א‬ E٣

t min.. =B/35 ‫א‬‫א‬ E٢

 

 K‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬B  

- ٤٦ -

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

   W‫א‬‫א‬‫א‬٣{٤

 W

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬  K?٢?‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬ i.e. L / b ≥ 1.0 ≤ 2.0  ‫א‬Zb‫א‬ZL

 J٤F‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬

K ‫א‬ ‫א‬ ‫א‬‫א‬‫א‬ ‫א‬KE٥

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬K‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬

   ‫א‬‫א‬‫א‬‫א‬E٥ J٤F

  

 KL/b ‫א‬E

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E

 αE‫א‬‫א‬F‫א‬‫א‬‫א‬

βE‫א‬‫א‬F‫א‬‫א‬‫א‬

- ٤٧ -

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬‫א‬‫א‬   t min.. =b/35 ‫א‬ E

  t min. =b/45  ‫א‬‫א‬ E

 Kb

 

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٤ J٤ ‫א‬‫א‬(Hook’s Law) (Bernoulli theorem) 

  ‫א‬  ‫א‬ ‫א‬ ‫א‬ K     ‫א‬  ‫א‬

 KW‫א‬‫א‬‫א‬‫א‬

(Pure Bending Moment or Pure ‫א‬ ‫א‬     ‫א‬    ١{٤{٤

 

 Flexure)  ‫א‬ •

(Bond slip )EF‫א‬‫א‬ •

‫א‬  ‫א‬  ‫א‬ ‫א‬ ‫א‬   ‫א‬  ‫א‬  ‫א‬ ‫• א‬  ‫א‬

    ‫א‬   (Plane cross sections) ‫א‬ ‫• א‬  KE٦ J٤F‫א‬‫א‬K‫א‬ fc

3 C

Z=d -x 3

R.C sec



s Strain diagram

 E٦ J٤F - ٤٨ -

fs n

Stress diagram

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  

 

(4-1)

M b

W‫אא‬‫א‬

   

 E‫א‬F‫א‬‫א‬Zb  ‫א‬‫א‬Zd

  (f c)  ‫א‬  ‫א‬       Z k1  KE١ J٤F‫א‬‫א‬K(f s)‫א‬‫א‬

 K‫א‬‫א‬‫א‬ZM  

 W‫א‬‫א‬

 

(4-2)

M k 2 × d

   

 (M)‫א‬‫א‬‫א‬ZAs  ‫א‬‫א‬Zd

‫א‬(f c)‫א‬‫א‬ZK2  KE١ J٤F‫א‬‫א‬K(f s)‫א‬

 K‫א‬‫א‬‫א‬ZM  

- ٤٩ -

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 ‫א‬E١ J٤F

Fs=2200

Fs=2000

Fs=1600

Fs=1400

Fs=1200

Fs=1000

fc α β k1 k2 α β k1 k2 α β k1 k2 α β k1 k2 α β k1 k2 α β k1 k2

45 50 .403 .428 .866 .857 .357 .330 866 857 .360 .385 .880 .872 .374 .345 1058 1048 .325 .349 .892 .884 .391 .360 1248 1237 .297 .319 .901 .894 .408 .375 1441 1430 .273 .909 .402 1818 .254 .915 .415 2013

55 .452 .849 .308 849 .407 .864 .322 1037 .372 .876 .335 1227 .340 .887 .347 1419 .292 .803 .371 1898 .273 .909 .383 2000

60 .474 .842 .289 842 .428 .857 .301 1029 .391 .870 .313 1217 .360 .880 .324 1408 .310 .897 .346 1793 .290 .903 .357 1987

65 .494 .835 .273 835 .448 .851 .284 1021 .411 .863 .295 1208 .379 .874 .305 1398 .328 .891 .328 1782 .307 .898 .334 1976

70 .512 .829 .259 829 .467 .844 .269 1013 .429 .857 .279 1200 .396 .868 .288 1389 .344 .885 .306 1771 .323 .892 .315 1962

75 .529 .824 .247 524 .484 .839 .256 1007 .446 .851 .265 1192 .413 .862 .274 1380 .360 .880 .290 1769 .338 .887 .298 1952

80 .545 .818 .237 818 .500 .833 .245 1000 .462 .846 .253 1185 .429 .857 .261 1371 .375 .875 .276 1750 .353 .882 .283 1940

90 .574 .809 .219 809 .529 .823 .226 988 .491 .836 .233 1171 .458 .847 .240 1367 .403 .866 .252 1731 .380 .873 .269 1921

95 .588 .804 .211 804 .543 .819 .218 983 .504 .832 .224 1165 .471 .843 .230 1349 .416 .861 .242 1723 .393 .869 .248 1912

100 .600 .800 .204 800 .555 .815 .210 978 .517 .826 .216 1162 .484 .839 .222 1342 .429 .857 .233 1715 .406 .865 .239 1903

105 .612 .796 .193 796 .567 .811 .204 973 .529 .824 .209 1154 .496 .835 .214 1335 .440 .853 .225 1706 .417 .861 .230 1894

   

- ٥٠ -

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 Diagonal Tension‫א‬‫א‬٢{٤{٤ Horizontal ‫א‬‫א‬‫א‬Vertical Shear‫א‬‫א‬‫א‬‫א‬‫א‬

 KShear

Wq‫א‬‫א‬  

(4-3)

q =

Q 0 . 87 × bd  

 K‫א‬‫א‬Zq

 K‫א‬‫א‬‫א‬‫א‬ ZQ

 W‫א‬‫א‬‫א‬W٣ J٤ J٤  W‫א‬W  E‫א‬ ‫א‬  ‫א‬  F ‫א‬ ‫א‬  ‫א‬     (١  K‫א‬‫א‬‫א‬٪٠{٢٥

E‫א‬‫א‬F ‫א‬‫א‬‫א‬‫א‬ (٢

‫א‬‫א‬K ‫א‬‫א‬E 1 F 5

KE٥F

E٪ ٢٠    F ‫א‬ ‫א‬     ‫א‬ ‫א‬ ‫א‬  (٣ ‫א‬‫א‬ ٥L١ ‫א‬‫א‬‫א‬ ‫א‬

‫א‬‫א‬‫א‬ ٤L ١‫א‬‫א‬‫א‬

K‫א‬‫א‬

‫א‬‫א‬ ‫א‬‫א‬ (٤

‫א‬‫א‬E٥F‫א‬ ٢٠

K١٠‫א‬

K٢{٠١{٥‫א‬ (٥

E ٣L ١F   ‫א‬  ‫א‬ ‫א‬ ‫א‬       (٦ K‫א‬‫א‬‫א‬‫א‬ - ٥١ -

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

K٨ (٧  

 W‫א‬W ‫א‬‫א‬‫א‬‫א‬٢L٤٠٠‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬

K‫א‬

K‫א‬

E١

 W

E٢

E٣

 

 W‫א‬W K ١٠‫א‬‫א‬  K١٥‫א‬  

 W‫א‬W‫א‬ ١{٠٥  ‫א‬    ‫א‬  ‫א‬    ‫א‬ ‫א‬   K‫א‬‫א‬K‫א‬‫א‬

 

- ٥٢ -

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 W ٤{٤{٤ ‫א‬   ‫א‬ KE٧ J٤F   ‫א‬ ‫א‬‫א‬ ‫א‬ ‫א‬ ‫א‬   WE١F   K

 W‫א‬

 Dead loadsW‫א‬‫א‬‫א‬

 ١٠Z(t)‫א‬‫א‬

  A

One - way slab

m 2.25

L=6

w = 0.6 t/m = 6 KN/m Loads

 

i.e.

B.M.d

2.25

 E٧ J٤F Own weight of slab =1×1× t ×γ c = t × γ c  = 0.1× 2.5 = 0.25 t/m2 = 2.5 KN / m2 Flooring (‫א‬) = 0.15 t / m2 = 1.5 KN / m2 Live Loads (L.L.) (‫א‬‫ = )א‬0.20 t/m2 = 2.0 KN / m2 = 0.60 t / m2 = 6.0 KN / m2

Total Loads (wt) (‫א‬‫)א‬ Bending Moments (‫א‬)

- ٥٣ -

 

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

Section A-A: M = wt ×L2/8 = 0.6 × (2.25)2 / 8 = 0.380 m.t /m Assume f c =60 kg / cm2

(f cu = 250 kg / cm2)

f s = 1400 kg/cm2

And

(mild steel 37)

i.e.

From table (4-1)

k 1= 0.313

and k 2 = 1217

 Eb=100cm.F١{٠‫א‬EdF‫א‬‫א‬ d = k1

M b

0 . 313

0 . 380 × 100000 100

= 6.10 cm.

‫א‬   ‫א‬    K  ٨ Z  EtF ‫א‬  ‫א‬  ‫א‬   

 K

I.e. take t min = 8.0 cm.

d act. = t – cover = t – (1.5: 2.0 cm) = 8.0 – 1.5 = 6.5 cm.

 W‫א‬

As main =

M × 10 5 k2× d

0.380 × 10 5 1217 × 6.5

= 4.8 cm2/m

Choose 7Ø10 mm/m (5.5cm2/m) Check: As min = 0.25% Ac = 0.25 / 100 ×10×100 = 2.5 cm2 i.e. As main chosen is okay. As secondary = 0.20 A s main = 0.20 × 4.8 = 0.96 cm2 /m Choose As secondary = 5 Ø 8 mm/m (2.51 cm2)  

- ٥٤ -

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 WE٢F    ‫א‬  ‫א‬ ‫א‬‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬ 

‫א‬KE٨ J٤F‫א‬‫א‬ ‫א‬‫א‬ ٣{٠٠  KE٢L٢٠٠Z‫א‬‫א‬F‫א‬ ‫א‬

L 6 = =2 b 3

 W‫א‬ (One way slab) Loads on Slab:

 

assume t s=10 cm.

O.w. of slab = 0.1 ×2.5 = 0.25 t/m2 = 2.5 KN/m2 Flooring

= 0.15 t/m2 = 1.5 KN/m2

L.L.

= 0.20 t/m2 = 2.0 KN/m2

Total load wt =

= 0.60 t/m2 = 6.0 KN/m2 3.0 m

3.0 m

W d.L + L.L Loads m 3.0

m 3.0

S wL2 24

--v M e

+ve M

wL2 24

m 6.0 B.M.d

+ve M

loads & B.M at section s-s

m L = 3.0

E٨ J٤F

- ٥٥ -

m L = 3.0

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

Bending Moments: 2 × wt l1 = 0.6 × 9 = 0.49 mt / m M +ve = 11 11 2 w × l 0.6 × 9 = 0.6 mt / m   M −ve = t 1 = 9 9 (Cases of ‫א‬٢L٤٠٠‫א‬‫א‬ W

 K(case of total loads)‫א‬‫א‬loading) Assume f c =60 kg / cm2

(f cu = 250 kg / cm2)

f s = 1400 kg/cm2

(mild steel 37—24/35)

And

i.e. k 1= 0.313

From table (4-1) and

k 2 = 1217

 Eb=100cm.F١{٠‫א‬EdF‫א‬‫א‬  

d = k1

M b

0 . 313

0 . 6 × 100000 100

= 7.74 cm.

Take t = 10.0 cm d act. = t – cover = t – (1.5: 2.0 cm) = 10.0 – 1.5 = 8.5 cm.

 

W‫א‬‫א‬‫א‬

A main = s1

M +ve ×10 k2 × d

0 . 49 × 10 5 = = 4.74 cm2/m 1217 * 8 . 5 Choose 7 Ø 10 mm/m (5.5cm2/m)

Check: As min = 0.25% Ac = 0.25/100 ×10×100 = 2.5 cm2 i.e. As1 main chosen is okay. As1 secondary = 0.20 As1 main = 0.20× 4.74 = 0.948 cm2 /m Choose As1 secondary = 5 Ø 8 mm/m (2.51 cm2)

- ٥٦ -

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 

W‫א‬‫א‬‫א‬ M −ve ×105 As2 main = k2 × d

0.6 ×105 = 5.8 cm2 / m 1217× 8.5

Choose 8 Ø 10 mm/m (6.28cm2/m) Check: As min = 0.25% Ac = 0.25/100 ×10×100 = 2.5 cm2 i.e. As2 main chosen is okay. As2 secondary = 0.20 As2 main = 0.20× 5.8 = 1.16 cm2 /m Choose As2 secondary = 5 Ø 8 mm/m (2.51 cm2)

‫א‬E٢F‫א‬‫א‬‫א‬‫א‬

KE٩ J٤F  

  K‫א‬‫א‬‫א‬‫א‬WE٩ J٤F  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٥{٤    WE١٠.٤F‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E١  K٥

٧٠‫א‬‫א‬‫א‬K‫א‬‫א‬ E٢ K٥‫א‬

- ٥٧ -

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 WE١١{٤F‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬ E٣ K‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬ ‫א‬ •  K‫א‬‫א‬‫א‬  

 

 ١٠ J٤  

 

 ١١ J٤

- ٥٨ -

 

 ‫א‬‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

‫א‬E١٢{٤F‫א‬W‫א‬

‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬K  

‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬

‫א‬‫א‬‫א‬ ‫א‬٦  KE١٠{٤F‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬٦٤‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬                

 

  K‫א‬W١٢{٤

- ٥٩ -

‫א‬

‫א‬‫א‬‫א‬

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬

‫א‬  ‫א‬ ‫א‬   ‫א‬   ‫א‬ ،‫א‬ ‫א‬ 

‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬K‫א‬

 K‫א‬‫א‬‫א‬‫א‬

W‫א‬‫א‬ ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E١

‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬   ‫א‬ ‫א‬   E٢  K‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٣

‫א‬‫א‬‫א‬‫א‬ ‫א‬ E٤

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬  ٪١٠٠‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ W‫א‬‫א‬‫א‬‫א‬ W‫א‬‫א‬  K‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

- ٦٠ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 W١{٥  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ E١    ‫א‬‫א‬    ‫א‬   K ‫א‬ ‫א‬

 K٢٠٢٠WKK‫א‬

 KE١ J٥F‫א‬F٢٥٢٥

T 12 cm b

20 cm

25 cm 12 cm b

b< T

12 cm b

25 cm b< 25 cm

20 cm b< 20 cm

 E١ J٥F  

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٢ ‫א‬‫א‬‫א‬‫א‬K‫א‬   K‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٣ K‫א‬‫א‬

‫א‬ ‫א‬‫א‬  ‫א‬‫א‬      ‫א‬  E٤ K‫א‬‫א‬‫א‬

K‫א‬ E٥

 

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

- ٦١ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬‫א‬‫א‬‫א‬٢{٥



 W‫א‬‫א‬‫א‬‫א‬   Main girders ‫א‬‫א‬‫ א‬E١ Secondary beams‫א‬‫א‬‫ א‬E٢

E‫א‬ F‫א‬ ‫א‬‫א‬‫א‬‫א‬    F ‫א‬ ‫א‬‫א‬  ‫א‬   ‫א‬  ‫א‬ ‫א‬‫א‬

 KE٢ J٥F‫א‬‫א‬E‫א‬‫א‬‫א‬  

4.00 m

Beam

0.3

Seconadry

 

0.2

m Seconadry

3.00

Beam Main

0.3

Beam m

3.00

 E٢ J٥F  

 F‫א‬ ‫א‬ ‫א‬‫א‬  KE‫א‬ ‫א‬‫א‬ ‫א‬

 K‫א‬

   K   E٣ J٥F  ‫א‬  ‫א‬ ‫א‬ ‫א‬ ،‫א‬  

‫א‬ (G1) ‫א‬ ‫א‬     (B1→B2→B3)     ‫א‬

 KC4‫א‬B1‫א‬‫א‬‫א‬‫א‬K - ٦٢ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

‫א‬     K  E٣ J٥F  ‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬ 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬G1‫א‬ ،C1‫א‬‫א‬ G1‫א‬‫א‬‫א‬B3،B2،B1

 K‫א‬‫א‬‫א‬C4،C3،C2

 

4.00

G1 C3

C4 3 3.00

m 2

B2 1

3.00

 

B3 B1

 E٣ J٥F

 W‫א‬‫א‬‫א‬‫א‬W١ J٢ J٥  

‫א‬ E‫א‬ ‫א‬ ‫א‬ ‫א‬‫א‬ ‫א‬  F ‫א‬   E١ (Embedded beams) ‫א‬ (Dropped beams)  ‫א‬  ‫א‬ 

 K‫א‬‫א‬

 

‫א‬‫א‬ (Loop of loading)E ٢

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

E‫א‬F‫א‬EF‫א‬E J٤ J٥F‫א‬ ‫א‬ a‫א‬‫א‬‫א‬ d c b a ‫א‬

 K‫א‬‫א‬‫א‬

KE J٤ J٥F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E J٤ J٥F‫א‬ cba‫א‬‫א‬E J٤ J٥F‫א‬‫א‬ - ٦٣ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

‫א‬K‫א‬‫א‬ D‫א‬ e d  K‫א‬‫א‬‫א‬

 ‫א‬ ‫א‬      E‫א‬ ‫א‬F ‫א‬ ‫א‬   

 ‫א‬ ،E J٥ J٥F ، E J٥ J٥F  ‫א‬  K E J٥ J٥F ‫א‬ ‫א‬  ‫א‬‫א‬  KE J٥ J٥F‫א‬‫א‬‫א‬

 

m D

m S

m D

e m D

m S

m D

 

 E٤ J٥F

- ٦٤ -

m S

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

X m

ks ac Cr

Cr ac ks

 

 E٥ J٥F  

 W‫א‬‫א‬‫א‬‫א‬ ٢.٢.٥

‫א‬‫א‬‫א‬E‫א‬‫א‬F‫א‬‫א‬‫א‬

‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ‫א‬ ‫א‬ ‫א‬  ‫א‬   K   ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٥ J١F‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬  

 W‫א‬‫א‬‫א‬٣{٥

 W‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬  E‫א‬F‫א‬‫א‬‫א‬ - ٦٥ -

(١ (٢

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

E‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬

(٣

 ‫א‬ ‫א‬ ‫א‬  ‫א‬‫א‬  ‫א‬ ‫א‬ ‫א‬   

‫א‬‫א‬ E٧{٦FE٦ J٥F  ‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 EF ‫א‬  K         EF ‫א‬    K

‫א‬‫א‬‫א‬‫א‬‫א‬

  ‫א‬ ‫א‬ ‫א‬ ‫א‬‫א‬   E٥{٧ F ‫א‬   

 KE١ J٥F  

   

 

  d/2

          L

 

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٦ J٥F

 

- ٦٦ -

d/2

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

L Y

45°

Beam A

Beam B

 

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٧ J٥F  E١ J٥F

 

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬β،α‫א‬

L/2x 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0  α 0.667 0.725 0.769 0.803 0.829 0.853 0.870 0.885 0.897 0.908 0.917  β 0.500 0.554 0.582 0.615 0.642 0.667 0.688 0.706 0.722 0.637 0.750

 W

 K‫א‬‫א‬‫א‬‫א‬‫א‬ZW  K‫א‬‫א‬ZL  KZX  W

 (Equivalent coefficient for moment)‫א‬‫א‬Zα  (Equivalent coefficient for shear)‫א‬‫א‬Zβ

 W

- ٦٧ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬Zα ×w ×x ‫א‬‫א‬‫א‬‫א‬ ‫א‬  K‫א‬‫א‬

E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬Zβ ×w ×x

 

  ‫א‬  ‫א‬  F ‫א‬‫א‬  ‫א‬  ‫א‬  KEα‫א‬‫א‬‫א‬

 

 KE٢ J٥F‫א‬‫א‬‫א‬‫א‬W  

 E٢ J٥F

0.5 0.667

 

L/2 L

0.5

From table

0.5 0.667

0.5 0.333

0.5

From table

Take = 1/2x for one trabizoidal

 E١ J٥F ‫א‬‫א‬‫א‬‫א‬  E٨ J٥F‫א‬ ‫א‬K‫א‬‫א‬E J٨ J٥F‫א‬KE J٨ J٥F

 W

 KE٣L١{٢‫א‬F٢٠‫א‬‫א‬‫א‬‫א‬

 W‫א‬KE J٨ J٥F‫א‬‫א‬K٣{٠Z‫א‬‫א‬‫א‬ - ٦٨ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

   

 KB2‫א‬‫א‬B1‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 1

m 6.00

6.00

C 5.00 m

 

5.00m

4.00 m

 E J٨ J٥F  

3 G2

A S2 m 6.00 B2

m B2 6.00

0.4 m

5.00 m

G2 4.00 m

 

0.2

C 5.00 m 3

 E J٢ J٥F  

- ٦٩ -

E١

E٢

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

h2 ( clear height )

 

 E J٢ J٥F  

 ‫א‬

 B2،B1‫א‬‫א‬‫א‬W

 E٩ J٥F‫א‬‫א‬B1‫א‬‫א‬

 

2.00

2.50

2.00

2.50

6.00 m

B1 w t t/m G1

B1 E٩ J٥F - ٧٠ -

 

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 Wt on beam B1 = loads from slab + o. w. of beam  Loads on slab:

Assume t s = 12 cm = 0.12 m O.W. of slab = 0.12 × 2.5 = 0.30 t/m2 = 3.0 KN / m2 O.W. of flooring

= 0.15 t/m2 = 1.5 KN / m2

L.L

= 0.30 t/m2 = 3.0 KN / m2

Total load on slab

= 0.75 t/m2 = 7.5 KN / m2 Slab s1

is 4 × 6 m

r1 = 6/4 = 1.5 α1 = 0.853

and

β1 = 0.667 (from table 5-1) Slab s2

is 5 × 6 m

r2 = 6/5 = 1.2 α1 = 0.769

and

β1 = 0.582 (from table 5-1)

Beam B1 has two equal span = 6.0 m Assume And

b =20 cm

t = span / 10 = 60 cm

 W

 W‫א‬B1‫א‬‫א‬(working loads)‫א‬ W α = total working load for moment

= 0.853 × 0.75 × 4/2 + 0.769 × 0.75 × 5/2 + 0.2 (0.6 – 0.12) × 2.5 = 2.96 t/m 

 W‫א‬B1‫א‬‫א‬(working loads)‫א‬ W β = total working load for shear

= 0.667 × 0.75 × 4/2 + 0.582 × 0.75 × 5/2 + 0.2 (0.6 – 0.12) × 2.5 = 2.33 t/m 

 K‫א‬B1‫א‬‫א‬‫א‬‫א‬‫א‬W  K‫א‬‫א‬‫א‬ B2‫א‬‫א‬ 

 K‫א‬G1(Main girder)‫א‬E‫א‬F‫א‬

 

 E١٠ J٥F‫א‬‫א‬B2‫א‬‫א‬ - ٧١ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

2.50

2.50 col

col

6.00 m

B2 w t/m t col

col

E١٠ J٥F Loads on slab: Assume t s = 12 cm = 0.12 m O.W. of slab = 0.12 × 2.5 = 0.30 t/m2 O.W. of flooring = 0.15 t/m2 L.L = 0.30 t/m2 Total load on slab = 0.75 t/m2 Slab s2 is 5 × 6 m r2 = 6/5 = 1.2 and β1 = 0.582 α1 = 0.769 Beam B2 has two equal span = 6.0 m Assume b =20 cm And t = span / 10 = 60 cm Loads from wall: = 3.0 – 0.6 = 2.4 m‫א‬‫א‬H wall = W wall = γ b × t w + o.w. of plaster = 1.2× 0.2 + 0.05 = 0.29 t/m2

 W

 WE‫א‬)B2‫א‬‫א‬(working loads)‫א‬ W α = total working load for moment

= 0.769 × 0.75 × 5/2 + 0.2 (0.6 – 0.12) × 2.5 + 0.29 × 2.4 = 2.38 t/m

WE‫א‬FB2‫א‬‫א‬(working loads)‫א‬

 

- ٧٢ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

W β = total working load for shear = 0.582 × 0.75 × 5/2 + 0.2 (0.6 – 0.12) × 2.5 + 0.29 × 2.4 = 2.38 t/m  

 :B2،B1‫א‬‫א‬‫א‬‫א‬W

 J٥FE١١ J٥F‫א‬‫א‬E‫א‬FB1‫א‬E١  E١٢

2.33 t/m Load for shear 6.00 m

0.4

6.00 m

0.6 0.6

0.4

K ( Shear factor) q

8.4 t 5.6 t S.F.D Q=K * w L q

5.6 t 8.4 t

 

 E١١ J٥F  

2.96 t/m

6.00 m

-24

6.00 m

-9 +11

-4.44

 

Load for moment

9.7

2 w L= 11.84 9

-24 K m ( moment factor)

+11

- 4.44

9.7

 E١٢ J٥F - ٧٣ -

2 B.M.d M= wL /Km

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 

 WE‫א‬FB2‫א‬E٢

W β (for shear) = 1.74 t/m W α (for moment) = 2.22 t/m

 

 KB2‫א‬‫א‬‫א‬‫א‬‫א‬W١

 

WDesign of R.C. Sections of Beams‫א‬‫א‬‫א‬٤{٥

 ‫א‬    ‫א‬ ‫א‬ ‫א‬   ‫א‬ ‫א‬ ‫א‬ 

‫א‬  K‫א‬‫א‬  ‫א‬ ‫א‬       K ‫א‬

‫א‬    K  ‫א‬ ‫א‬  ‫א‬    ‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٣ J٥F‫א‬

 

 E١٣ J٥F

  

‫א‬(Deflection)‫א‬‫א‬A-B‫א‬E١٤ J٥F‫א‬

‫א‬‫א‬ ‫א‬K‫א‬‫א‬

 WEB-B‫א‬F‫א‬‫א‬EA-A‫א‬F

 

- ٧٤ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 

 E١٤ J٥F    

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬E١٥ J٥F‫א‬‫א‬KE١٥ J٥FE١٥ J٥F‫א‬

E١

‫א‬      K ‫א‬   ‫א‬ ‫א‬  ‫א‬

‫א‬‫א‬‫א‬K‫א‬     T       ‫א‬   

E١٥ J٥F‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

KE١٥ J٥F‫א‬‫א‬

A-A

B-B

- ٧٥ -

A-A T

E٢  

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 E١٥ J٥F  

W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 E١٥ J٥‫א‬‫א‬F‫א‬‫א‬‫א‬E

 E١٥ J٥‫א‬‫א‬FT‫א‬‫א‬TE L‫א‬ (L-shaped)L ‫א‬‫א‬ K(L-Section)>

 

 W‫א‬‫א‬‫א‬‫א‬١{٤{٥

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬ (Linear) ‫א‬ 

E١

‫א‬‫א‬‫א‬  ‫א‬

E٢

KE١٦ J٥F

‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ‫א‬  f

  ‫א‬ ‫א‬         Kf s‫א‬‫א‬‫א‬‫א‬

- ٧٦ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

fc Stress diagram

 

Strain diagram

 E١٦ J٥F  

‫א‬        ‫א‬  ‫א‬ ‫א‬  

E٣

W‫א‬‫א‬d‫א‬‫א‬

E٤

 K‫א‬‫א‬(Q)‫א‬‫א‬‫א‬‫א‬(M)

 

(5-1) d =

M b

 W

‫א‬‫א‬(Depth of R.C. Sec.)‫א‬‫א‬‫א‬Zd

 EE١٧ J٥F&E١٦ J٥F‫א‬‫א‬F

    (f c)  ‫א‬ ‫א‬        Z k1  K‫א‬‫א‬‫א‬‫א‬E١ J٤F‫א‬‫א‬(f s)‫א‬‫א‬

K‫א‬‫א‬‫א‬ZB

 f s,bf c f cuE٥  - ٧٧ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

f cu = 250 kg/cm2

 W‫א‬W

f c = 80 kg/cm2

So, k1 = 0.253

and f s = 1400 kg/cm2

k 2= 1185 



 E١ J٤F‫א‬‫א‬‫א‬d‫א‬‫א‬E٦ W‫א‬‫א‬‫א‬As‫א‬ E٧  

(5-2)

M × d 2

 From figure (5-21)

t = d +d′ Where; d′ = 3 + Ø /2 + (2.5 + Ø /2) × (n-1)

 K‫א‬ZnW

 W٢٠ZØ،‫א‬Z(n)‫א‬‫א‬ d′ = 3 + Ø /2 ≈ 4 cm. KE١٧ J٥F‫א‬‫א‬K‫א‬

fs / n

b  

 E١٧ J٥F  

- ٧٨ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 

 E‫א‬‫א‬‫א‬‫א‬F LT‫א‬‫א‬‫א‬٢{٤{٥   L‫א‬T‫א‬I‫א‬∏‫א‬K‫א‬‫א‬‫א‬  KE١٨ J٥‫א‬FL‫א‬T‫א‬‫א‬‫א‬‫א‬

   ‫א‬  ‫א‬       ‫א‬  ‫א‬‫א‬    K‫א‬‫א‬‫א‬‫א‬

‫א‬ K T    ‫א‬ ‫א‬  ‫א‬    ‫א‬  ‫א‬ 

 (Floor) K‫א‬ ‫א‬‫א‬  KL‫א‬‫א‬

 ‫א‬‫א‬ ‫א‬‫א‬ (B)‫א‬‫א‬

 WL‫א‬T  

 W‫א‬‫א‬‫א‬‫א‬‫א‬B‫א‬‫א‬ T

B = 12 ts + b Or

B = L/3 (for simple beams)

B = L/4.5 (for continuous beams)

E

 

(5-3)  

 LE

B = 4.5 t s + b Or

B = L/6 (for simple beams)

(5-4)

B = L/9 (for continuous beams)

t sK٨K‫א‬Z

LK‫א‬‫א‬Z

    - ٧٩ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 

M B

B ts

 

ts d

bO T - section

bO L - section

 E١٨ J٥F

‫א‬‫א‬‫א‬(Maximum B)‫א‬‫א‬W KE١٩ J٥F

 

- ٨٠ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

6.30 L sec

T sec bo

 

L sec

 E١٩ J٥F  

 WLT‫א‬

 WT

E‫א‬F‫א‬  (Z)‫א‬

E١

‫א‬F ‫א‬     (Z) ‫א‬     

E٢

 K‫א‬‫א‬E٢٠ J٥F

KT‫א‬‫א‬KE٢٠ J٥FE

- ٨١ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

B z

z d

 

 E٢٠ J٥F  

 W‫א‬‫א‬ (neutral axis distance (z))‫א‬‫א‬  



Z = 0 . 14

M B

(5-5)

‫א‬ ‫א‬‫א‬‫א‬ BK B‫א‬ (r)‫א‬ 

WK‫א‬‫א‬Br



(5-6)

Br= r × B

 

B/b0&ts/z‫א‬K(r)‫א‬E٣ J٥F‫א‬  

- ٨٢ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

(Br=r.B) (r)‫א‬E٣ J٥F B/b0 2.0 2.5 3.0 3.5 4.0 5.0

1.0 1.0 1.0 1.0 1.0 1.0 1.0

0.9 1.0 .99 .99 .99 .99 .99

0.8 .98 .98 .97 .97 0.97 0.97

0.7 .96 .95 .94 .94 .93 .93

ts/z 0.6 .92 .90 .89 .89 .88 .87

0.5 .88 .85 .83 .82 .81 .80

0.4 .82 .78 .76 .74 .73 .71

0.3 .76 .70 .67 .65 .63 .61

0.2 .68 .62 .57 .54 .52 .49

 

 W‫א‬‫א‬ d =

M 1

 :k1‫א‬W f c′= 0.75fc 

T = d + d′

 

 K‫א‬‫א‬‫א‬ f cW 

 K(t)‫א‬‫א‬

W‫א‬T‫א‬‫א‬‫א‬

 

M × d 2

  Kf s , (f c′)‫א‬E١ J٤F‫א‬k2W

‫א‬‫א‬ (shear stress)‫א‬‫א‬ (Check)‫א‬   K‫א‬‫א‬

 W‫א‬ ‫א‬LT‫א‬‫א‬‫א‬E١  K‫א‬‫א‬‫א‬ - ٨٣ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

‫א‬‫א‬(L)‫א‬E٢ ‫א‬‫א‬‫א‬E‫א‬‫א‬F‫א‬ K‫א‬‫א‬‫א‬٪١٥

: Shear stress‫א‬‫א‬‫א‬٥{٥

(q)  ‫א‬  ‫א‬ ‫א‬  ‫א‬ (shear forces (Q)) ‫א‬  

‫א‬‫א‬(Diagonal Tension)(T)(shear stress)  KE٢١ J٥F‫א‬‫א‬

W‫א‬‫א‬q‫א‬  

q =

Q 0 . 87 × b × d

Kg / cm2  

T q q

q q

T E٢١ J٥F  

 W‫א‬

 K٢L٧‫א‬‫א‬‫א‬  E١

١٨  E   F        E٢ K‫א‬‫א‬‫א‬‫א‬‫א‬H‫א‬‫א‬‫א‬K٢L - ٨٤ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 :‫א‬‫א‬‫א‬‫א‬‫א‬١{٥{٥

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬

 KE١٣ J٥١١ J٥F‫א‬‫א‬K(Shear force diagram) (S.F.D)‫א‬‫ א‬E١ W‫א‬‫א‬‫א‬‫א‬‫א‬E٢

max

Q 0 . 87 × b × d

  q maxK (Linearity)‫א‬ Q qW  K(Face of column)‫א‬‫א‬

K(7kg/cm2)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٣  KE٢٢ J٥F‫א‬‫א‬‫א‬

Q q

By concrete

S.F.D

7 kg/cm q = 1: 1 q st 3 2 max

q max

 

E٢٢ J٥F

- ٨٥ -

 

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 Kq max½⅓‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٤ I.e.

q stirrups =(⅓: ½) q max =

n × Ast ×

b× s

 K(No. of branches of stirrups)‫א‬‫א‬‫א‬ZnW

 K(Area of bar of one branch of stirrups)‫א‬ZA st

 (A st = 0.503 cm2)W٨‫א‬

 K٢L١٤٠٠‫א‬‫א‬Zf s  (breadth of beam)‫א‬ Zb

 K‫א‬Zs

 

W‫א‬‫א‬(A sb)‫א‬‫א‬E٥

Where;

× b

 

A b = area from diagram of shear stress.

 

- ٨٦ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 K٦{٥

 K‫א‬‫א‬E١ J٥F‫א‬‫א‬B1‫א‬  

 W‫א‬  

Design data: L= Effective Span =6.0 m ton Q max. +ve = 8.4 ton Q max. – ve = 5.6 M max. –ve = 11.84 t.m. M max. +ve = 9.7 t.m. Assume f cu = 250 kg/cm2 kg/cm2 f c = 90 f s =1400 kg/cm2 8.4 ton Therefore: Q Design = At Sec. 2-2 M –ve = 11.84 t.m. t.m. At Sec. 1-1 M +ve = 9.7 From table k1 = 0.233 k2 = 1171 Design of Sec. 2-2 (Slab lies in Tension zone) So design as a rectangular Sec. d =

× 10 b

= 0 . 233

11 . 84 × 10 20

Take:

= 56 . 7 cm

t = 60 cm d act. = 56 cm

M × 10 k ×d 2

act

11 . 84 × 10 1171 × 56

= 18 . 06

Take 6 Ø 20 mm (18.8 cm2) Check on section 1-1 (slab is in compression zone) So design as a T section B (breadth of flange) is taken the least of: B = 12 t s + b = 12 × 10 + 20 = 140 cm Or B = L/4.5 = 600/4.5 = 133.33 cm Or B = ¢ :¢ =450 cm I.e. B =133.33 cm

- ٨٧ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

And

Z = 0 .14

+ ve

9 .7 × 10

= 0 .14

133 .33

= 11 .94 cm

Z > t s > 10 cm So: the sec. is actually T sec. f c′ = 0.75 f c = 0.75× 90 = 67.5 kg/cm2 Take f c′ = 70 kg/cm2 I.e. k1= 0.279 k2= 1200 d act.= 56 cm

As at sec .1 =

M × 10 k ×d

act

9 .7 × 10 5 = 14 .43 cm 2 1200 × 56

Take 5 Ø 20 mm (15.7 cm2)

8.4 t

sec 2

255 q

max

8.62 kg/cm

7 kg/cm

 

E٢٣ J٥  Check of shear:

2 max .

 

8 . 4 × 10 3 = 8 . 62 kg / cm 2 > 7 kg/cm2 0 . 87 × 20 × 56

Take stirrups 2 branches 5 Ø 8 mm/m - ٨٨ -

45°

3.6 m

x 2.4 m

5.6 t

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

bent

n × Ast ×

b× s

2 × 0.503×1400 1 1 = 3.52 = ( : ) q 20× 20 3 2 2 max.

A ×b = × b A f f

= (45 ×

8.62 − 3.52 + 7 − 3.52 20 2 )× = 2.28 cm 2 1400

Take 2 Ø 20 mm (6.28 cm2 for more safety)  KB1‫א‬‫א‬E٢٤ J٥F‫א‬‫א‬  

 ٧{٥

- ٨٩ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 K‫א‬  

 

 B1‫א‬E٢٤ J٥F    

2Φ18

٦Φ٢٠

   

  ‫ آﺎﻧﺎت‬Φ      

5Φ20

٢Φ٢٠

  ‫ﻓﻲ وﺳﻂ اﻟﻜﻤﺮة‬

   

‫ﻓﻮق اﻟﺮآﻴﺰة‬

 B1‫א‬‫א‬WE٢٥ J٥F  

W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬E١

 K٣٥٠H٣٠{٤H٣٠{٨

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢ - ٩٠ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

‫א‬٢٨‫א‬‫א‬‫א‬‫א‬E٣  ٢L٢٥٠

 K٢٤‫א‬‫א‬‫א‬E٤

 KE‫א‬‫א‬F٣٥L٢٤‫א‬‫א‬‫א‬‫א‬E٥

 K‫א‬‫א‬٤L١‫א‬٥L١‫א‬‫א‬‫א‬E٦  K‫א‬‫א‬٧L١‫א‬‫א‬‫א‬E٧  K٣٥‫א‬‫א‬‫א‬E٨

‫ א‬‫א‬EF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٩

 K‫א‬‫א‬٤L١‫א‬

 ‫א‬‫א‬‫א‬‫א‬E١٠  

 E٣٥L٢٤F‫א‬  

 

  ‫א‬‫א‬

 ‫א‬‫א‬ 



 

 L٨Ø٥

 ١٦Ø٢

 

 L٨Ø٥

 ١٨Ø٢

٢٠Ø٢ ٢٠Ø٢  ٢

 

 L١٠Ø٦

 ٢٠Ø٢

٢٥Ø٣ ٢٢Ø٣  ٣

 

 L١٠Ø٦

 ٢٥Ø٢

٢٢Ø٥ ٢٢Ø٥  ٤

- ٩١ -

  J

 

١٦Ø٢  ١

‫א‬

‫א‬‫א‬

‫ א‬‫ א‬ 

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

W‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ K‫א‬ ‫א‬‫א‬ ‫א‬ ‫א‬ ،‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   W‫א‬‫א‬ K‫א‬‫א‬‫א‬ E١

 K‫א‬‫א‬‫א‬‫א‬‫א‬

E٢

K‫א‬‫א‬‫א‬

E٣

W‫א‬‫א‬  ٪١٠٠‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬  • W‫א‬‫א‬  K‫א‬‫א‬

- ٩٢ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

 W‫א‬‫א‬١{٦ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬  ‫א‬    ‫א‬  ‫א‬ ‫א‬   ‫א‬  

‫א‬  ‫א‬ ‫א‬          K ‫א‬ ‫א‬ 

 K‫א‬

    ‫א‬  ‫א‬  ‫א‬  K  ‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬E١ J٦F‫א‬‫א‬K‫א‬‫א‬‫א‬  

 

 W(Braced and un-braced column) ‫א‬‫א‬‫א‬١{١{٦  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

  ‫א‬ ‫א‬   (Shear walls)‫א‬ ‫א‬   ‫א‬ 

‫א‬‫א‬ ‫א‬K‫א‬K  K‫א‬‫א‬‫א‬‫א‬

 WE٢ J٦F‫א‬W

‫א‬‫א‬‫א‬‫א‬ (Shear wall A and B)‫א‬ Y ‫א‬‫א‬‫א‬‫א‬

 E‫א‬ F ٥‫א‬K ٨ ← ١ X ‫א‬  KX‫א‬(un-braced)Y‫א‬(Braced)  - ٩٣ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

 E٢ J٦F    W‫א‬‫א‬٢{١{٦ (λ i = He/ i)‫א‬(λ b=He/b)‫א‬‫א‬‫א‬‫א‬  KE١ J٦F‫א‬‫א‬‫א‬‫א‬

 WK‫א‬‫א‬‫א‬‫א‬ZiW

i = 0.3b for rectangular section i = 0.25 D for circular section  K‫א‬‫א‬‫א‬‫א‬D،‫א‬‫א‬‫א‬bW

 

- ٩٤ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬E١ J٦F ‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬  λ i  λb λb  ٥٠  ١٢  ١٥    ٣٥

 ٨

 ١٠

 

 

K‫א‬‫א‬‫א‬‫א‬‫א‬•  W‫א‬‫א‬٢{٦  W‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬ E١

   ‫א‬ F K‫א‬  ‫א‬ ‫א‬‫א‬  ‫א‬   

(٢

KE‫א‬  W‫א‬‫א‬‫א‬١{٢{٦

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬E‫א‬‫א‬F‫א‬‫א‬‫א‬ E١ KE٣ J٦F‫א‬‫א‬K(Y)‫א‬(X)‫א‬‫א‬‫א‬‫א‬

  (B-3) ‫א‬   ‫א‬‫א‬ ‫א‬ E‫א‬ ‫א‬ F ‫א‬   E٢ K(A)‫א‬‫א‬‫א‬‫א‬‫א‬

- ٩٥ -

 

 ‫א‬‫א‬ ‫א‬‫א‬

 

 ٢٥١

 ‫א‬

 ‫א‬

 

 E٣ J٦F  W‫א‬‫א‬‫א‬‫א‬(B-3)‫א‬‫א‬P‫א‬‫ א‬E٣

 

 KEA‫א‬‫א‬‫א‬F‫א‬‫ א‬E

K‫א‬‫א‬‫א‬‫א‬ E 

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E K‫א‬‫א‬‫א‬ E

Therefore; total load P of each floor is equal to: P = W slab ×A + weight of beams + weight of walls + own weight of column - ٩٦ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

Where; W slab = t s × 2.5 + weight of flooring + Live Loads. If Weight of flooring = 150 kg/m2

t s = 12 cm,

and Live Loads = 300 kg/m2

So, W slab = 0.12 × 2.5 + 0.15 + 0.3 = 0.75 t/m2 Weight of beams = b × t × 2.5 × ∑ L beams

KE٢٠ZF‫א‬Z b W K(t = span / 10: 14) ‫א‬Z t  

‫א‬‫א‬‫א‬ (A)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬Z ∑ L beams K

Weight of walls = γ wall × h wall ×t wall × ∑ L walls  K‫א‬Zγ wallW

 KEF‫א‬‫א‬‫א‬Z h wall

 KE‫א‬‫א‬‫א‬F‫א‬Z t wall

‫א‬ ‫א‬  F ‫א‬ ‫א‬  ‫א‬‫א‬  ‫א‬‫א‬ ‫א‬  Z ∑ L



walls

  KE‫א‬

For example; If γ wall = 1.2 t/m3; t wall = 0.2 m

;

∑ L walls = 6.0 m ; h wall = 2.4 m

;

And, own weight of plaster = 50 kg/ m2 = 0.05 t/m2 i.e., Weight of wall = (1.2 × 0.2 + 0.05) × 2.4 × 6.0 = 4.176 tons / floor Own weight of column / floor = b c × t c × 2.5 × h c Where;

 E٠{٦F٠{٦←٠{٢Z‫א‬Zb c  ٢{٠←٠{٢٥Z‫א‬Zt c

- ٩٧ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬Zh c

 WPc‫א‬‫א‬‫א‬ Pc = total vertical load on column = N × Pc/floor  K‫א‬‫א‬ZNW  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ZPc/floor

 W

‫א‬  E‫א‬  ‫א‬ ‫א‬ ‫א‬ F ‫א‬           ‫א‬ ‫א‬    ٪ ١٠ ±       ‫א‬

‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬  W‫א‬‫א‬٣{٦  

‫א‬‫א‬EF‫א‬‫א‬

   K ‫א‬  ‫א‬    EF   Ke min.‫א‬‫א‬

e min = 0.05 t or 20 mms (Whichever is bigger)

 ‫א‬ ‫א‬   ‫א‬  ‫א‬ ‫א‬    ‫א‬   W‫א‬‫א‬‫א‬‫א‬

P = fc0 × Ac + 0.44 f y ×A sc

(6-1)

 

 W

 KEE٤ J١F‫א‬‫א‬Kf cu FZfc0

 K‫א‬‫א‬‫א‬ZAc

 K‫א‬‫א‬‫א‬‫א‬‫א‬Zf y  K‫א‬‫א‬‫א‬‫א‬ZA sc

 A sc = 1% ×AcW‫א‬µ = A sc/Ac = 1%‫א‬

E١ J٦F‫א‬‫א‬‫א‬‫א‬ ‫א‬  W  K‫א‬

- ٩٨ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

    ‫א‬‫א‬W٤ J٦ ‫א‬   ٪ ٠{٨  ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬  ‫א‬ ‫א‬  E١ ‫א‬‫א‬ ‫א‬‫א‬٪ ٠{٦‫א‬

 KE١ J٦F‫א‬‫א‬‫א‬(λ i)‫א‬(λ b)

‫א‬   ٪ ١  ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬  ‫א‬ ‫א‬ E٢  K‫א‬‫א‬‫א‬٪١{٢‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٣  W‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬٪٤ •  K‫א‬‫א‬‫א‬‫א‬٪٥ •

 K‫א‬‫א‬‫א‬‫א‬٪٦ •

 K‫א‬E٤  K١٢‫א‬E٥

 K٢٠‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٦

K ٣٠‫א‬‫א‬‫א‬ E٧ ‫א‬‫א‬‫א‬K ٢٥

 KE٤ J٦F ‫א‬ ‫א‬ F  ١٥  ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬

 KEF٦‫א‬‫א‬‫א‬‫א‬‫א‬

 E٤ J٦F - ٩٩ -

 

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

 

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٨  KE١٥FE

 K٢٠‫א‬‫א‬‫א‬E

 K٨¼E٩

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٠

‫א‬  K ٣    K ٨  ‫א‬     E١١ ‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬١٠١٠‫א‬‫א‬‫א‬

K‫א‬‫א‬٤٠‫א‬‫א‬E١٢

- ١٠٠ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

 W٥{٦

W‫א‬K١٠٠Z‫א‬‫א‬‫א‬W١  ‫א‬٣Z‫א‬‫• א‬

 K(36/52)‫א‬‫א‬‫• א‬

K٢L٢٥٠Z(f cu)‫א‬ •

 

Assume:

 ‫א‬

µ (total steel ratio) = 1% ; f co = 60 kg/cm2

(for f cu =250 kg/cm2)

And

f y = 3600 kg/cm2

i.e.,

applying in equation (6-1)

100×1000 = 60×Ac + 0.44×0.01×Ac×3600 = 75.84 Ac Ac = 1318.56 cm2

b = breadth of column = 25 cm; Take 1318 . 56 = 52 . 74 cm 25

t =

Take

t = 60 cm A sc = 1% ×25×60 = 15 cm2 Choose 8 Ø 16 mm

- ١٠١ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

 W٢

W‫א‬K150Z‫א‬‫א‬  ‫א‬4Z‫א‬‫• א‬

 K(36/52)‫א‬‫א‬‫• א‬

K٢L300Z(f cu)‫א‬ • Assume:

 ‫א‬

µ (total steel ratio) = 1% ; f co = 70 kg/cm2

(for f cu =300 kg/cm2)

And

f y = 3600 kg/cm2

i.e.,

applying in equation (6-1)

150×1000 = 70×Ac + 0.44×0.01×Ac×3600 = 85.84 Ac Ac = 1747.43 cm2

d = diameter of column = 50 cm; Take So

Ac =

π × (50 )2 4

= 1962 . 5 cm

A sc = 1% ×1962.5 = 19.62 cm2 Choose 8 Ø 18 mm =20.4 cm2

- ١٠٢ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

 W‫א‬‫א‬

٦{٦  

 K١ ‫א‬E٥ J٦F‫א‬

 

 ‫א‬E٥ J٦F

 

       

  ٨Φ١٨

 

‫ ﺳﻢ‬٥٠

     

 ‫א‬‫א‬‫א‬E٦ J٦F

   

- ١٠٣ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

 W3

 W‫א‬‫א‬E٦F‫א‬‫א‬‫א‬E٧ J٦F‫א‬  (C5 ; C6)٦W٥‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K (C5 ; C6) ٦W ٥‫א‬

K‫א‬

 

E١

E٢

 ‫א‬‫א‬‫א‬E٧ J٦F

 

 ‫א‬

 W

 (L.L = 200 kg/m2)‫א‬‫• א‬

 K‫א‬‫א‬E٨ J٦F‫א‬‫א‬ •

٧٠Z‫א‬‫א‬‫א‬K٢{٩٠Z‫א‬‫א‬ • - ١٠٤ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

 E‫א‬‫א‬FA5‫א‬(C5)٥‫א‬‫א‬

 E‫א‬‫א‬FA6‫א‬(C6)٦‫א‬‫א‬  

 E٨ J٦F For column (C5): • Slabs: W slab = t s× γ c + flooring + L.L = 0.1×2.5 +0.15 + .200 = 0.6 t/m2 Area (A5) = (3.0 + 1.0) ×(3.5/2) = 7 m2 ∑ loads from slabs = 0.6×7 + (0.12 -0.1) × 2.5× (3.5/2) ×3 = 4.463 tons - ١٠٥ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

• Beams: ∑ L (of Beams) = (3.5/2) + 1 +3 +1 = 6.75 ms O.W. of Beams = 0.2× (0.7 – 0.1) ×2.5 = 0.3 t/m ∑ loads of Beams = 6.75 ×0.3 = 2.025 tons. • Walls: γ wall = 1.2 t/m3 O.W. of wall = 0.2 ×1.2 +0.05 (Plaster) = 0.29 t/m2 ∑ L (of Walls) = 1 + 3 + (3.5/2) +1 = 6.75 ms h wall = 2.9 – 0.6 = 2.3 ms ∑ loads of walls = 6.75 ×0.29×2.3 = 4.5 tons. • Columns:

assume column dimension = 20 × 60 cm O.W. of column = 0.2 ×0.6 ×2.5 ×3 = 0.9 ton Total load P on column C5 = (Pc5) Pc5 (per one floor) = 4.463 + 2.025 + 4.5 + 0.9 =11.888 tons Pt = 11.888 × 6 = 71.328 tons = 72.0 tons For column (C6):

• Slabs: W slab = t s× γ c + flooring + L.L = 0.1×2.5 +0.15 + .200 = 0.6 t/m2 Area (A6) = (2.5/2 + 2.0) × (3.5/2 + 3.5/2) = 3.25 × 3.5 = 11.375 m2 ∑ loads from slabs = 0.6×11.375+ (0.12 -0.1)×2.5×(3.5/2)×3.25 =

7.11 tons

• Beams: ∑ L (of Beams) = (2.5/2) + 2 +3.5/2 +2.5/2 +3.5/2 = 8.0 ms O.W. of Beams = 0.2× (0.7 – 0.1) ×2.5 = 0.3 t/m - ١٠٦ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

∑ loads of Beams = 8.0 ×0.3 = 2.4 tons. • Walls: γ wall = 1.2 t/m3 O.W. of wall = 0.2 ×1.2 +0.05 (Plaster) = 0.29 t/m2 ∑ L (of Walls) = 8.0 ms h wall = 2.9 – 0.6 = 2.3 ms ∑ loads of walls = 8.0 ×0.29×2.3 = 5.336 tons. • Columns:

assume column dimension = 20 × 70 cm O.W. of column = 0.2 ×0.7 ×2.5 ×3 = 1.05 ton Total load P on column C5 = (Pc6) Pc6 (per one floor) = 7.11 + 2.4 + 5.336 + 1.05 =15.896= 16 tons Pt = 16 × 6 = 96 tons Design of column C5: Assume: f c0 = 60 kg/cm2

for

f y = 3600 kg/cm2 So;

f cu = 250 kg/cm2; and A sc= 1 % Ac

Pc5 = Ac × fc0 + 0.44× A sc× f y

72×1000 = 60 × Ac + 0.44×0.01×Ac×3600 = 60 Ac +12.32 Ac = 75.84 Ac Ac = 72000/ 75.84 = 949.3 cm2 Take b = 20 cm i.e.

t = 949.3 /20 = 47.4 cm

Take column section = 20 × 50 cm Area of required steel reinforcement (A sc) = 1/100 × 20×50 = 10 cm2 Take 6 Ø16 mm (A sc = 12.1 cm2) Use stirrups 5 Ø 8 mm/m

. C5 ‫( واﻟﺬي ﻳﻮﺿﺢ ﻗﻄﺎﻋًﺎ ﻋﺮﺿﻴًﺎ ﻓﻲ اﻟﻌﻤﻮد‬٩-٦) ‫اﻧﻈﺮ اﻟﺸﻜﻞ رﻗﻢ‬

- ١٠٧ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

C5‫א‬E٩ J٦F Design of column C6: Assume: f c0 =60 kg/cm2 f y = 3600 kg/cm2 So;

f cu = 250 kg/cm2;

for

and A sc= 1 % Ac

Pc6 = Ac × fc0 + 0.44× A sc× f y

96×1000 = 60 × Ac + 0.44×0.01×Ac×3600 = 60 Ac +12.32 Ac = 75.84 Ac Ac = 96000/ 75.84 = 1265.8 cm2 Take i.e.

b = 20 cm

t = 1265.8 /20 = 63.3 cm ≈ 70 cm Take column section = 20 × 70 cm

Area of required steel reinforcement (A sc) = 1/100 × 20×70 = 14 cm2 Take 8 Ø 16 mm (A sc = 16.1 cm2) Use stirrups 5 Ø 8 mm/m

KC6‫א‬  ‫א‬E١٠ J٦F‫א‬‫א‬

- ١٠٨ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

 C6‫א‬E١٠ J٦F

- ١٠٩ -

 

 

 ‫א‬‫א‬ ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

   W‫א‬‫א‬E٨ J٦F‫א‬  ‫א‬ (C1-C2-C3-C4-C7) ٧– ٤– ٣– ٢– ١‫א‬  ‫א‬‫א‬

‫א‬K ٧٠Z‫א‬‫א‬‫א‬K ٢{٩٠Z‫א‬‫א‬‫א‬

  E١

  

K‫א‬ (C1-C2-C3-C4-C7) ٧– ٤– ٣– ٢– ١‫א‬  (36/52)‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬

E٢

K٢L300Z(f cu)‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬

- ١١٠ -

E٣

‫א‬

‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫ א‬

١٠٣

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬ ‫א‬‫• א‬ ‫א‬   ‫א‬ ‫א‬ ‫א‬‫א‬   ‫א‬ ‫א‬ ‫א‬ ‫א‬  

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬ ،‫א‬‫א‬

 K‫א‬‫א‬   W‫א‬‫• א‬

‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬‫א‬    ‫א‬   ‫א‬ ‫א‬K‫א‬‫א‬‫א‬

K‫א‬

‫א‬ ‫א‬  ‫א‬  ‫א‬ ‫א‬   ‫א‬ ‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬

E١

E٢ E٣

E٤ 

W‫א‬‫א‬‫א‬ •  ٪١٠٠‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫• א‬  • W‫א‬‫א‬ •  K‫א‬‫א‬  K‫א‬‫א‬‫א‬ K‫א‬‫א‬

- ١١١ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬W١ J٧ ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬ K ‫א‬     ‫א‬     ‫ א‬    ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬

Shallow  ‫א‬  ‫א‬   ‫א‬      ‫א‬

 ‫א‬  ‫א‬   ‫א‬F ‫א‬   ‫א‬ ‫א‬    K foundation

‫א‬ ،‫א‬‫א‬‫א‬ E‫א‬

 K‫א‬‫א‬‫א‬KDeep foundation‫א‬

 

،‫א‬‫א‬‫א‬ ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬

  W‫א‬ ‫א‬ ‫א‬‫א‬   ‫א‬ ‫א‬    K‫א‬ ‫א‬ 

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬

  ‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬ ‫א‬‫א‬KE‫א‬‫א‬،‫א‬‫א‬

 W‫א‬‫א‬‫א‬

‫א‬‫א‬K (Strip footings)‫א‬‫א‬

  (١

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K(Spread footings)‫א‬‫א‬

(٢

       K (Combined footings) ‫א‬ ‫א‬

(٣

K‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬K،‫א‬ K

- ١١٢ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

    K ‫א‬  K (Raft foundations) ‫א‬ ‫א‬

(٤

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،    

  W‫א‬‫א‬‫א‬‫א‬‫א‬W٢ J٧ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬(D f)‫א‬(q all.)‫א‬‫א‬  

γ 1−



P a

  (7-1)

all

 

 K‫א‬ZPW

 K‫א‬‫א‬‫א‬ZPT

 KE٣L٢٠Z٣L٢ZF‫א‬‫א‬Zγ a  K‫א‬ZD f

 (Gross allowable bearing stress of the soil)‫א‬‫א‬‫א‬Zq all 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬PT‫א‬  

‫א‬   K‫א‬         ‫א‬ ‫א‬‫א‬ 

‫א‬  ‫א‬ ‫א‬‫א‬   E١ J٧F  ‫א‬ K ‫א‬  ‫א‬

 K‫א‬

 Two Way Footings ‫א‬‫א‬‫א‬E - ١١٣ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 One Way Footings‫א‬‫א‬‫א‬E



 

 ‫א‬‫א‬‫א‬‫א‬‫א‬E١ J٧F

   

‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬ ‫א‬‫א‬ K‫א‬  ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬  WK‫א‬‫א‬‫א‬

(L - l) = (B - b)

(7-2)

 

 W‫א‬‫א‬‫א‬

A = L × B = PT/q all

(7-3)

q all = P T / (L × B)

(7-4) - ١١٤ -

 

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

‫א‬  B ، LE3 J٧F،E2 J٧F 

 KE١ J٧F‫א‬PTKE٥F‫א‬

 

‫א‬‫א‬‫א‬E١ J٧F‫א‬‫א‬PT K(B,L)‫א‬‫א‬PTK

 

 ‫א‬‫א‬‫א‬E2 J٧F  

‫א‬‫א‬ ‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬ ‫א‬  ‫א‬   ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬ 

 K‫א‬KE٢ J٧F

 W‫א‬‫א‬ Section a -a:

P = A

⎡ ⎛ L − l ⎞2 ⎟ / 2 + ⎢b ⎜ ⎢⎣ ⎝ 2 ⎠

(B − b )⎛⎜ L − l ⎞⎟ ⎝ 2 ⎠

- ١١٥ -

⎤ / 3⎥ ⎥⎦

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

(7-5) M

P 24 × A

)(L

B + b

− l

)2 Section a′- a′:

(7-6) M

P 24 × A

L + l

)(B

− b

)2  W‫א‬‫א‬ Section a -a:

(7-7)

(7-8)

P L

−

P B

−



/ 8

 

  ‫א‬ ‫א‬   KE6 J٧F ، E5 J٧F  ‫א‬ ‫א‬  ‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬  ‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬

 WQ b‫א‬

Fn=P/A

(7-9)

 

W‫א‬‫א‬Q b For section a -a: Q b =¼ (B + b) (L - l) × F n

(7-10) For section a′- a′: - ١١٦ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

Q b =¼ (L + l) (B - b) × F n

(7-11)  Punching Depth ‫א‬‫א‬W١ J٢ J٧

   (L × B) ‫א‬ ‫א‬   (l × b)  ‫א‬   ‫א‬  

‫א‬‫א‬K(Direct Shear)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬

 K٢L٨q P‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

KE3 J٧F‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬

E‫א‬‫א‬F‫א‬˚٤٥‫א‬

 W‫א‬‫א‬K‫א‬‫א‬  

2 ⎞ ⎛ 2 ⎞ ⎛ = P − Fn ⎜ b + d ⎟ × ⎜ l + d ⎟ P 3 ⎠ ⎝ 3 ⎠ ⎝

(7-12)      

 W‫א‬‫א‬‫א‬‫א‬  

qP =

QP 2 d (l + b + 1 .33 d ) 

 

- ١١٧ -

(7-13)  

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 

E3 J٧F  WW3 J٧  ١

K ١{٠‫א‬K ١٠٠ ٤٥ × ٤٥

 E١٨ø٨‫א‬F٢L١{٧٥‫א‬

 

 ‫א‬

 

 E٤ J٧F - ١١٨ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 

Footing Dimensions:

= 1 −

P a

× D q all

= f

100 = 112 . 9 ton 2 ×1 1 − 17 . 5

A = 112.9 / 17.5 = 6.452 m2

A = 2.54 = 2.55m Concrete Sections:

P (2B + b)(L − l )2 = 100 2 (5.1 + 0.45)(2.55 − 0.45)2 = 15.683m.t 24 × A 24 × (2.55)

Q b =¼ (B + b) (L - l) × F n =¼ (2.55 + 0.45) (2.55 -0.45) × 15.38 = 24.221 ton

Q But

2 ⎞ ⎛ 2 ⎞ ⎛ = P − Fn ⎜ b + d ⎟ × ⎜ l + d ⎟ P 3 ⎠ ⎝ 3 ⎠ ⎝ 15 . 683 × 10 5 = 49 cm (45 + 20 )

d = 0 . 313 ×

Take d =50 cm so, Q P = 100 −

t = 55 cm

100 ⎛ 2 2 ⎞ ⎞⎛ 0 . 45 0 . 5 0 . 45 + × 0.5 ⎟ = 90.564ton + × ⎟ ⎜ ⎜ 2 3 3 2.55 ⎝ ⎠ ⎠⎝

QP 90 . 564 × 10 3 = 5 . 78 kg / cm = = 2 d (l + b + 1 . 33 d ) 2 × 50 (45 + 45 + 66 . 7 )

M 15.68 × 10 5 2 As = k 2 × d = 1217 × 50 = 25.75cm Choose 13 Ø 16 mm

Q 24.221× 1000 = = 8.57 < 10kg / cm2 0.87 × d × ∑ o o o o 0.87 × 50 × (13π × 1.6) Footing is 2.55 ×2.55 ×0.55 (13 Ø 16 in each direction)

 W‫א‬‫א‬ ٤ J٧ - ١١٩ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

‫א‬ ‫א‬ ‫א‬  ‫א‬  ‫א‬   ‫א‬  E٥ J٧F  ‫א‬ ‫א‬  K‫א‬

 

 E٥ J٧F

- ١٢٠ -

 

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 W٢

 ١٥٠ K ١٦ Ø ١٢E٧٥ × ٣٠F

   ‫א‬‫א‬‫א‬K ٢L ٢{٠‫א‬‫א‬  KEq p = 8 kg/cm2‫א‬‫א‬‫א‬FK‫א‬  

W‫א‬  

A = P / F all.net = 150 / 20 = 7.5 m2 Take B=2.5 m;

i.e. (L - l) = (B - b) L = (2.5 – 0.30) + 0.75 = 2.95 m Choose L = 3.0 m , B = 2.5 m  i.e. L x B = 3 x 2.5 = 7.5 m2

 

 E٦ J٧F  

- ١٢١ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

M a−a =

P (2 B + b )(L − l )2 = 150 (5 . 3 )(2 . 25 )2 = 22 . 36 t .m 24 × A 24 × 7 . 5

M a ′− a ′ =

P (2 L + l )(B − b )2 = 150 (6 . 75 )(2 . 2 )2 = 27 .225 t .m 24 × A 24 × 7 . 5

Q b a-a =¼ (B + b) (L - l) × P/A = ¼ × 150/7.5(2.8) (2.25) = 31.50 ton Q b a′-a′ =¼ (L + l) (B - b)× P/A = ¼ × 150/7.5(3.75) (2.2) = 41.25 ton Concrete Sections; d = 0 . 313 ×

22 . 360 × 10 5 = 66 . 16 cm (30 + 20 )

t = 70 cm

M 22.360 × 105 2 As = k 2 × d = 1217 × 65 = 28.24cm M 27.225 × 10 5 2 As′ = k 2 × d = 1217 × 63 = 35.5cm

Choose 15 Ø 16 mm

Choose 18 Ø 16 mm

Q 41.25 × 103 qb = 0.87 × d × ∑ o o o o = 0.87 × 63 × (18π × 1.6) = 8.36 < 10kg / cm2 (Safe) Q p = 150-20(0.3+0.44)(0.75+0.44) = 132.4 ton

QP 132 . 4 × 10 3 qP = = = 5 . 04 < 8 kg / cm 2 ( Safe ) 2 d (l + b + 1 . 33 d ) 2 × 65 (75 + 30 + 97 )

- ١٢٢ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

   E٧ J٧F  

- ١٢٣ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬ K١٨φ١٢٨٠×٣٠E

‫א‬ ‫א‬ K ٢L ٢{٤  ‫א‬ ‫א‬   K  ١٨٠ 

E١

 

K‫א‬‫א‬

  ‫א‬   ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬ ‫א‬ E  K‫א‬

K ٢٢ φ ١٢ ٣٥× ٣٥ E ١{٥ ٢L ٣{٠٠‫א‬K ٨٥ 

   

 

E٢

K‫א‬‫א‬

   

 W  

‫א‬‫א‬‫א‬‫א‬E١

 K٢L٨q P‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬  K١٠‫א‬‫א‬‫א‬

E٢

K‫א‬‫א‬١٢٥‫א‬

E٣

 K‫א‬‫א‬‫א‬‫א‬

E٥

K٥{٠٣{٠‫א‬

- ١٢٤ -

E٤

 

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬W‫א‬‫א‬

  W‫א‬‫• א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ ‫א‬   ‫א‬ ‫א‬ ‫א‬‫א‬  E‫א‬ ‫א‬  ‫א‬ ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬

  W‫א‬‫• א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E١  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٢ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٣ 

W‫א‬‫א‬‫א‬ •  ٪١٠٠‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ W‫א‬‫א‬‫א‬‫• א‬  K‫א‬‫א‬ •  K‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

- ١٢٥ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

  ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬‫א‬ ‫א‬  ‫א‬  

W‫א‬‫א‬‫א‬‫א‬١{٨  

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫• א‬  K‫א‬‫א‬‫א‬‫א‬‫• א‬

 

 W‫א‬‫א‬‫א‬‫א‬‫א‬١{١{٨

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬    

- ١٢٦ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 

K‫א‬‫א‬WE١{٨F

 

KWE٢{٨F

- ١٢٧ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 KWE٣{٨F

 

‫א‬‫א‬‫א‬‫א‬‫א‬

     ‫א‬  ٤W١ ‫א‬       ‫א‬ ‫א‬  H ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 12

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KE٤{٨F٣٥ ‫א‬‫א‬‫א‬K‫א‬

 K‫א‬‫א‬‫א‬

 W‫א‬‫א‬  ‫א‬‫ א‬ J

 

K‫א‬‫א‬  J  

 

- ١٢٨ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

   

 

   

 W   H  H ZD 6

 

  2H  H ZB 3

   

 

 K‫א‬‫א‬WE٤{٨F

   

 W‫א‬‫א‬‫א‬‫א‬‫א‬٢{١{٨  

‫א‬EheelF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬

  cantilever wallW‫א‬‫א‬‫א‬ J

 counterfort wallW‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ J

 W‫א‬‫א‬

 

 ‫א‬ •  ‫א‬‫א‬ •

  - ١٢٩ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

cantilever wallW‫א‬‫א‬‫א‬ J



 K٢٥‫א‬‫א‬‫א‬‫א‬E٥{٨F  



  

 K‫א‬‫א‬E٥{٨F

   

K‫א‬  ‫א‬ ‫א‬ ‫א‬‫א‬    E٦{٨  F ‫א‬ ‫א‬‫א‬ 

 ‫א‬   ‫א‬ ‫א‬      ‫א‬  ‫א‬‫א‬ 

 H F‫א‬‫א‬‫א‬‫א‬ H ٣٠K‫א‬ 12

 K‫א‬‫א‬‫א‬E H  10

 

‫א‬‫א‬   ‫א‬  ‫א‬ ‫א‬  ‫א‬   ‫א‬  ‫א‬   K‫א‬‫א‬

   

- ١٣٠ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

   

 

     

 W   H ZD 12

 

  2H  H ZB 3



 

 K‫א‬‫א‬WE٦{٨F

     

 counterfort wallW‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ J

‫א‬  KE٧{٨F،

K‫א‬‫א‬WE٧{٨F - ١٣١ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫ א‬٢{٨  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬E١  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٣  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٤ 

 W‫א‬‫א‬‫א‬‫א‬٣{٨

 W‫א‬‫א‬‫א‬‫א‬ E١  W‫א‬‫א‬‫א‬‫א‬ ⎡1 − Sinφ ⎤   P = W .H .K a = W .H ⎢1 + Sinφ ⎥ ⎦ ⎣

 W  ‫א‬‫א‬WW  ‫א‬‫א‬‫א‬WH  KE١{٨F‫א‬‫א‬WΦ  K‫א‬‫א‬WKa  W‫א‬‫א‬‫א‬‫א‬

 

P.H 2  K‫א‬‫א‬٣L١

- ١٣٢ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١{٨F

Φ‫א‬‫א‬  E٣LF‫א‬  ‫ﺑﺎﻟﺪرﺟﺔ‬

 ‫א‬

 ٣٧

 ١٥٠٠

 

 ٣٥

 ١٧٠٠

 

 ٣٢

 ١٩٠٠

 

 ٢٤–١٦

 ٢١٠٠

 

 ٤٨

 ١٨٠٠ J١٦٠٠

 ‫א‬

 ٤٥

 ١٩٠٠ J١٨٠٠

 ‫א‬

 ٢٠ J١٧

 ٢٠٠٠ J١٩٠٠

 ‫א‬

 ٥٠

 ١٧٠٠

 

 ٤٥

 ١٨٠٠

 

 ١٥

 ١٩٠٠

 

 ٤٥–٣٨

 ١٨٠٠

 

 ٣٥–٢٦

 ٢٣٠٠

 

 ٣٨

 ٢٣٠٠

 

 ٣٥

 ١٧٥٠

     W١

‫א‬ ٣L ١{٥‫א‬ ٣٠‫א‬‫א‬ ٥{٠‫א‬

 K‫א‬  

- ١٣٣ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬ 1 − 0.5 ⎤ = 2.50  ⎣1 + 0.5 ⎥⎦

⎡   P = 1.5 × 5.0⎢

   P =

2 .5 × 5 .0 = 6.25  2

   W‫א‬‫א‬‫א‬‫א‬E٢ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬ WS‫א‬‫א‬ P

  ‫א‬  ‫א‬ F ‫א‬  ‫א‬   ‫א‬ ‫א‬  ‫א‬  K X ‫א‬‫א‬‫א‬EToeF‫א‬  X =

∑M ∑W  W  KEToeF‫א‬‫א‬W ∑ M  K‫א‬‫א‬W ∑W  

B=‫א‬‫א‬‫א‬e‫א‬  e =

B −X 2  K B e‫א‬ 6

 

- ١٣٤ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 ١{٥٠‫א‬‫א‬‫א‬‫א‬

 K‫א‬٢{٠٠‫א‬  

∑   FSL =

resisting. forces

∑ driving. forces

f 1.5

  ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬    K‫א‬   ‫א‬ ‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬ 

 K‫א‬٢{٠٠‫א‬١{٥٠‫א‬   M

St   Fov = M ≥ 1.5 OV

 W  K‫א‬‫א‬W M St  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W M OV    W٢ ٧{٥٠‫א‬ ٢L ١{٥٠‫א‬‫א‬    

‫א‬‫א‬‫א‬‫א‬١{٥٠‫א‬

K٣٠٠‫א‬‫א‬‫א‬‫א‬٣L١{٧‫א‬‫א‬  

- ١٣٥ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

+0.00

   W‫א‬  K‫א‬‫א‬

B =4,5 m  K١{٢٥Z‫א‬  W‫א‬E١   K a = ⎡⎢1 − Sinφ ⎤⎥ = 1 / 3 ⎣1 + Sinφ ⎦ - ١٣٦ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

  Kp =   P = W × H × Ka

1 =3 Ka

⎡1 − Sinφ ⎤ =W ×H ×⎢ ⎥ ⎣1 + Sinφ ⎦

 Pa1=1.5x(1/3)x7.5=3.75 t/m

Pa2=(1/2) x1.7x(7.5)2x (1/3)=15.94 t/m Pp=(1/2) x1.7x(1.5)2x (3)=5.74 t/m

 W  K‫א‬‫א‬ZPp    W‫א‬‫א‬E٢   W1= 1.5x2.6 +(6.85x2.6x1.7) = 34.177 t/m W2= 0.3x6.85x2.5 = 5.138 t/m W3= 0.35x6.85x2.5/2 = 2.997 t/m W4= 0.65x4.5x2.5 = 7.313 t/m ΣV = 34.177 + 5.138 + 2.997 + 7.313 = 49.625 t/m  

  Wall Stability W‫א‬‫א‬‫א‬

ΣM/Toe W‫א‬‫א‬ ΣM/Toe = (34.177x3.2) + (5.138x1.75) + (2.997x1.48) + (7.313 x2.25)+  (5.74x0.50)-(3.75x3.75)-(15.94x2.5) = 142.118 – 53.913 = 86.22 t.m/m.

     (over-turning)‫א‬‫א‬‫א‬‫א‬‫א‬ - ١٣٧ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

    Fov =

M St = M OV

∑ Re sisting.Moment = 142.17 = 2.635 ≥ 1.5 ∑ Overturning.moment 53.913 O.K.

:e‫א‬ X=

88.22 = 1.78m 49.625

  e = B − X = 4.5 − 1.78 = 0.47 p B = 4.5 0.75 2

O.K.

ΣM/base = ΣV x e = 49.625 x 0.47 = 23.324 tm/m. ‫إﺟﻬﺎد ﻋﻨﺪ اﻟﻘﺪم‬ 49.625 23.324 × 6 + = 11.03 + 6.91 = 17.94t / m 2 2 4.5 (4.5)

f toe =

‫إﺟﻬﺎد ﻋﻨﺪ اﻟﻜﻌﺐ‬ f heel =

49.625 23.324 × 6 − = 11.03 − 6.91 = 4.12t / m 2 2 4.5 (4.5)

   W(Sliding)‫א‬‫א‬‫א‬‫א‬‫א‬ Driving Force = Pa1 + Pa2 = 3.75 + 15.94 =19.69 t/m Resisting Force = Pp + V tan Φ = 5.74 + 49.625 x 0.5774 = 34.39 t/m.

FSL =

∑ resisting. forces = 34.39 = 1.75 f 1.5 ∑ driving. forces 19.69 - ١٣٨ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

OK Design of Stem:    K٦{٨٥Z٠{٦٥–٧{٥٠Z‫א‬‫א‬‫א‬‫א‬  K٦{٨٥‫א‬stem‫א‬‫א‬‫א‬‫א‬ W‫א‬‫א‬‫א‬

 

  WEarth Pressure W‫א‬

PD = (1.5 x1/3) + (1.7 x 1.725 x 1/3) = 0.5 + 0.977 = 1.477 t/m2. PC = (1.5 x1/3) + (1.7 x 3.45 x 1/3) = 0.5 + 1.955 = 2.455 t/m2. PB = (1.5 x1/3) + (1.7 x 5.15 x 1/3) = 0.5 + 2.918 = 3.418 t/m2. PA = (1.5 x1/3) + (1.7 x 6.85 x 1/3) = 0.5 + 3.881 = 4.381 t/m2.

 Shear ForceW‫א‬ VD = (0.5 x 1.725) + (0.977 x 1.725 x 1/2) =0.862 + 0.843 = 1.705 t. VC = (0.5 x 3.45) + (1.955 x 3.45 x 1/2) =1.725 + 3.372 = 5.097 t. - ١٣٩ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 VB = (0.5 x 5.15) + (2.918 x 5.15 x 1/2) =2.575 + 7.513 = 10.089 t.

VA = (0.5 x 6.85) + (3.881 x 6.85 x 1/2) =3.425 + 13.292 = 16.717 t.

Bending Moment W‫א‬  MD

0.5 × (1.725) 2 ⎛ 0.977 × 1.725 1.725 ⎞ +⎜ × ⎟ = 0.744 + 0.484 = 1.228 t.m 2 2 3 ⎠ ⎝

t.m. M C =

0.5 × (3.45) 2 ⎛ 1.955 × 3.45 3.45 ⎞ +⎜ × ⎟ = 2.975 + 3.878 = 6.853 2 2 3 ⎠ ⎝

t.m. M B =

0.5 × (5.15) 2 ⎛ 2.918 × 5.15 5.15 ⎞ +⎜ × ⎟ = 6.630 + 12.900 = 19.530 2 2 3 ⎠ ⎝

t.m. M A =

0.5 × (6.85) 2 ⎛ 3.881 × 6.85 6.85 ⎞ +⎜ × ⎟ = 11.730 + 30.356 = 42.086 2 2 3 ⎠ ⎝

Section A: Assume And

f c =60 kg / cm2

(f cu = 250 kg / cm2)

f s = 1400 kg/cm2

(mild steel 37—24/35)

i.e. k 1= 0.313

From table (4-1) and

k 2 = 1217

Eb=100cm.F١{٠‫א‬EdF‫א‬‫א‬

   

d = k1

M b

0 . 313

42 , 086 × 100000 100

= 64.21 cm.

Take t = 70.0 cm d act. = t – cover = 70.0 – 5 = 65.0 cm.

 

W‫א‬‫א‬ M ×105 As = k2 × d

42.86×105 = 54.18 cm2/m 1217× 65

  Choose 12 Ø 24 mm/m (54.24cm2/m) - ١٤٠ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

Section B: d = 0 . 313

19 . 530 × 100000 = 43 . 74 cm. 100

t = 60.0 cm d act. = t – cover = 60.0 – 5 = 55.0 cm. M ×105 As = k2 × d

19.55×105 = 29.20 cm2/m 1217× 55

Choose 12 Ø 20 mm/m (39.6 cm2/m)

Section C: 6 . 853 × 100000 = 25 . 91 cm. 100

d = 0 . 313

t = 50.0 cm d act. = t – cover = 50.0 – 5 = 45.0 cm.

As =

M ×105 k2 × d

6.853×105 = 12.51 cm2/m 1217× 45

Choose 6 Ø 20 mm/m (19.8 cm2/m) Check: As min = 0.25% Ac = 0.25/100 ×70×100 = 17.5 cm2

 K‫א‬‫א‬E٨{٨F

- ١٤١ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

+0.00

16 6

 

6 +

19 22

 K‫א‬‫א‬WE٨{٨F - ١٤٢ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 ‫א‬W٢{٨  ١٦

 ١٩

 ٢٢

 ٢٠

 ٢٤

 EFΦ

 ٨

 ٦

 ١٢

 

 

 

 

 ٧٢٠

 ٣٠٠

 ٦٦٠

 ٣٠٠

 ٣٦٠

EF

  ٩٩٠

   

 



 



 

- ١٤٣ -

 ‫א‬‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

 (References) ‫א‬‫א‬

1) BS 8110 – 1985

 

2) CP 110 , 1972 3) Jack C. McCormack ˝Design of Reinforced Concrete˝ Fourth Edition Copyright © 1998 by Addison Wesley Longman, Inc. 4) James G. Macgregor ˝Reinforced Concrete – Mechanics and Design˝ Third Edition © 1997 Prentice-Hall, Inc. ‫א‬‫א‬‫א‬‫א‬˝‫א‬K E٥  K‫א‬ J‫א‬˝‫א‬ K١٩٩٥‫א‬١٩٨٩˝‫א‬‫א‬‫א‬‫א‬‫ ˝א‬E٦

7) M. Hillal ˝Fundamentals of reinforced and pre-stressed concrete˝ Dar ElNashr Cairo 1992. 8) Reynolds, C.E and Steadman, J.C ˝Reinforced Concrete Designers˝ Handbook 9th Edition. -1981. 9) Robert Park and William L. Gamble. ˝Reinforced Concrete Slabs˝ Second Edition John Wiley & Sons Inc 2000. 10) Shaker El-Behairy, ˝Reinforced Concrete Design Handbook˝ Part I , II and III Fifth Edition Dar-El-Nashr-Cairo 1998.  

 ‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

 ‫א‬  ‫א‬

 

  

 ‫א‬‫א‬‫א‬W‫א‬‫א‬

 ‫א‬‫א‬–‫א‬‫א‬–‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬W١ J١

 ‫א‬W٢ J١

 ‫א‬‫א‬W١ J٢ J١

 ‫א‬‫א‬W٢ J٢ J١

 ‫א‬W٣ J١

 ‫א‬‫א‬‫א‬‫א‬W٤ J١

 ‫א‬W١ J٤ J١

 ‫א‬E‫א‬F‫א‬‫א‬W٢ J٤ J١

 ‫א‬W٣ J٤ J١

 ‫א‬‫א‬‫א‬‫א‬W٤ J٤ J١

 ‫א‬‫א‬‫א‬W٥ J١

 ‫א‬W١ J٥ J١

 E‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬W٢ J٥ J١

١٠

 ‫א‬‫א‬W٣ J٥ J١

١١

 ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬

‫א‬‫א‬–‫א‬‫א‬–‫א‬‫א‬

١٢

 ‫א‬‫א‬W١ J٢

١٢

 ‫א‬‫א‬W١ J١ J٢

١٣

 ‫א‬‫א‬‫א‬‫א‬W٢ J١ J٢

١٤

 ‫א‬‫א‬W٢ J٢

 ‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

١٦

 K‫א‬‫א‬‫א‬W٣ J٢

١٦

 ‫א‬‫א‬‫א‬W١ J٣ J٢

١٦

 ‫א‬‫א‬W٢ J٣ J٢

١٦

 W٢ J٤ J٢

١٩

 ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬

 ‫א‬‫א‬–‫א‬‫א‬–‫א‬‫א‬

٢٠

 ‫א‬‫א‬W١ J٣

٢١

 ‫א‬‫א‬‫א‬W٢ J٣

٢١

 W١ J٢ J٣

٢١

 ‫א‬‫א‬W٢ J٢ J٣

٢٢

 ‫א‬‫א‬‫א‬‫א‬W٣ J٣

٢٣

 ‫א‬‫א‬W٤ J٣

٢٨

 ‫א‬‫א‬‫א‬W٥ J٣

٢٩

 W٦ J٣

٣٢

‫א‬‫א‬W‫א‬‫א‬‫א‬

 ‫א‬‫א‬–‫א‬‫א‬–‫א‬‫א‬

٣٣

 ‫א‬‫א‬‫א‬W١ J٤

٣٥

 ‫א‬‫א‬‫א‬‫א‬‫א‬W٢ J٤

٣٦

 ‫א‬‫א‬‫א‬W٣ J٤

٣٦

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٤{٤

٣٧

 ‫א‬‫א‬‫א‬W١ J٤ J٤

٣٩

 ‫א‬‫א‬W٢ J٤ J٤

٣٩

 ‫א‬‫א‬‫א‬W٣ J٤ J٤

٤٠

 W٤ J٤ J٤

٤٤

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٥ J٤

 ‫א‬

 ٢٥١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬W‫א‬‫א‬ ٤٦

 ‫א‬‫א‬–‫א‬‫א‬–‫א‬‫א‬

٤٧

 W١ J٥

٤٧

 K‫א‬‫א‬‫א‬‫א‬‫א‬W٢ J٥

٤٩

 K‫א‬‫א‬‫א‬‫א‬W١ J٢ J٥

٥٠

 K‫א‬‫א‬‫א‬‫א‬ ٢{٢{٥

٥٠

 ‫א‬‫א‬‫א‬W٣ J٥

٥٨

  ‫א‬‫א‬‫א‬٤ J٥

٥٩

 ‫א‬‫א‬‫א‬‫א‬W١ J٤ J٥

٦١

 L&T‫א‬‫א‬W٢ J٤ J٥

٦٥

 ‫א‬‫א‬‫א‬W٥ J٥

٦٦

 ‫א‬‫א‬‫א‬‫א‬W١ J٥ J٥

٦٨

 W٦ J٥

٧٠

 ‫א‬ W٧ J٥  ‫א‬‫א‬‫א‬W‫א‬‫א‬

٧٢

 ‫א‬‫א‬–‫א‬‫א‬–‫א‬‫א‬

٧٣

 ‫א‬‫א‬W١ J٦

٧٣

 ‫א‬‫א‬‫א‬١{١{٦

٧٤

 ‫א‬‫א‬٢{١{٦

٧٥

 ‫א‬‫א‬W٢ J٦

٧٥

 ‫א‬‫א‬‫א‬W١ J٢ J٦

٧٧

 ‫א‬‫א‬W٣ J٦

٧٧

 ‫א‬‫א‬W٤ J٦

٧٩

 W٥ J٦

 ‫א‬

٨٠

 ٢٥١

 ‫א‬

 ‫א‬

 

 K‫א‬‫א‬W٦ J٦  ‫א‬W‫א‬‫א‬

٨٧

 ‫א‬‫א‬–‫א‬‫א‬–‫א‬‫א‬

٨٨

 ‫א‬‫א‬W١ J٧

٨٨

 K‫א‬‫א‬‫א‬‫א‬‫א‬W٢ J٧

٩٢

 ‫א‬‫א‬W١ J٢ J٧

٩٣

 W٣ J٧

٩٥

 K‫א‬‫א‬ W٤ J٧  ‫א‬‫א‬‫א‬W‫א‬‫א‬

٩٩

 ‫א‬‫א‬–‫א‬‫א‬–‫א‬‫א‬

١٠٠

 ‫א‬‫א‬‫א‬‫א‬W١ J٨

١٠٠

 K‫א‬‫א‬‫א‬‫א‬‫א‬W١ J١ J٨

١٠٢

 ‫א‬‫א‬‫א‬‫א‬‫א‬W٢ J١ J٨

١٠٥

 ‫א‬‫א‬W٢ J٨

١٠٥

 ‫א‬‫א‬‫א‬‫א‬W٣ J٨

١١٦  

 



(References)

‫א‬‫א‬

   

                         