تصميم كل العناصر الانشائية

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 K‫א‬W١J ٢

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

 W‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬

E١

‫א‬‫א‬

E٣

‫א‬‫א‬ ‫א‬

‫א‬

E٢

E٤

E٥

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

E١

‫א‬

E٢

‫א‬

E

E 

E٣

 EDead LoadsF‫א‬‫א‬‫א‬W١J ١J 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 

 KKKKKKKKK‫א‬‫א‬ 

 (Slab Dead load)‫א‬‫א‬W١J ١J ١J 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  O.W of slab = A × t × γ c،i.e

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

- ١٦ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬ E١J ٢F‫א‬  K‫א‬‫א‬

 E١J ٢F EF‫א‬‫א‬

EF‫א‬

 ٢L٢٠٠

 ٨

 ٢L٢٥٠

 ١٠

 ٢L٣٠٠

 ١٢

 ٢L٣٥٠

 ١٤

 ٢L٤٠٠

 ١٦

 ٢L٤٥٠

 ١٨

 ٢L٥٠٠

 ٢٠    ‫א‬W

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

٥J ٣HE‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬F  ٢L١٥٠Z‫א‬E١J ٢F  Tiles Mortar 3-5cm sand isolated sheets

R.C slab

(plaster)

 E١J ٢F - ١٧ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

‫א‬ ٢L ٢٥٠J ٢٠٠‫א‬‫א‬‫א‬‫א‬  K٥‫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 •



 ‫א‬‫א‬‫א‬‫א‬‫א‬W٢J ١J ١J ٢  W‫א‬‫א‬‫א‬‫א‬‫א‬

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

E

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

E 

‫א‬F(O.W of slab)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E KE١J ١J ١J ٢‫א‬ ‫א‬‫א‬‫א‬‫א‬

E

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

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

١٠J ٨L‫א‬ZtZ‫א‬

  For simple beams choose t = span / 8

‫א‬‫א‬

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

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

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

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

Where;

= 10 cm = 0.1 m‫ ﺳﻤﻚ اﻟﺒﻼﻃﺔ‬γc = 2.5 t/ m3 , ts = =1.0 m E١{٠‫א‬F L0 = length of beam O.w. of beam = 1.0 × 0.2 × (0.6 – 0.1) ×2.5 = 0.25 t/m i.e.  L٠{٢٥Z‫א‬‫א‬‫א‬ - ١٨ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

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

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

 γ wall = 1.20

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

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

 γ wall = 0.75:1.2 t/m3 ‫א‬‫א‬‫א‬E٣  γ wall = 0.6 :0.8 t/m3 ‫א‬‫א‬‫א‬E٤ γ wall = 1.8

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

 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،‫א‬‫א‬‫א‬‫א‬

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

 W wall = γ wall × t wall × 1

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

 K‫א‬‫א‬‫א‬‫א‬‫א‬  (Live Loads)‫א‬‫א‬W٢J ١J ٢

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

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

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

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W١J ٢J ١J ٢ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬

٢L١٢٥J ٧٥‫א‬‫א‬‫א‬‫א‬‫א‬  K٢L١٥٠J 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

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢J ٢F‫א‬‫א‬

K‫א‬KKKKK ‫א‬‫א‬ ‫א‬F‫א‬‫א‬E١F BS 8110‫א‬‫א‬

 KEE٦F‫א‬‫א‬‫א‬

 (working life loads )‫א‬‫א‬F‫א‬‫א‬E٢J ٢F



٢L‫א‬‫א‬ 

 ‫א‬

  W‫א‬‫ א‬ ١

 ٥٠

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

 ١٠٠

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

 ٤٠٠

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

 ٢٠٠

 E



 ٢٠٠  ٣٠٠

 W  ٢

 ‫א‬‫א‬E

 E‫א‬F‫א‬‫א‬E



 ٣٠٠  ٤٠٠

 W‫א‬‫א‬‫ א‬ ٣

 ‫א‬E

 E‫א‬F‫א‬‫א‬E

 ١٠٠٠J ٥٠٠

 E‫א‬F‫א‬E

  ٣٠٠

 W‫א‬‫ א‬ ٤  E‫א‬F‫א‬‫א‬E - ٢٠ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 ٤٠٠

 ‫א‬‫א‬‫א‬E

 ٥٠٠

 ‫א‬‫א‬E

 W‫ א‬ ٥

  ٣٠٠  ٤٠٠

 E‫א‬F‫א‬‫א‬E

‫א‬‫א‬‫א‬‫א‬‫א‬E

 ‫א‬



 ‫א‬‫א‬‫א‬E

 ٥٠٠J ٣٠٠

 ‫א‬E

 ٨٠٠J ٥٠٠   ٥٠٠

 ٦٠٠

 W(Halls)W‫א‬‫ א‬ ٦  ‫א‬‫א‬‫א‬‫א‬E

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

  ٥٠٠

 ١٠٠٠

 E‫א‬F‫א‬‫ א‬ ٧  E‫א‬F‫א‬‫א‬E

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



 ٢٠٠  ٤٠٠

 W‫ א‬ ٨

 ‫א‬E

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



 W‫ א‬ ٩

 ٤٠٠

 ‫א‬E

 ١٠٠٠

 ‫א‬E



 ٣٠٠

 W‫א‬‫ א‬ ١٠

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



 ٢{٤

 ٤٠٠

 ‫א‬‫א‬‫א‬E

 ٥٠٠

 ‫א‬‫א‬E   - ٢١ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬W٢J ٢J ١J ٢ ‫א‬‫א‬  ‫א‬  ‫א‬ ‫א‬    ‫א‬ ‫א‬ ‫א‬‫א‬   W

   ‫א‬‫א‬   ‫א‬ ‫א‬   ‫א‬    

‫א‬

E

 K‫א‬ EF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ ‫א‬‫א‬ ،EF

E 

‫א‬ ‫א‬   ‫א‬   ‫א‬ ‫א‬   ‫א‬‫א‬ 

E٣J ٢F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬E‫א‬F‫א‬‫א‬P  

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٣J ٢F 

 ‫א‬‫א‬‫א‬

 ‫א‬

P

 E‫א‬F‫א‬‫א‬

P

 ‫א‬‫א‬‫א‬

0.9P

 ‫א‬‫א‬‫א‬

0.8P

 ‫א‬‫א‬‫א‬

0.7P

 ‫א‬‫א‬‫א‬‫א‬

0.6P

 ‫א‬‫א‬‫א‬

0.5P

 ‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬(0.5P)‫א‬  (Design Loads)‫א‬‫א‬W٢J ٢  ‫א‬‫א‬(Working Loads) ‫א‬W١J ٢J ٢

  ‫א‬ ‫א‬    ‫א‬ ‫א‬  ‫א‬   ‫א‬K‫א‬٪٥ ‫א‬ - ٢٢ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬‫א‬

 ‫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

E

,,L,,(live loads)‫א‬‫א‬

E 

 (Ultimate loads)‫א‬‫א‬W٢J ٢J ٢ J ٣J ٢F‫א‬‫א‬F‫א‬‫א‬ ‫א‬ ‫א‬

 W‫א‬EE١

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

E١

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

U = 1.4 D + 1.7 L



(2-1)

 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

- ٢٣ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

‫א‬‫א‬

 Structural Analysis

 

 ‫א‬‫א‬W١J ٣  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬J ١

 Member Analysis‫א‬‫א‬ ‫א‬‫א‬  (Beams)‫א‬‫א‬ (slabs)‫א‬،

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

Slabs‫א‬E‫א‬

 Beams‫א‬‫א‬E٢  Girders‫א‬‫א‬E٣ Columns‫א‬E٤

 Footings‫א‬E٥ 

 ‫א‬‫א‬J ٢  Section Analysis‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬   ‫א‬KK‫א‬‫א‬‫א‬‫א‬–‫א‬‫א‬K‫א‬‫א‬‫א‬  J W‫א‬

 UL،T،،،

 K‫א‬‫א‬‫א‬‫א‬E١J ٣F‫א‬  K‫א‬‫א‬‫א‬E٢J ٣F‫א‬

- ٢٥ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 

Over hanging beam

Simple slab or beam

continous slab or beam

(Column)

Simple frame

(Column)

 ‫א‬‫א‬‫א‬E١J ٣F  

U

L

U - section

L - section

T circular sec

T - section square sec

 ‫א‬‫א‬‫א‬E٢J ٣F

- ٢٦ -

Rectangular sec

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬W٢J ٣ ‫א‬ Statically System‫א‬‫א‬‫א‬ ‫א‬

 ‫א‬ ‫א‬     K‫א‬    ‫א‬ ‫א‬ 

 K‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬

 J WW١J ٢J ٣ ‫א‬E‫א‬‫א‬F‫א‬‫א‬

‫א‬‫א‬E٣J ٣F (Knife Edge Support)

 ‫א‬

 K

d

L

Knife edge support



 E٣J ٣F

   ‫א‬‫א‬W٢J ٢J ٣

‫א‬‫א‬ ‫א‬‫א‬ (Linear Elastic Theory)‫א‬‫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 - ٢٧ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 Moment Distribution‫א‬E ‫א‬‫א‬E‫א‬‫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 

 (Effective Span l0)‫א‬‫א‬‫א‬‫א‬W٣J ٣  ‫א‬‫א‬‫א‬E

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

•

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

•

•

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

 E٤J ٣F‫א‬‫א‬‫א‬‫א‬Zd

d

L L

1

L 2 = 1.05 L

C L



C L

 ‫א‬‫א‬‫א‬E٤J ٣F

   

- ٢٨ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 



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

‫א‬F‫א‬E‫א‬F‫א‬‫א‬‫א‬‫א‬E١  J 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KE‫א‬‫א‬  –  K‫א‬‫א‬‫א‬‫א‬‫א‬



Or

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

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

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

•

 (l01)‫א‬‫א‬

•

 J W‫א‬‫א‬ L02 = l0 + d2

 E٥J ٣F‫א‬‫א‬ 

C

L

d1 d2

L L 1

C

L



 E٥J ٣F - ٢٩ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 (Straining Actions)‫א‬‫א‬W٤J ٣ (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 

  Simple Slab or Simple BeamE‫א‬‫א‬FE١  W‫א‬‫א‬(D.L + L.L )‫א‬‫א‬

•

 Z(N)‫א‬‫א‬

•

 W‫א‬‫א‬(Q)‫א‬ 

Q = K q × wt × L

(3-1)



 EJ ٦J ٣F‫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J  

M = w × L2 / Km

 EJ ٦J ٣F‫א‬‫א‬



(3-2)

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

- ٣٠ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

w t/m Loads L

wL 2 K q = 0.5

Q=

S.F.D

Q B.M.D

K m= 8 2

wL M= 8



 E٦J ٣F  Over Hanging Slab or Beam‫א‬‫א‬E٢

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

•

(D.L+L.L) ‫א‬‫א‬  ‫א‬  ‫א‬  ‫א‬           ‫א‬    KKKK (D.L only)  ‫א‬‫א‬  E‫א‬ ‫א‬‫א‬F ‫א‬‫א‬  KEJ ٧J ٣F‫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

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

 Span of Slab or beam 

‫א‬‫א‬ZL

- ٣١ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

•

W(M)‫א‬‫א‬ 

(D.L+L.L)‫א‬‫א‬‫א‬‫א‬E K EJ ٧J ٣F  ‫א‬ ‫א‬  (D.L)  ‫א‬‫א‬  E‫א‬‫א‬F ‫א‬‫א‬   

W

2

2

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 

(D.L. ‫א‬‫א‬‫א‬‫א‬ ‫א‬E

J ٧J ٣F‫א‬‫א‬(D.L+L.L.)‫א‬E‫א‬‫א‬F‫א‬‫א‬Only) 2

Max. M-ve = w × L1 /2

(3-5)

  

- ٣٢ -

 WE

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

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

w

D.L

w

Loads L

1

L

L

w1L 2

1

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

 E٧J ٣F  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

M = w×L2 / Km

(3-7)W(M)‫א‬‫א‬

 E٨J ٣F‫א‬‫א‬(moment factor)‫א‬ZKm

 EffectiveSpan of Slab or beam ‫א‬‫א‬‫א‬ZL - ٣٣ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 



Q = K q × wt × L

(3-6

(Q)‫א‬ 



 E٩J ٣F‫א‬‫א‬ (shear factor) ‫א‬ZK q

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

 Effective Span of Slab or beam ‫א‬‫א‬‫א‬ZL

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

Where,

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

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

w t/m or w1

 WL2L1‫א‬

w t/m or w2 Loads

L or L

-24

L or L

2

1

-24

-9 +11 w L2 24

( Moment factor)

+11 w L2 9

Km

w L2 24 B.M.D



w L2 11

w L2 11

 ‫א‬E٨J ٣F

- ٣٤ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 0.4

0.6

0.6

0.4 K q ( Shear factor)

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

 ‫א‬E٩J ٣F  .‫א‬‫א‬‫א‬‫א‬W (Q)‫א‬ Q = K q × wt × L

(3-8)

•

 

 E١٠J ٣F‫א‬‫א‬٠ (shear factor) ‫א‬ZK q

 (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)



  E١٢J ٣FE١١J ٣F‫א‬‫א‬(moment factor)‫א‬ZKm  EffectiveSpan of Slab or beam ‫א‬‫א‬‫א‬ZL - ٣٥ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 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

0.5

0.5

0.5

0.5

Kq

 ‫א‬‫א‬‫א‬‫א‬‫א‬E١٠J ٣F

-24

-10

-12 +12

+10

-12 +12

Km ( Moment factor)

‫א‬‫א‬E١١J ٣F

-24

-10 +12

-12 +16

-12 +16

Km ( Moment factor)

‫א‬‫א‬‫א‬‫א‬E١٢J ٣F - ٣٦ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬W٥J ٣ ‫א‬‫א‬‫א‬‫א‬E١J ٣F‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬K‫א‬‫א‬K

W‫א‬E‫א‬FE‫א‬‫א‬F E

 EE٦J ٣F‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬ •

 K‫א‬‫א‬‫א‬ • K‫א‬‫א‬ E 

  F ‫א‬   ‫א‬   ‫א‬  ‫א‬ ‫א‬  •  E٧J ٣‫א‬‫א‬FE‫א‬

 ‫א‬‫א‬‫א‬ •  E‫א‬FE

 E١٠J ٣F‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬ •

‫א‬ F‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬ •  E١٢J ٣FE١١J ٣F‫א‬ 

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 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 W١J ٤  W‫א‬‫א‬‫א‬،‫א‬،‫א‬  Solid Slabs‫א‬‫א‬E١

 Hollow Block Slabs‫א‬‫א‬E٢

 Flat Slabs‫א‬‫א‬E٣

 Waffle Slabs‫א‬‫א‬‫א‬‫א‬E٤

 Lift Slabs‫א‬‫א‬E٥

 Pre-Slabs‫א‬‫א‬E٦

‫א‬‫א‬ (Solid Slabs)‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬(Working Stress Design Method)

 (Solid Slabs)‫א‬‫א‬٢J ٤ ‫א‬  F ‫א‬‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬    ‫א‬  ‫א‬ ‫א‬

(Beams)‫א‬‫א‬‫א‬‫א‬‫א‬KE‫א‬KKKKK‫א‬‫א‬‫א‬

 K‫א‬(girders)‫א‬  W‫א‬‫א‬‫א‬

 One way Solid Slabs

 Two Way Solid Slabs

‫א‬‫א‬‫א‬

E

‫א‬

E 

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

 One way Solid Slabs ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W١J ٢J ٤  W

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

i.e. r = L / B ≥ 2

 E١J ٤‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬

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

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 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

m 1

d

2

b d

2

L



 E١J ٤F



‫א‬F‫א‬‫א‬ ‫א‬ ‫א‬‫א‬E١J ٤F‫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   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٣J ٤

Section Analysis by Working Stress Method ‫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 W١J ٣J ٤

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



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

‫א‬  ‫א‬  ‫א‬ ‫א‬ ‫א‬   ‫א‬  ‫א‬  ‫א‬‫• א‬  ‫א‬ - ٤٠ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

    ‫א‬   (Plane cross sections) ‫א‬ ‫• א‬  KE٢J ٤F‫א‬‫א‬K‫א‬ fc

c

x

 

3 C

x

Z=d -x 3

d

T fs n

s Strain diagram

R.C sec



Stress diagram

 E٢J ٤F 

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



d

=

k

1

M b

(4-1)

J W‫אא‬‫א‬

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

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

  (f c)  ‫א‬  ‫א‬       Z k1  KE١J ٤F‫א‬‫א‬K(f s)‫א‬‫א‬

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

- ٤١ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 J W‫א‬‫א‬ 

A

s

=

M k 2 × d

 

(4-2)



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

‫א‬(f c)‫א‬‫א‬ZK2  KE١J ٤F‫א‬‫א‬K(f s)‫א‬

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

 Diagonal Tension‫א‬‫א‬W٢J ٣J ٤ Horizontal ‫א‬‫א‬‫א‬Vertical Shear‫א‬‫א‬‫א‬‫א‬‫א‬  KShear

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

q =

Q 0 . 87 × bd

(4-3)

  ‫א‬‫א‬Zq  K‫א‬‫א‬‫א‬‫א‬ ZQ  Bond‫א‬W٣J ٣J ٤ 

 ‫א‬ ‫א‬   ‫א‬  ‫א‬  ‫א‬  (Bond Stress) ‫א‬ 

Flexure ‫א‬      ‫א‬    ‫א‬ K ‫א‬   ‫א‬  K‫א‬‫א‬KShear Strength‫א‬  Flexure Bond‫א‬

E

Anchorage Bond‫א‬ E 

- ٤٢ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

Flexural Rigidity ‫א‬W٤J ٣J ٤ ،‫א‬‫א‬‫א‬ (EI) ‫א‬

‫ آﻤﺎ‬E с ‫א‬ Es‫א‬  DeflectionE‫א‬F  -: ‫ﻳﻠﻲ‬ n =E s / E c = 15 ‫א‬‫א‬‫א‬E ‫א‬‫א‬‫א‬Elastic Deformation ‫א‬‫א‬ (‫ب‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ n = 10 . ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬E١J ٤F

Design coefficients for bending (working Stress Method)

Fs=2000

Fs=1600

Fs=1400

Fs=1200

Fs=1000

fs

Fs=2200



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

- ٤٣ -

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

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 ٥J ٣J ٤ ‫א‬  ‫א‬KE٣J ٤F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  WE١F  K

 ‫א‬

 Dead loadsW‫א‬‫א‬‫א‬  ١٠Z(t)‫א‬‫א‬

 A

One - way slab

m 2.25

L=6

m

A

2

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



i.e.

M

m

B.M.d

2.25

 E٣J ٤F

 

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) Section A-A:

M = wt ×L2/8 = 0.6 × (2.25)2 / 8 = 0.380 m.t /m - ٤٤ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

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 = 6.10 cm.

0 . 313

0 . 380 × 100000 100

d = k1

M b

=

‫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 = 4.8 cm2/m

0.380 × 10 5 1217 × 6.5

= As main = M × 10 ×d

k

5

2

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)

 W‫א‬‫א‬W

  ‫א‬       K  ٨Z (t) ‫א‬   E١  K٨‫א‬

‫א‬K ١٠ ٧‫א‬‫א‬ ‫א‬‫א‬E٢  ٨‫א‬‫א‬E٥F‫א‬

K‫א‬‫א‬٪٠{٢٠‫א‬‫א‬E٣

٪٠{٢٥E‫א‬‫א‬F‫א‬‫א‬E٤ K‫א‬‫א‬

- ٤٥ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 J WE٢F

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬ KE٤J ٤F‫א‬‫א‬‫א‬‫א‬ ٣{٠٠  KE٢L٢٠٠Z‫א‬‫א‬F‫א‬  ‫א‬ (One way slab) r = Loads on Slab: 

L 6 = =2 b 3

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

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

E٤J ٤F



Bending Moments: 2 × l 1 0 .6 × 9 w t M +ve = 11 = 11 = 0.49 mt / m 2 × l 1 0 .6 × 9 w t M −ve = 9 = 9 = 0.6 mt / m - ٤٦ -

m L = 3.0

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

(Cases of ‫א‬٢L٤٠٠‫א‬‫א‬ W

 K(case of total loads)‫א‬‫א‬loading) Assume

And

f c =60 kg / cm2

(f cu = 250 kg / cm2)

f s = 1400 kg/cm2

(mild steel 37—24/35)

i.e.

From table (4-1)

k 1= 0.313

and

k 2 = 1217

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

= 7.74 cm. 0 . 313

0 . 6 × 100000 100

d = k1

M b

=

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

0 . 49 × 10 5 M +ve ×105 2 main = = 4.74 cm /m 1217 * 8 . 5 = As1 k2 × d 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)



W‫א‬‫א‬‫א‬ = 5.8 cm2 / m

0.6 ×105 1217× 8.5

=

As2 main =

M −ve ×105 k2 × d

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) - ٤٧ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 W‫א‬‫א‬‫א‬W٦J ٣J ٤  ‫א‬W E‫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  ٢٠  K١٠‫א‬

K٢{٠١{٥‫א‬ (٥ E ٣L ١F   ‫א‬  ‫א‬ ‫א‬ ‫א‬       (٦ K‫א‬‫א‬‫א‬‫א‬

K٨ (٧

    E٢F   ‫א‬ ‫א‬ ‫א‬ ‫א‬    (٨ KE٥J ٤F‫א‬

- ٤٨ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 E٥J ٤F   ‫א‬W

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

E١

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

E٣

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

 W

E٢ 

 ‫א‬W

K ١٠‫א‬ ‫א‬

 K١٥‫א‬   ‫א‬‫א‬W‫א‬

(Deflection)F‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  t min.. =L/30

 WE‫א‬

‫א‬ E١

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

t min.. =L/40

‫א‬ E٣

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬L - ٤٩ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

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

 Tow Way Slabs‫א‬‫א‬‫א‬‫א‬‫א‬W٤J ٤  W١J ٤J ٤

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

J ٤F‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬KE٦

‫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E٦J ٤F

 

 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 - ٥٠ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬‫א‬W٢J ٤J ٤  W‫א‬‫א‬‫א‬‫א‬   t min.. =b/35 ‫א‬ E

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

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

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٣J ٤J ٤ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬    K‫א‬ ‫א‬  ‫א‬ ‫א‬‫א‬  ‫א‬   ‫א‬ ‫א‬

 K‫א‬‫א‬K(b)‫א‬‫א‬(L)‫א‬  E‫א‬F‫א‬‫א‬‫א‬Zb W

 E‫א‬F‫א‬‫א‬‫א‬ZL

‫א‬  ‫א‬     ‫א‬   ‫א‬ ‫א‬  Z m b



 Kb‫א‬(b)‫א‬‫א‬ ‫א‬  ‫א‬     ‫א‬   ‫א‬ ‫א‬  Z m L KL‫א‬(L)‫א‬‫א‬

 K‫א‬m L m b

 Wm L m b‫א‬‫א‬‫א‬ m b = m L = 1.0W‫א‬

m b =m L = 0.87W‫א‬

 m b =m L = 0.76W ‫א‬ ‫א‬  (r) ‫א‬   ‫א‬   ‫א‬ ‫א‬   (4-4)

r=

m ×l  m ×b l

 W‫א‬‫א‬ 

b

  ‫א‬  ‫א‬ (β) (α)‫א‬E٢J ٤F‫א‬

 K‫א‬r‫א‬‫א‬‫א‬(L)‫א‬(b)‫א‬‫א‬ - ٥١ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 r‫א‬(β)(α)‫א‬E٢J ٤F r α β

 ‫א‬‫א‬E‫א‬F‫א‬‫א‬

1.0 0.35 0.35

1.1 0.40 0.29

1.2 0.45 0.25

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.21 0.18 0.16 0.14 0.12 0.11 0.09 0.08  β = 0.35/ r2W

 

 W‫א‬‫א‬‫א‬

  W α =Wt × α(b)‫א‬‫א‬‫א‬  W β =Wt × β(L)‫א‬‫א‬‫א‬

 EWL.L‫א‬‫א‬WD.L‫א‬‫א‬‫א‬F‫א‬‫א‬wt

 

 W‫א‬‫א‬

 W‫א‬‫א‬(Bending Moments)‫א‬ W‫א‬‫א‬‫א‬‫א‬‫א‬ E١ 

×b2

  M b = ± wα  (4-5)‫א‬‫א‬‫א‬ 10 

×L

2

  M L = ± wβ  (4-6) 10

‫א‬‫א‬‫א‬  

 W‫א‬‫א‬‫א‬‫א‬‫א‬E٢



×b2

  M b = ± wα 12  M L = ± w β

×L

12



(4-7)

‫א‬‫א‬‫א‬

  2

‫א‬‫א‬‫א‬

 (4-8)

  

- ٥٢ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬‫א‬W٤J ٤J ٤ ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬  ‫א‬‫א‬KE٣J ٤F

E‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬

‫א‬F‫א‬ ‫א‬‫א‬  ‫א‬

     ‫א‬ ‫א‬  ‫א‬ ‫א‬    ‫א‬ E ‫א‬  ‫א‬‫א‬E٢J ٤F‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬

 K Rigid Beams  ‫א‬  ‫א‬ ‫א‬  ‫א‬‫א‬    ‫א‬  K٢٠‫א‬١٥‫א‬ 

 EFr‫א‬(β)(α)‫א‬E٣J ٤F r α β

1.0 .396 .396

1.1 .473 .323

 ‫א‬‫א‬‫א‬ 1.2 .542 .262

1.3 .606 .212

1.4 .660 .172

1.5 .706 .140

1.6 .746 .113

1.7 .778 .093

1.8 .806 .077

1.9 2.0 .830 .849 .063 .053

  ‫א‬‫א‬‫א‬٥J ٤J ٤  J WE١F

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬   ‫א‬  K E٧J ٤F       ٤{٥  

 KE٢L٢٠٠Z‫א‬‫א‬F  ‫א‬ (Two way slab) r =

 ٤{٥Z‫א‬‫א‬

m × l = 0.87 × 4.5 = 1.0 m × b 0.87 × 4.5 l

b



From table (4-1)

α = β =0.35 Slab is continues

- ٥٣ -

i.e. t = 450/ 45 =10 cm

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

4.50 m

4.50 m

0.40 m

4.50

m

1

1 0.20 m

0.40 m

4.50

m

0.20 m 0.40 m

  E٧J ٤F Loads on Slab:

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

 

W α =Wt × α= Load in short direction = 0.6 × 0.35 = 0.21t/m2 Wt × β = Load in long direction = 0.6 × 0.35 = 0.21 t/m2=W β 

- ٥٤ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬



 ٢٠١

 ‫א‬

 ‫א‬

 

Bending Moments:

 WK‫א‬‫א‬

Mα Mβ

+ ve

=

+ ve

=

Mα

− ve

Mβ

− ve

× = wα l =

2 1

10 2 wβ × l 2

0.21 × 4.5 2 = = 0.425 mt / m 10 =

10

0 .21 × 4 .5 2 = 0 .425 mt / m 10

(Cases of    ‫א‬  ٢L  ٤٠٠   ‫א‬ ‫א‬   W 

 K(Case of total loads)‫א‬‫א‬loading) Assume f c =60 kg / cm2 f s = 1400 kg/cm2

And

(f cu = 250 kg/cm2)

(mild steel 37—24/35) i.e. From table (4-1)

k1= 0.313

and

k 2 = 1217

 Eb=100cm.F١{٠‫א‬EdF‫א‬‫א‬ = 6.45 cm. 0 . 313

0 . 425 × 100000 100

M b

d = k1

=

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 0.425 × 10 5 = 4.11 cm /m 1217 × 8.5 2

= A main = M α k

+ ve

sL

2

× 10 5

×d

Choose 6 Ø 10 mm/m (4.71cm2/m) 0.425 × 10 5 = 4.65 cm /m = 1217 × 7.5 2

Mβ A Secondary = k

+ ve

sl

2

× 10 5

×d

Choose 6 Ø 10 mm/m (4.71cm2/m)



W‫א‬‫א‬‫א‬ = 4.11 cm2/m

0.425 × 10 5 = 1217 × 8.5

Asu main =

Mβ

− ve

× 10 5

k2 × d

Choose 6 Ø 10 mm/m (4.71cm2/m) - ٥٥ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

0.425 × 10 = 4.65 cm /m = 1217 × 7.5 2

A

su

Mβ sec ondary =

− ve

× 10 5

k2 × d

Choose 6 Ø 10 mm/m (4.71cm2/m)

3

10 m m m

3

10 m m m

10 mm m

10 mm m

3 3

4.50

10 m m m

m 1

10 m m m

4.50

m

3

3

1

3

3

10 mm m

10 mm m

E٨J ٤F‫א‬‫א‬

4.50 m

4.50 m

6

3 +3

3 +3

10 m m m 10 m m m

10 m m m

10 m m m 10 m m m

S ec ( 1-1 )



 ‫א‬E٨J ٤F



 J WE٢F

‫א‬ ‫א‬ ٣{٥Z‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 KE٩J ٤F‫א‬

 ‫א‬

 ٣{٥Z‫א‬‫א‬

(Two way slab) r =

m × l = 1.0 × 3.5 = 1 .0 m × b 1.0 × 3.5 l

b

- ٥٦ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

‫א‬٢٠‫א‬‫א‬‫א‬ 

E٣J ٤F‫א‬ From table (4-3)

α = β =0.396

Slab is Simple

i.e. t = 350/ 35 =10 cm Loads on Slab:

O.w. of slab = 0.1 × 2.5 = 0.25 t/m2 = 2.5 KN/m2 = 0.15 t/m2 = 1.5 KN/m2

Flooring L.L.

= 0.20 t/m2 = 2.0 KN/m2



Total load wt =

= 0.60 t/m2 = 6.0 KN/m2

 

W α =W β= 0.6 × 0.396 = 0.21t/m2

 

Bending Moments:

 WKEF‫א‬‫א‬‫א‬

Mα

+ ve

=

Mβ

+ ve

× = wα l 8

2 1

0.2376 × 3.5 2 = = 0.364 mt / m 8 (f cu = 250 kg/cm2) Assume f c =60 kg / cm2 2 And f s = 1400 kg/cm (mild steel 37—24/35) i.e. From table (4-1) k1= 0.313 and k2 = 1217

 Eb=100cm.F١{٠‫א‬EdF‫א‬‫א‬ = 6.0 cm. 0 . 313

0 . 367 × 10 100

5

M b

d = k1

=

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

 = 3.52 cm2/m

W‫א‬ 0.364 × 10 5 1217 × 8.5

× 10 5

= AsL main = M α +ve *d

k

2

Choose 7 Ø 8 mm/m (3.52cm2/m) 0.364 × 10 5 = 3.98 cm /m = 1217 × 7.5 2

Mβ A Secondary = k

+ ve

sl

2

× 10 5

×d



Choose 8 Ø 8 mm/m (4.02cm2/m) - ٥٧ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

  ‫א‬ KE β F‫א‬ ‫א‬  ‫א‬   E α F‫א‬ ‫א‬  ‫א‬  ‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W i.e. A s α. ≥ A s β.  2

10 mm m

8 m

0.2

5

m

8 mm m

4

8 mm / m

Concrete seat

4

8 m

2

m 3.50

10 mm m 8

8 mm m

m 3.50

Sec ( i - i )



i

8

i

 E٩J ٤F



 ‫א‬‫א‬‫א‬‫א‬: ٥J ٤ ‫א‬‫א‬‫א‬‫א‬E١   K‫א‬‫א‬‫א‬‫א‬K٢٠

 K(Ø=8mm)٨‫א‬E٢ E٤L١F‫א‬‫א‬‫א‬‫א‬‫א‬E٣  ‫א‬E٥F‫א‬K‫א‬‫א‬

K٢{٠W١{٥‫א‬‫א‬E٤K  K‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٥  

- ٥٨ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٦J ٤ E‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ (Flexure)‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬

 K(No need to check shear stress)‫א‬‫א‬  EDeflection in SlabsF‫א‬‫א‬W٧J ٤  K‫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١٩٨٥ BS8110 CP110‫א‬‫א‬‫א‬ ACI‫א‬

‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬  ١٩٩٥‫א‬

‫א‬      E٤J ٤F  ‫א‬ ‫א‬  (ACI-318-71)  ١٩٧١  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 (L/d)‫א‬‫א‬‫א‬E٤J ٤F ACI‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬     

 ‫א‬

‫א‬

‫א‬

 ‫א‬

‫א‬ (Fy kg/cm2)  ٢٨٠٠ ‫א‬‫א‬‫א‬

١٢{٥

 ٣٥

 ٣٠

 ٢٥

 ١٠

 ٢٦

 ٢٣

 ٢٠

 ٢٨٠٠

‫א‬‫א‬

 ١١

 ٣١

 ٢٧

 ٢٢

 ٣٥٠٠

‫א‬‫א‬‫א‬

 ٩

 ٢٣{٥

 ٢٠{٥

 ١٨

 ٣٥٠٠

‫א‬‫א‬

 ١٠

 ٢٨

 ٢٤

 ٢٠

 ٤٢٠٠

‫א‬‫א‬‫א‬

 ٨

 ٢١

 ١٨{٥

 ١٦

 ٤٢٠٠

‫א‬‫א‬

 ‫א‬‫א‬

 ‫א‬‫א‬

 ‫א‬‫א‬

١٠{٠٠‫א‬‫א‬ (L/d)‫א‬ ‫א‬‫א‬E٥J ٤F‫א‬  K‫א‬‫א‬‫א‬‫א‬ - ٥٩ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 (L/d)‫א‬‫א‬‫א‬E٥J ٤F  E.C.O.P‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬   



 

 ‫א‬

 ‫א‬

‫א‬ (Fy kg/cm2)

 ٣٥

 ٣٠

 ٢٥



 ‫א‬‫א‬

 ٢٦

 ٢٣

 ١٨



‫א‬‫א‬‫א‬

 ٢٨

 ٢٤

 ٢٠

 ٢١

 ١٧

 ١٤

٢٨٠٠J ٢٤٠٠

 ‫א‬

٢٨٠٠J ٢٤٠٠

 ‫א‬‫א‬



 ‫א‬‫א‬

 ‫א‬

٤٢٠٠J ٣٥٠٠

‫א‬‫א‬‫א‬  ‫א‬‫א‬ 

 ‫א‬‫א‬‫א‬W ‫א‬‫א‬‫א‬(ACI-318-83)K١٩٨٣‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬  ‫א‬      K ٣٥J ٣٣  ‫–א‬ K ١٩٨٣  ACI-318-83  K‫א‬‫א‬‫א‬

 E١٢F١٢٠(Drop panels)‫א‬‫א‬‫א‬‫א‬ E٢J ٣J ٥J ٩F‫א‬‫א‬ E١٠F١٠٠‫א‬‫א‬

 ٢{٠٠‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ E٩F٩٠

- ٦٠ -

E١

E٢ E٣

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬ ١٠‫א‬ ١٠Z‫א‬

١٠ Ø٦Z ‫א‬

٨J ٤ E١

 KL

١٢‫א‬ ١٢Z‫א‬ ١٢ Ø٧Z ‫א‬

 KL

١٤‫א‬ ١٤Z‫א‬

E٢

E٣

١٤ ø٨Z ‫א‬

 KL

١٦‫א‬ ١٦Z‫א‬

١٦ Ø٩Z ‫א‬

E٤

KL١٠Ø٥‫א‬KL

 ‫א‬٩J ٤ ‫א‬K ٢٠‫א‬ ‫א‬E‫א‬FE١  W‫א‬K٩{٠٤{٢Z

 K‫א‬‫א‬E

 K‫א‬‫א‬‫א‬‫א‬E  K‫א‬‫א‬E 

‫א‬ ‫א‬E١٠J ٤F‫א‬E١F‫א‬‫א‬‫א‬E٢

‫א‬K ‫א‬K ٦{٥ ٤{٥Z‫א‬K ٢٠   W‫א‬K٢{٠Z‫א‬‫א‬‫א‬١٢Z‫א‬

 K‫א‬‫א‬‫א‬E

 K‫א‬‫א‬‫א‬‫א‬E

 K‫א‬‫א‬E - ٦١ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 6.50 m

6.50 m

1 0.2

m

4.50

0.2

m

4.50

6.50 m



m

m

6.50 m

 E١٠J ٤F

 

  KE١١J ٤F  ‫א‬  ‫א‬ E٣J ٢J ١F  ‫א‬ ‫א‬ ‫א‬  E٣  W‫א‬K٢٠‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬E٣،٢،١F‫א‬E  K‫א‬‫א‬‫א‬E

‫א‬ ‫א‬    ‫א‬        E  K‫א‬‫א‬

    - ٦٢ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

5.00 m

5.00

m

1

5.00 m

6.00 m

0.2

m

2

0.2

m

5.00

0.2

6.00

6.00

5.00

6.00 m

 E١١J ٤F

- ٦٣ -

m

m

m

5.00 m



m

3

m

0.2

5.00

m

5.00 m

m

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 WW١J ٥ ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬      KKK  ‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬  K‫א‬E‫א‬F‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬W٢J 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

 KE١J ٥F‫א‬F٢٥٢٥

T 12 cm b

12 cm b

b< T

20 cm

25 cm

12 cm b

25 cm b< 25 cm

20 cm b< 20 cm

 E١J ٥F 

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

 K‫א‬‫א‬‫א‬‫א‬

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

‫א‬ ‫א‬‫א‬  ‫א‬‫א‬      ‫א‬  E٤ K‫א‬‫א‬‫א‬ - ٦٥ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

(To reduce buckling length of columns)‫א‬ E٥ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٣J ٥

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

E١

Secondary beams‫א‬‫א‬‫א‬

E٢

E‫א‬ F‫א‬ ‫א‬‫א‬‫א‬‫א‬    F ‫א‬ ‫א‬‫א‬  ‫א‬   ‫א‬  ‫א‬ ‫א‬‫א‬  KE٢J ٥F‫א‬‫א‬E‫א‬‫א‬‫א‬  4.00 m

4.00 m

Beam

0.3

0.2

Seconadry



m Seconadry

3.00

m

Beam Main

0.3

Beam m

m

3.00

 E٢J ٥F 

- ٦٦ -

m

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

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

 K‫א‬

   K   E٣J ٥F  ‫א‬  ‫א‬ ‫א‬ ‫א‬ ،‫א‬  

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

 KC4‫א‬B1‫א‬‫א‬‫א‬‫א‬K   4.00

4.00

4

G1 C3

C4 3 3.00

m 2

C5

B2 1

3.00

m

B3 B1

C2



C1

 E٣J ٥F

‫א‬    KE٣J ٥F  ‫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،

 K‫א‬‫א‬‫א‬‫א‬W١J ٣J ٥ ‫א‬ E‫א‬ ‫א‬ ‫א‬ ‫א‬‫א‬ ‫א‬  F ‫א‬   E١ (Embedded beams)  ‫א‬  (Dropped beams)‫א‬ ‫א‬

 K‫א‬‫א‬ - ٦٧ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫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J ٤J ٥F‫א‬

 ‫א‬ a‫א‬‫א‬ ‫א‬ d  c  b  a ‫א‬  K‫א‬‫א‬

  ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬ ‫א‬  EJ ٤J ٥F  ‫א‬  a‫א‬‫א‬EJ ٤J ٥F‫א‬‫א‬KEJ ٤J ٥F ‫א‬K‫א‬ ‫א‬  D‫א‬  e  d  c  b  K‫א‬‫א‬‫א‬ 

m

m D

m S

m D

S

m D

m D

m

b

c

a

d

S

m

b

c

a

d

S

m S

m D

m D

e m D



m

D

m D

S

 E٤J ٥F 

- ٦٨ -

m S

m S

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

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

E٣

J ٥F،EJ ٥J ٥F‫א‬KEJ ٥J ٥F‫א‬‫א‬‫א‬‫א‬‫א‬

 KEJ ٥J ٥F‫א‬‫א‬‫א‬‫א‬،EJ ٥  X m

X m

ks ac Cr

Y

m

Y

Cr ac ks

X

m

Y



m

m

 E٥J ٥F 

 ‫א‬‫א‬‫א‬KW٤J ٥    ‫א‬     ‫א‬  ‫א‬‫א‬      W‫א‬‫א‬

- ٦٩ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 W‫א‬‫א‬  (Uniformly distributed load) ‫א‬   ‫א‬ ‫א‬ ‫א‬‫א‬    KE١J ٦J ٥F‫א‬‫א‬K٥{٠‫א‬‫א‬  

Loads L

b< 5.00 m 

 E١J ٦J ٥F  

 W‫א‬‫א‬   K ‫א‬   ‫א‬   ‫א‬ ‫א‬ ‫א‬‫א‬   KE٢J ٦J ٥FK٧،٠‫א‬‫א‬‫א‬

- ٧٠ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 



w t/m

Loads

L

b<7.00 m L 

 E٢J ٦J ٥F 

 W‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬١٠{٠‫א‬‫א‬K

 KE٣J ٦J ٥F  

P

w t/m Loads

L

b< 7.00 m 

 E٣J ٦J ٥F - ٧١ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 W‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K٧{٠

 W‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬

 K٨{٠

 W‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  K

 W‫א‬‫א‬  F       ‫א‬   ‫א‬ ‫א‬‫א‬  ‫א‬  K‫א‬ ‫א‬‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬   E‫א‬  KE٤J ٦J ٥F‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W  

w t/m



w t/m

 E٤J ٦J ٥F  - ٧٢ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 K‫א‬‫א‬‫א‬‫א‬ :٥-٥

‫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K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬ E٤J ١F‫א‬‫א‬  Allowable working stress ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

 K‫א‬‫א‬‫א‬‫א‬‫א‬

 

 K‫א‬‫א‬‫א‬W١J ٥J ٥

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

‫א‬ ‫א‬ ‫א‬  K‫א‬‫א‬  ‫א‬ (Slabs) ‫א‬  

(١

 EJ ١J ٢J ٢J ٢F‫א‬‫א‬

 EJ ٢J ٢J ٢J ٢F‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬

(٢

J ٢J ٢F‫א‬‫א‬ E‫א‬F‫א‬‫א‬ ‫א‬ ‫א‬‫א‬

(٣

EJ ٢J ٢

 K‫א‬‫א‬‫א‬W٢J ٥J ٥  ‫א‬ ‫א‬ ‫א‬  ‫א‬‫א‬  ‫א‬ ‫א‬ ‫א‬     ‫א‬ E٧J ٥F ‫א‬‫א‬

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

- ٧٣ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

L Y

X

45°

Beam A

2X

Beam B



 K‫א‬‫א‬‫א‬‫א‬E٧J ٥F   EF ‫א‬  K         EF ‫א‬    K

 ‫א‬ ‫א‬ ‫א‬‫א‬‫א‬  KE١J ٥F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

 E١J ٥F

 ‫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

 

 K‫א‬‫א‬‫א‬‫א‬‫א‬ZW  K‫א‬‫א‬ZL

 KZX - ٧٤ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

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

 W

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



 KE٢J ٥F‫א‬‫א‬‫א‬‫א‬W 

 E٢J ٥F

0.5 0.667



L/2 L

1

0.5

0.5

2

=

From table

3

0.5 0.667

4

0.5 0.333

5

=

0.5

6

=

From table

7

Take = 1/2x for one trabizoidal

- ٧٥ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 KE‫א‬‫א‬‫א‬E،،٣J ٣F‫א‬‫א‬F‫א‬‫א‬‫א‬W٣J ٥J ٥  KE‫א‬‫א‬E٤J ٣F‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬W٤J ٥J ٥

 KE‫א‬‫א‬E٥J ٣F‫א‬‫א‬F‫א‬‫א‬‫א‬W٥J ٥J ٥  E١J ٥F ‫א‬‫א‬‫א‬‫א‬  E٨J ٥F‫א‬

‫א‬K ‫א‬‫א‬EJ ٨J ٥F‫א‬KEJ ٨J ٥F

 W

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

 W‫א‬KEJ ٨J ٥F‫א‬‫א‬K٣{٠Z‫א‬‫א‬‫א‬ 

 KG1‫א‬‫א‬B2،B1‫א‬‫א‬‫א‬‫א‬

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

2

3

4

A

A

m 6.00

B

6.00

B m

C

C 5.00 m



5.00m

4.00 m

1

2

3

 EJ ٨J ٥F 

- ٧٦ -

4

E١

E٢

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 1

2

4

3 G2

A

A S2 m 6.00 B2

S1

S2

B B1

S2

B

1

B1

0.4 m

S1

5.00 m

G2 4.00 m

C

2

C 5.00 m 3

 EJ ٨J ٥F

h2 ( clear height )

 EJ ٨J ٥F - ٧٧ -

B2

S2





B2

m

G1

m B2 6.00



0.2

4

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 ‫א‬

 G1،B2،B1‫א‬‫א‬‫א‬W

 E٩J ٥F‫א‬‫א‬B1‫א‬‫א‬  2.00

G2

2.50

2.00

G1

G2

2.50

6.00 m

6.00 m

B1 w t t/m G1

G2

G2

B1 E٩J ٥F



 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 - ٧٨ -

and

β1 = 0.582 (from table 5-1)

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

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

 E١٠J ٥F‫א‬‫א‬B2‫א‬‫א‬

2.50

2.50 col

col

col 6.00 m

6.00 m B2 w t/m t col

col B2

E١٠J ٥F - ٧٩ -

col

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

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 α1 = 0.769

and

β1 = 0.582

Beam B2 has two equal span = 6.0 m Assume And

b =20 cm

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 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

- ٨٠ -



 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 KE١١J ٥F‫א‬‫א‬G1‫א‬‫א‬

R

R B1

2.50

B1

2.00

2.50

col

2.50 2.50

2.00

5.00 m

4.00 m

5.00 m

G1



 E١١J ٥F



 ٠{٤Z٤٠ZG1‫א‬ 

 W٠{٩Z٩٠Z

K‫א‬‫א‬L‫א‬Z‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬ 

‫א‬‫א‬ W (‫א‬‫א‬ ) ‫א‬‫א‬K‫א‬

E٢J ٥F‫א‬‫א‬K (α = β = 0.5). ‫ ﺣﻴﺚ‬.W β

Wt = total working load on G1 = ∑ loading area / span + o.w. of girder i.e.

W α = W β = ( 2 × 0.75 × 0.5 × 4 × 4/2 + 2 × 2 × 0.75 × 0.5 × 5 × 5/2 ) / 14 + 0.4 × (0.9 – 0.12) × 2.5 = 1.77 + 0.78 = 2.55 t/m - ٨١ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 W‫א‬G1‫א‬‫א‬B1‫א‬‫א‬‫א‬  B1 ‫א‬  (working reaction) ‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬ 

E١

،  ‫א‬ E‫א‬F ‫א‬ ‫א‬‫א‬  ‫א‬ ‫א‬‫א‬   

E٢

 KRB1G1‫א‬‫א‬

(load for   ‫א‬ ‫א‬     ، ‫א‬  ‫א‬ 

WKKKKKKKKshear coefficient) (w β)

RB1 = R w + R m  K‫א‬‫א‬‫א‬ZR wW

 KB1‫א‬‫א‬‫א‬ZR m

 KB1‫א‬‫א‬‫א‬‫א‬E١٢J ٥F‫א‬‫א‬       

- ٨٢ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

w t/m or w1 Beam B1 Loads

w = 2.33 t/m

G1

G2

G2

6.00 m

6.00 m

w L2 2.33 * 6 * 6 = 10.485 m.t M= = 8 8

B.M.d G1

G2

10.485

Reaction 10.485 6

10.485 10.485 *2 = Rm 6 6 6.00 m



G2

10.485

6.00 m

 E١٢J ٥F 

 W‫א‬‫א‬

R w = (wβ×L/2) ×2 = (2.33 ×6/2) ×2 = 13.98 ton

R m = (M - ve /L) ×2 = (wβ×L2/8L) ×2 = (2.33 ×6×6 / (8×6))×2 = 3.495 ton i.e. RB1 = 3.495 + 13.98 = 17.5 ton

 KE١٣J ٥FG1‫א‬‫א‬‫א‬‫א‬

- ٨٣ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

R

 ٢٠١

 ‫א‬

 ‫א‬

 

= 17.5 t B1 w = 2.55 t/m

R B1

= 17.5 t

col

col 5.0

4.00 m

5.0

14.00 m



E١٣J ٥F  E١J ٥F‫א‬  G1،B2،B1‫א‬‫א‬‫א‬‫א‬W E١٤J ٥F‫א‬‫א‬E‫א‬FB1‫א‬

E١

E١٥J ٥F

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

B

5.6 t 8.4 t

  E١٤J ٥F 

- ٨٤ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 2.96 t/m

Load for moment

6.00 m

-24

-9 +11

-4.44



6.00 m

-24 K m ( moment factor)

+11

2 w L= 11.84 9

- 4.44

9.7

2 B.M.d M= wL /Km

9.7

 E١٥J ٥F 

 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W   KE١٦J ٥F‫א‬‫א‬G1 ‫א‬E٣   

- ٨٥ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 17.5 t 2.55 t/m

Loads 35.35 t

17.5 t

5.00 m

4.00 m

5.00 m

35.35 t

35.35 22.6 5.1 S.F.D 5.1 22.6 35.35 B.M.d

144.88

8 mt

w L2 = 8 mt 8 Mmax= 144.88 + 5.1 =150 mt

5.1

 E١٦J ٥F

 

Design of R.C. Sections of Beams‫א‬‫א‬‫א‬W٦J ٥

 ‫א‬    ‫א‬ ‫א‬ ‫א‬   ‫א‬ ‫א‬ ‫א‬  ‫א‬  K‫א‬‫א‬  ‫א‬ ‫א‬       K ‫א‬

‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٧J ٥F   - ٨٦ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 





 E١٧J ٥F

 

‫א‬(Deflection)‫א‬A-B‫א‬E١٨J ٥F‫א‬ ‫א‬      ‫א‬    ‫א‬  K  ‫א‬ ‫א‬

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



 E١٨J ٥F  - ٨٧ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

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

E١

‫א‬    E١٩J ٥F ‫א‬ ‫א‬  KE١٩J ٥F  E١٩J ٥F ‫א‬

K‫א‬‫א‬‫א‬‫א‬ (Neutral Axis) ‫א‬‫א‬‫א‬K‫א‬‫א‬

T‫א‬ E١٩J ٥F‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

E٢

KE١٩J ٥F‫א‬‫א‬

 b

B-B

A-A

A-A T

 E١٩J ٥F 

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

،E١٩J ٥F‫א‬‫א‬F‫א‬‫א‬‫א‬ E  EEF،(F

‫א‬‫א‬ F T ‫א‬‫א‬ (T-shaped) T E  E١٩J ٥ ‫א‬ (L-shaped)L‫א‬‫א‬ W K(L-Section)>L

- ٨٨ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬‫א‬W١J ٦J ٥  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬

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

KE٢٠J ٥F

E١

ft

d

+

d

fc Stress diagram



Strain diagram

 E٢٠J ٥F  ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ‫א‬  f

c

E٢

  ‫א‬ ‫א‬        

Kf s‫א‬‫א‬‫א‬‫א‬

E١J ٥J ٥F  ‫א‬     ‫א‬  ‫א‬ ‫א‬  

 ‫א‬ (M) ‫א‬     E٤J ٥J ٥F ،E٣J ٥J ٥F ،E٢J ٥J ٥F،  K‫א‬‫א‬(Q)‫א‬‫א‬‫א‬ W‫א‬‫א‬d‫א‬‫א‬ - ٨٩ -

E٣

E٤

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬



d

=

k

1

 ٢٠١

 ‫א‬

 ‫א‬

 

M b

(4-1)  W

‫א‬‫א‬(Depth of R.C. Sec.)‫א‬‫א‬‫א‬Zd  EE٢٠J ٥F&E١٩J ٥F‫א‬‫א‬F

    (f c)  ‫א‬ ‫א‬        Z k1  K‫א‬‫א‬‫א‬‫א‬E١J ٤F‫א‬‫א‬(f s)‫א‬‫א‬

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

 f s,b‫א‬f c f cuE٥   W‫א‬W f cu = 250 kg/cm2

f c = 80 kg/cm2

,

So, k1 = 0.253

and f s = 1400 kg/cm2

,

k 2= 1185 



 E١J ٤F‫א‬‫א‬‫א‬d‫א‬‫א‬

E٦

W‫א‬‫א‬‫א‬As‫א‬

E٧ 

(4-2)

A

s

=

k

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.

KE٢١J ٥F‫א‬‫א‬K‫א‬

- ٩٠ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

fc

t

d

+

d

fs / n

b 

 E٢١J ٥F  

 E‫א‬‫א‬‫א‬‫א‬F LT‫א‬‫א‬‫א‬W٢J ٦J ٥  (Flanged Beam)  L‫א‬T‫א‬I‫א‬∏‫א‬K‫א‬‫א‬‫א‬  KE٢٢J ٥‫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

- ٩١ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 W‫א‬‫א‬‫א‬‫א‬‫א‬B‫א‬‫א‬ T B = 12 ts + b Or

B = L/3

(for simple beams)

Or

B = L/4.5 (for continuous beams)

E

 

(4-3) 

 LE

B = 4.5 t s + b Or

B = L/6 (for simple beams)

(4-4)

Or

B = L/9 (for continuous beams)

t sK٨K‫א‬Z LK‫א‬‫א‬Z



M

M B

B ts

d



ts d

As

As

bO T - section

bO L - section

 E٢٢J ٥F 

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

 KE٢٣J ٥FK

- ٩٢ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 C

L

C

L

S

S

S

6.30 L sec

m

T sec bo

L sec

C



L

C

L

 E٢٣J ٥F 

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

 J WT E‫א‬F‫א‬ (Z)‫א‬  K‫א‬‫א‬E٢٤J ٥F

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

KT‫א‬‫א‬KE٢٤J ٥F

- ٩٣ -

E١ E٢

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

B

B z

ts

ts

z d

t

t

bO

bO



 E٢٤J ٥ 

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

Z = 0 . 14

M B

(4-5)

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

WK‫א‬‫א‬Br



(4-5)

Br= r × B



B/b0&ts/z‫א‬K(r)‫א‬E٣J ٥F‫א‬  

- ٩٤ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

(Br=r.B) (r)‫א‬E٣J ٥F 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 =

k

M 1

B

r

 :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 

A

s

=

k

M × d 2

  Kf s , (f c′)‫א‬E١J ٤F‫א‬k2W

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

- ٩٥ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

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

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

 Shear stress‫א‬W٣J ٦J ٥

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

‫א‬‫א‬ (Diagonal Tension) (T) (shear stress)  KE٢٥J ٥F‫א‬‫א‬

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

q =

Q 0 . 87 × b × d

Kg / cm2 

T q q

q q

T E٢٥J ٥F 

 W‫א‬ - ٩٦ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 K٢L٧‫א‬‫א‬‫א‬ E١ ١٨  E   F        E٢ K‫א‬‫א‬‫א‬‫א‬‫א‬H‫א‬‫א‬‫א‬K٢L

 .‫א‬‫א‬‫א‬‫א‬‫א‬W٤J ٦J ٥

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

 W‫א‬ J ٥ ١٤J ٥F‫א‬‫א‬   K(Shear force diagram) (S.F.D)‫א‬  E١  KE١٦

W‫א‬‫א‬‫א‬‫א‬‫א‬E٢

q

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  KE٢٦J ٥F‫א‬‫א‬‫א‬

- ٩٧ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

Q Q

By concrete

q

S.F.D

st

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

Ab

q max



E٢٦J ٥F 

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

n × Ast × b× s

f

s

I.e.

q stirrups =(⅓: ½) q max =

 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

- ٩٨ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

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

A

sb

A

=

b

f

Where;



× b s

A b = area from diagram of shear stress.



 ‫א‬‫א‬W٥J ٦J ٥ ‫א‬‫א‬E١J ٥F‫א‬‫א‬B1‫א‬  ‫א‬

 KE١٥J ٥&١٤J ٥F‫א‬ 

Design data: L= Effective Span =6.0 m Q max. +ve = 8.4

ton

Q max. – ve = 5.6

ton

M max. –ve = 11.84 t.m.

M max. +ve = 9.7

t.m. kg/cm2

Assume f cu = 250 f c = 90

kg/cm2

f s =1400

kg/cm2

Therefore: Q Design =

8.4

ton

At Sec. 2-2 M –ve =

11.84 t.m.

At Sec. 1-1 M +ve =

9.7

t.m.

From table k1 = 0.233 k2 = 1171 Design of Sec. 2-2

(Slab lies in Tension zone)

So design as a rectangular Sec. - ٩٩ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

d =

k

1

M

× 10

2

5

= 0 . 233

b

11 . 84 × 10

5

20

= 56 . 7 cm

Take:

t = 60 cm d act. = 56 cm

A

s

=

M × 10 k ×d

5

=

2

2

act

11 . 84 × 10 1171 × 56

5

= 18 . 06

cm

2

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 Z = 0 .14

M

+ ve

B

9 . 7 × 10

= 0 .14

133 . 33

6

= 11 .94 cm

And

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 = Take 5 Ø 20 mm (15.7 cm2)

- ١٠٠ -

M × 10 k ×d

5

1

2

act

=

9 .7 × 10 5 = 14 .43 cm 2 1200 × 56

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

8.4 t

sec 2

q

255 q

max

8.62 kg/cm

Ab

st

45°

3.6 m

x 2.4 m

5.6 t

7 kg/cm



E٢٧J ٥    Check of shear:

 > 7 kg/cm2

q

2 max .

=

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

Take stirrups 2 branches 5 Ø 8 mm/m

q

st

=

n × Ast × b× s

f

s

=

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

A

bent

=

A ×b = × b A f f

= (45 ×

b

b

s

s

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)

- ١٠١ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 KB1‫א‬‫א‬E٢٨J ٥F‫א‬‫א‬  



B1  B1‫א‬E٢٨J ٥F    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٧J ٥  W‫א‬‫א‬E١  K٣٥٠H٣٠{٤H٣٠{٨  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢

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

 K٢٤‫א‬‫א‬‫א‬E٤ ‫א‬F ٣٥L٢٤ ‫א‬‫א‬‫א‬‫א‬E٥  KE‫א‬

 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EF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٩  K‫א‬‫א‬٤L١‫א‬‫א‬

- ١٠٢ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬‫א‬E١٠  

 E٣٥L٢٤F‫א‬   

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

 ‫א‬‫א‬ 

 





 L٨Ø٥

 ١٦Ø٢

 J

١٦Ø٢ 

١



 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

- ١٠٣ -

   

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

 ٢٠١

 ‫א‬

 ‫א‬

 

 W١J ٦ K‫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E١J ٦F‫א‬‫א‬K‫א‬‫א‬‫א‬ 





 K‫א‬‫א‬W٢J ٦ ‫א‬‫א‬ ‫א‬  ‫א‬  W‫א‬‫א‬‫א‬‫א‬  (i.e 0.05t or 0.05b) K‫א‬٠{٠٥ K٢٠

E

E 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 KE‫א‬‫א‬‫א‬‫א‬F

- ١٠٣ -

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

 ٢٠١

 ‫א‬

 ‫א‬

 

 (Braced and un-braced column) ‫א‬‫א‬‫א‬W٣J 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E٢J ٦F‫א‬W

‫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)‫א‬  

 E٢J ٦F  - ١٠٤ -

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

 ٢٠١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬W٤J ٦ (λ i = He/ i)‫א‬(λ b=He/b)‫א‬‫א‬‫א‬ ‫א‬  KE١J ٦F‫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



 ‫א‬‫א‬‫א‬E١J ٦F ‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬  λi  λb  λ b  ٥٠  ١٢  ١٥  ٣٥

 ٨

 ١٠

‫א‬    

 K‫א‬‫א‬‫א‬‫א‬‫א‬

•

 ‫א‬‫א‬‫א‬W٥J ٦  W‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬ E١

   ‫א‬ F K‫א‬  ‫א‬ ‫א‬‫א‬  ‫א‬   

(٢

KE‫א‬  K‫א‬‫א‬‫א‬W١J ٥J ٦

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬E‫א‬‫א‬F‫א‬‫א‬‫א‬ E١ KE٣J ٦F‫א‬‫א‬K(Y)‫א‬(X)‫א‬‫א‬‫א‬‫א‬

‫א‬(B-3)‫א‬‫א‬‫א‬‫א‬E‫א‬‫א‬F‫א‬ E٢ K(A)‫א‬‫א‬‫א‬‫א‬ - ١٠٥ -

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

 ٢٠١

 ‫א‬

 ‫א‬

 





 E٣J ٦F  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

- ١٠٦ -

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

 ٢٠١

 ‫א‬

 ‫א‬

 

Therefore; total load P of each floor is equal to: P = W slab ×A + weight of beams + weight of walls + own weight of column Where; W slab = t s × 2.5 + weight of flooring + Live Loads. t s = 12 cm,

If Weight of flooring = 150 kg/m2

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 

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; - ١٠٧ -

walls



KE‫א‬

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

 ٢٠١

 ‫א‬

 ‫א‬

 

 E٠{٦F٠{٦←٠{٢Z‫א‬Zb c  ٢{٠←٠{٢٥Z‫א‬Zt c  ‫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  ‫א‬‫א‬W٦J ٦  W‫א‬‫א‬ W‫א‬‫א‬‫א‬‫א‬ E١ t / b ≤ 5

and

h/b ≥ 5

 ‫א‬ZbW

  ‫א‬Zt  ‫א‬‫א‬Zh

W‫א‬‫א‬‫א‬ E٢ andE‫א‬Fλ b = he / b ≤ 15 for braced columns E‫א‬Fλ b = he / b ≤ 10 for un-braced columns

 (buckling length of column)‫א‬‫א‬Zhe W  EE١J ٦F‫א‬‫א‬F ‫א‬Zλ b

- ١٠٨ -

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

 ٢٠١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬W١J ٦J ٦   K‫א‬ ‫א‬ ‫א‬      ‫א‬ ‫א‬ 

 K‫א‬

 W‫א‬(Fixed end)‫א‬‫א‬WE١

 KE٤J ٦F‫א‬‫א‬K‫א‬

‫א‬ ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬





 E٤J ٦F 

‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ WE٢ K(Partially restrained)‫א‬‫א‬‫א‬‫א‬‫א‬

- ١٠٩ -

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

 ٢٠١

 ‫א‬

 ‫א‬

 

‫א‬‫א‬‫א‬ WE٣  K‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ WE٤  K‫א‬‫א‬

E٢J ٦F‫א‬ β = He / H0 β‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  β‫א‬‫א‬‫א‬E٣J ٦F‫א‬ (Braced column)‫א‬β‫א‬E٢J ٦F‫א‬K‫א‬‫א‬

 K(Un-braced column)‫א‬β‫א‬E٣J ٦F‫א‬K 

(Braced column)‫א‬β = He / H0E٢J ٦F

 ‫א‬‫א‬

‫א‬‫א‬

 ٣

 ٢

 ١

 

 ٠{٩٠

 ٠{٨٠

 ٠{٧٥

 ١

 ٠{٩٥

 ٠{٨٥

 ٠{٨٠

 ٢

 ١{٠

 ٠{٩٥

 ٠{٩٠

 ٣



(un-Braced column)‫א‬β = He / H0E٣J ٦F

 ‫א‬‫א‬

‫א‬‫א‬

 ٣

 ٢

 ١

 

 ١{٦٠

 ١{٣٠

 ١{٢٠

 ١

 ١{٨

 ١{٥٠

 ١{٣٠

 ٢

 J

 ١{٨

 ١{٦٠

 ٣

 J

 J

 ٢{٢٠

 ٤    

- ١١٠ -

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

 ٢٠١

 ‫א‬

 ‫א‬

 

 EF‫א‬‫א‬‫א‬‫א‬W٧J 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‫א‬

P = fc0 × Ac + 0.44 f y ×A sc



(6-1)

 W

 KEE٤J ١F‫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

E١J ٦F ‫א‬‫א‬‫א‬‫א‬‫א‬ W K‫א‬ 

 WW١J ٧J ٦

 W‫א‬K١٠٠Z‫א‬‫א‬‫א‬  K(Mild steel 24-35)‫א‬‫• א‬

K٢L٢٥٠Z(f cu)‫א‬ • Assume:

µ (total steel ratio) = 1% ; f co = 60 kg/cm2

 ‫א‬

(for f cu =250 kg/cm2)

And

f y = 2800 kg/cm2

i.e.,

applying in equation (6-1)

So

100×1000 = 60×Ac + 0.44×0.01×Ac×2800 = 72.32 Ac - ١١١ -

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

 ٢٠١

 ‫א‬

 ‫א‬

 

Ac = 1382.27 cm2 b = breadth of column = 25 cm; Take t =

1382 . 27 = 55 . 3 cm So 25

Take

t = 60 cm A sc = 1% ×25×60 = 15 cm2 Choose 8 Ø 16 mm

 K‫א‬E٥J ٦F‫א‬



 ‫א‬E٥J ٦F 

 ‫א‬‫א‬W٨J ٦  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫ א‬E١ KE٦J ٦F‫א‬‫א‬K‫א‬‫א‬‫א‬‫ א‬E٢

KE٧J ٦F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٣

- ١١٢ -

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

 ٢٠١

 ‫א‬

 ‫א‬

 





‫א‬‫א‬‫א‬E٦J ٦F

- ١١٣ -

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

 ٢٠١

 ‫א‬

 ‫א‬

 





 E٧J ٦F  

KE٨J ٦F‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬

E٤   

- ١١٤ -

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



 ٢٠١

 ‫א‬

 ‫א‬

 

 E٨J ٦F KE٩J ٦F‫א‬K‫א‬‫א‬‫א‬



 E٩J ٦F

- ١١٥ -



E٥

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

 ٢٠١

 ‫א‬

 ‫א‬

 

     ‫א‬ ‫א‬   ‫א‬    

E٦

WE١٠J ٦F‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬ D=

b

2

2

+ t Minimum diameter

 K‫א‬‫א‬‫א‬ZDW  K‫א‬‫א‬Z b  K‫א‬‫א‬Zt  

 E١٠J ٦F   ‫א‬‫א‬W٩J ٦ ‫א‬   ٪ ٠{٨  ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬  ‫א‬ ‫א‬  E١ ‫א‬‫א‬‫א‬ ‫א‬٪ ٠{٦‫א‬

 KE٤J ٦FE١J ٦F‫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 • - ١١٦ -

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

 ٢٠١

 ‫א‬

 ‫א‬

 

 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  KE١١J ٦F  ‫א‬ ‫א‬ F  ١٥  ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬

 KEF٦‫א‬‫א‬‫א‬‫א‬‫א‬



 E١١J ٦F 

   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

- ١١٧ -

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

 ٢٠١

 ‫א‬

 ‫א‬

 

‫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

 W١J ٩J ٦

 W‫א‬‫א‬E٦F‫א‬‫א‬‫א‬E١٢J ٦F‫א‬  (C5 ; C6)٦W٥‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K (C5 ; C6) ٦W ٥‫א‬

K‫א‬



 ‫א‬‫א‬‫א‬E١٢J ٦F

- ١١٨ -

E١

E٢

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

 ٢٠١

 ‫א‬

 ‫א‬

 

 ‫א‬  W

 (L.L = 200 kg/m2)‫א‬‫• א‬

 K‫א‬‫א‬E١٣J ٦F‫א‬‫א‬ •

٧٠Z‫א‬‫א‬‫א‬K٢{٩٠Z‫א‬‫א‬ •

 E‫א‬‫א‬FA5‫א‬(C5)٥‫א‬‫א‬  E‫א‬‫א‬FA6‫א‬(C6)٦‫א‬‫א‬ 

 E١٣J ٦F

- ١١٩ -

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

 ٢٠١

 ‫א‬

 ‫א‬

 

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 • 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 - ١٢٠ -

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

 ٢٠١

 ‫א‬

 ‫א‬

 

= 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 ∑ 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 = 2800 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×2800 = 60 Ac +12.32 Ac = 72.32 Ac Ac = 72000/ 72.32 = 995.6 cm2 Take i.e.

- ١٢١ -

b = 20 cm

t = 995.6 /20 = 49.8 cm

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

 ٢٠١

 ‫א‬

 ‫א‬

 

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 ﻗﻄﺎع ﻋﺮﺿﻲ ﻓﻲ اﻟﻌﻤﻮد‬١٤-٦) ‫اﻧﻈﺮ اﻟﺸﻜﻞ رﻗﻢ‬

C5 ‫( ﻗﻄﺎع ﻋﺮﺿﻲ ﻓﻲ اﻟﻌﻤﻮد‬١٤-٦) ‫ﺷﻜﻞ رﻗﻢ‬ Design of column C6: Assume: f c0 =60 kg/cm2 f y = 2800 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×2800 = 60 Ac +12.32 Ac = 72.32 Ac Ac = 96000/ 72.32 = 1327.4 cm2 Take i.e.

b = 20 cm

t = 1327.4 /20 = 66.4 cm ≈ 70 cm Take column section = 20 × 70 cm

Area of required steel reinforcement (A sc) = 1/100 × 20×70 = 14 cm2 - ١٢٢ -

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

 ٢٠١

 ‫א‬

 ‫א‬

 

Take 8 Ø 16 mm (A sc = 16.1 cm2) Use stirrups 5 Ø 8 mm/m

. C6 ‫( واﻟﺬي ﻳﻮﺿﺢ ﻗﻄﺎع ﻋﺮﺿﻲ ﻓﻲ اﻟﻌﻤﻮد‬١٥-٦) ‫اﻧﻈﺮ اﻟﺸﻜﻞ رﻗﻢ‬

 C6 ‫( ﻗﻄﺎع ﻋﺮﺿﻲ ﻓﻲ اﻟﻌﻤﻮد‬١٥-٦) ‫ﺷﻜﻞ رﻗﻢ‬



  W١٠J ٦  W‫א‬‫א‬E١٢J ٦F‫א‬

 (C1-C2-C3-C4-C7) ٧– ٤– ٣– ٢– ١ ‫א‬  ‫א‬ ‫א‬ 

 K‫א‬

E١

K‫א‬(C1-C2-C3-C4-C7)٧–٤–٣–٢–١‫א‬

E٢

K‫א‬‫א‬‫א‬‫א‬‫א‬

E٣

K‫א‬‫א‬

K‫א‬‫א‬

- ١٢٣ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

 W١J ٧    ‫א‬ K‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬  ‫א‬ ‫א‬     ‫א‬     ‫א‬    ‫א‬ 

 ‫א‬  ‫א‬ ‫א‬   ‫א‬     ‫א‬ ‫א‬ K K  K‫א‬‫א‬‫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W٢J ٧ ‫א‬‫א‬  ‫א‬ ‫א‬  K ‫א‬ ‫א‬ ‫א‬ ‫א‬ 

W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬،‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KK‫א‬   ‫א‬‫א‬‫א‬W٣J ٧ ‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬KE‫א‬‫א‬،‫א‬‫א‬

 W‫א‬

‫א‬  ‫א‬   K (Strip footings) ‫א‬ ‫א‬

(١

‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 K

‫א‬ ‫א‬    K (Spread footings) ‫א‬ ‫א‬

(٢

K‫א‬‫א‬‫א‬ K (Combined footings)‫א‬‫א‬ ‫א‬ ‫א‬   K     ،  ‫א‬  

KK‫א‬

- ١٢٥ -

(٣

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

K‫א‬K(Raft foundations)‫א‬‫א‬

(٤

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،   (Design of Strip footings)‫א‬‫א‬W٤J ٧ ‫א‬ ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬E١J ٧F ‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬ ‫א‬K B‫א‬ K‫א‬‫א‬    K B ‫א‬   b ‫א‬  ‫א‬   ‫א‬ ‫א‬

 K(Reinforcement)(Thickness)‫א‬

،‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬

‫א‬       ‫א‬   ‫א‬   ‫א‬‫א‬  

 K‫א‬(D f)‫א‬(q all.)‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

(7-1)

PT = 1−

γ

P

a

×

q

D

f

all



 K‫א‬‫א‬‫א‬ZPW

 K‫א‬‫א‬،‫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 B×1.0 = PT / q all

(7-2)

- ١٢٦ -



 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

 K‫א‬،B‫א‬E٢J ٧F‫א‬  



 E١J ٧F

  

- ١٢٧ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

 W‫א‬‫א‬W١J ٤J ٧ ‫א‬‫א‬‫א‬K‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

((PT-P)/B)‫א‬‫א‬   (PT/B)‫א‬‫א‬‫א‬  W‫א‬F net‫א‬‫א‬‫א‬‫א‬K F net = P /B



(7-3)

K Double Cantilever  ‫א‬‫א‬‫א‬  W‫א‬

 W‫א‬‫א‬ 

(7-4)

S = (B-b) / 2

   W‫א‬‫א‬‫א‬ S = (B-b/2) / 2



(7-5)

   E٦J ٧F‫א‬‫א‬‫א‬ 2

M = F net × S / 2

 K

(7-6)

   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬Q b‫א‬

Q b = F net × S

(7-7)  

 W ‫א‬  ‫א‬ ‫א‬ ‫א‬‫א‬    ‫א‬ ‫א‬  ‫א‬   K(Bond stress)‫א‬‫א‬‫א‬‫א‬‫א‬ - ١٢٨ -

E١

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

‫א‬   K  ‫א‬ ‫א‬ ‫א‬     

E٢

K‫א‬ 

K‫א‬‫א‬‫א‬

  E‫א‬ ‫א‬ ‫א‬F ‫א‬    ‫א‬ ‫א‬ 

 ‫א‬ ‫א‬ ‫א‬  ‫א‬     ‫א‬  

E٣

‫א‬‫א‬‫א‬‫א‬‫א‬FK‫א‬ ‫א‬‫א‬       ‫א‬ ‫א‬   K E‫א‬ ‫א‬  ‫א‬

‫א‬K‫א‬K‫א‬   ‫א‬ ‫א‬   ‫א‬ ‫א‬   ‫א‬

   ‫א‬   ‫א‬   E٣J ٧F  E١J ٧F  K‫א‬‫א‬‫א‬ W = Pc / Sc

(7-8)

 ‫א‬‫א‬K‫א‬‫א‬‫א‬ZWW  K‫א‬ZPc  K‫א‬‫א‬ZSc

 

(Strip ‫א‬‫א‬‫א‬‫א‬

‫א‬K‫א‬‫א‬K footing)  K‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ 

 ‫א‬‫א‬W٢J ٤J ٧  ١

KL٢٠‫א‬‫א‬٣٠

‫א‬K‫א‬‫א‬‫א‬K٢L١{٠‫א‬١{٠‫א‬K  K‫א‬

- ١٢٩ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

 ‫א‬  



 E٢J ٧F 

P

T

P

= 1−



γa × D q all

= f

20 = 25 t / m 2 × 1 .0 1− 10 B= 25/10 =2.5 m Concrete Section: F n = 20/2.5 = 8 t/m

S = (B –b/2)/2 = (2.5 - 0.3/2)/2 = 1.175 m M = F n ×S2/2 = 8 × (1.175)2/2 = 5.523 t.m. /m Q b = F n ×S = 8 × 1.175 = 9.4 t/m Assume: f c = 60 f s = 1400

kg/cm2 kg/cm2 k1 = 0.313 k2 = 1217

- ١٣٠ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

d = k1

M 5.523 × 10 5 = 0.313 = 23.26cm b 100

d min = b Take

or 25 cm d = 30 cm

t = 30 + cover = 30 +5 = 35 cm

A

s

2 5 .523 × 100000 M cm = = = 15 .127 × 1217 × 30 d k2

Take 8 Ø 16 mm/m (16.1 cm2) 2

< 10 kg /cm

9.4×1000

Q

= = 8.96 (safe) q = 0.87× d × ∑o o o o 0.87×30×(8π ×1.6) b

As′ ≥ 0.2 % Ac = 0.2 % ×30×100 = 6 cm2 As′ = 5 Ø 16 (min. Reinforcement)

 E٣J ٧F - ١٣١ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

 ٢ ٥{٠٠‫א‬ ٤٠‫א‬ 

F٢L٠{٧٢‫א‬‫א‬K‫א‬١{٢‫א‬  KE١٤ Ø٨ ‫ وﺗﺴﻠﻴﺤﻪ‬. ٣٠ ×٣٠‫א‬

 ‫א‬ 



 E٤J ٧F  

Design of long beam Load per meter = 40/5 = 8 t/m

M

max

=

W ×l

2

12

=

8×5 12

↑

2

= 16 .67 m.t

Choose b = 40 cm

d = k1 Take

- ١٣٢ -

M 16.67×100000 = 0.313 = 64.3cm b 40 t = 75 cm

and

d = 68 cm

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

As =

2 16.67 × 100000 M = = 20.13cm 1217 × 68 k2 × d

Choose

8 Ø 18 mm

Shear

Q = 20 ton

kg /cm2 q = Choose

20 × 1000 = 8 .45 0 .87 × 40 × 68

4 branches Ø 8 mm @ 15 cm Stirrups 2

kg /cm

q

stirr

=

4 × 0.503×1400 = 4.67 15× 40

The rest to be resisted by four (4) bent up bars Ø 18 mm Design of slab:

P

T

=

8 8 = = 12 . 0 t / m 1 .2 × 2 2/3 1− 7 .2 B = 12 / 7.2 = 1.67 → 1.7 m F net = 8 / 1.7 = 4.7 t/m S = (1.7 – 0.4) / 2 = 0.65 m M = 4.7 (0.65)2 /2 = 0.993 m.t/m Q b = 4.7×0.65 = 3.055 t/m

d = k1

M = 0 . 313 b

0 . 993 × 100000 100

= 10 cm

For rigidity requirements take t = 20 cm d act = 17 cm

A

s

=

M 0.993 × 100000 = = 4.8cm 2 / m k2 × d 1217 × 17 Take

kg./cm2(safe)

q

b

=

A s min = 6 Ø 14 mm / m

Q 3.055 × 1000 = = 7.83 < 10 0.87 × d × ∑ o o o o 0.87 × 17 × (6π × 1.4) - ١٣٣ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

As′ ≥ 0.2 % Ac = 0.2 % ×20×100 = 4cm2 As′ = 5 Ø 12 mm/m (min. Reinforcement)

 K‫א‬‫א‬E٥J ٧F‫א‬‫א‬ 

 E٥J ٧F       - ١٣٤ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

 Design of Spread Footings ‫א‬‫א‬‫א‬W٥J ٧ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬        ‫א‬ ‫א‬‫א‬  K‫א‬

‫א‬‫א‬‫א‬E٦J ٧F‫א‬K‫א‬‫א‬‫א‬

 K‫א‬‫א‬

 Two Way Footings ‫א‬‫א‬‫א‬E One Way Footings‫א‬‫א‬‫א‬E 



 ‫א‬‫א‬‫א‬‫א‬‫א‬E٦J ٧F

 

‫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   - ١٣٥ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

(L - l) = (B - b)

(7-9)  W‫א‬‫א‬‫א‬

A = L × B = PT/q all



(7-10)

q all = P T / (L × B) (7-11) ‫א‬     B ، L  E١١J ٧F ، E١٠J ٧F    Or

    E١J ٧F ‫א‬    PT   KE ٥F ‫א‬    K

 W FK‫א‬E١١J ٧F‫א‬qall‫א‬‫א‬ E١  KE‫א‬‫א‬

‫א‬‫א‬ ‫א‬ E١J ٧F ‫א‬  ‫א‬ PT   E٢

 ‫א‬ ‫א‬  PT   K      

K(B,L)



 ‫א‬‫א‬‫א‬E٧J ٧F - ١٣٦ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

‫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KE٧J ٧F

 W‫א‬‫א‬ Section a -a:

M

=

(7-12) M

=

P A

⎡ ⎛ L − l ⎞2 ⎟ / 2 + ⎢b ⎜ ⎢⎣ ⎝ 2 ⎠

(2

P 24 × A

B + b

)(L

⎛ L − l ⎞ − b )⎜ ⎟ ⎝ 2 ⎠

(B − l

2

⎤ / 3⎥ ⎥⎦

)2 Section a′- a′:

(7-13) M

=

P 24 × A

(2

L + l

)(B

− b

)2

 W‫א‬‫א‬ Section a -a: (7-14) M

=

P L

(L

−

l

)2

/ 8

(7-15) M

=

P B

(B

−

b

)2

/ 8



 ‫א‬ ‫א‬KE١٤J ٧F،E١٢J ٧F‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ ‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬  WQ b‫א‬ - ١٣٧ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

Fn=P/A

(7-16)



W‫א‬‫א‬Q b For section a -a: Q b =¼ (B + b) (L - l) × F n

(7-17) For section a′- a′:

Q b =¼ (L + l) (B - b) × F n

(7-18)  Punching Depth ‫א‬‫א‬W١J ٥J ٧

   (L × B) ‫א‬ ‫א‬   (l × b)  ‫א‬   ‫א‬  

‫א‬ ‫א‬   K (Direct Shear) ‫א‬ ‫א‬ ‫א‬  ‫א‬ ‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬  K٢L٨q P‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ KE٨J ٧F‫א‬‫א‬‫א‬‫א‬ ‫א‬

E‫א‬‫א‬F‫א‬˚٤٥‫א‬  W‫א‬‫א‬K‫א‬‫א‬ 

(7-19)

Q

P

2 ⎞ ⎛ 2 ⎞ ⎛ = P − Fn ⎜ b + d ⎟ × ⎜ l + d ⎟ 3 ⎠ ⎝ 3 ⎠ ⎝

    - ١٣٨ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

 W‫א‬‫א‬‫א‬‫א‬  (7-20)  q P =

QP 2 d (l + b + 1 .33 d ) 





E٨J ٧F   

 ‫א‬‫א‬W٢J ٥J ٧  ١

K ١{٠‫א‬K ١٠٠ ٤٥ × ٤٥  E١٨ø٨‫א‬F٢L١{٧٥‫א‬

- ١٣٩ -

 ‫א‬‫א‬

 ٢٠١

 ‫א‬

 ‫א‬

 ‫א‬

 

 ‫א‬  



 E٩J ٧F  

P

T

Footing Dimensions:

= 1 −

γ

P a

× D q all

= f

100 = 112 . 9 ton 2 ×1 1 − 17 . 5

A = 112.9 / 17.5 = 6.452 m2

B=

A = 2.54 = 2.55m Concrete Sections:

M=

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 - ١٤٠ -

2 ⎞ ⎛ 2 ⎞ ⎛ = P − Fn ⎜ b + d ⎟ × ⎜ l + d ⎟ P 3 ⎠ ⎝ 3 ⎠ ⎝

 ‫א‬‫א‬

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 ‫א‬

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 

d = 0 . 313 ×

15 . 683 × 10 5 = 49 cm But (45 + 20 )

Take d =50 cm

Q P = 100 − qP

100 2.55 2

&

t = 55 cm

2 2 ⎞⎛ ⎞ ⎛ ⎜ 0.45 + × 0.5 ⎟⎜ 0.45 + × 0.5 ⎟ = 90.564 ton so, 3 3 ⎝ ⎠⎝ ⎠

QP 90 . 564 × 10 3 = = = 5 . 78 kg / cm 2 d (l + b + 1 . 33 d ) 2 × 50 (45 + 45 + 66 . 7 )

2

M 15.68 × 10 5 2 As = k2 × d = 1217 × 50 = 25.75cm Choose 13 Ø 16 mm

q

b

=

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) 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٠J ٧F‫א‬‫א‬  K‫א‬

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 ١٥٠ K ١٦ Ø ١٢E٧٥ × ٣٠F

‫א‬‫א‬K ٢L ٢{٠‫א‬‫א‬

 KEq p = 8 kg/cm2‫א‬‫א‬‫א‬FK‫א‬

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A = P / F all.net = 150 / 20 = 7.5 m2 Choose L = 3.0 m

,

B = 2.5 m



 E١١J ٧F  

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 × - ١٤٣ -

22 .360 × 10 5 = 66 . 16 cm (30 + 20 )

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 ‫א‬

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 ‫א‬

 

t = 70 cm

M 22.360 × 10 5 = = 28.24cm 2 Choose 15 Ø 16 mm As = k2 × d 1217 × 65 M 27.225 × 10 5 = = 35.5cm 2 Choose 18 Ø 16 mm As′ = k2 × d 1217 × 63

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 )

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