Individual components Lim Choon Wah
1
2
4
5
4A
3
6
4B
7
5A
8
9
10
7C 19700
2000
600 1200 1300
500
1200 900
1500
3600
600 1800
1500
3000
1800
I
1700
H 700
G
1800
Ff F
1650
Void
3200
D
1300
17200
550
Ee
E
C/3-5
C3 2500
C
C-B / 4
B 2000
B4
B / 4-5
D-A/5
B-A/ 4
A A4
A/ 4-5
A5
Structural First Floor Plan I had assigned to a. To analysis minimum 6 beams (each beam must subject to different types of load, i.e. UDL from one or more than one slabs, beam with point load(s) or combination of UDL and PL) 1) C-B/4 is UDL type C
B
3) B-A / 4 is UDL type B
5) C / 3-5 is combination type
A
5
6 C4
2) B / 4-5 is UDL type 4
5
4) A / 4-5 is UDL type 4
6) D-A / 5 combination type
5
5
7 5C 5B
b. To analysis minimum 4 columns by using tributary method (from roof to foundation level) 1) C3 2) B4 3) A4
4) A5
Roof Floor
Roof Floor
Roof Floor
Roof Floor
First Floor
First Floor
First Floor
First Floor
Ground Floor
Ground Floor
Ground Floor
Ground Floor
Evelyn Sinugroho 0318217
Beam Analysis Calculation First Floor Beam, C-B/4 1) Carry Self Weight- Dead Load 2) Slab Dead Load & Live Load > C-B / 4-5 3) Brick Wall - Dead Load
-Total Dead Load Diagram C
B 2.50m
8.55kN/m -Dead load on Brick Wall Brick Wall Weight = Wall height x thickness x density Brick Wall Load
= 8.55kN/m
3kN/m -Dead load on Slab C-B / 4-5 (two way slab) Load is transferred to beam C-B / 4-5 in a triangular form. Convert the triangle load into UDL Dead Load from Slab C-B / 4-5 = Dead load on slab x (Lx/2) x 32
DL from Slab C-B/4-5
2 3
= 3kN/m 1.08kN/m
-Dead load on Concrete Beam Beam Self Weight = Beam size x concrete density
Beam Self Weight
= 1.08kN/m 12.63kN/m
-Total Dead load Total for beam C-B / 4-5 = 8.55kN/m + 3kN/m + 1.08kN/m = 12.63kN/m
Total Dead load
-Total Live Load Diagram C
B 2.50m
1.25kN/m
LL from Slab C-B/ 4-5
-Live load on Slab C-B / 4-5 (two way slab) Load is transferred to beam C-B / 4-5 in a triangular form. Convert the triangle load into UDL Live Load Load from Slab C-B / 4-5 = Live load on slab x (Lx/2) 2 3
= 1.25kN/m
Evelyn Sinugroho 0318217
-Total Ultimate Load Diagram B
C 2.50m
17.68kN/m -Total Ultimate Dead load Apply factor of 1.4 to dead load Total Ultimate Dead Load
Ultimate Dead load for beam C-B / 4 = 12.63kN/m x 1.4 = 17.68kN/m 2.0kN/m
-Total Ultimate Live load Apply factor of 1.6 to live load Ultimate Live load for beam C-B / 4 = 1.25kN/m x 1.6 = 2.0kN/m
Total Ultimate Live Load
19.68kN/m -Total Ultimate load Combining the ultimate dead load and ultimate live load Total Ultimate Load
Evelyn Sinugroho 0318217
Ultimate load for beam C-B / 4 = 17.68kN/m + 2.0kN/m = 19.68kN/m
-Total Live Load Diagram
C
B
19.68kN/m
2.50m
19.68kN/m
Load Diagram C
B 2.50m
RBy = 24.6kN
RCy = 24.6kN
= -2.50m(RBy) + 19.68kN/m(2.50m)(2.50m/2) +2.5mRBy = 61.50kN/m RBy = 24.6kN
= RCy + RBy - 19.68kN/m(2.5m) -RCy = -24.6kN RCy= 24.6kN
Shear Force Diagram At point C there is a 24.6kN force acting upwards (+ve)
24.6kN
(+) 0kN
0kN
C
0kN (-)
B
-24.6kN 2.50m
At middle of the beam there were no point load. so UDL was converted to PL only for calculation of reaction forces. 19.68kN/m x 1.25 = 24.6kN 24.6kN - 24.6kN = 0kN At point B there is a 24.6kN force acting downwards (-ve) 0kN-24.6kN = -24.6kN
15.38kN-M
Bending Moment Diagram At point C there is only a line so no area = 0kN (+)
0kN-m
0kN C
B 2.50m
Evelyn Sinugroho 0318217
At middle of the beam = Area of triangle between C and middle = 24.6kN(1.25m)(0.5) = 15.38kN-m At point B, = Area of triangle (+ve) + area of triangle (-ve) = 15.38kN + -24.6kN(1.25m)(0.5) = 0kN-m
Beam Analysis Calculation First Floor Beam, B-A/4 1) Carry Self Weight- Dead Load 2) Slab Dead Load & Live Load > B-A / 4-5 3) Brick Wall - Dead Load
-Total Dead Load Diagram B
A 2.00m
8.55kN/m -Dead load on Brick Wall Brick Wall Weight = Wall height x thickness x density Brick Wall Load
= 8.55kN/m
2.4kN/m -Dead load on Slab B-A/4-5 (two way slab) Load is transferred to beam B-A / 4-5 in a triangular form. Convert the triangle load into UDL Dead Load from Slab B-A / 4-5 = Dead load on slab x (Lx/2) x 23
DL from Slab B-A/4-5
2 3
= 2.4kN/m 1.08kN/m
-Dead load on Concrete Beam Beam Self Weight = Beam size x concrete density
Beam Self Weight
= 1.08kN/m 12.03kN/m
-Total Dead load Total for beam B-A / 4-5 = 8.55kN/m + 2.4kN/m + 1.08kN/m = 12.03kN/m
Total Dead load
-Total Live Load Diagram B
A 2.00m
1.00kN/m
LL from Slab B-A/ 4-5
-Live load on Slab B-A/ 4-5 (two way slab) Load is transferred to beam B-A / 4-5 in a triangular form. Convert the triangle load into UDL Live Load Load from Slab B-A / 4-5 = Live load on slab x (Lx/2) 2 3
= 1.00kN/m
Evelyn Sinugroho 0318217
-Total Ultimate Load Diagram B
A 2.00m
16.84kN/m -Total Ultimate Dead load Apply factor of 1.4 to dead load Total Ultimate Dead Load
Ultimate Dead load for beam B-A / 4 = 12.03kN/m x 1.4 = 16.84kN/m 1.6kN/m
-Total Ultimate Live load Apply factor of 1.6 to live load Ultimate Live load for beam B-A / 4 = 1.00kN/m x 1.6 = 1.6kN/m
Total Ultimate Live Load
18.44kN/m -Total Ultimate load Combining the ultimate dead load and ultimate live load Total Ultimate Load
Evelyn Sinugroho 0318217
Ultimate load for beam B-A / 4 = 16.84kN/m + 1.6kN/m = 18.44kN/m
-Total Live Load Diagram
B
A
18.44kN/m
2.00m
18.44kN/m
Load Diagram B
A 2.00m
RAy = 18.44kN
RBy = 18.44kN
= -2.00m(RAy) + 18.44kN/m(2.00m)(2.00m/2) +2.00mRAy = 36.88kN/m RAy = 18.44kN
= RBy + RAy - 18.44kN/m(2.0m) -RBy = -18.44kN RBy= 18.44kN
Shear Force Diagram At point C there is a 18.44kN force acting upwards (+ve)
18.44kN
(+) 0kN
0kN
B
0kN (-)
A
-18.44kN 2.00m
At middle of the beam there were no point load. so UDL was converted to PL only for calculation of reaction forces. 18.44kN/m x 1.00 = 18.44kN 18.44kN - 18.44kN = 0kN At point A there is a 18.44kN force acting downwards (-ve) 0kN-18.44kN = -18.44kN
9.22kN-M
Bending Moment Diagram At point B there is only a line so no area = 0kN (+)
0kN-m
0kN B
A 2.00m
Evelyn Sinugroho 0318217
At middle of the beam = Area of triangle between B and middle = 18.44kN(1.00m)(0.5) = 9.22kN-m At point A, = Area of triangle (+ve) + area of triangle (-ve) = 9.22kN + -18.44kN(1.00m)(0.5) = 0kN-m
Beam Analysis Calculation First Floor Beam, B/4-5 1) Carry Self Weight- Dead Load 2) Slab Dead Load & Live Load > C-B / 4-5 > B-A / 4-5 3) Brick Wall - Dead Load
-Total Dead Load Diagram 4
5 3.00m
4.5kN/m -Dead load on Slab C-B /4-5 (two way slab) Load is transferred to beam B / 4-5 in a trapezium form. Convert the Trapezium load into UDL Dead Load from Slab C-B / 4-5 = Dead load on slab x (Lx/2)
DL from Slab C-B/4-5
= 4.5kN/m 3.6kN/m -Dead load on Slab B-A / 4-5 (two way slab) Load is transferred to beam B / 4-5 in a trapezium form. Convert the trapezium load into UDL Dead Load from Slab B-A / 4-5 = Dead load on slab x (Lx/2)
DL from Slab B-A/4-5
= 3.6kN/m
1.08kN/m
-Dead load on Concrete Beam Beam Self Weight = Beam size x concrete density
Beam Self Weight
= 1.08kN/m 17.73kN/m
Total Dead load
Evelyn Sinugroho 0318217
-Total Dead load Total for beam B / 4-5 = 4.5kN/m + 3.6kN/m + 1.08kN/m = 9.18kN/m
-Total Live Load Diagram 4
5 3.00m
1.88kN/m
-Live load on Slab C-B / 4-5 (two way slab) Load is transferred to beam B / 4-5 in a trapezium form. Convert the trapezium load into UDL Live Load Load from Slab C-B / 4-5 = Live load on slab x (Lx/2)
LL from Slab C-B/4-5
= 1.88kN/m 1.5kN/m
-Live load on Slab B-A / 4-5 (two way slab) Load is transferred to beam B / 4.5 in a trapezium form. Convert the trapezium load into UDL Live Load from Slab B-A / 4-5 = Live load on slab x (Lx/2)
LL from Slab B-A/4-5
= 1.5kN/m
3.38kN/m -Total Live load Total for beam B / 4-5 = 1.88kN/m + 1.50kN/m = 3.38kN/m
Total Live load
-Total Ultimate Load Diagram 4
5 3.00m
24.82kN/m -Total Ultimate Dead load Apply factor of 1.4 to dead load Total Ultimate Dead Load
Ultimate Dead load for beam B / 4-5 = 9.18kN/m x 1.4 = 12.85kN/m 5.41kN/m
-Total Ultimate Live load Apply factor of 1.6 to live load Ultimate Live load for beam B / 4-5 = 3.38kN/m x 1.6 = 5.41kN/m
Total Ultimate Live Load
30.23kN/m -Total Ultimate load Combining the ultimate dead load and ultimate live load Total Ultimate Load
Evelyn Sinugroho 0318217
Ultimate load for beam B / 4-5 = 12.85kN/m + 5.41kN/m = 18.26kN/m
-Total Live Load Diagram
4
5
18.26kN/m
3.00m
18.26kN/m
Load Diagram 4
5 3.00m
R5y = 27.39kN
R4y = 27.39kN
= -3.0m(R5y) + 18.26kN/m(3.00m)(3.00m/2) +3.0mR5y = 82.17kN/m R5y = 27.39kN
= R4y + R5y - 18.26kN/m(3.0m) -R4y = -27.39kN R4y = 27.39kN
Shear Force Diagram At point 4 there is a 27.39kN force acting upwards (+ve)
27.39kN
(+) 0kN
0kN
4
0kN (-)
5
-27.39kN 3.00m
At middle of the beam there were no point load. so UDL was converted to PL only for calculation of reaction forces. 18.26kN/m x 1.50 = 27.39kN 27.39kN - 27.39kN = 0kN At point 5 there is a 27.39kN force acting downwards (-ve) 0kN-27.39kN = -27.39kN
27.39kN-M
Bending Moment Diagram At point 4 there is only a line so no area = 0kN (+)
0kN-m
0kN 4
5 3.00m
Evelyn Sinugroho 0318217
At middle of the beam = Area of triangle between 4 and middle =27.39kN(1.50m)(0.5) =20.54kN-m At point 5, = Area of triangle (+ve) + area of triangle (-ve) = 20.54kN + -27.39kN(1.50m)(0.5) = 0kN-m
Beam Analysis Calculation First Floor Beam, A/4-5 1) Carry Self Weight- Dead Load 2) Slab Dead Load & Live Load > B-A / 4-5 3) Brick Wall - Dead Load
-Total Dead Load Diagram 4
5 3.00m
8.55kN/m -Dead load on Brick Wall Brick Wall Weight = Wall height x thickness x density Brick Wall Load
= 8.55kN/m 3.6kN/m -Dead load on Slab B-A / 4-5 (two way slab) Load is transferred to beam A/ 4-5 in a trapezium form. Convert the trapezium load into UDL Dead Load from Slab B-A / 4-5 = Dead load on slab x (Lx/2)
DL from Slab B-A/4-5
= 3.6kN/m
1.08kN/m -Dead load on Concrete Beam Beam Self Weight = Beam size x concrete density
Beam Self Weight
= 1.08kN/m 17.73kN/m -Total Dead load Total for beam A / 4-5 = 8.55kN/m + 3.6kN/m + 1.08kN/m = 13.23kN/m
Total Dead load
-Total Live Load Diagram 4
5 3.00m
1.50kN/m
LL from Slab B-A/4-5
-Live load on Slab B-A / 4-5 (two way slab) Load is transferred to beam B / 4-5 in a trapezium form. Convert the trapezium load into UDL Live Load from Slab B-A / 4-5 = Live load on slab x (Lx/2) = 1.5kN/m
Evelyn Sinugroho 0318217
-Total Ultimate Load Diagram 4
5 3.00m
18.52kN/m -Total Ultimate Dead load Apply factor of 1.4 to dead load Total Ultimate Dead Load
Ultimate Dead load for beam A / 4-5 = 13.23kN/m x 1.4 = 18.52kN/m 2.4kN/m
-Total Ultimate Live load Apply factor of 1.6 to live load Ultimate Live load for beam A / 4-5 = 1.5kN/m x 1.6 = 2.4kN/m
Total Ultimate Live Load
20.92kN/m -Total Ultimate load Combining the ultimate dead load and ultimate live load Total Ultimate Load
Evelyn Sinugroho 0318217
Ultimate load for beam A / 4-5 = 18.52kN/m + 2.4kN/m = 20.92kN/m
-Total Live Load Diagram
4
5
20.92kN/m
3.00m
20.92kN/m
Load Diagram 4
5 3.00m
R5y = 31.38kN
R4y = 31.38kN
= -3.0m(R5y) + 20.92kN/m(3.00m)(3.00m/2) +3.0mR5y = 94.14kN/m R5y = 31.38kN
= R4y + R5y - 20.92kN/m(3.0m) -R4y = -31.38kN R4y = 31.38kN
Shear Force Diagram At point 4 there is a 31.38kN force acting upwards (+ve)
31.38kN
(+) 0kN
0kN
4
0kN (-)
5
-31.38kN 3.00m
At middle of the beam there were no point load. so UDL was converted to PL only for calculation of reaction forces. 20.92kN/m x 1.50 = 31.38kN 31.38kN - 31.38kN = 0kN At point 5 there is a 31.38kN force acting downwards (-ve) 0kN-31.38kN = -31.38kN
23.54kN-M
Bending Moment Diagram At point 4 there is only a line so no area = 0kN (+)
0kN-m
0kN 4
5 3.00m
Evelyn Sinugroho 0318217
At middle of the beam = Area of triangle between 4 and middle = 31.38kN(1.50m)(0.5) =23.54kN-m At point 5, = Area of triangle (+ve) + area of triangle (-ve) = 23.54kN + -31.38kN(1.50m)(0.5) = 0kN-m
Beam Analysis Calculation First Floor Beam, C / 3-5 1) Carry Self Weight- Dead Load 2) Slab Dead Load & Live Load > D-C / 3-5 > C-B / 4-5 3) Brick Wall - Dead Load
-Total Dead Load Diagram 4
3
5 3.0m
1.2m
8.55kN/m -Dead load on Brick Wall Brick Wall Weight = Wall height x thickness x density Brick Wall Load = 8.55kN/m 5.76kN/m
-Dead load on Slab D-C / 3-5 (two way slab) Load is transferred to beam C / 3-5 in a trapezium form. Convert the trapezium load into UDL Dead Load from Slab D-C/ 3-5 = Dead load on slab x (Lx/2)
DL from Slab D-C / 3-5 = 5.76kN/m
4.5kN/m
DL from Slab C-B / 4-5
-Dead load on Slab C-B / 4-5 (two way slab) Load is transferred to beam C / 3-5 in a trapezium form. Convert the trapezium load into UDL Dead Load from Slab C-B / 4-5 = Dead load on slab x (Lx/2) =4.5kN/m
1.08kN/m -Dead load on Concrete Beam Beam Self Weight = Beam size x concrete density
= 1.08kN/m
Beam Self Weight
15.39kN/m
Total Dead load
Evelyn Sinugroho 0318217
19.89kN/m
-Total Dead load Total for 3-4 = 8.55kN/m + 5.76kN/m + 1.08kN/m = 15.39kN/m Total for 4-5 = 8.55kN/m + 5.76kN/m + 4.5kN/m + 1.08kN/m = 19.89kN/m
-Total Live Load Diagram 3
5
4 1.2m
3.0m
2.4kN/m
-Live load on Slab D-C / 3-5 (two way slab) Load is transferred to beam C / 3-5 in a trapezium form. Convert the trapezium load into UDL Live Load from Slab D-C/ 3-5 = Live load on slab x (Lx/2)
LL from Slab D-C / 3-5
= 2.4kN/m
1.88kN/m -Live load on Slab C-B / 4-5 (two way slab) Load is transferred to beam C / 3-5 in a Trapezium form. Convert the trapezium load into UDL Live Load from Slab C-B / 4-5 = Live load on slab x (Lx/2)
LL from Slab C-B / 4-5
= 1.88kN/m
2.4kN/m
4.28kN/m
-Total Live load Total for 3-4 = 2.4kN/m + 0kN/m = 2.4kN/m Total for 4-5 = 2.4kN/m + 1.88kN/m = 4.28kN/m
Total Live load
-Total Ultimate Load Diagram 3
5
4 1.2m
21.55kN/m
3.0m
27.85kN/m
Total Ultimate Dead Load
-Total Ultimate Dead load Apply factor of 1.4 to dead load Ultimate Dead load for 3-4 = 15.39N/m x 1.4 = 21.55kN/m Ultimate Dead load for 4-5 = 19.89kN/m x 1.4 = 27.85kN/m
-Total Ultimate Live load Apply factor of 1.6 to live load 6.85kN/m 3.84kN/m Total Ultimate Live Load
34.7kN/m
Ultimate Live load for 3-4 = 2.4kN/m x 1.6 = 3.84kN/m Ultimate Live load for 4-5 = 4.28kN/m x 1.6 = 6.85kN/m
-Total Ultimate load Combining the ultimate dead load and ultimate live load
25.39kN/m Total Ultimate Load
Evelyn Sinugroho 0318217
Ultimate Load for 3-4 = 21.55kN/m + 3.84kN/m = 25.39kN/m Ultimate Load for 4-5 = 27.85kN/m + 6.85kN/m = 34.7kN/m
-Total Live Load Diagram 3
5
4 24.6kN 34.7kN/m
Point Load 4 = RCy of C-B / 4 = 24.6kN
25.39kN/m
1.2m
3.0m
Load Diagram 24.6kN 34.7kN/m
25.39kN/m
3
4
5
1.2m
3.0m
R5y = 78.3kN
R3y = 80.86kN
80.86kN
+4.2mR5y R5y
= -4.2m(R5y) + [25.39kN/m(1.2m)(1.2m/2)]+ 24.6kN/m(1.2m) + [34.7kN/m(3.0m)(1.2+(3.0/2))] = 328.87kN/m =78.3kN
= R3y + R5y - 24.6kN 25.39kN/m(1.2m) - 34.7kN/m(3.0m) -R3y = -80.86kN R3y=80.86kN
Shear Force Diagram At point 3 there is a 80.86kN force acting upwards (+ve) 50.39kN
(+) 25.79kN 0kN 5
0kN 3
4
0kN
UDL was converted to PL only for calculation of reaction forces 25.39kN/m x 1.2 = 30.47kN 80.86kN - 30.47kN = 50.39kN At point 4 there is a 24.6kN force acting downwards (-ve) 50.39kN - 24.6kN = 25.79kN
(-)
At point 5 there is a 104.1kN (34.7kn/m x 3m) force acting downwards (-ve) 25.79kN - 104.1kN= -78.3kN 1.2m
0.74m
2.26m 3.0m
-78.3kN
Bending Moment Diagram At point 3 there is only a line so no area = 0kN-m 88kN-M
At point 4 = Area of trapezium between 3 and 4 (80.86+50.39)(1.2)(0.5)=78.75kN-m At point 4 = Area of triangle (24.6)(0.74)(0.5)=9.102kN-m 78.75kN-m +9.102kN-m =88kN-m
(+) 0kN-m
0kN-m 3
4 1.2m
Evelyn Sinugroho 0318217
5 3.0m
At point 5, = Area of left trapezoid (+ve) and triangle (+ve) + area of right triangle (-ve) -78.3kN(2.26m)(0.5) = -88kN-m 88kN-m - 88kN-m = 0
Beam Analysis Calculation First Floor Beam, D-A/ 5 1) Carry Self Weight- Dead Load 2) Slab Dead Load & Live Load > D-A / 5-7 > D-C / 3-5 > C-B / 4-5 > B-A / 4-5 3) Brick Wall - Dead Load
-Total Dead Load Diagram D
3.2m
A
B
C
2.5m
2.0m
8.55kN/m -Dead load on Brick Wall Brick Wall Weight = Wall height x thickness x density Brick Wall Load = 8.55kN/m 10.8kN/m
-Dead load on Slab A-D /5-7 (two way slab) Load is transferred to beam 5 / A-D in a trapezoid form. Convert the trapezoid load into UDL Dead Load from Slab A-D /5-7 = Dead load on slab x (Lx/2)
DL from Slab A-D / 5-7
= 10.8kN/m
3.84kN/m
-Dead load on Slab D-C /3-5 (two way slab) Load is transferred to beam 5 / A-D in a triangular form. Convert the triangle load into UDL Dead Load from Slab D-C/ 3-5 = Dead load on slab x (Lx/2) x 2/3
DL from Slab D-C/ 3-5
= 3.84kN/m
3.00kN/m -Dead load on Slab C-B / 4-5 (two way slab) Load is transferred to beam 5 / A-D in a triangular form. Convert the triangle load into UDL Dead Load from Slab C-B / 4-5 = Dead load on slab x (Lx/2) x 2/3 x 2/3 = 3.00kN/m
DL from Slab C-B / 4-5
2.4kN/m
DL from Slab B-A / 4-5
-Dead load on Slab B-A / 4-5 (two way slab) Load is transferred to beam D-A / 5 in a triangular form. Convert the triangular load into UDL Dead Load from Slab B-A / 4-5 = Dead load on slab x (Lx/2) x 2/3 = 2.4kN/m
1.08kN/m
-Dead load on Concrete Beam Beam Self Weight = Beam size x concrete density
= 1.08kN/m
Beam Self Weight
23.43kN/m 15.72kN/m Total Dead load
Evelyn Sinugroho 0318217
22.83kN/m
-Total Dead load Total for D-C = 10.8kN/m + 3.84kN/m + 1.08kN/m = 15.72kN/m Total for C-B = 8.55kN/m + 10.8kN/m + 3.00kN/m + 1.08kN/m = 23.43kN/m Total for B-A = 8.55kN/m + 10.8kN/m +2.4kN/m + 1.08kN/m = 22.83kN/m
-Total Live Load Diagram
D 3.2m
A
B
C 2.5m
-Live load on Slab D-A /5-7 (two way slab) Load is transferred to beam D-A / 5 in a trapezoid form. Convert the trapezoid load into UDL Live Load from Slab D-A /5-7 = Live load on slab x (Lx/2)
2.0m
4.5kN/m
LL from Slab D-A / 5-7
= 4.5kN/m
-Live load on Slab D-C /3-5 (two way slab) Load is transferred to beam D-A / 5 in a triangular form. Convert the triangle load into UDL Live Load from SlabD-C / 3-5 = Live load on slab x (Lx/2) x 2/3
1.6kN/m
LL from Slab D-C/ 3-5
= 1.6kN/m
-Live load on Slab C-B / 4-5 (two way slab) Load is transferred to beam D-A / 5 in a triangular form. Convert the triangle load into UDL Live Load from Slab C-B / 4-5 = Live load on slab x (Lx/2) x 2/3 x 2/3 = 1.25kN/m
1.25kN/m
LL from Slab C-B / 4-5
-Live load on Slab B-A / 4-5 (two way slab) Load is transferred to beam D-A / 5 in a triangular form. Convert the triangular load into UDL Live Load from Slab B-A / 4-5 = Live load on slab x (Lx/2) x 2/3
1.00kN/m
LL from Slab B-A / 4-5
= 1.00kN/m
6.1kN/m
5.75kN/m
-Total Live load Total for D-C = 4.5kN/m + 1.6kN/m = 6.1kN/m Total for C-B = 4.5kN/m + 1.25kN/m = 5.75kN/m Total for B-A = 4.5kN/m + 1.0kN/m = 5.5kN/m
5.5kN/m
Total Live load
-Total Ultimate Load Diagram
D 3.2m
22.01kN/m
A
B
C 2.5m
2.0m
32.80kN/m 31.96kN/m
Total Ultimate Dead Load
9.76kN/m
9.2kN/m
8.8kN/m
-Total Ultimate Dead load Apply factor of 1.4 to dead load Ultimate Dead load for D-C = 15.72N/m x 1.4 = 22.01kN/m Ultimate Dead load for C-B = 23.43kN/m x 1.4 = 32.80kN/m Ultimate Dead load for B-A = 22.83kN/m x1.4 = 31.96kN/m -Total Ultimate Live load Apply factor of 1.6 to live load Ultimate Live load for D-C = 6.1kN/m x 1.6 = 9.76kN/m Ultimate Live load for C-B = 5.75kN/m x 1.6 = 9.2kN/m Ultimate Live load for B-A = 5.5kN/m x1.6 = 8.8kN/m
Total Ultimate Live Load
31.77kN/m
42kN/m
40.76kN/m -Total Ultimate load Combining the ultimate dead load and ultimate live load
Total Ultimate Load
Evelyn Sinugroho 0318217
Ultimate Load for 5-5A = 22.01kN/m + 9.76kN/m = 31.77kN/m Ultimate Load for 5A-6 = 32.80kN/m + 9.2kN/m = 42kN/m Ultimate Load for 6-7 = 31.96kN/m + 8.8kN/m = 40.76kN/m
-Total Live Load Diagram D
A
B
C 78.3kN
27.39kN
3.2m
2.5m
2.0m
42.0kN/m
31.77kN/m
3.2m
40.76kN/m
2.5m
Point Load C = RDy of C / 3-5 = 78.3kN Point Load B = RDy of B / 4-5 = 27.39kN
2.0m
Load Diagram 78.3kN 42.0kN/m
31.77kN/m
D RDy = 205.56kN
27.39kN
C
40.76kN/m
B
3.2m
2.5m
2.0m
A RAy = 188.32kN
= -7.7m(RAy) +[31.77kN/m(3.2m)(3.2m/2)]+ 78.3kN(3.2m) + [42.0kN/m(2.5m)(3.2+(2.5/2))] + 27.39kN(5.7m) + [40.76kN/m(2.0m)(5.7m+(2.0/2))] 7.7mRAy= 1582.77kN/m RAy = 205.56kN
= RDy + RAy - 78.3kN - 27.39kN 31.77kN/m(3.2m) - 42.0kN/m(2.5m) 40.76kN/m(2.0m) - RDy = 205.56kN - 393.87kN -RDy= -188.32kN RDy= 188.32 kN 205.56kN
Shear Force Diagram At point D there is a 205.56kN force acting upwards (+ve) 103.39kN
(+) 25.6kN 0kN
0kN D
0kN
C
B
A
(-) -79.4kN
-188.32kN 1.89m 0.61m
Evelyn Sinugroho 0318217
2.5m
At point C there is a 78.3kN force acting downwards (-ve) 103.9kN - 78.3kN = 25.59kN UDL was converted to PL only for calculation of reaction forces 42.0kN/m x 2.5m = 105kN 25.6kN - 105kN = -79.41kN
-106.79kN
3.2m
UDL was converted to PL only for calculation of reaction forces 31.77kN/m x 3.2m = 101.664kN 205.56kN - 101.66kN = 103.89kN
2.0m
At point B there is a 27.39kN force acting downwards (-ve) -79.4kN - 27.39kN = -106.79kN UDL was converted to PL only for calculation of reaction forces 40.76kN/m x 2.0m = 81.52kN -106.79kN - 81.52kN = -188.32kN
370.14kN-M
(+) 0kN-m D
C
0kN-m A
B 2.06m 0.44m
3.2m
2.5m
Bending Moment Diagram At point D there is only a line so no area = 0kN-m At point C = Area of right trapezoid between D & C (205.56+103.39)(3.2)(0.5)=362.33 kN-m
At point B = Area of 2 triangles between C & B 25.6kN(0.61m)(0.5) =7.81kN-m 79.4kN(1.89m)(0.5) = 75.03kN-m
At point A, = Area of right trapezoid (+ve) (188.32+106.79)(2)(0.5)=295.11 kN-m 362.33 + 7.81 =370.14 kN-m 75.03+295.11= 370.14 kN-m 370.14-370.14= 0 kN-m
Evelyn Sinugroho 0318217
2.0m
Column Analysis Calculation Tributary Area Method (Live Load Only) To determine 4 columns: D5 , D7C , F5 , F6 1
2
4
5
6
7
8
9
10
3 19700 600 2000
1200
3000
2400
3600
2400
1500
3000
I 1800
H 1700
G 2500
F
E D
17200
2200
1300
3200
GF C3
C 2500
GF B4
B 2000
A GF A4
GF A5
Ground Floor Plan (Showing Distribution of load from slab to column)
Column
Area
GF C3
(2.1m x 1.7m) + (0.9m x 1.19m) = 3.8m + 1.07m = 4.87m
GF B4
1.5m x 2.31m = 3.47 m
Live Load
4.87m
3.47m
GF A4
1.5m x 1.0m = 1.5m
1.5m
GFA5
[(3.31m x 1.5m) + (3m x 3.85m)] = 16.52m
16.52m
Evelyn Sinugroho 0318217
-Total Live Load Diagram 1
2
4
5
6
7
8
9
10
3 19700 600 2000
1200
3000
2400
3600
2400
1500
3000
I 1800
H 1700
G 2500
F 2200 17200
E D
1300
3200
FF C3
C 2500
FF B4
B 2000
A FF A4
FF A5
First Floor Plan (Showing Distribution of load from slab to column)
Column
Area
FF C3
(2.1m x 1.7m) + (0.9m x 1.19m) = 3.8m + 1.07m = 4.87m
FF B4
1.5m x 2.31m = 3.47 m
Live Load
4.87m
3.47m
FF A4
1.5m x 1.0m = 1.5m
1.5m
FFA5
[(3.31m x 1.5m) + (3m x 3.85m)] = 16.52m
16.52m
Evelyn Sinugroho 0318217
-Total Live Load Diagram
1
2
4
5
6
7
8
9
10
3 19700 600 2000
1200
3000
2400
3600
2400
1500
3000
I 1800
H 1700
G 2500
F
E D
17200
2200
1300
3200
RF C3
C 2500
RF B4
B 2000
A RF A4
RF A5
Roof Floor Plan (Showing Distribution of load from slab to column)
There were no live load on roof floor plan. Column
Area
RF C3
(2.1m x 1.7m) + (0.9m x 1.19m) = 3.8m + 1.07m = 4.87m
RF B4
1.5m x 2.31m = 3.47 m
Live Load
4.87m
3.47m
RF A4
1.5m x 1.0m = 1.5m
1.5m
RFA5
[(3.31m x 1.5m) + (3m x 3.85m)] = 16.52m
16.52m
Evelyn Sinugroho 0318217
Column Analysis Calculation Tributary Area Method Column C3
Determine the load acting on column C3 1
2
4
5
6
7
8
9
10
3
Dead Load
I
Roof Level Dead Load Slab Roof Beam Total
H G F E D
First Floor Dead Load Walls Slabs Beams Column Total
GF C3
C B A
Ground Floor Plan
1
2
4
5
6
7
8
9
10
3 I H G
Ground Floor Dead Load Walls Slabs Beams Column Total
4.87 4.56m x 1.08kN/m = 4.92kN 9.79kN
4.56m x 8.55kN/m = 38.99kN 4.56m x 1.08kN/m = 4.92kN 0.3m x 0.4m x3m x 24kN/m3 = 8.64kN 70.08kN
4.56m x 8.55kN/m = 38.99kN 4.56m x 1.08kN/m = 4.92kN 0.3m x 0.4m x3m x 24kN/m3 = 8.64kN 70.08kN
F
Total Dead Load E D
Apply 1.4 Factor
9.79kN + 70.08kN + 70.08kN = 149.95 kN 149.95kN x 1.4 = 209.93kN
FF C3
C B
Live Load
A
First Floor Plan
1
2
4
5
6
7
8
9
10
First Floor Live Load Slabs
4.87m
Ground Floor Live Load Slabs
4.87m
Total Live Load Apply 1.6 Factor
7.31kN + 7.31kN = 14.62kN 14.62kN x 1.6 =23.39kN
3 I H G F E D FF C3
C
Total Ultimate Dead load + Ultimate Live load 209.93kN + 23.39kN = 233.32kN
B A
Roof Floor Plan
So, ultimate load acting on column D5 is 233.32kN Evelyn Sinugroho 0318217
Column Analysis Calculation Tributary Area Method Column B4
Determine the load acting on column B4 1
2
4
5
6
7
8
9
10
3
Dead Load
I
Roof Level Dead Load Slab Roof Beam Total
H G F E D
First Floor Dead Load Walls Slabs Beams Column Total
C GF B4
B A
Ground Floor Plan
1
2
4
5
6
7
8
9
10
3 I H G
Ground Floor Dead Load Walls Slabs Beams Column Total
3.26m x 1.08kN/m = 3.52kN 6.99kN
1.91m x 8.55kN/m = 16.33kN 3.26m x 1.08kN/m = 3.52kN 0.3m x 0.4m x3m x 24kN/m3 = 8.64kN 40.98kN
1.91m x 8.55kN/m = 38.99kN 1.91m x 1.08kN/m = 2.06kN 0.3m x 0.4m x3m x 24kN/m3 = 8.64kN 62.18kN
F
Total Dead Load E D
Apply 1.4 Factor
6.99kN + 40.98kN + 62.18kN = 110.15 kN 110.15kN x 1.4 = 154.2kN
C FF B4
B
Live Load
A
First Floor Plan
1
2
4
5
6
7
8
9
10
First Floor Live Load Slabs
3.47m
3 I H
Ground Floor Live Load Slabs
3.47m
Total Live Load Apply 1.6 Factor
5.21kN + 5.21kN = 10.41kN 10.41kN x 1.6 =16.66kN
G F E D
C B
RF B4
A
Roof Floor Plan
Total Ultimate Dead load + Ultimate Live load 154.2kN + 16.66kN = 170.86kN So, ultimate load acting on column B4 is 170.86kN Evelyn Sinugroho 0318217
Column Analysis Calculation Tributary Area Method Column A4
Determine the load acting on column A4 1
2
4
5
6
7
8
9
10
3
Dead Load
I
Roof Level Dead Load Slab Roof Beam Total
H G F E D
First Floor Dead Load Walls Slabs Beams Column Total
C B GF A4
A
Ground Floor Plan
1
2
4
5
6
7
8
9
10
3 I H G
Ground Floor Dead Load Walls Slabs Beams Column Total
F
Total Dead Load E D
Apply 1.4 Factor
2.5m x 1.08kN/m = 2.7kN 4.2kN
2.5m x 8.55kN/m = 21.38kN 2.5m x 1.08kN/m = 2.7kN 0.3m x 0.4m x3m x 24kN/m3 = 8.64kN 38.12kN
2.5m x 8.55kN/m = 21.38kN 2.5m x 1.08kN/m = 2.7kN 0.3m x 0.4m x3m x 24kN/m3 = 8.64kN 38.12kN 4.2kN + 38.12kN + 38.12kN = 80.44 kN 80.44kN x 1.4 = 112.62kN
C B
Live Load
FF A4
A
First Floor Plan
1
2
4
5
6
7
8
9
10
First Floor Live Load Slabs 1.5m
3
Ground Floor Live Load Slabs
I H
1.5m
G
Total Live Load Apply 1.6 Factor
F
2.25kN + 2.25kN = 4.5kN 4.5kN x 1.6 =7.2kN
E D
Total Ultimate Dead load + Ultimate Live load 112.62kN + 7.2kN = 119.82kN
C B RF A4
A
Roof Floor Plan
So, ultimate load acting on column A4 is 119.82kN Evelyn Sinugroho 0318217
Column Analysis Calculation Tributary Area Method Column A5
Determine the load acting on column A4 1
2
4
5
6
7
8
9
10
3
Dead Load
I
Roof Level Dead Load Slab Roof Beam Total
H G F E D
First Floor Dead Load Walls Slabs Beams Column Total
C B A
GF A5
Ground Floor Plan
1
2
4
5
6
7
8
9
10
3 I H G
Ground Floor Dead Load Walls Slabs Beams Column Total
9.28m x 1.08kN/m = 10.02kN 26.54kN
7.85m x 8.55kN/m = 21.38kN 9.28m x 1.08kN/m = 10.02kN 0.3m x 0.4m x3m x 24kN/m3 = 8.64kN 99.5kN
4.2m x 8.55kN/m = 35.91kN 4.2m x 1.08kN/m = 4.54kN 0.3m x 0.4m x3m x 24kN/m3 = 8.64kN 108.56kN
F
Total Dead Load E D
Apply 1.4 Factor
26.54kN + 99.5kN + 108.56kN = 234.6 kN 234.6kN x 1.4 = 328.44kN
C B
Live Load
A
FF A5
First Floor Plan
1
2
4
5
6
7
8
9
10
First Floor Live Load Slabs
16.52m
Ground Floor Live Load Slabs
16.52m
Total Live Load Apply 1.6 Factor
24.78kN + 24.78kN = 49.56kN 49.56kN x 1.6 =79.30kN
3 I H G F E D
Total Ultimate Dead load + Ultimate Live load 328.44kN + 79.30kN = 407.74kN
C B A RF A5
Roof Floor Plan
So, ultimate load acting on column A4 is 407.74kN Evelyn Sinugroho 0318217