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This document contains calculations for the dead loads, live loads, and ultimate loads on various beams and slabs in a building. It first calculates the loads on beam C-D, finding the total ultimate load to be 35.14 kN/m. It then calculates loads on beam C/2-3, with ultimate loads of 37.514 kN/m and 21.7 kN/m. Similar load calculations are provided for beams A1/3-4.1 and A1-B/3.1 and 4, finding ultimate point loads on these beams. The document includes details on the slab thicknesses, beam sizes, densities, and live load assumptions used in the calculations.

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Wong Kai Chiang 0323341 1 Beam Calculation 1. Beam C-D/ 2.2 Ground floor plan Structural plan Basic information Slab thickness : 0.15m Brick wall thickness : 0.225m Wall height : 3m Beam size : Primary beam : 0.2m x 0.4m : Secondary beam: 0.2m x 0.3m Brick wall density : 19 kN/m3 RC density : 24 kN/m3 Live Load UBBL : Living area: 1.5 kN/m2 : Bedroom : 1.5 kN/m2
Wong Kai Chiang 0323341 2 Dead Load 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab C-D/ 2-2.1 3.6 kN/m2 x (2.075/ 2) = 3.735 kN/m c. Dead load on slab C-D/ 2.1- 3 3.6 kN/m2 x (2/ 2) = 3.6 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load (3.735 + 3.6 + 2.825 + 1.44) kN/m = 21.6 kN/m Live Load Live load on slab C-D/ 2-2.2 (bedroom) 1.5 kN/m2 x (2.075/ 2) = 1.56 kN/m Live load on slab C-D/ 2.2-3 (living area) 1.5 kN/m2 x (2/ 2) = 1.5 kN/m Total Live Load (1.56 + 1.5) kN/m = 3.06 kN/m Ultimate Load Ultimate dead load C-D: 1.4 x 21.6 kN/m = 30.24 kN/m Ultimate live load C-D: 1.6 x 3.06 kN/m = 4.9 kN/m Total ultimate load C-D: (30.24 + 4.9) kN/m = 35.14 kN/m
Wong Kai Chiang 0323341 3 Ultimate Load Diagram ∑Fy = 0 Therefore, RC = RD 35.14 kN/m x 3.5m = 123 kN 123 kN/ 2 = 61.5 kN RC = RD = 61.5 kN Shear Force Diagram Positive area (61.5 x 1.75)/ 2 = 53.81 kN/m Negative area (61.5 x 1.75)/ 2 = 53.81 kN/m Bending Moment Diagram
Wong Kai Chiang 0323341 4 2. Beam C/ 2-3 Ground floor plan Structural plan Basic information Slab thickness : 0.15m Brick wall thickness : 0.225m Wall height : 3m Beam size : Primary beam : 0.2m x 0.4m : Secondary beam: 0.2m x 0.3m Brick wall density : 19 kN/m3 RC density : 24 kN/m3 Live Load UBBL : Living area: 1.5 kN/m2 : Bedroom : 1.5 kN/m2
Wong Kai Chiang 0323341 5 Dead Load 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab B1-C/ 2-3 3.6 kN/m2 x (3.15/ 2) = 5.67 kN/m c. Dead load on slab C-D/ 2-2.2 2 3 [3.6 kN/m2 x (2.075/ 2)] = 2.49 kN/m d. Dead load on slab C-D/ 2.2-3 2 3 [3.6 kN/m2 x (2/ 2)] = 2.4 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load For 2-2.1 (2.36 + 1.04) kN/m = 3.4 kN/m For 2.1-3 (2.36 + 1) kN/m = 3.36 kN/m Live Load Live load on slab C-D/ 2-2.2 (bedroom) 2 3 [1.5 kN/m2 x (2.075/ 2)] = 1.04 kN/m Live load on slab C-D/ 2.2-3 (living area) 1.5 kN/m2 x (3.15/ 2) = 2.36 kN/m Live load on slab C-D/ 2-2.2 (living area) 2 3 [1.5 kN/m2 x (2/ 2)] = 1 kN/m
Wong Kai Chiang 0323341 6 Total Live Load For 2-2.2 (2.36 + 1.04) kN/m = 3.4 kN/m For 2.2-3 (2.36 + 1) kN/m = 3.36 kN/m Ultimate Load Ultimate load on 2-2.2 Ultimate dead load: 1.4 x 22.91 kN/m = 32.074 kN/m Ultimate live load : 1.6 x 3.4 kN/m = 5.44 kN/m Total ultimate load: (32.074 + 5.44) kN/m = 37.514 kN/m Ultimate load on 2.2-3 Ultimate dead load: 1.4 x 11.66 kN/m = 16.32 kN/m Ultimate live load : 1.6 x 3.36 kN/m = 5.38 kN/m Total ultimate load: (16.32 + 5.38) kN/m = 21.7 kN/m
Wong Kai Chiang 0323341 7 Ultimate Load Diagram *PL of 61.5 kN/m is obtained from pg.7, which is the value of RC ∑M2 = 0 = -R3 (4.075) + 37.514 (2.075)(1.038) + 61.5 (2.075) + 21.7 (2)(3.075) = -4.075 R3 + 341.87 R3 = 341.87/ 4.075 = 83.89 kN ∑Fy = 0 R2 + R3 – 61.5 – 77.84 – 43.4 = 0 R2 + 83.89 – 182.74 = 0 R2 – 98.85 = 0 R2 = 98.85 kN Shear Force Diagram Positive area [(98.85 + 21.01)/ 2] x 2.075 = 124.35 kN/m ≈ 124 kN/m Negative area [(40.49 + 83.89)/ 2] x 2 = 124.38 kN/m ≈ 124 kN/m Bending Moment Diagram
Wong Kai Chiang 0323341 8 3. Beam A1/ 3-4.1 Ground floor plan Structural plan Basic information Slab thickness : 0.15m Brick wall thickness : 0.225m Wall height : 3m Beam size : Secondary beam: 0.2m x 0.3m Brick wall density : 19 kN/m3 RC density : 24 kN/m3 Live Load UBBL : Living area: 1.5 kN/m2 : Bedroom : 1.5 kN/m2
Wong Kai Chiang 0323341 9 Dead Load 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A-A1/ 3-4 3.6 kN/m2 x (3.5/ 2) = 6.3 kN/m c. Dead load on slab A1-B/ 3-3.1 3.6 kN/m2 x (1.5/ 2) = 2.7 kN/m d. Dead load on slab A1-B/ 3.1-4 3.6 kN/m2 x (1.5/ 2)] = 2.7 kN/m e. Dead load on slab A1-B/ 3.1-4 2 3 [3.6 kN/m2 x (1.03/ 2)] = 1.236 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load For 3-3.1 (6.3 + 2.7 + 12.825 + 1.44) kN/m = 23.27 kN/m For 3.1-4 (6.3 + 2.7 + 12.825 + 1.44) kN/m = 23.27 kN/m For 4-4.1 (1.236 + 12.825 + 1.44) kN/m = 15.5 kN/m Live Load Live load on slab A-A1/ 3-4 (bedroom) 1.5 kN/m2 x (3.5/ 2)] = 2.625 kN/m Live load on slab A1-B/ 3-3.1 (living area) 1.5 kN/m2 x (1.5/ 2) = 1.125 kN/m
Wong Kai Chiang 0323341 10 Live load on slab A1-B/ 3.1-4 (bedroom) 1.5 kN/m2 x (1.5/ 2)] = 1.125 kN/m Live load on slab A1-B/ 4-4.1 (bedroom) 1.5 kN/m2 x (1.025/ 2)] = 0.77 kN/m Total Live Load For 3-3.1 (2.625 + 1.125) kN/m = 3.75kN/m For 3.1-4 (2.625 + 1.125) kN/m = 3.75 kN/m For 4-4.1 0.77 kN/m Ultimate Load Ultimate load on 3-3.1 Ultimate dead load: 1.4 x 23.27 kN/m = 32.58 kN/m Ultimate live load : 1.6 x 3.75 kN/m = 6 kN/m Total ultimate load: (32.58 + 6) kN/m = 38.58 kN/m Ultimate load on 3.1-4 Ultimate dead load: 1.4 x 23.27 kN/m = 32.58 kN/m Ultimate live load : 1.6 x 3.75 kN/m = 6 kN/m Total ultimate load: (32.58 + 6) kN/m = 38.58 kN/m Ultimate load on 4-4.1 Ultimate dead load: 1.4 x 15.5 kN/m = 21.7 kN/m Ultimate live load : 1.6 x 0.77 kN/m = 1.23 kN/m Total ultimate load: (21.7 + 1.23) kN/m = 22.93 kN/m ___________________________________________________________________________
Wong Kai Chiang 0323341 11 Beam A1-B/ 3.1 (Point Load) 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A1-B/ 3-3.1 2 3 [3.6 kN/m2 x (1.5/ 2)] = 2.9 kN/m c. Dead load on slab A1-B/ 3.1-4 2 3 [3.6 kN/m2 x (1.5/ 2)] = 2.9 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load (2.9 + 2.9 + 12.825 + 1.44) kN/m = 20.07 kN/m Live Load Live load on slab A-A1/ 3-4 (living area) 2 3 [1.5 kN/m2 x (1.5/ 2)] = 0.75 kN/m Live load on slab A1-B/ 3-3.1 (living area) 2 3 [1.5 kN/m2 x (1.5/ 2)] = 0.75 kN/m Total Live Load (0.75 + 0.75) kN/m = 1.5kN/m Ultimate Load Ultimate dead load A1-B: 1.4 x 20.07 kN/m = 28.1 kN/m Ultimate live load A1-B: 1.6 x 1.5 kN/m = 2.4 kN/m Total ultimate load A1-B: (28.1 + 2.4) kN/m = 30.5 kN/m
Wong Kai Chiang 0323341 12 Ultimate Load Diagram ∑Fy = 0 Therefore, RA1 = RB 30.5 kN/m x 1.5m = 45.75 kN 45.75 kN/ 2 = 22.88 kN RA1 = RB = 22.88 kN ___________________________________________________________________________ Beam A1-B/ 4 (Point Load) 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A1-B/ 3-3.1 2 3 [3.6 kN/m2 x (1.5/ 2)] = 2.9 kN/m c. Dead load on slab A1-B/ 3.1-4 3.6 kN/m2 x (1.025/ 2)] = 1.845 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load (2.9 + 1.845 + 12.825 + 1.44) kN/m = 19.01kN/m Live Load Live load on slab A1-B/ 3.1-4 (living area) 2 3 [1.5 kN/m2 x (1.5/ 2)] = 0.75 kN/m Live load on slab A1-B/ 3-3.1 (bedroom) 1.5 kN/m2 x (1.025/ 2) = 0.77 kN/m
Wong Kai Chiang 0323341 13 Total Live Load (0.75 + 0.77) kN/m = 1.52kN/m Ultimate Load Ultimate dead load A1-B: 1.4 x 19.01 kN/m = 26.61 kN/m Ultimate live load A1-B: 1.6 x 1.52 kN/m = 2.43 kN/m Total ultimate load A1-B: (26.61 + 2.43) kN/m = 29.04 kN/m Ultimate Load Diagram ∑Fy = 0 Therefore, RA1 = RB 29.04 kN/m x 1.5m = 43.56 kN 43.56 kN/ 2 = 21.78 kN RA1 = RB = 21.78 kN ___________________________________________________________________________ Beam A-A1/ 4 (Point Load) 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A-A1/ 3-3.1 2 3 [3.6 kN/m2 x (3.5/ 2)] = 4.2 kN/m c. Dead load on slab A-A1/ 3.1-4 3.6 kN/m2 x (1.025/ 2)] = 1.845 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load (4.2 + 1.845 + 12.825 + 1.44) kN/m = 20.31kN/m
Wong Kai Chiang 0323341 14 Live Load Live load on slab A-A1/ 3-3.1 (bedroom) 2 3 [1.5 kN/m2 x (3.5/ 2)] = 1.75 kN/m Live load on slab A-A1/ 3.1-4 (bedroom) 1.5 kN/m2 x (1.025/ 2) = 0.77 kN/m Total Live Load (1.75 + 0.77) kN/m = 2.52kN/m Ultimate Load Ultimate dead load A1-B: 1.4 x 20.31 kN/m = 28.43 kN/m Ultimate live load A1-B: 1.6 x 2.52 kN/m = 4.03 kN/m Total ultimate load A1-B: (28.43 + 4.03) kN/m = 32.46 kN/m Ultimate Load Diagram ∑Fy = 0 Therefore, RA1 = RB 32.46 kN/m x 3.5m = 113.61 kN 113.61 kN/ 2 = 56.81 kN RA1 = RB = 56.81 kN ___________________________________________________________________________ Ultimate Load Diagram of Beam A1/ 3-4.1 *PL of 22.88 kN/m obtained from pg.; PL of 21.78 kN/m obtained from pg.; PL of 56.81 kN/m obtained from pg.. ∑M3 = 0 = -R4.1 (4.95) + 38.58 (1.7)(0.85) + 22.88 (1.7) + 38.58 (2.225)(2.8) + 56.81 (3.9) + 21.78 (3.9) + 22.93 (1.025)(4.44)
Wong Kai Chiang 0323341 15 = -4.95 R4.1 + 745.85 R4.1 = 745.85/ 4.95 = 150.68kN ∑Fy = 0 = R3 + R4.1 – 65.59 – 22.88 – 85.84 - 56.81 – 21.78 – 23.5 = R3 + 150.68 – 276.4 = 0 R3 – 125.72 = 0 R3 = 125.72 kN Shear Force Diagram To find the triangle area, x y = 37.25 48.59 ~1 x + y = 2.225 ~2 x = 2.225 – y ~3 sub 3 into 1, 108.11 – 48.59y = 37.25y 108.11 = 85.84y y = 1.26m ~4 then, sub 4 into 3, x = 2.225 – 1.26 = 0.965m Positive area [(125.72 + 60.13)/ 2] x 1.7 = 157.97 kNm (37.25 x 0.965)/ 2 = 17.97 kNm 157.97 + 17.97 = 175.94 kNm ≈ 174.5 kNm Negative area [(127.18 + 150.68)/ 2] x 1.025 = 142.4 kN/m
Wong Kai Chiang 0323341 16 (48.59 x 1.26)/ 2 = 30.61 kNm 142.4 + 30.61 = 173.01 kNm ≈ 174.5 kNm Bending Moment Diagram
Wong Kai Chiang 0323341 17 4. Beam A1/ 2-3 Ground floor plan Structural plan Basic information Slab thickness : 0.15m Brick wall thickness : 0.225m Wall height : 3m Beam size : Secondary beam: 0.2m x 0.3m Brick wall density : 19 kN/m3 RC density : 24 kN/m3 Live Load UBBL : Living area: 1.5 kN/m2 : Bedroom : 1.5 kN/m2 : Toilet : 2.0 kN/m2 Dead Load 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A-A1/ 2.1-2.2 2 3 [3.6 kN/m2 x (1.9/ 2)] = 2.28 kN/m
Wong Kai Chiang 0323341 18 c. Dead load on slab A1-B/ 2-3 3.6 kN/m2 x (1.5/ 2) = 2.7 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load For 2.1-2.2 (2.28 + 2.7 + 12.825 + 1.44) kN/m = 19.245 kN/m For 2-2.1, 2.2-3 (2.7 + 12.825 + 1.44) kN/m = 16.97 kN/m Live Load Live load on slab A-A1/ 2.1-2.2 (toilet) 2 3 [2 kN/m2 x (1.9/ 2)] = 1.27kN/m Live load on slab A1-B/ 2-2.1 (bedroom) 1.5 kN/m2 x (1.5/ 2) = 1.13 kN/m Total Live Load For 2.1-2.2 (1.27 + 1.13) kN/m = 2.4kN/m For 2-2.1, 2.2-3 1.13 kN/m Ultimate Load Ultimate load on 2-2.1 Ultimate dead load: 1.4 x 16.97 kN/m = 23.76 kN/m Ultimate live load : 1.6 x 1.13 kN/m = 1.81 kN/m Total ultimate load: (23.76 + 1.81) kN/m = 25.57 kN/m
Wong Kai Chiang 0323341 19 Ultimate load on 2.1-2.2 Ultimate dead load: 1.4 x 19.245 kN/m = 26.94 kN/m Ultimate live load : 1.6 x 2.4 kN/m = 3.84 kN/m Total ultimate load: (26.94 + 3.84) kN/m = 30.78 kN/m Ultimate load on 2.2-3 Ultimate dead load: 1.4 x 16.97 kN/m = 23.76 kN/m Ultimate live load : 1.6 x 1.13 kN/m = 1.81 kN/m Total ultimate load: (23.76 + 1.81) kN/m = 25.57 kN/m ___________________________________________________________________________ Beam A1-B/ 3.1 (Point Load) 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A-A1/ 2-2.1 3.6 kN/m2 x (1.1/ 2)] = 1.98 kN/m c. Dead load on slab A-A1/ 2.1-2.2 3.6 kN/m2 x (1.9/ 2)] = 3.42 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load (1.98 + 3.42 + 12.825 + 1.44) kN/m = 19.67 kN/m Live Load Live load on slab A-A1/ 2-2.1 (bedroom) 1.5 kN/m2 x (1.1/ 2)] = 0.83 kN/m Live load on slab A1-B/ 2.1-2.2 (living area) 2 kN/m2 x (1.9/ 2)] = 1.9 kN/m
Wong Kai Chiang 0323341 20 Total Live Load (0.83 + 1.9) kN/m = 2.73kN/m Ultimate Load Ultimate dead load A-A1: 1.4 x 19.67 kN/m = 27.54 kN/m Ultimate live load A-A1: 1.6 x 2.73 kN/m = 4.37 kN/m Total ultimate load A-A1: (27.54 + 4.37) kN/m = 31.91 kN/m Ultimate Load Diagram ∑Fy = 0 Therefore, RA1 = RB 31.91 kN/m x 3.5m = 111.69 kN 111.69 kN/ 2 = 55.85 kN RA1 = RB = 55.85 kN ___________________________________________________________________________ Beam A-A1/ 2.2 (Point Load) 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A-A1/ 2.1-2.2 3.6 kN/m2 x (1.9/ 2)] = 3.42 kN/m c. Dead load on slab A-A1/ 2.2-3 3.6 kN/m2 x (1.075/ 2)] = 1.94 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load (3.42 + 1.94 + 12.825 + 1.44) kN/m = 19.63 kN/m
Wong Kai Chiang 0323341 21 Live Load Live load on slab A-A1/ 2.1-2.2 (toilet) 2.0 kN/m2 x (1.9/ 2)] = 1.9 kN/m Live load on slab A1-B/ 2.2-3 (bedroom) 1.5 kN/m2 x (1.075/ 2)] = 0.81 kN/m Total Live Load (1.9 + 0.81) kN/m = 2.71kN/m Ultimate Load Ultimate dead load A-A1: 1.4 x 19.63 kN/m = 27.48 kN/m Ultimate live load A-A1: 1.6 x 2.71 kN/m = 4.34 kN/m Total ultimate load A-A1: (27.48 + 4.34) kN/m =31.82 kN/m Ultimate Load Diagram ∑Fy = 0 Therefore, RA1 = RB 31.82 kN/m x 3.5m = 111.37 kN 111.37 kN/ 2 = 55.69 kN RA1 = RB = 55.69 kN ___________________________________________________________________________ Ultimate Load Diagram of Beam A1/ 3-4.1 ∑M2 = 0 = -R3 (4.075) + 25.57 (1.1)(0.55) + 55.84 (1.1) + 30.78 (1.9)(2.05) + 55.69 (3) + 25.57 (1.075)(3.54) = -4.075 R3 + 461.16 R3 = 461.16/ 4.075 = 113.17kN ∑Fy = 0
Wong Kai Chiang 0323341 22 = R2 + R3 – 28.13 – 55.84 – 58.48 - 55.69 – 27.49 = R2 + 113.17 – 225.63 = 0 R2 – 112.46 = 0 R2 = 112.46 kN Shear Force Diagram To find the triangle area, x y = 28.49 29.99 ~1 x + y = 1.9 ~2 x = 1.9 – y ~3 sub 3 into 1, 56.98 – 29.99y = 28.49y 56.98 = 58.48y y = 0.97m ~4 then, sub 4 into 3, x = 1.9 – 0.97 = 0.93m Positive area [(112.46 + 84.33)/ 2] x 1.1 = 108.23 kNm (28.49 x 0.93)/ 2 = 13.25 kNm 108.23 + 13.25 = 121.48 kNm ≈ 121 kNm Negative area [(113.17 + 85.68)/ 2] x 1.075 = 106.88 kN/m (29.99 x 0.97)/ 2 = 14.55 kNm 106.88 + 14.55 = 121.43 kNm ≈ 121 kNm
Wong Kai Chiang 0323341 23 Bending Moment Diagram
Wong Kai Chiang 0323341 24 5. Beam A-B/ 3 Ground floor plan Structural plan Basic information Slab thickness : 0.15m Brick wall thickness : 0.225m Wall height : 3m Beam size : Primary beam : 0.2m x 0.4m : Secondary beam: 0.2m x 0.3m Brick wall density : 19 kN/m3 RC density : 24 kN/m3 Live Load UBBL : Living area: 1.5 kN/m2 : Bedroom : 1.5 kN/m2 Dead Load 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A-A1/ 2.2-3 3.6 kN/m2 x (1.075/ 2)] = 1.935 kN/m
Wong Kai Chiang 0323341 25 c. Dead load on slab A1-B/ 3-4 2 3 [3.6 kN/m2 x (3.5/ 2)] = 4.2 kN/m d. Dead load on slab A1-B/ 3-3.1 2 3 [3.6 kN/m2 x (1.5/ 2)] = 1.8 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load For A-A1 (1.935 + 4.2 + 12.825 + 1.44) kN/m = 20.4 kN/m For A1-B (1.8 + 12.825 + 1.44) kN/m = 16.07 kN/m Live Load Live load on slab A-A1/ 2.2-3 (bedroom) 1.5 kN/m2 x (1.075/ 2) = 0.81 kN/m Live load on slab A1-B/ 2-2.1 (bedroom) 2 3 [1.5 kN/m2 x (3.5/ 2)] = 1.75kN/m Live load on slab A1-B/ 3-3.1 (living area) 2 3 [1.5 kN/m2 x (3.5/ 2)] = 0.75kN/m Total Live Load For A-A1 (0.81 + 1.75) kN/m = 2.56kN/m For A1-B 0.75 kN/m
Wong Kai Chiang 0323341 26 Ultimate Load Ultimate load on A-A1 Ultimate dead load: 1.4 x 20.4 kN/m = 28.56 kN/m Ultimate live load : 1.6 x 2.56 kN/m = 4.1 kN/m Total ultimate load: (28.56 + 4.1) kN/m = 32.66 kN/m Ultimate load on A1-B Ultimate dead load: 1.4 x 16.07 kN/m = 22.5 kN/m Ultimate live load : 1.6 x 0.75 kN/m = 1.2 kN/m Total ultimate load: (22.5 + 1.2) kN/m = 23.7 kN/m Ultimate Load Diagram of Beam A1/ 3-4.1 *PL of 113.17 kN/m obtained from pg.21; PL of 125.72 kN/m obtained from pg.15; ∑MA = 0 = -RB (5) + 32.66 (3.5)(1.75) + 113.17 (3.5) + 125.72 (3.5) + 23.7 (1.5)(4.25) = -5 RB + 1187.25 RB = 1187.25/ 5 = 237.45kN ∑Fy = 0 = RA + RB – 114.31 – 113.17 – 125.72 - 35.55 = RA + 237.45 – 388.75 RA – 151.3 = 0 RA = 151.3 kN Shear Force Diagram Positive area [(151.3 + 36.99)/ 2] x 3.5 = 329.5 kNm
Wong Kai Chiang 0323341 27 Negative area [(201.9 + 237.45)/ 2] x 1.5 = 329.5 kN/m Bending Moment Diagram
Wong Kai Chiang 0323341 28 6. Beam B/ 2-4 Structural plan Basic information Slab thickness : 0.15m Brick wall thickness : 0.225m Wall height : 3m Beam size : Largest beam : 0.2m x 0.5m : Secondary beam: 0.2m x 0.3m RC density : 24 kN/m3 Brick wall density : 19 kN/m3 Live Load UBBL : Living area: 1.5 kN/m2 Dead Load 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A1-B/ 2-3 3.6 kN/m2 x (1.5/ 2)] = 2.7 kN/m c. Dead load on slab A1-B/ 3-3.1 3.6 kN/m2 x (1.5/ 2)] = 2.7 kN/m d. Dead load on slab B-C/ 3-3.1
Wong Kai Chiang 0323341 29 2 3 [3.6 kN/m2 x (4.075/ 2)] = 4.89 kN/m e. Dead load on slab A1-B/ 3.1-4 3.6 kN/m2 x (1.5/ 2)] = 2.7 kN/m f. Dead load on slab B-C/ 3.1-4 2 3 [3.6 kN/m2 x (2.225/ 2)] = 2.67 kN/m 2. Beam self-weight 0.2m x 0.5m x 24 kN/m3 = 2.4 kN/m Total Dead Load For 2-3 (2.7 + 4.89 + 2.4) kN/m = 9.99 kN/m For 3-3.1 (2.7+ 2.4) kN/m = 5.1 kN/m For 3.1-4 (2.7 + 2.67 + 2.4) kN/m = 7.77kN/m Live Load Live load on slab A1-B/ 2-3 (living area) 1.5 kN/m2 x (1.5/ 2) = 1.125 kN/m Live load on slab A1-B/ 3-3.1 (living area) 1.5 kN/m2 x (1.5/ 2)] = 1.125 kN/m Live load on slab A1-B/ 3-3.1 (living area) 2 3 [1.5 kN/m2 x (4.075/ 2)] = 2.04 kN/m Live load on slab A1-B/ 3.1-4 1.5 kN/m2 x (1.5/ 2)] = 1.125 kN/m Live load on slab B-C/ 3.1-4 2 3 [1.5 kN/m2 x (2.225/ 2)] = 1.1125 kN/m
Wong Kai Chiang 0323341 30 Total Live Load For 2-3 (1.125 + 2.04) kN/m = 3.165kN/m For 3-3.1 1.125 kN/m For 3.1-4 (1.125 + 2.04) kN/m = 2.24 kN/m Ultimate Load Ultimate load on 2-3 Ultimate dead load: 1.4 x 9.99 kN/m = 14 kN/m Ultimate live load : 1.6 x 3.165 kN/m = 5.064 kN/m Total ultimate load: (14 + 5.064) kN/m = 19.06 kN/m Ultimate load on 3-3.1 Ultimate dead load: 1.4 x 5.1 kN/m = 7.14 kN/m Ultimate live load : 1.6 x 1.125 kN/m = 1.8 kN/m Total ultimate load: (7.14 + 1.8) kN/m = 8.94 kN/m Ultimate load on 3.1-4 Ultimate dead load: 1.4 x 7.77 kN/m = 10.88 kN/m Ultimate live load : 1.6 x 2.24 kN/m = 3.58 kN/m Total ultimate load: (10.88 + 3.58) kN/m = 14.46 kN/m ___________________________________________________________________________ Beam B-C/ 3 (Point Load) 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab B-C/ 2-3 2 3 [3.6 kN/m2 x (4.075/ 2)] = 4.89 kN/m c. Dead load on slab B-C/ 3-3.1 3.6 kN/m2 x (1.7/ 2)] = 3.06 kN/m
Wong Kai Chiang 0323341 31 2. Beam self-weight 0.2m x 0.4m x 24 kN/m3 = 1.92 kN/m Total Dead Load (4.89 + 3.06 + 1.92) kN/m = 9.87 kN/m Live Load Live load on slab B-C/ 2-3 (living area) 1.5 kN/m2 x (4.075/ 2)] = 3.06 kN/m Live load on slab B-C/ 3-3.1 (living area) 1.5 kN/m2 x (1.7/ 2)] = 1.28 kN/m Total Live Load (3.06 + 1.28) kN/m = 4.34 kN/m Ultimate Load Ultimate dead load B-C: 1.4 x 9.87 kN/m = 13.82 kN/m Ultimate live load B-C: 1.6 x 4.34 kN/m = 6.94 kN/m Total ultimate load B-C: (13.82 + 6.94) kN/m = 20.76 kN/m Ultimate Load Diagram ∑Fy = 0 Therefore, RB = RC 20.76 kN/m x 4.35m = 90.31 kN 90.31 kN/ 2 = 45.16 kN RB = RC = 45.16 kN ___________________________________________________________________________ Beam B-C/ 3.1 (Point Load) 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab B-C/ 3.1-4 3.6 kN/m2 x (1.5/ 2)] = 2.7 kN/m
Wong Kai Chiang 0323341 32 c. Dead load on slab B-C/ 3-3.1 2 3 [3.6 kN/m2 x (2.225/ 2)] = 2.67 kN/m 2. Beam self-weight 0.2m x 0.4m x 24 kN/m3 = 1.92 kN/m Total Dead Load (2.7 + 2.67 + 1.92) kN/m = 7.29 kN/m Live Load Live load on slab B-C/ 2-3 (bedroom) 1.5 kN/m2 x (1.5/ 2)] = 1.125 kN/m Live load on slab B-C/ 3-3.1 (bedroom) 2 3 [1.5 kN/m2 x (2.225/ 2)] = 1.113 kN/m Total Live Load (1.125 + 1.113) kN/m = 4.34 kN/m Ultimate Load Ultimate dead load B-C: 1.4 x 7.29 kN/m = 10.21 kN/m Ultimate live load B-C: 1.6 x 4.34 kN/m = 6.94 kN/m Total ultimate load B-C: (10.21 + 6.94) kN/m = 17.15 kN/m Ultimate Load Diagram ∑Fy = 0 Therefore, RB = RC 17.15 kN/m x 4.35m = 74.6 kN 74.6 kN/ 2 = 37.3 kN RB = RC = 37.3 kN Ultimate Load Diagram of Beam A1/ 3-4.1 ∑M2 = 0
Wong Kai Chiang 0323341 33 = -R4 (8) + 19.06 (4.075)(2.038) + 237.45 (4.075) + 45.16 (4.075) + 8.94 (1.7)(4.93) + 22.88 (5.78) + 37.3 (5.78) + 14.46 (2.225)(6.89) = -8 R4 + 1954.37 R4 = 1954.37/ 8 = 244.3kN ∑Fy = 0 = R2 + R4 – 77.67 – 237.45 – 45.16 - 15.2 – 22.88 – 37.3 – 32.17 = R2 + 244.3 – 467.83 = 0 R2 – 223.53 = 0 R2 = 223.53 kN Shear Force Diagram Positive area [(230.66 + 146.19)/ 2] x 4.075 = 767.83 kNm ≈ 767 kNm Negative area [(136.42 + 154.92)/ 2] x 1.7 = 247.64 kN/m [(215.1 + 251.01)/ 2] x 2.225 = 518.55 kN/m 247.64 + 518.55 = 766.19 kNm ≈ 767 kNm Bending Moment Diagram

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individual part

  • 1. Wong Kai Chiang 0323341 1 Beam Calculation 1. Beam C-D/ 2.2 Ground floor plan Structural plan Basic information Slab thickness : 0.15m Brick wall thickness : 0.225m Wall height : 3m Beam size : Primary beam : 0.2m x 0.4m : Secondary beam: 0.2m x 0.3m Brick wall density : 19 kN/m3 RC density : 24 kN/m3 Live Load UBBL : Living area: 1.5 kN/m2 : Bedroom : 1.5 kN/m2
  • 2. Wong Kai Chiang 0323341 2 Dead Load 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab C-D/ 2-2.1 3.6 kN/m2 x (2.075/ 2) = 3.735 kN/m c. Dead load on slab C-D/ 2.1- 3 3.6 kN/m2 x (2/ 2) = 3.6 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load (3.735 + 3.6 + 2.825 + 1.44) kN/m = 21.6 kN/m Live Load Live load on slab C-D/ 2-2.2 (bedroom) 1.5 kN/m2 x (2.075/ 2) = 1.56 kN/m Live load on slab C-D/ 2.2-3 (living area) 1.5 kN/m2 x (2/ 2) = 1.5 kN/m Total Live Load (1.56 + 1.5) kN/m = 3.06 kN/m Ultimate Load Ultimate dead load C-D: 1.4 x 21.6 kN/m = 30.24 kN/m Ultimate live load C-D: 1.6 x 3.06 kN/m = 4.9 kN/m Total ultimate load C-D: (30.24 + 4.9) kN/m = 35.14 kN/m
  • 3. Wong Kai Chiang 0323341 3 Ultimate Load Diagram ∑Fy = 0 Therefore, RC = RD 35.14 kN/m x 3.5m = 123 kN 123 kN/ 2 = 61.5 kN RC = RD = 61.5 kN Shear Force Diagram Positive area (61.5 x 1.75)/ 2 = 53.81 kN/m Negative area (61.5 x 1.75)/ 2 = 53.81 kN/m Bending Moment Diagram
  • 4. Wong Kai Chiang 0323341 4 2. Beam C/ 2-3 Ground floor plan Structural plan Basic information Slab thickness : 0.15m Brick wall thickness : 0.225m Wall height : 3m Beam size : Primary beam : 0.2m x 0.4m : Secondary beam: 0.2m x 0.3m Brick wall density : 19 kN/m3 RC density : 24 kN/m3 Live Load UBBL : Living area: 1.5 kN/m2 : Bedroom : 1.5 kN/m2
  • 5. Wong Kai Chiang 0323341 5 Dead Load 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab B1-C/ 2-3 3.6 kN/m2 x (3.15/ 2) = 5.67 kN/m c. Dead load on slab C-D/ 2-2.2 2 3 [3.6 kN/m2 x (2.075/ 2)] = 2.49 kN/m d. Dead load on slab C-D/ 2.2-3 2 3 [3.6 kN/m2 x (2/ 2)] = 2.4 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load For 2-2.1 (2.36 + 1.04) kN/m = 3.4 kN/m For 2.1-3 (2.36 + 1) kN/m = 3.36 kN/m Live Load Live load on slab C-D/ 2-2.2 (bedroom) 2 3 [1.5 kN/m2 x (2.075/ 2)] = 1.04 kN/m Live load on slab C-D/ 2.2-3 (living area) 1.5 kN/m2 x (3.15/ 2) = 2.36 kN/m Live load on slab C-D/ 2-2.2 (living area) 2 3 [1.5 kN/m2 x (2/ 2)] = 1 kN/m
  • 6. Wong Kai Chiang 0323341 6 Total Live Load For 2-2.2 (2.36 + 1.04) kN/m = 3.4 kN/m For 2.2-3 (2.36 + 1) kN/m = 3.36 kN/m Ultimate Load Ultimate load on 2-2.2 Ultimate dead load: 1.4 x 22.91 kN/m = 32.074 kN/m Ultimate live load : 1.6 x 3.4 kN/m = 5.44 kN/m Total ultimate load: (32.074 + 5.44) kN/m = 37.514 kN/m Ultimate load on 2.2-3 Ultimate dead load: 1.4 x 11.66 kN/m = 16.32 kN/m Ultimate live load : 1.6 x 3.36 kN/m = 5.38 kN/m Total ultimate load: (16.32 + 5.38) kN/m = 21.7 kN/m
  • 7. Wong Kai Chiang 0323341 7 Ultimate Load Diagram *PL of 61.5 kN/m is obtained from pg.7, which is the value of RC ∑M2 = 0 = -R3 (4.075) + 37.514 (2.075)(1.038) + 61.5 (2.075) + 21.7 (2)(3.075) = -4.075 R3 + 341.87 R3 = 341.87/ 4.075 = 83.89 kN ∑Fy = 0 R2 + R3 – 61.5 – 77.84 – 43.4 = 0 R2 + 83.89 – 182.74 = 0 R2 – 98.85 = 0 R2 = 98.85 kN Shear Force Diagram Positive area [(98.85 + 21.01)/ 2] x 2.075 = 124.35 kN/m ≈ 124 kN/m Negative area [(40.49 + 83.89)/ 2] x 2 = 124.38 kN/m ≈ 124 kN/m Bending Moment Diagram
  • 8. Wong Kai Chiang 0323341 8 3. Beam A1/ 3-4.1 Ground floor plan Structural plan Basic information Slab thickness : 0.15m Brick wall thickness : 0.225m Wall height : 3m Beam size : Secondary beam: 0.2m x 0.3m Brick wall density : 19 kN/m3 RC density : 24 kN/m3 Live Load UBBL : Living area: 1.5 kN/m2 : Bedroom : 1.5 kN/m2
  • 9. Wong Kai Chiang 0323341 9 Dead Load 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A-A1/ 3-4 3.6 kN/m2 x (3.5/ 2) = 6.3 kN/m c. Dead load on slab A1-B/ 3-3.1 3.6 kN/m2 x (1.5/ 2) = 2.7 kN/m d. Dead load on slab A1-B/ 3.1-4 3.6 kN/m2 x (1.5/ 2)] = 2.7 kN/m e. Dead load on slab A1-B/ 3.1-4 2 3 [3.6 kN/m2 x (1.03/ 2)] = 1.236 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load For 3-3.1 (6.3 + 2.7 + 12.825 + 1.44) kN/m = 23.27 kN/m For 3.1-4 (6.3 + 2.7 + 12.825 + 1.44) kN/m = 23.27 kN/m For 4-4.1 (1.236 + 12.825 + 1.44) kN/m = 15.5 kN/m Live Load Live load on slab A-A1/ 3-4 (bedroom) 1.5 kN/m2 x (3.5/ 2)] = 2.625 kN/m Live load on slab A1-B/ 3-3.1 (living area) 1.5 kN/m2 x (1.5/ 2) = 1.125 kN/m
  • 10. Wong Kai Chiang 0323341 10 Live load on slab A1-B/ 3.1-4 (bedroom) 1.5 kN/m2 x (1.5/ 2)] = 1.125 kN/m Live load on slab A1-B/ 4-4.1 (bedroom) 1.5 kN/m2 x (1.025/ 2)] = 0.77 kN/m Total Live Load For 3-3.1 (2.625 + 1.125) kN/m = 3.75kN/m For 3.1-4 (2.625 + 1.125) kN/m = 3.75 kN/m For 4-4.1 0.77 kN/m Ultimate Load Ultimate load on 3-3.1 Ultimate dead load: 1.4 x 23.27 kN/m = 32.58 kN/m Ultimate live load : 1.6 x 3.75 kN/m = 6 kN/m Total ultimate load: (32.58 + 6) kN/m = 38.58 kN/m Ultimate load on 3.1-4 Ultimate dead load: 1.4 x 23.27 kN/m = 32.58 kN/m Ultimate live load : 1.6 x 3.75 kN/m = 6 kN/m Total ultimate load: (32.58 + 6) kN/m = 38.58 kN/m Ultimate load on 4-4.1 Ultimate dead load: 1.4 x 15.5 kN/m = 21.7 kN/m Ultimate live load : 1.6 x 0.77 kN/m = 1.23 kN/m Total ultimate load: (21.7 + 1.23) kN/m = 22.93 kN/m ___________________________________________________________________________
  • 11. Wong Kai Chiang 0323341 11 Beam A1-B/ 3.1 (Point Load) 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A1-B/ 3-3.1 2 3 [3.6 kN/m2 x (1.5/ 2)] = 2.9 kN/m c. Dead load on slab A1-B/ 3.1-4 2 3 [3.6 kN/m2 x (1.5/ 2)] = 2.9 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load (2.9 + 2.9 + 12.825 + 1.44) kN/m = 20.07 kN/m Live Load Live load on slab A-A1/ 3-4 (living area) 2 3 [1.5 kN/m2 x (1.5/ 2)] = 0.75 kN/m Live load on slab A1-B/ 3-3.1 (living area) 2 3 [1.5 kN/m2 x (1.5/ 2)] = 0.75 kN/m Total Live Load (0.75 + 0.75) kN/m = 1.5kN/m Ultimate Load Ultimate dead load A1-B: 1.4 x 20.07 kN/m = 28.1 kN/m Ultimate live load A1-B: 1.6 x 1.5 kN/m = 2.4 kN/m Total ultimate load A1-B: (28.1 + 2.4) kN/m = 30.5 kN/m
  • 12. Wong Kai Chiang 0323341 12 Ultimate Load Diagram ∑Fy = 0 Therefore, RA1 = RB 30.5 kN/m x 1.5m = 45.75 kN 45.75 kN/ 2 = 22.88 kN RA1 = RB = 22.88 kN ___________________________________________________________________________ Beam A1-B/ 4 (Point Load) 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A1-B/ 3-3.1 2 3 [3.6 kN/m2 x (1.5/ 2)] = 2.9 kN/m c. Dead load on slab A1-B/ 3.1-4 3.6 kN/m2 x (1.025/ 2)] = 1.845 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load (2.9 + 1.845 + 12.825 + 1.44) kN/m = 19.01kN/m Live Load Live load on slab A1-B/ 3.1-4 (living area) 2 3 [1.5 kN/m2 x (1.5/ 2)] = 0.75 kN/m Live load on slab A1-B/ 3-3.1 (bedroom) 1.5 kN/m2 x (1.025/ 2) = 0.77 kN/m
  • 13. Wong Kai Chiang 0323341 13 Total Live Load (0.75 + 0.77) kN/m = 1.52kN/m Ultimate Load Ultimate dead load A1-B: 1.4 x 19.01 kN/m = 26.61 kN/m Ultimate live load A1-B: 1.6 x 1.52 kN/m = 2.43 kN/m Total ultimate load A1-B: (26.61 + 2.43) kN/m = 29.04 kN/m Ultimate Load Diagram ∑Fy = 0 Therefore, RA1 = RB 29.04 kN/m x 1.5m = 43.56 kN 43.56 kN/ 2 = 21.78 kN RA1 = RB = 21.78 kN ___________________________________________________________________________ Beam A-A1/ 4 (Point Load) 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A-A1/ 3-3.1 2 3 [3.6 kN/m2 x (3.5/ 2)] = 4.2 kN/m c. Dead load on slab A-A1/ 3.1-4 3.6 kN/m2 x (1.025/ 2)] = 1.845 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load (4.2 + 1.845 + 12.825 + 1.44) kN/m = 20.31kN/m
  • 14. Wong Kai Chiang 0323341 14 Live Load Live load on slab A-A1/ 3-3.1 (bedroom) 2 3 [1.5 kN/m2 x (3.5/ 2)] = 1.75 kN/m Live load on slab A-A1/ 3.1-4 (bedroom) 1.5 kN/m2 x (1.025/ 2) = 0.77 kN/m Total Live Load (1.75 + 0.77) kN/m = 2.52kN/m Ultimate Load Ultimate dead load A1-B: 1.4 x 20.31 kN/m = 28.43 kN/m Ultimate live load A1-B: 1.6 x 2.52 kN/m = 4.03 kN/m Total ultimate load A1-B: (28.43 + 4.03) kN/m = 32.46 kN/m Ultimate Load Diagram ∑Fy = 0 Therefore, RA1 = RB 32.46 kN/m x 3.5m = 113.61 kN 113.61 kN/ 2 = 56.81 kN RA1 = RB = 56.81 kN ___________________________________________________________________________ Ultimate Load Diagram of Beam A1/ 3-4.1 *PL of 22.88 kN/m obtained from pg.; PL of 21.78 kN/m obtained from pg.; PL of 56.81 kN/m obtained from pg.. ∑M3 = 0 = -R4.1 (4.95) + 38.58 (1.7)(0.85) + 22.88 (1.7) + 38.58 (2.225)(2.8) + 56.81 (3.9) + 21.78 (3.9) + 22.93 (1.025)(4.44)
  • 15. Wong Kai Chiang 0323341 15 = -4.95 R4.1 + 745.85 R4.1 = 745.85/ 4.95 = 150.68kN ∑Fy = 0 = R3 + R4.1 – 65.59 – 22.88 – 85.84 - 56.81 – 21.78 – 23.5 = R3 + 150.68 – 276.4 = 0 R3 – 125.72 = 0 R3 = 125.72 kN Shear Force Diagram To find the triangle area, x y = 37.25 48.59 ~1 x + y = 2.225 ~2 x = 2.225 – y ~3 sub 3 into 1, 108.11 – 48.59y = 37.25y 108.11 = 85.84y y = 1.26m ~4 then, sub 4 into 3, x = 2.225 – 1.26 = 0.965m Positive area [(125.72 + 60.13)/ 2] x 1.7 = 157.97 kNm (37.25 x 0.965)/ 2 = 17.97 kNm 157.97 + 17.97 = 175.94 kNm ≈ 174.5 kNm Negative area [(127.18 + 150.68)/ 2] x 1.025 = 142.4 kN/m
  • 16. Wong Kai Chiang 0323341 16 (48.59 x 1.26)/ 2 = 30.61 kNm 142.4 + 30.61 = 173.01 kNm ≈ 174.5 kNm Bending Moment Diagram
  • 17. Wong Kai Chiang 0323341 17 4. Beam A1/ 2-3 Ground floor plan Structural plan Basic information Slab thickness : 0.15m Brick wall thickness : 0.225m Wall height : 3m Beam size : Secondary beam: 0.2m x 0.3m Brick wall density : 19 kN/m3 RC density : 24 kN/m3 Live Load UBBL : Living area: 1.5 kN/m2 : Bedroom : 1.5 kN/m2 : Toilet : 2.0 kN/m2 Dead Load 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A-A1/ 2.1-2.2 2 3 [3.6 kN/m2 x (1.9/ 2)] = 2.28 kN/m
  • 18. Wong Kai Chiang 0323341 18 c. Dead load on slab A1-B/ 2-3 3.6 kN/m2 x (1.5/ 2) = 2.7 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load For 2.1-2.2 (2.28 + 2.7 + 12.825 + 1.44) kN/m = 19.245 kN/m For 2-2.1, 2.2-3 (2.7 + 12.825 + 1.44) kN/m = 16.97 kN/m Live Load Live load on slab A-A1/ 2.1-2.2 (toilet) 2 3 [2 kN/m2 x (1.9/ 2)] = 1.27kN/m Live load on slab A1-B/ 2-2.1 (bedroom) 1.5 kN/m2 x (1.5/ 2) = 1.13 kN/m Total Live Load For 2.1-2.2 (1.27 + 1.13) kN/m = 2.4kN/m For 2-2.1, 2.2-3 1.13 kN/m Ultimate Load Ultimate load on 2-2.1 Ultimate dead load: 1.4 x 16.97 kN/m = 23.76 kN/m Ultimate live load : 1.6 x 1.13 kN/m = 1.81 kN/m Total ultimate load: (23.76 + 1.81) kN/m = 25.57 kN/m
  • 19. Wong Kai Chiang 0323341 19 Ultimate load on 2.1-2.2 Ultimate dead load: 1.4 x 19.245 kN/m = 26.94 kN/m Ultimate live load : 1.6 x 2.4 kN/m = 3.84 kN/m Total ultimate load: (26.94 + 3.84) kN/m = 30.78 kN/m Ultimate load on 2.2-3 Ultimate dead load: 1.4 x 16.97 kN/m = 23.76 kN/m Ultimate live load : 1.6 x 1.13 kN/m = 1.81 kN/m Total ultimate load: (23.76 + 1.81) kN/m = 25.57 kN/m ___________________________________________________________________________ Beam A1-B/ 3.1 (Point Load) 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A-A1/ 2-2.1 3.6 kN/m2 x (1.1/ 2)] = 1.98 kN/m c. Dead load on slab A-A1/ 2.1-2.2 3.6 kN/m2 x (1.9/ 2)] = 3.42 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load (1.98 + 3.42 + 12.825 + 1.44) kN/m = 19.67 kN/m Live Load Live load on slab A-A1/ 2-2.1 (bedroom) 1.5 kN/m2 x (1.1/ 2)] = 0.83 kN/m Live load on slab A1-B/ 2.1-2.2 (living area) 2 kN/m2 x (1.9/ 2)] = 1.9 kN/m
  • 20. Wong Kai Chiang 0323341 20 Total Live Load (0.83 + 1.9) kN/m = 2.73kN/m Ultimate Load Ultimate dead load A-A1: 1.4 x 19.67 kN/m = 27.54 kN/m Ultimate live load A-A1: 1.6 x 2.73 kN/m = 4.37 kN/m Total ultimate load A-A1: (27.54 + 4.37) kN/m = 31.91 kN/m Ultimate Load Diagram ∑Fy = 0 Therefore, RA1 = RB 31.91 kN/m x 3.5m = 111.69 kN 111.69 kN/ 2 = 55.85 kN RA1 = RB = 55.85 kN ___________________________________________________________________________ Beam A-A1/ 2.2 (Point Load) 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A-A1/ 2.1-2.2 3.6 kN/m2 x (1.9/ 2)] = 3.42 kN/m c. Dead load on slab A-A1/ 2.2-3 3.6 kN/m2 x (1.075/ 2)] = 1.94 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load (3.42 + 1.94 + 12.825 + 1.44) kN/m = 19.63 kN/m
  • 21. Wong Kai Chiang 0323341 21 Live Load Live load on slab A-A1/ 2.1-2.2 (toilet) 2.0 kN/m2 x (1.9/ 2)] = 1.9 kN/m Live load on slab A1-B/ 2.2-3 (bedroom) 1.5 kN/m2 x (1.075/ 2)] = 0.81 kN/m Total Live Load (1.9 + 0.81) kN/m = 2.71kN/m Ultimate Load Ultimate dead load A-A1: 1.4 x 19.63 kN/m = 27.48 kN/m Ultimate live load A-A1: 1.6 x 2.71 kN/m = 4.34 kN/m Total ultimate load A-A1: (27.48 + 4.34) kN/m =31.82 kN/m Ultimate Load Diagram ∑Fy = 0 Therefore, RA1 = RB 31.82 kN/m x 3.5m = 111.37 kN 111.37 kN/ 2 = 55.69 kN RA1 = RB = 55.69 kN ___________________________________________________________________________ Ultimate Load Diagram of Beam A1/ 3-4.1 ∑M2 = 0 = -R3 (4.075) + 25.57 (1.1)(0.55) + 55.84 (1.1) + 30.78 (1.9)(2.05) + 55.69 (3) + 25.57 (1.075)(3.54) = -4.075 R3 + 461.16 R3 = 461.16/ 4.075 = 113.17kN ∑Fy = 0
  • 22. Wong Kai Chiang 0323341 22 = R2 + R3 – 28.13 – 55.84 – 58.48 - 55.69 – 27.49 = R2 + 113.17 – 225.63 = 0 R2 – 112.46 = 0 R2 = 112.46 kN Shear Force Diagram To find the triangle area, x y = 28.49 29.99 ~1 x + y = 1.9 ~2 x = 1.9 – y ~3 sub 3 into 1, 56.98 – 29.99y = 28.49y 56.98 = 58.48y y = 0.97m ~4 then, sub 4 into 3, x = 1.9 – 0.97 = 0.93m Positive area [(112.46 + 84.33)/ 2] x 1.1 = 108.23 kNm (28.49 x 0.93)/ 2 = 13.25 kNm 108.23 + 13.25 = 121.48 kNm ≈ 121 kNm Negative area [(113.17 + 85.68)/ 2] x 1.075 = 106.88 kN/m (29.99 x 0.97)/ 2 = 14.55 kNm 106.88 + 14.55 = 121.43 kNm ≈ 121 kNm
  • 23. Wong Kai Chiang 0323341 23 Bending Moment Diagram
  • 24. Wong Kai Chiang 0323341 24 5. Beam A-B/ 3 Ground floor plan Structural plan Basic information Slab thickness : 0.15m Brick wall thickness : 0.225m Wall height : 3m Beam size : Primary beam : 0.2m x 0.4m : Secondary beam: 0.2m x 0.3m Brick wall density : 19 kN/m3 RC density : 24 kN/m3 Live Load UBBL : Living area: 1.5 kN/m2 : Bedroom : 1.5 kN/m2 Dead Load 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A-A1/ 2.2-3 3.6 kN/m2 x (1.075/ 2)] = 1.935 kN/m
  • 25. Wong Kai Chiang 0323341 25 c. Dead load on slab A1-B/ 3-4 2 3 [3.6 kN/m2 x (3.5/ 2)] = 4.2 kN/m d. Dead load on slab A1-B/ 3-3.1 2 3 [3.6 kN/m2 x (1.5/ 2)] = 1.8 kN/m 2. Brick wall self-weight 3m x 0.225m x 19 kN/m3 = 12.825 kN/m 3. Beam self-weight 0.2m x 0.3m x 24 kN/m3 = 1.44 kN/m Total Dead Load For A-A1 (1.935 + 4.2 + 12.825 + 1.44) kN/m = 20.4 kN/m For A1-B (1.8 + 12.825 + 1.44) kN/m = 16.07 kN/m Live Load Live load on slab A-A1/ 2.2-3 (bedroom) 1.5 kN/m2 x (1.075/ 2) = 0.81 kN/m Live load on slab A1-B/ 2-2.1 (bedroom) 2 3 [1.5 kN/m2 x (3.5/ 2)] = 1.75kN/m Live load on slab A1-B/ 3-3.1 (living area) 2 3 [1.5 kN/m2 x (3.5/ 2)] = 0.75kN/m Total Live Load For A-A1 (0.81 + 1.75) kN/m = 2.56kN/m For A1-B 0.75 kN/m
  • 26. Wong Kai Chiang 0323341 26 Ultimate Load Ultimate load on A-A1 Ultimate dead load: 1.4 x 20.4 kN/m = 28.56 kN/m Ultimate live load : 1.6 x 2.56 kN/m = 4.1 kN/m Total ultimate load: (28.56 + 4.1) kN/m = 32.66 kN/m Ultimate load on A1-B Ultimate dead load: 1.4 x 16.07 kN/m = 22.5 kN/m Ultimate live load : 1.6 x 0.75 kN/m = 1.2 kN/m Total ultimate load: (22.5 + 1.2) kN/m = 23.7 kN/m Ultimate Load Diagram of Beam A1/ 3-4.1 *PL of 113.17 kN/m obtained from pg.21; PL of 125.72 kN/m obtained from pg.15; ∑MA = 0 = -RB (5) + 32.66 (3.5)(1.75) + 113.17 (3.5) + 125.72 (3.5) + 23.7 (1.5)(4.25) = -5 RB + 1187.25 RB = 1187.25/ 5 = 237.45kN ∑Fy = 0 = RA + RB – 114.31 – 113.17 – 125.72 - 35.55 = RA + 237.45 – 388.75 RA – 151.3 = 0 RA = 151.3 kN Shear Force Diagram Positive area [(151.3 + 36.99)/ 2] x 3.5 = 329.5 kNm
  • 27. Wong Kai Chiang 0323341 27 Negative area [(201.9 + 237.45)/ 2] x 1.5 = 329.5 kN/m Bending Moment Diagram
  • 28. Wong Kai Chiang 0323341 28 6. Beam B/ 2-4 Structural plan Basic information Slab thickness : 0.15m Brick wall thickness : 0.225m Wall height : 3m Beam size : Largest beam : 0.2m x 0.5m : Secondary beam: 0.2m x 0.3m RC density : 24 kN/m3 Brick wall density : 19 kN/m3 Live Load UBBL : Living area: 1.5 kN/m2 Dead Load 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab A1-B/ 2-3 3.6 kN/m2 x (1.5/ 2)] = 2.7 kN/m c. Dead load on slab A1-B/ 3-3.1 3.6 kN/m2 x (1.5/ 2)] = 2.7 kN/m d. Dead load on slab B-C/ 3-3.1
  • 29. Wong Kai Chiang 0323341 29 2 3 [3.6 kN/m2 x (4.075/ 2)] = 4.89 kN/m e. Dead load on slab A1-B/ 3.1-4 3.6 kN/m2 x (1.5/ 2)] = 2.7 kN/m f. Dead load on slab B-C/ 3.1-4 2 3 [3.6 kN/m2 x (2.225/ 2)] = 2.67 kN/m 2. Beam self-weight 0.2m x 0.5m x 24 kN/m3 = 2.4 kN/m Total Dead Load For 2-3 (2.7 + 4.89 + 2.4) kN/m = 9.99 kN/m For 3-3.1 (2.7+ 2.4) kN/m = 5.1 kN/m For 3.1-4 (2.7 + 2.67 + 2.4) kN/m = 7.77kN/m Live Load Live load on slab A1-B/ 2-3 (living area) 1.5 kN/m2 x (1.5/ 2) = 1.125 kN/m Live load on slab A1-B/ 3-3.1 (living area) 1.5 kN/m2 x (1.5/ 2)] = 1.125 kN/m Live load on slab A1-B/ 3-3.1 (living area) 2 3 [1.5 kN/m2 x (4.075/ 2)] = 2.04 kN/m Live load on slab A1-B/ 3.1-4 1.5 kN/m2 x (1.5/ 2)] = 1.125 kN/m Live load on slab B-C/ 3.1-4 2 3 [1.5 kN/m2 x (2.225/ 2)] = 1.1125 kN/m
  • 30. Wong Kai Chiang 0323341 30 Total Live Load For 2-3 (1.125 + 2.04) kN/m = 3.165kN/m For 3-3.1 1.125 kN/m For 3.1-4 (1.125 + 2.04) kN/m = 2.24 kN/m Ultimate Load Ultimate load on 2-3 Ultimate dead load: 1.4 x 9.99 kN/m = 14 kN/m Ultimate live load : 1.6 x 3.165 kN/m = 5.064 kN/m Total ultimate load: (14 + 5.064) kN/m = 19.06 kN/m Ultimate load on 3-3.1 Ultimate dead load: 1.4 x 5.1 kN/m = 7.14 kN/m Ultimate live load : 1.6 x 1.125 kN/m = 1.8 kN/m Total ultimate load: (7.14 + 1.8) kN/m = 8.94 kN/m Ultimate load on 3.1-4 Ultimate dead load: 1.4 x 7.77 kN/m = 10.88 kN/m Ultimate live load : 1.6 x 2.24 kN/m = 3.58 kN/m Total ultimate load: (10.88 + 3.58) kN/m = 14.46 kN/m ___________________________________________________________________________ Beam B-C/ 3 (Point Load) 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab B-C/ 2-3 2 3 [3.6 kN/m2 x (4.075/ 2)] = 4.89 kN/m c. Dead load on slab B-C/ 3-3.1 3.6 kN/m2 x (1.7/ 2)] = 3.06 kN/m
  • 31. Wong Kai Chiang 0323341 31 2. Beam self-weight 0.2m x 0.4m x 24 kN/m3 = 1.92 kN/m Total Dead Load (4.89 + 3.06 + 1.92) kN/m = 9.87 kN/m Live Load Live load on slab B-C/ 2-3 (living area) 1.5 kN/m2 x (4.075/ 2)] = 3.06 kN/m Live load on slab B-C/ 3-3.1 (living area) 1.5 kN/m2 x (1.7/ 2)] = 1.28 kN/m Total Live Load (3.06 + 1.28) kN/m = 4.34 kN/m Ultimate Load Ultimate dead load B-C: 1.4 x 9.87 kN/m = 13.82 kN/m Ultimate live load B-C: 1.6 x 4.34 kN/m = 6.94 kN/m Total ultimate load B-C: (13.82 + 6.94) kN/m = 20.76 kN/m Ultimate Load Diagram ∑Fy = 0 Therefore, RB = RC 20.76 kN/m x 4.35m = 90.31 kN 90.31 kN/ 2 = 45.16 kN RB = RC = 45.16 kN ___________________________________________________________________________ Beam B-C/ 3.1 (Point Load) 1.a. Slab self-weight 0.15m x 24 kN/m3 = 3.6 kN/m2 b. Dead load on slab B-C/ 3.1-4 3.6 kN/m2 x (1.5/ 2)] = 2.7 kN/m
  • 32. Wong Kai Chiang 0323341 32 c. Dead load on slab B-C/ 3-3.1 2 3 [3.6 kN/m2 x (2.225/ 2)] = 2.67 kN/m 2. Beam self-weight 0.2m x 0.4m x 24 kN/m3 = 1.92 kN/m Total Dead Load (2.7 + 2.67 + 1.92) kN/m = 7.29 kN/m Live Load Live load on slab B-C/ 2-3 (bedroom) 1.5 kN/m2 x (1.5/ 2)] = 1.125 kN/m Live load on slab B-C/ 3-3.1 (bedroom) 2 3 [1.5 kN/m2 x (2.225/ 2)] = 1.113 kN/m Total Live Load (1.125 + 1.113) kN/m = 4.34 kN/m Ultimate Load Ultimate dead load B-C: 1.4 x 7.29 kN/m = 10.21 kN/m Ultimate live load B-C: 1.6 x 4.34 kN/m = 6.94 kN/m Total ultimate load B-C: (10.21 + 6.94) kN/m = 17.15 kN/m Ultimate Load Diagram ∑Fy = 0 Therefore, RB = RC 17.15 kN/m x 4.35m = 74.6 kN 74.6 kN/ 2 = 37.3 kN RB = RC = 37.3 kN Ultimate Load Diagram of Beam A1/ 3-4.1 ∑M2 = 0
  • 33. Wong Kai Chiang 0323341 33 = -R4 (8) + 19.06 (4.075)(2.038) + 237.45 (4.075) + 45.16 (4.075) + 8.94 (1.7)(4.93) + 22.88 (5.78) + 37.3 (5.78) + 14.46 (2.225)(6.89) = -8 R4 + 1954.37 R4 = 1954.37/ 8 = 244.3kN ∑Fy = 0 = R2 + R4 – 77.67 – 237.45 – 45.16 - 15.2 – 22.88 – 37.3 – 32.17 = R2 + 244.3 – 467.83 = 0 R2 – 223.53 = 0 R2 = 223.53 kN Shear Force Diagram Positive area [(230.66 + 146.19)/ 2] x 4.075 = 767.83 kNm ≈ 767 kNm Negative area [(136.42 + 154.92)/ 2] x 1.7 = 247.64 kN/m [(215.1 + 251.01)/ 2] x 2.225 = 518.55 kN/m 247.64 + 518.55 = 766.19 kNm ≈ 767 kNm Bending Moment Diagram