This document contains calculations of loads, reactions, and shear forces for several beams in a building plan. It calculates dead loads from self-weight of beams and brick walls, as well as live loads. Total loads are determined and distributed equally along the length of each beam. Reactions and shear forces are then calculated at critical points along each beam.

1. 1. Beam 1-2,B (Ground Floor Plan) Teo Vi Vien
Dead load
Beam self weight
= 0.15m x 0.45m x 24kN/m
=​ ​1.62kN/m
Brick wall weight
= 3m x 0.15m x 19kN/m
=​ ​8.55kN/m
Dead load at 1-2,A-B
= 3.6kN/m² x 1.875m/2
=​ ​3.375kN/m
Dead load at 1-2,B-C
= 3.6kN/m² x 2.9m/2
=​ ​5.22kN/m
Total dead load
= (1.62 + 8.55 + 3.375 + 5.22)kN/m
=​ ​18.765kN/m
Ultimate dead load
= 18.765kN/m x 1.4
=​ ​26.3kN/m
Live load
Live load at 1-2,A-B
= 1.5kN/m² x 1.875m/2
= 1.41kN/m
Live load at 1-2,B-C
= 1.5kN/m² x 2.9m/2
= 2.175kN/m
Total live load
= (1.41 + 2.175)kN/m
= 3.59kN/m
Ultimate live load
= 3.59kN/m x 1.6
= 5.74kN/m
Total ultimate load
= 26.3kN/m + 5.74kN/m
= 32.04kN/m
Distributed load
= (32.04kN/m x 3.775m)
= 120.95kN ​/2 (UDL)
= 60.48kN ​(Reaction Force) 60.48kN x 1.89m x 1/2 = ​57.15kNm

2. 2. Beam 2-Y,C (Ground Floor Plan) Lim Zanyu
Beam self weight
= 0.15m x 0.45m x 24kN/m
= 1.62kN/m
Dead load at 2-Y,A-C
= 3.6kN/m² x 4.78m/2
= 8.6kN/m
Dead load 2-Y,C-D
= 3.6 kN/m² x 1.75m/2
= 3.15kN/m
Total dead load
= (8.6 + 3.15 + 1.62)kN/m
= 13.37kN/m
Ultimate dead load
= 13.37kN/m x 1.4
= 18.72kN/m
Live load
Live load at 2-Y,A-C
= 1.5kN/m² x 4.78m/2
= 3.59kN/m
Live load at 2-Y,C-D
= 1.5kN/m² x 1.75m/2
= 1.31kN/m
Total live load
= (3.59 + 1.31)kN/m
= 4.9kN/m
Ultimate live load
= 4.9kN/m x 1.6
= 7.84kN/m
Total ultimate load
= 7.84kN/m + 18.72kN/m
= 26.56kN/m
Distributed load
= (26.56kN/m x 5.2m)
= 138.11kN​ /2 (UDL)
= 69.06kN ​(Reaction Force)
Shear force diagram
69.06kN x 2.6m x 1/2 = ​89.78kNm

3. 3. Beam 2,A-D (Ground Floor Plan) Teo Vi Vien
Beam self weight
= 0.15m x 0.45m x 24kN/m
= 1.62kN/m
Brick wall weight
= 3m x 0.15m x 19kN/m
= 8.55kN/m
Dead load at 2-4,A-C
= 3.6kN/m² x 4.775m/2 x 2/3
= 5.73kN/m
Dead load at 1-2,B-C
= 3.6kN/m² x 2.9m/2 x 2/3
= 3.48kN/m
Dead load at U-2,C-D
= 3.6kN/m² x 1.6m/2
= 2.88kN/m
Total dead load at grid A-B
= (1.62 + 8.55 + 5.73)kN/m
= 15.9kN/m
Total dead load at grid B-C
= (1.62 + 8.55 + 5.73 + 3.48)kN/m
= 19.38kN/m
Total dead load at grid C-D
= (1.62 + 8.55 + 2.88)kN/m
= 13.05kN/m
Ultimate dead load of grid A-B
= 15.9kN/m x 1.4
= 22.26kN/m
Ultimate dead load of grid B-C
= 19.38kN/m x 1.4
= 27.13kN/m
Ultimate dead load of grid C-D
= 13.05kN/m x 1.4
= 18.27kN/m

4. Live load
Live load at 2-4,A-C
= 1.5kN/m² x 4.775m/2 x 2/3
= 2.39kN/m
Live load at 1-2,B-C
= 1.5kN/m² x 2.9m/2 x 2/3
= 1.45kN/m
Live load at U-2,C-D
= 1.5kN/m² x 1.6m/2
= 1.2kN/m
Total live load on grid A-B
= 2.39kN/m
Total live load on grid B-C
= (2.39 + 1.45)kN/m
= 3.84kN/m
Total live load on grid C-D
= 1.2kN/m
Ultimate live load for grid A-B
= 2.39kN/m x 1.6
= 3.824kN/m
Ultimate live load for grid B-C
= 3.84kN/m x 1.6
= 6.144kN/m
Ultimate live load for grid C-D
= 1.2kN/m x 1.6
= 1.92kN/m
Total ultimate load on grid A-B
= (22.26 + 3.824)kN/m
26.08kN/m
Total ultimate load on grid B-C
= (27.13 + 6.144)kN/m
= 33.28kN/m
Total ultimate load on grid C-D
= (18.27 + 1.92)kN/m
= 20.19kN/m
Take point load from 1-2,B
= 60.48kN
Take point load from 2-4,C and 1-2,C
= 69.06kN + 73.19kN
= 142.25kN

5. Take moment at point A,
48.9kN/m(0.9375m) + 60.48kN/m(1.875m) + 96.51kN/m(3.325m) + 142.25kN/m(4.775m) +
35.33kN/m(5.65m) - DkN/m(6.525m) = 0
6.525D = 1358.998
D = 208.28kN
Take moment at point D,
35.33kN/m(0.875m) + 142.25kN/m(1.75m) + 96.51kN/m(3.2m) + 60.48kN/m(4.65m) +
48.9kN/m(5.59m) - AkN/m(6.525m) = 0
6.525A = 1143.266
A = 175.21kN
Shear area diagram
A = 1/2 x (126.31 + 175.21)kN x 1.875m
= 282.68kNm
B = 1/2 x 65.83kN x 1.978m
= 65.11kNm
C = 1/2 x 30.68kN x 0.921m
= 14.13kNm
D = 1/2 x (172.93 + 208.26)kN x 1.75m
= 333.54kNm

6. 4. Beam U,C-D (Ground Floor Plan) Teo Vi Vien
Beam self weight
= 0.15m x 0.45m x 24kN/m
= 1.62kN/m
Brick wall weight
= 3m x 0.15m x 19kN/m
= 8.55kN/m
Dead load at 1-U,C-D
= 3.6kN/m² x 1.4m/2
= 2.52kN/m
Dead load at U-2,C-D
= 3.6kN/m² x 1.75m/2 x 2/3
= 2.1kN/m
Total dead load
= (1.62 + 8.55 + 2.52 + 2.1)kN/m
= 14.79kN/m
Ultimate dead load
= 14.79kN/m x 1.4
= 20.71kN/m
Live load
Live load at 1-U,C-D
= 1.5kN/m² x 1.4m/2
= 1.05kN/m
Live load at U-2,C-D
= 1.5kN/m² x 1.75m/2 x 2/3
= 0.875kN/m
Total live load
= (1.05 + 0.875)kN/m
= 1.925kN/m
Ultimate live load
= 1.925kN/m x 1.6
= 3.08kN/m
Total ultimate load
= (20.71 + 3.08) kN/m
= 23.79kN/m
Distributed load
= 23.79kN/m x 1.75m
= 41.63kN​ /2 (UDL)
= 20.82kN ​(Reaction Force/Point Load at 1-2,C) 20.82kN x 0.875m x 1/2 = ​9.11kNm

7. 5. Beam 1-2,C (Ground Floor Plan) Teo Vi Vien
Beam self weight
= 0.15m x 0.45m x 24kN/m
= 1.62kN/m
Brick wall weight
= 3m x 0.15m x 19kN/m
= 8.55kN/m
Dead load at 1-2,B-C
= 3.6kN/m² x 2.9m/2
= 5.22kN/m
Dead load at U-2,C-D
= 3.6kN/m² x 1.4m/2 x 2/3
= 1.68kN/m
Dead load at 1-U,C-D
= 3.6kN/m² x 1.75m/2
= 3.15kN/m
Total dead load
= (1.62 + 8.55 + 5.22 + 1.68 + 3.15)kN/m
= 20.22kN/m
Ultimate dead load
= 20.22kN/m x 1.4
= 28.3kN/m
Live load
Live load at 1-2,B-C
= 1.5kN/m² x 2.9m/2
= 2.175kN/m
Live load at U-2,C-D
= 1.5kN/m² x 1.4m/2 x 2/3
= 0.7kN/m
Live load at 1-U,C-D
= 1.5kN/m² x 1.75m/2
= 1.31kN/m
Total live load
= (2.175 + 0.7 + 1.31)kN/m
= 4.19kN/m
Ultimate live load
= 4.19kN/m x 1.6
= 6.71kN

8. Total ultimate load
= (28.3 + 6.71)kN/m
= 35.01kN/m ​x 3.775m
= 132.16kN ​(UDL)
Point load from ​Beam 4. U,C-D
= 20.82kN
Take moment at point 2C,
20.8kN(1.4m) + 132.16kN(1.8875m) - 2CkN(3.775m) = 0
Reaction force at 2C = 73.79kN
Reaction force at 1C
= 20.8kN + 132.16kN - 73.79kN
= 79.17kN
Shear graph area
A = 1/2 x (30.16kN + 79.17kN) x 1.4m = ​76.53kNm
x/2.375 = 9.36/83.15
x = 0.267
B = 1/2 x 9.36kN x 0.267m = ​1.25kNm
C = 1/2 x 73.79kN x 2.108m = ​77.77kNm

9. 6. Beam T-2,D’ Lim Zanyu
Beam self weight
= 0.15m x 0.45m x 24kN/m
= 1.62kN/m
Brick wall weight
= 3m x 0.15m x 19kN/m
= 8.55kN/m
Dead load T-2,D-D’
= 3.6kN/m² x 1.2m/2
= 2.16kN/m
Dead load T-2,D’-E
= 3.6kN/m² x 1.2m/2
= 2.16kN/m
Total dead load
= (1.62 + 8.55 + 2.16 + 2.16)kN/m
= 14.49kN/m
Ultimate dead load
= 14.49kN/m x 1.4
= 20.29kN/m
Live load
Live load at T-2,D-D’
= 1.5kN/m² x 1.2m/2
= 0.9kN/m
Live load at T-2,D’-E
= 1.5kN/m² x 1.2m/2
= 0.9kN/m
Total live load
= (0.9 + 0.9)kN/m
= 1.8kN/m
Ultimate live load
= 1.8kN/m x 1.6
= 2.88kN/m
Total ultimate load
= (20.29 + 2.88)kN/m
= 23.17kN/m
Distributed load
= 23.17kN/m x 2.1m
=48.66kN /2
= 24.33kN (Point load)
Shear area diagram = 24.33kN x 1.05m x 1/2 = ​12.77kNm

10. 7. Beam T,D-E Lim Zanyu
Beam self weight
= 0.15m x 0.45m x 24kN/m
= 1.62kN/m
Brick wall weight
= 3m x 0.15m x 19kN/m
= 8.55kN/m
Dead load at T-2,D-D’
= 3.6kN/m² x 1.2m/2 x 2/3
= 1.44kN/m
Dead load at T-2,D’-E
= 3.6kN/m² x 1.2/2 x 2/3
= 1.44kN/m
Dead load 1-T,D-E
= 3.6kN/m² x 1.5m/2
= 2.7kN/m
Total dead load
= (1.62 + 8.55 + 1.44 + 1.44 + 2.7)kN/m
= 15.75kN/m
Ultimate dead load
= 15.75kN/m x 1.4
= 22.05kN/m
Live load at T-2,D-D’
= 1.5kN/m² x 1.2m/2 x 2/3
= 0.6kN/m
Live load at T-2,D’-E
= 1.5kN/m² x 1.2m/2 x 2/3
= 0.6kN/m
Live load at 1-T,D-E
= 1.5kN/m² x 1.5m/2
= 1.125kN/m
Total live load
= (0.6 + 0.6 + 1.125)kN/m
= 2.325kN/m
Ultimate live load
= 2.325kN/m x 1.6
= 3.72kN/m

11. Total ultimate load
= (22.05 + 3.72)kN/m
= 25.77kN/m x 2.7m
= 69.58kN
Point load from beam T-2,D’
= 24.33kN
Take moment at point D,
69.58kN(1.35m) + 24.33kN(1.35m) - DkN(2.7m) = 0
Reaction force at ​D = 46.95kN
Reaction force at E
= 24.32kN + 69.58kN - 46.95kN
= 46.95kN
Shear area diagram
= 1/2 x (46.95 + 12.16)kN x 1.35m
=39.9kNm

12. 8. Beam 1-2,D (Ground Floor Plan) Lim Zanyu
Beam self weight
= 0.15m x 0.45m x 24kN/m
= 1.62kN
Brick wall weight
= 3m x 0.15m x 19kN/m
= 8.55kN/m
Dead load at U-2,C-D
= 3.6kN/m² x 1.5m/2 x 2/3
= 1.8kN/m
Dead load at 1-U,C-D
= 3.6kN/m² x 1.75m/2
= 3.15kN/m
Dead load at T-2,D-D’
= 3.6kN/m² x 1.2m/2
= 2.16kN/m
Dead load at 1-T,D-D’
= 3.6kN/m² x 1.6m/2 x 2/3
= 1.92kN/m
Total dead load at grid 2-U
= (1.62 + 1.8 + 2.16)kN/m = ​5.58kN/m
Total dead load at grid U-T
= (1.62 + 8.55 + 3.15 + 2.16)kN/m = ​15.48kN/m
Total dead load at grid T-1
= (1.62 + 8.55 + 3.15 + 1.92)kN/m = ​15.24kN/m
Ultimate dead load at grid U-2
= 5.58kN/m x 1.4
= 7.81kN/m
Ultimate dead load at grid T-U
= 15.48kN/m x 1.4
= 21.67kN/m
Ultimate dead load at grid 1-T
= 15.24kN/m x 1.4
= 21.34kN/m

13. Live load
Live load at U-2,CD
= 1.5kN/m² x 1.5m/2 x 2/3
= 0.75kN/m
Live load at 1-U,CD
= 1.5kN/m x 1.75m/2
= 1.31kN/m
Live load at T-2,D-D’
= 1.5kN/m² x 1.2m/2
= 0.9kN/m
Live load 1-T,D-D’
= 1.5kN/m² x 1.6m/2 x 2/3
= 0.8kN/m
Total live load at grid 2-U
= (0.75 + 0.9)kN/m
= 1.65kN/m
Total live load at grid U-T
= (1.31 + 0.9)kN/m
= 1.21kN/m
Total live load at grid T-1
= (1.31 + 0.8)kN/m
= 2.11kN/m
Ultimate load at grid U-2
= 1.65kN/m x 1.6
= 2.64kN/m
Ultimate load at grid T-U
= 1.21kN/m x 1.6
= 1.936kN/m
Ultimate load at grid 1-T
= 2.11kN/m x 1.6
= 3.376kN/m
Total ultimate load on grid U-2
= (7.81 + 2.64)kN/m
= 10.45kN/m
Total ultimate load on grid T-U
= (21.67 + 1.936)kN/m
= 23.61kN/m
Total ultimate load on grid 1-T
= (21.34 + 3.376)kN/m
= 24.71kN/m
Point load of grid U-2

14. = (7.81 + 2.64)kN/m
= 10.45kN/m​ ​x 1.5m
= 15.68kN
Point load of grid T-U
= (21.67 + 1.936)kN/m
= 23.61kN/m x 0.5m
= 11.8kN
Point load of grid 1-T
= (21.34 + 3.376)kN/m
= 24.71kN/m x 1.6m
= 39.54kN/m
Point load from ​Beam 4. U,C-D
= 20.8kN
Reaction force as point load from ​Beam 7. T,D-E
= 46.95kN
Take moment at point A,
15.68kN/m(0.75m) + 20.8kN/m(1.5m) + 11.8kN/m(1.75m) + 46.95kN/m(2m) + 39.54kN/m(2.8m)
- B(3.6m) = 0
3.6B = 268.22kN/m
B = 74.51kN
Take moment at point B,
-39.54kN/m(0.8m) - 46.95kN/m(1.6m) - 11.8kN/m(1.85m) - 20.8kN/m(2.1m) - 15.68kN/m(2.85m)
+ A(3.6m) = 0
3.6A = 216.95kN/m
A = 60.26kN
Shear area diagram
Area A
= 1/2 x (44.58kN + 60.26kN) x 1.5m
= 78.63kNm
Area B
= 1/2 x (11.98kN + 23.78kN) x 0.5m
= 8.94kNm
Area C
= 1/2 x (34.97kN + 74.51kN) x 1.6m
= 87.58kNm

15. Beam 4-2, E (First Floor Plan) Yen Wei Zheng
Beam self weight
= 0.15m x 0.45m x 24kN/m
= 1.62kN/m
Brick wall weight
= 3m x 0.15m x 19kN/m
= 8.55kN/m
Dead load at 2-4, E-F
= 3.6kN/m² x 5.6m/2
= 10.08kN/m
Dead load 1-X, D-E
= 3.6kN/m² x 2.6m/2
= 4.68kN/m
Total dead load X-4, E
= (1.62 + 8.55 + 10.08) kN/m
= 20.25kN/m
Total dead load 2-X, E
= (1.62 + 8.55 + 10.08 + 4.68) kN/m
= 24.93kN/m
Ultimate dead load X-4, E
=20.25kN/m x 1.4
= 28.35kN/m
Ultimate dead load 2-X, E
= 24.93kN/m x 1.4
= 34.9kN/m
Live load 2-4, E-F
= 1.5kN/m² x 5.6m/2
= 4.2kN/m
Live load 1-X, D-E
= 1.5kN/m² x 2.6m/2
=1.95kN/m
Total live load at X-4, E
= 4.2kN/m
Total live load 2-X, E
= (4.2 + 1.95) kN/m
= 6.15kN/m
Ultimate live load X-4, E
= 4.2kN/m x 1.6
= 6.72kN/m
Ultimate live load 2-X, E
= 6.15kN/m x 1.6

16. = 9.84kN/m
Total ultimate load X-4, E
= (28.35 + 6.72) kN/m
= 35.07kN/m
Total ultimate load 2-X, E
= (34.9 + 9.84) kN/m
= 44.74kN/m
Point load from beam X, D-E
= ​11.34kN/m
Distributed load X-4, E
= 35.07kN/m x 4m
= 140.28kN
Distribution load 2-X, E
= 44.74kN/m x 1.6m
= 71.58kN/m
Total moment of point 4E
= 140.28kN(2m) + 11.34kN(4m) + 71.58kN(4.8m) - 2E(5.6m)
2E(5.6m) = 669.5kNm
2E reaction force = 119.55kN
4E reaction force
= (140.28 + 11.34 + 71.58 - 119.55) kN
= 103.65kN
Shear graph area
x/4 = 36.63/140.28
x = 1.04m
A = ½ (103.65kN x 2.96m)
= 153.4kNm
B = ½ (36.63kN x 1.04m)
= 19.05kNm
C = ½ (47.97kN+ 119.55kN) x 1.6m
= 134.02kNm

17. Beam X, D-E (First Floor Plan) Yen Wei Zheng
Beam self weight
= 0.15m x 0.45m x 24kN/m
= 1.62kN/m
Dead load at 1-X, D-E
= 3.6kN/m² x 2.6m/2 x ⅔
= 3.12kN/m
Total dead load
= (3.12 + 1.62) kN/m
= 4.74kN/m
Ultimate dead load
= 4.74kN/m x 1.4
= 6.64kN/m
Live load 1-X, D-E
= 1.5kN/m² x 2.6m/2 x ⅔
= 1.3kN/m
Ultimate live load 1-X, D-E
= 1.3kN/m x 1.6
= 2.08kN/m
Total ultimate load
= 6.64kN/m + 2.08kN/m
=8.72kN/m
Distributed load
= 8.72kN/m x 2.6m
= 22.67kN/m​ /2
= 11.34kN
Shear force area
= ½ (11.34kN + 1.3m)
= 6.32kNm

18. Beam 2 E-E’ (First Floor Plan) Yen Wei Zheng
Beam self weight
= 0.15m x 0.45m x 24kN/m
=​ ​1.62kN/m
Brick wall weight
= 3m x 0.15m x 19kN/m
=​ ​8.55kN/m
Dead load 1-2, E-E’
= 3.6kN/m² x 3.4m/2 x ⅔
4.08kN/m
Dead load 2-4, E-F
= 3.6kN/m² x 5.6m/2 x ⅔
= 6.72kN/m
Total dead load
= (1.62 + 8.55 + 4.08 + 6.72) kN/m
= 20.97kN/m
Ultimate dead load
= 20.97kN/m x 1.4
= 29.36kN/m
Live load 1-2, E-E’
= 1.5kN/m² x 3.4m/2 x ⅔
= 1.7kN/m
Live load 2-4, E-F
= 1.5kN/m² x 5.6m/2 x ⅔
= 2.8kN/m
Total live load
= (1.7 + 2.8)kN/m
= 4.5kN/m
Ultimate live load
= 4.5kN/m x 1.6
= 7.2kN/m
Total ultimate load
= (29.36 + 7.2)kN/m
= 36.56kN/m
Distributed load
= 36.56kN/m x 3.4m
= 124.3kN​ / 2
= 62.15kN

19. Shear force area
= ½ (62.15kN x 1.7m)
= 52.83kNm

20. Beam T, E’-F (First Floor Plan) Yen Wei Zheng
Beam self weight
= 0.15m x 0.45m x 24kN/m
=​ ​1.62kN/m
Brick wall weight
= 3m x 0.15m x 19kN/m
=​ ​8.55kN/m
Dead load T-2, E’-F
= 3.6kN/m² x 2/2 x ⅔
= 2.4kN/m
Total dead load
= (1.62 +8.55 + 2.4) kN/m
= 12.57kN/m
Ultimate dead load
= 12.57kN/m x 1.4
= 17.6kN/m
Live load T-2, E’-F
= 1.5kN/m² x 2/2 x ⅔
= 1kN/m
Ultimate live load
= 1kN/m x 1.6
= 1.6kN/m
Total ultimate load
= (17.6 + 1.6) kN/m
= 19.2kN/m
Distributed load
= 19.2kN/m x 2m
= 38.4kN​ / 2
= 19.2kN/m
Shear force area
= ½ (1m x 19.2kN)
= 9.6kNm

21. Beam 1-2, E’ (First Floor Plan) Yen Wei Zheng
Beam self weight
= 0.15m x 0.45m x 24kN/m
=​ ​1.62kN/m
Brick wall weight
= 3m x 0.15m x 19kN/m
=​ ​8.55kN/m
Dead load 1-2, E-E’
= 3.6kN/m² x 3.5m/2
= 6.3kN/m
Dead load T-2, E’-F
= 3.6kN/m² x 2m/2
= 3.6kN/m
Total dead load T-2, E’
= (1.62 + 8.55 + 6.3 + 3.6)kN/m
= 20.07kN/m
Total dead load 1-T, E’
= (1.62 + 8.55 + 6.3)kN/m
= 16.47kN/m
Ultimate dead load T-2, E’
= 20.07kN/m x 1.4
= 28.1kN/m
Ultimate dead load 1-T, E’
= 16.47kN/m x 1.4
= 23.06kN/m
Live load 1-2, E-E’
= 1.5kN/m x 3.5m/2
= 2.63kN/m
Live load T-2, E’-F
= 1.5kN/m x 2m/2
= 1.5kN/m
Total live load T-2, E’
= (2.63 + 1.5)kN/m
= 4.13kN/m
Ultimate live load T-2, E’
= 4.13kN/m x 1.6
= 6.61kN/m
Ultimate live load 1-1’E’
= 2.63kN/m x 1.6
= 4.21kN/m

22. Total ultimate load T-2, E’
= (28.1 + 6.61)kN/m
= 34.71kN/m
Total ultimate load 1-T, E’
= (23.06 + 4.21)kN/m
= 27.27kN/m
UDL (T-2, E’) to point load
= 34.71kN/m x 2m
= 69.42kN
UDL (1-T, E’) to point load
= 27.27kN/m x 1.5m
= 40.9kN
Point load from Beam T, E’-F
= 19.2kN
Total moment of point 2E’
= 69.42kN(1m) + 19.2kN(2m) + 40.9kN(2.75m) - 1E’(3.5m)
1E’(3.5m) = 220.3kN
Reaction force 1E’ = 62.94kN
Reaction force 2E’
= (69.42 + 19.2 + 40.9 - 62.94)kN
= 66.58kN
Shear force area
x/2 = 2.84/69.42
x = 0.08m
A = ½ (66.58kN x 1.92m)
= 63.92kNm
B = ½ ( 0.08m x 2.84kN)
= 0.11kNm
C = ½ (22.04kN + 62.94kN) x 1.5m
= 63.74kNm

23. Beam W-Y, C winter
Beam self weight
= 0.15m x 0.45m x 24kN/m
=​ ​1.62kN/m
Brick wall weight
= 3m x 0.15m x 19kN/m
=​ ​8.55kN/m
Dead load WY, CD
= 3.6kN/m² x 1.75m/2
= 3.15kN/m
Dead load WY, A’C
= 3.6kN/m² x 2.9m/2
= 5.22kN/m
Total dead load 3Y, C
= (1.62 + 8.55 + 3.15 + 5.22) kN/m
= 18.54kN/m
Total dead load 3W, C
= (1.62 + 3.15 + 5.22) kN/m
= 9.99kN/m
Ultimate dead load 3Y, C
= 18.54kN/m x 1.4
= 26.3kN/m
Ultimate dead load 3W, C
= 9.99kN/m x 1.4
= 13.986kN/m
Live load WY, CD
= 1.5kN/m² x 1.75m/2
= 1.313kN/m
Live load WY, A’C
= 1.5kN/m² x 2.9m/2
= 2.175kN/m²
Total live load
= (1.313 + 2.175)kN/m
= 3.488kN/m
Ultimate live load
= 3.488kN/m x 1.6
= 5.581kN/m
Total ultimate load 3Y, C
= (26.3 + 5.581) kN/m
= 31.881kN/m

24. Point load 3Y, C
= 31.881kN/m x 2.9m
= 92.455kN
Point load 3W, C
= 19.567kN/m x 1.6m
= 31.307kN
Total moment YC
= 92.455kN(1.45m) + 31.307kN(3.7) - WC(4.5)
WC(4.5) = 249.896kN
Reaction force WC = 55.532kN
Reaction force YC = (92.455 + 31.307 - 55.532)
= 68.23kN
Shear force area
x/2.9 = 24.225/92.455
x = 0.76m
A = ½ (68.23kN x 2.14m)
​= 73kNm
B = ½ (24.225kN x 0.76m)
​= 9.21kNm
C = ½ (24.225kN + 55.532kN) x 1.6m
​ = 63.81

25. Beam Y, A’D winter
Beam self weight
= 0.15m x 0.45m x 24kN/m
=​ ​1.62kN/m
Brick wall weight
= 3m x 0.15m x 19kN/m
=​ ​8.55kN/m
Dead load WY, A’C
= 3.6kN/m² x 3.5m/2 x ⅔
= 4.2kN/m
Dead load YZ, A’D
= 3.6kN/m² x 1m/2
= 1.8kN/m
Total dead load Y, A’C
= (1.8+4.2+1.62+8.55)
= 16.17kN/m
Ultimate dead load Y, A’C
= 16.17kN/m x 1.4
= 22.64kN/m
Total dead load Y, CD
= (1.8+1.62+8.55)kN/m
= 11.97kN/m
Ultimate dead load Y, CD
= 11.97kN/m x 1.4
= 16.758kN/m
Live load WY, A’C
= 1.5kN/m² x 3.5m/2 x ⅔
= 1.75kN/m
Live load YZ, A’D
= 1.5kN/m² x 1m/2
= 0.75kN/m
Total ultimate load Y, A’C
= (0.75+1.75) kN/m
= 2.5kN/m
Ultimate live load Y, A’C
= 2.5kN/m x 1.6
= 4kN/m
Live load Y,CD
=1.75kN/m

26. Ultimate live load Y, CD
= 1.75kN/m x 1.6
= 2.8kN/m
Total ultimate load Y, A’C
= (22.638+4) kN/m
= 26.64kN/m
Total ultimate load Y, CD
= (16.758+2.8) kN/m
= 19.558kN/m
Point load at Y, A’C
= 26.638kN/m x 3.5m
= 93.24kN
Point load Y, CD
= 19.558kN/m x 1.75m
= 34.2265kN
Total moment of YD
= 34.2265kN(0.875m) + 68.23kN(1.75m) + 93.24kN(3.5m) - YA’(5.25m)
YA’(5.25) = 475.69
YA’ reaction force = 90.61kN
YD reaction force = (34.2265+68.23+93.24-90.61)
= 105.09kN
Shear force area
x/3.5 = 2.63/93.24
x = 0.0987m
A = ½ (105.09kN+70.86kN) x 1.75m
​ = 153.96kNm
B = ½ (0.0987m x 2.63kN)
= 0.13kN
C = ½ (90.61kN x 3.4m)
= 154.04kNm

27. Beam X-4, D winter
Beam self weight
= 0.15m x 0.45m x 24kN/m
= 1.62kN/m
Brick wall weight
= 3m x 0.15 x 19kN/m
=8.55kN/m
Dead load WY, CD
= 3.6kN/m x 1.75m/2
= 3.15kN/m
Total dead load Y-4, D
= (1.62+8.55)
= 10.17kN/m
Ultimate dead load Y-4, D
= 10.17kN/m x 1.4
= 14.238kN/m
Total dead load X-Y, D
= (1.62+8.55+3.15)
= 13.32kN/m
Ultimate dead load X-Y, D
= 13.32kN/m x 1.4
= 18.648kN/m
Live load WY, CD
= 1.5kN/m x 1.75m/2
= 2.625kN/m
Ultimate live load
= 2.625kN/m x 1.6
= 4.2kN/m
Total ultimate load Y-4, D
= 14.238kN/m
Total ultimate load X-Y, D
= (18.648+4.2) kN/m
= 22.848kN/m
Point load from beam Y, A’D
= 105.09kN
Point load at Y-4
= 14.238kN/m x 0.4m
= 5.695kN

28. Point load at X-Y
= 22.848kN/m x 3.8m
= 86.822kN
Total moment at 4,D
= 5.695kN(0.2m) + 105.09kN(0.4m) + 86.822kN(2.3m) - XD(4.2)
XD(4.2) = 242.87Kn
Reaction force at XD = 57.83kN
Reaction force at 4D
= (5.695+105.09+86.822-57.83)kN
= 139.78kN
Shear force area
x/3.8 = 29/86.83
x = 1.27m
A = ½ (139.78kN+132.09kN) x 0.4m
​ = 54.37kNm
B = ½ (29kN x 1.27m)
​ = 18.42kNm
C = ½ (2.53m x 57.83kN)
​= 73.15kNm

29. Beam V, C-D (First Floor Plan) Teo Chong Yih
Beam self weight
= 0.15m x 0.45m x 24kN/m
= 1.62kN/m
Brick wall weight
= 3m x 0.15 x 19kN/m
=8.55kN/m
Dead load 1-V, CD
= 3.6kN/m² x 1.75/2 x ⅔
= 2.1kN/m
Dead load V-W, CD
= 3.6kN/m² x 1.75/2 x ⅔
= 2.1kN/m
Total dead load
= (1.62 + 8.55 + 2.1 + 2.1 ) kN/m
= 14.37kN/m
Ultimate dead load
= 14.37kN/m x 1.4
= 20.118kN/m
Live load 1-V, CD
= 1.5kN/m² x 1.75/2
= 1.31kN/m
Live load V-W, CD
= 1.5kN/m² x 1.75/2
= 1.31kN/m
Total live load
= (1.31 + 1.31 )kN/m
= 2.62kN/m
Ultimate live load
= 2.62kN/m x 1.6
= 4.19kN/m
Total ultimate load
= (20.118 + 4.19 )kN/m
= 24.31kN/m
Distributed load
= 24.31kN/m x 1.75m
= 42.54kN / 2
= 21.27kN/m
Shear force area
= ½ (0.87m x 21.27kN/m)
= 9.3kNm

30. Beam W, C-D (First Floor Plan) Teo Chong Yih
Beam self weight
= 0.15m x 0.45m x 24kN/m
= 1.62kN/m
Brick wall weight
= 3m x 0.15 x 19kN/m
=8.55kN/m
Dead load V-W, CD
= 3.6kN/m² x 1.75/2 x ⅔
= 2.1kN/m
Dead load W-Y, CD
= 3.6kN/m² x 1.75/2
= 3.15kN/m
Total dead load
= (1.62 + 8.55 + 2.1 + 3.15 ) kN/m
=15.42kN/m
Ultimate dead load
= 15.42kN/m x 1.4
= 21.588kN/m
Live load W, C-D
= 1.5kN/m² x 1.75/2
= 1.31kN/m
Live load W, C-D
= 1.5kN/m² x 1.75/2
= 1.31kN/m
Total live load
= (1.31 + 1.31 )kN/m
= 2.62kN/m
Ultimate live load
= 2.62kN/m x 1.6
= 4.19kN/m
Total ultimate load
= (21.59 + 4.19 )kN/m
= 25.78kN/m
Distributed load
= 25.78kN/m x 1.75m
= 45.12kN / 2
= 22.56kN/m
Shear force area
= ½ (0.87m x 22.56kN/m)
= 9.87kNm

31. Beam 1-X, D (First Floor Plan) Teo Chong Yih
Beam self weight
= 0.15m x 0.45m x 24kN/m
= 1.62kN/m
Brick wall weight
= 3m x 0.15 x 19kN/m
=8.55kN/m
Dead load 1-V, D
= 3.6kN/m² x 2.65/2 x ⅔
= 3.18kN/m
Dead load V-W, D
= 3.6kN/m² x 2/2 x ⅔
= 2.4kN/m
Dead load 1-X
= 3.6kN/m² x 5.3
= 19.08kN/m
Dead load W-X,D
= 3.6kN/m² x 0.875m
= 3.15kN/m
Total dead load
= (1.62 + 8.55 + 19.08 + 3.15 ) kN/m, (1.62 + 2.4 + 19.08)kN/m, (1.62 + 8.55 + 3.18 +
19.08)kN/m
= 32.4kN/m , 23.1kN/m, 32.43kN/m
Ultimate dead load
= 32.4kN/m x 1.4, 23.1kN/m x 1.4, 32.43kN/m x 1.4
= 45.36kN/m, 32.34kN/m, 45.4kN/m
Live load 1-V, D
= 1.5kN/m² x 2.65/2
= 1.99kN/m
Live load V-W, D
= 1.5kN/m² x 2/2
= 1.5kN/m
Live load W-X, D
= 1.31kN/m
Live load 1-X
= 1.5 x 5.3/2
= 3.98kN/m

32. Total live load
= (1.31 + 3.98 )kN/m , (1.5 + 3.98)kN/m , (1.99 + 3.98)kN/m
= 5.29kN/m , 5.48kN/m , 5.97kN/m
Ultimate live load
= (5.29kN/m x 1.6) , (5.48kN/m x 1.6) , (5.97kN/m x 1.6)
= 8.46kN/m , 8.77kN/m , 9.55kN/m
Total ultimate load
= (45.36 + 8.46)kN/m , (32.34 + 8.77 )kN/m , (45.4 + 9.55)kN/m
= 53.82kN/m, 41.11kN/m, 54.95kN/m
Distributed load
= 53.82kN/m x 0.7m , 41.11kN/m x 2m , 54.95 x 2.65m
= 37.67kN, 82.22kN, 145.62kN
Take moment at point XD,
(37.67kN x 0.35m) + (22.56kN x 0.7m) + (82.22kN x 1.7m) + (21.27 x 2.7m) + (145.62kN x
4.025m) - 5.35z = 13.18kNm + 15.79kNm + 139.77kNm + 57.43kNm + 586.12kNm - 5.35z
= 812.29Nm - 5.35z
(5.35m)z = 812.29kNm
z = 151.83kN
(145.62kN x 1.325m) + (21.27kN x 2.65m) + (82.22kN x 3.65m) + (22.56kN x 4.65) + (37.67kN x
5.025m ) = 5.35x
192.95kNm + 56.37kNm + 300.1kNm + 104.9kNm + 189.29kNm = (5.35m)x
x = 157.68kN
Shear graph area
A = ½ (157.68kN + 120.01kN) x 0.7 = 97.19kNm
B = ½ (97.45kN + 15.23kN) x 2 = 112.68kNm
C = ½ (-6.04kN - 151.66kN) x 2.65 = -208.95kNm

33. Beam W, A’-C (First Floor Plan) WINTER
Beam self weight
= 0.15m x 0.45m x 24kN/m
= 1.62kN/m
Brick wall weight
= 3m x 0.15m x 19kN/m
= 8.55kN/m
Dead load at W-Y, A’-C
= 3.6kN/m² x 3.5m/2 x 2/3
= 4.2kN/m
Dead load at 1-W, A’-C
= 3.6kN/m² x 1.2/2 x 2/3
= 4.2kN/m
Total dead load
= (1.62 + 8.55 + 4.2 + 4.2)kN/m
= 18.57kN/m
Ultimate dead load
= 18.57kN/m x 1.4
= 26kN/m
Live load at W-Y, A’-C
= 1.5kN/m² x 3.5m/2 x 2/3
= 1.75kN/m
Live load at 1-W, A’-C
= 1.5kN/m² x 3.5m/2 x 2/3
= 1.75kN/m
Total live load
= (1.75 + 1.75)kN/m
= 3.5kN/m
Ultimate live load
= 3.5kN/m x 1.6
= 5.6kN/m
Total ultimate load
= (26 + 5.6)kN/m
= 31.6kN/m
Distributed load
31.6kN/m x 3.5m/2
= 55.3kN
Shear graph area
= ½ x 55.3kN x 1.75m
= 48.3kNm

34. Beam A’, 2-Y (First Floor Plan) WINTER
Beam self weight
= 0.15m x 0.45m x 24kN/m
= 1.62kN/m
Brick wall weight
= 3m x 0.15m x 19kN/m
= 8.55kN/m
Dead load at 1-Y, A-A’
= 3.6kN/m² x 1.2m/2
= 2.16N/m
Dead load at W-Y, A’-C
= 3.6kN/m² x 3.5m/2
= 6.3kN/m
Dead load at 2-W, A’-C
= 3.6kN/m² x 3.5m/2
= 6.3kN/m
Total dead load at grid W-Y
= (1.62 + 8.55 + 2.16 + 6.3)kN/m
= 18.63kN/m
Total dead load at grid 2-W
= (1.62 + 8.55 + 2.16 + 6.3)kN/m
= 18.63kN/m
Ultimate dead load at grid W-Y
= (18.63kN/m x 1.4)
= 26.08kN/m
Ultimate dead load at grid 2-W
= (18.63kN/m x 1.4)
= 26.08kN/m
Live load at 1-Y, A-A’
= 1.5kN/m² x 1.2m/2
= 0.9kN/m
Live load at W-Y, A’-C
= 1.5kN/m² x 3.5m/2
= 2.63kN/m
Live load at 2-W, A’-C
= 1.5kN/m² x3.5m/2
= 2.63kN/m
Total live load at grid W-Y
= (0.9 + 2.63)kN/m
= 3.53kN/m
Total live load at grid 2-W

35. = (0.9 + 2.63)kN/m
= 3.53kN/m
Ultimate live load at grid W-Y
= (3.53kN/m x 1.6)
= 5.65kN/m
Ultimate live load at grid 2-W
= (3.53kN/m x 1.6)
= 5.65kN/m
Total ultimate load at grid W-Y
= (26.08 + 5.65)kN/m
= 31.73kN/m
Total ultimate load at grid 2-W
= (26.08 + 5.65)kN/m
= 31.73kN/m
Distributed load of gid W-Y
= 31.73kN/m x 4.5m
= 142.79kN
Distributed load of grid 2-W
= 31.73kN/m x 1m
= 31.73kN
Take moment at point YA’
(142.79kN x 2.25m) + (55.3kN x 4.5m) + (31.73kN x 5m) = (5.5m)YA’
(5.5m)YA’ = 728.78kNm
YA’ = 132.51kN
Take moment at point A’2
(31.73kN x 0.5m) + (55.3kN x 1m) + (142.79kN x 3.25m) = (5.5m)2A’
(5.5m)2A’ = 535.23kNm
2A’ = 97.32kN
Shear graph area
x/4.5 = 97.32/142.79
x = 3.07
A = ½ x 3.07m x 97.32kN = 149.24kNm
B = ½ x 1.23m x 45.47kN = 32.51kNm
C = ½ x (100.77kN + 132.5kN) x 1m = 116.64