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Building structure

Y
yenweizheng

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.

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

  • 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