b structure
TRANSCRIPT
School of Architecture, Building and Design
Bachelor of Science (Hons) in Architecture
Building Structure (ARC 2523/BLD 61003)
Project 2 Beam and Column Analysis
Tutor : Mr. Mohd Adib Ramli
Group Member
Student Name Student ID
Andy Heng Wee Xiang 0327152
Leong Yu Shi 0322586
Yeoh Xiang An 0322691
Table of Content
1. Introduction to Project
2. Architectural Plan Drawings
3. Structural Plan Drawings
4. Slab System Analysis
5. 3D Digital Skeletal Model
6. Individual Analysis
- 6.1 – Andy Heng Wee Xiang
- 6.2 – Leong Yu Shi
- 6.3 – Yeoh Xiang An
7. Conclusion
8. References
1. Introduction to Project
In this project, we are to be in a group of 3 and select 2 different floor shapes
with dimensions and plan our own bungalow spaces. We are to identify and
analyze 6 different load beams and 3 different types of columns. At first, we are to
produce architectural and structural plan drawings of each floors for further
analysis due to calculation has to be carried out.
From the information we have gathered on the structural plan drawings, we need
to calculate and identify the slab system and load distribution for the beams and
columns. Each of us is required to calculate minimum of 6 different load beams
and 3 columns from both ground floor and first floor. Formulas used are as
follow :
Slab System
Beam Calculation
Ly/Lx > 2 - One way slab system
Ly/Lx < 2 - Two way slab system
Beam Self-Weight = beam size x density of reinforced concrete
Slab Dead Load = thickness x density of reinforced concrete x Lx/2
(Trapezoid)
= thickness x density of reinforced concrete x Lx/2 x 2/3
(Triangular)
Slab Live Load = live load (UBBL) x Lx/2 (Trapezoid)
= live load (UBBL) x Lx/2 x 2/3 (Triangular)
Brick Wall Dead Load = wall height x thickness x density of bricks
Column Calculation
Specifications
UBBL
Reinforced Concrete Density = 24kN/m3
Bricks Density = 19kN/m3
Room
1. Bedrooms (1 Master Bedroom and 2 Bedrooms)
2. Changing Room
3. Main Room
4. Guest Room
5. Bathrooms
6. Storage Room
7. Laundry Area
8. Garden
9. Kitchen
10. Corridor
11. Living Room
12. Gathering Space
13. Study Room
*According to UBBL, all residential buildings (bungalow) live load factor should be
1.5kN/m2
Beam Self-Weight = beam size x density of reinforced concrete x length
Slab Dead Load = thickness x density of reinforced concrete x
tributary area
Slab Live Load = live load (UBBL) x tributary area
Brick Wall Self-Weight = thickness x wall height x density of bricks x length
Column Self-Weight = width x length x height x density of reinforced concrete
2. Architectural Drawings
A
B1
C
D
E
F
B
34
00
13
25
52
00
27
50
50
00
51
00
22
00
28
00
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
A
B1
C
D
E
F
B
3400
1325
5200
2750
5000
5100
2200
2800
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
3. Structural Plan Drawings
A
B1
C
D
E
F
B
3400
1325
5200
2750
5000
5100
2200
2800
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
A
B1
C
D
E
F
B
34
00
13
25
52
00
27
50
50
00
51
00
22
00
28
00
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
A
B1
C
D
E
F
B
3400
1325
5200
2750
5000
5100
2200
2800
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
A
B1
C
D
E
F
B
34
00
13
25
52
00
27
50
50
00
51
00
22
00
28
00
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
A
B1
C
D
E
F
B
3400
1325
5200
2750
5000
5100
2200
2800
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
A
B1
C
D
E
F
B
3400
1325
5200
2750
5000
5100
2200
2800
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
4. Slab System Drawings
A
B1
C
D
E
F
B
3400
1325
5200
2750
5000
5100
2200
2800
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
A
B1
C
D
E
F
B
3400
1325
5200
2750
5000
5100
2200
2800
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
A
B1
C
D
E
F
B
3400
1325
5200
2750
5000
5100
2200
2800
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
A
B1
C
D
E
F
B
34
00
13
25
52
00
27
50
50
00
51
00
22
00
28
00
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
A
B1
C
D
E
F
B
34
00
13
25
52
00
27
50
50
00
51
00
22
00
28
00
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
A
B1
C
D
E
F
B
1 4 6 75 8
34
00
13
25
52
00
27
50
50
00
2500 2700 4000 2000 4000
51
00
2150
3
22
00
28
00
C1
C2
2
1375
5. Column
(Tributary Area Method)
A
B1
C
D
E
F
B
34
00
13
25
52
00
27
50
50
00
51
00
22
00
28
00
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
A
B1
C
D
E
F
B
34
00
13
25
52
00
27
50
50
00
51
00
22
00
28
00
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
A
B1
C
D
E
F
B
34
00
13
25
52
00
27
50
50
00
51
00
22
00
28
00
C1
C2
1 4 6 75 8
2500 2700 4000 2000 40002150
32
1375
6. 3D Model
3D Model of the Structural System
Beams and Columns
ANDY HENG WEE XIANG
BEAM AND COLUMN ANALYSIS
Ground Floor Beam (2/C1-D)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab Self Weight = 0.15m x 24kN/m
= 3.6 kN/m²
Slab 1-2/C1-D = 3.6kN/m² x (2.5/2)m
= 4.5kN/m
Slab 2-4/C1-D = 2/3[3.6kN/m² x (2.95/2)]m
= 3.54kN/m
Brick Wall Self-Weight = (3x0.15)m² x 19kN/m³
= 8.55 kN/m
Total Dead Load = (1.44 + 4.5 + 3.54 + 8.55)kN/m
= 18.03kN/m
Slab 1‐2/C1‐D = 2875/2500
= 1.15 < 2 (Two Way Slab)
Slab 2‐4/C1‐D = 3500/2875
= 1.22 < 2 (Two Way Slab)
Reinforced Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Live Load
(Assuming storage = 2.0kN/m², others = 1.5kN/m² )
Slab 1-2/C1-D = 2kN/m² x (lx/2)m
= 2kN/m² x (2.5/2)m
= 2.5kN/m
Slab 2-4/C1-D = 2/3[1.5kN/m² x (2.95/2)]m
= 1.48 kN/m
Total Live Load = 3.98 kN/m
Ultimate Load
Total Dead Load (1.4) + Total Live Load (1.6)
= 18.03kN/m(1.4) + 3.98kN/m(1.6)
= (25.24 + 6.37) kN/m
= 31.61kN/m
Total Point Load
= 31.61kN/m x 2.95m
= 93.25kN
Reaction Force
Calculate Moment at Point D
M(D) = 0
2.95RCy – 93.25(1.475) = 0
RCy = 46.625 kN (46.63kN)
Calculate Vertical Forces = 0
ΣFy = 0
-93.25kN + 46.625kN + R(Dy) = 0
R(Dy) = 46.625kN (46.63kN)
Shear Force Diagram
From Uniform Distribution Load,
0 + 46.63 = 46.63kN
46.63 – 93.25 = -46.63
-46.63 + 46.63 = 0
(Assuming 46.63 = 46.625)
Bending Moment Diagram
Calculate Area in Sheer Force Diagram
= ½ x 46.63kN x 1.475m
= 34.39kNm
Ground Floor Beam (3/D-E)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab Self Weight = 0.15m x 24kN/m
= 3.6 kN/m²
Slab 1-3/D-E = 2/3[3.6kN/m² x (2.75/2)]m
= 3.3kN/m
Slab 3-4/D-E = 3.6kN/m² x (2.15/2)m
= 3.87kN/m
Brick Wall Self-Weight = (3x0.15)m² x 19kN/m³
= 8.55 kN/m
Total Dead Load = (1.44 + 3.3 + 3.87 + 8.55)kN/m
= 17.16kN/m
Slab 1‐3/D‐E = 3850/2750
= 1.4 < 2 (Two Way Slab)
Slab 3‐4/D‐E = 2750/2150
= 1.28 < 2 (Two Way Slab)
Reinforced Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Live Load
(Assuming Bathroom = 2.0kN/m², others = 1.5kN/m² )
Slab 1-3/D-E = 2/3[1.5kN/m² x (2.75/2)]m
= 1.38kN/m
Slab 3-4/D-E = 2kN/m² x (2.15/2)]m
= 2.15 kN/m
Total Live Load = 3.53 kN/m
Ultimate Load
Total Dead Load (1.4) + Total Live Load (1.6)
= 24.02kN/m(1.4) + 3.53kN/m(1.6)
= (24.02 + 5.65) kN/m
= 29.67kN/m
Total Point Load
= 29.67kN/m x 2.75m
= 81.59kN
Reaction Force
Calculate Moment at Point D
M(E) = 0
2.75RDy – 81.59(1.375) = 0
RDy = 40.8 kN
Calculate Vertical Forces = 0
ΣFy = 0
-81.59kN + 40.8kN + R(Ey) = 0
R(Ey) = 40.8 kN
Shear Force Diagram
From Uniform Distribution Load,
0 + 40.8 = 40.8kN
40.8 – 81.59 = -40.8
-40.8 + 40.8 = 0
Bending Moment Diagram
Calculate Area in Sheer Force Diagram
= ½ x 40.8kN x 1.375m
= 28.05kNm
Ground Floor Beam (1-4/D)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab Self Weight = 0.15m x 24kN/m
= 3.6 kN/m²
Slab 1-2/C1-D = 2/3[3.6kN/m² x (2.5/2)m]
= 3kN/m
Slab 2-4/C1-D = 3.6kN/m² x (2.95/2)
= 5.31kN/m
Slab 1-3/D-E = 3.6kN/m² x (2.75/2)m
= 4.95kN/m
Slab 3-4/D-E = 2/3[3.6kN/m² x (2.15/2)]m
= 2.58 kN/m
Brick Wall Self-Weight = (3x0.15)m² x 19kN/m³
= 8.55 kN/m
Slab 1‐2/C1‐D = 2875/2500
= 1.15 < 2 (Two Way Slab)
Slab 2‐4/C1‐D = 3500/2875
= 1.22 < 2 (Two Way Slab)
Slab 1‐3/D‐E = 3850/2750
= 1.4 < 2 (Two Way Slab)
Slab 3‐4/D‐E = 2750/2150
= 1.28 < 2 (Two Way Slab)
Total Dead Load
Slab 1-2 = 1.44 + 8.55 + 3 + 4.95
= 17.94kN/m
Slab 2-3 = 1.44 + 8.55 + 5.31 + 4.95
= 20.25kN/m
Slab 3-4 = 1.44 + 8.55 + 5.31 + 2.58
= 17.63 kN/m
Live Load
Slab 1-2, C1-D = 2/3(2kN/m2 x 2.5/2)
= 1.67kN/m
Slab 2-4, C1-D = (1.5 x 2.95/2)
= 2.21kN/m
Slab 1-3, D-E = (1.5 x 2.75/2)
= 2.06kN/m
Slab 3-4, D-E = 2/3 (2kN/m2 x 2.15/2)
= 1.43 kN/m
Total Live Load
Slab 1-2 = 1.67 + 2.06
= 3.73kN/m
Slab 2-3 = 2.21 + 2.06
= 4.27kN/m
Slab 3-4 = 2.16 + 1.43
= 3.59 kN/m
Ultimate Load
Slab 1-2 = Total Dead Load (1.4) + Total Live Load (1.6)
= 17.94kN/m(1.4) + 3.73kN/m(1.6)
= (25.11 + 5.97) kN/m
= 31.08kN/m
Slab 2-3 = Total Dead Load (1.4) + Total Live Load (1.6)
= 20.25kN/m(1.4) + 4.27kN/m(1.6)
= (28.35 + 6.83) kN/m
= 35.18kN/m
Slab 3-4 = Total Dead Load (1.4) + Total Live Load (1.6)
= 17.63kN/m(1.4) + 3.59kN/m(1.6)
= (24.68 + 5.74) kN/m
= 30.42kN/m
Total Point Load
Slab 1-2 = 31.08kN/m x 2.5
= 77.7kN
Slab 2-3 = 35.18 kN/m x 1.35
= 47.49kN
Slab 3-4 = 30.42kN/m x 2.15
= 65.4kN
Reaction Force
Adding point load from beam 2, C1-D and 3, D-E
Calculate Moment at Point 2
M(2) = 0
6R1y – 4.75(77.7) – 3.5(46.63) – 2.825(47.49) – 2.15(40.22) – 1.075(65.4) = 0
6R1y = 823.23 kN
R1y = 137.21kN
Calculate Vertical Forces = 0
ΣFy = 0
-77.7 – 46.63 – 47.49 – 40.22 – 65.4 + 137.21kN + R(2y) = 0
R(2y) = 140.23 kN
Shear Force Diagram
From Uniform Distribution Load,
0 + 137.21 = 137.21
137.21 – 77.7 = 59.51
59.51-46.63 = 12.88
12.88 – 47.49 = -34.61
-34.61 – 40.22= -74.83
-74.83 – 65.4 = -140.23
-140.23 + 140.23 = 0
Bending Moment Diagram
Calculate Area in Sheer Force Diagram
Positive
½ (59.51 + 137.21) x 2.5 = 245.9
½ (0.37x12.88) = 2.38
Total = 245.9 + 2.38
= 248.28 (248kNm)
Negative
½ (34.61 x 0.98) = 16.96
½ (74.83 + 140.23) x 2.15 = 231.18
Total = 16.96 + 231.18
= 248.14 (248kNm)
First Floor Beam (4-5/A1)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab Self Weight = 0.15m x 24kN/m
= 3.6 kN/m²
Slab 4-5/A-A1 = 2/3[3.6kN/m² x (2.7/2)]m
= 3.24kN/m
Slab 4-5/A1-C = 3.6kN/m² x (1.95/2)m
= 3.51kN/m
Brick Wall Self-Weight = (3x0.15)m² x 19kN/m³
= 8.55 kN/m
Total Dead Load = (1.44 + 3.24 + 3.51 + 8.55)kN/m
= 16.74kN/m
Slab 4‐5/A‐A1 = 2800/2700
= 1.04 < 2 (Two Way Slab)
Slab 3‐4/A1‐C = 2700/1950
= 1.38 < 2 (Two Way Slab)
Reinforced Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Live Load
(Assuming Bathroom = 2.0kN/m², others = 1.5kN/m² )
Slab 4-5/A-A1 = 2/3[2kN/m² x (2.7/2)]m
= 1.8kN/m
Slab 4-5/A1-C = 1.5kN/m² x (1.95/2)m
= 1.46 kN/m
Total Live Load = 3.26 kN/m
Ultimate Load
Total Dead Load (1.4) + Total Live Load (1.6)
= 16.74kN/m(1.4) + 3.26kN/m(1.6)
= (23.44 + 5.22) kN/m
= 28.66kN/m
Total Point Load
= 28.66kN/m x 2.7m
= 77.38kN
Reaction Force
Calculate Moment at Point 5
M(5) = 0
2.7R4y – (77.38 x1.35) = 0
R4y = 38.69 kN
Calculate Vertical Forces = 0
ΣFy = 0
-77.38kN + 38.69kN + R(5y) = 0
R(5y) = 38.69 kN
Shear Force Diagram
From Uniform Distribution Load,
0 + 38.69 = 38.69kN
38.69 – 77.38 = -38.69
-38.69 + 38.69 = 0
Bending Moment Diagram
Calculate Area in Sheer Force Diagram
= ½ x 38.69kN x 1.35m
= 26.12kNm
First Floor Beam (4/A-C)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab Self Weight = 0.15m x 24kN/m
= 3.6 kN/m²
Slab 1-4/A-C = 2/3[3.6kN/m² x (4.75/2)]m
= 5.7kN/m
Slab 4-5/A-A1 = 3.6kN/m² x (2.7/2)m
= 4.86kN/m
Brick Wall Self-Weight = (3x0.15)m² x 19kN/m³
= 8.55 kN/m
Total Dead Load
A-A1 = (1.44 + 5.7 + 4.86 + 8.55)kN/m
= 20.55kN/m
A1-C = (1.44 + 8.55 + 5.7 + 3.51)kN/m
= 19.2kN/m
Slab 1‐4/A‐C = 6000/4750
= 1.26 < 2 (Two Way Slab)
Slab 4‐5/A‐A1 = 2800/2700
= 1.04 < 2 (Two Way Slab)
Slab 3‐4/A1‐C = 2700/1950
= 1.38 < 2 (Two Way Slab)
Reinforced Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Live Load
(Assuming Bathroom = 2.0kN/m², others = 1.5kN/m² )
Slab 1-4/A- C = 2/3[1.5kN/m² x (4.75/2)]m
= 2.38kN/m
Slab 4-5/A-A1 = 2kN/m² x (2.7/2)]m
= 2.7 kN/m
Slab 4-5/A1-C = 1.5kN/m² x (1.95/2)]m
= 1.46 kN/m
Total Live Load
A-A1 = 2.38 + 2.7 = 5.08 kN/m
A1-C = 2.38 + 1.46 = 3.84 kN/m
Ultimate Load
Dead Load
A-A1 = 20.55kN/m(1.4) = 28.77 kN/m
A1-C = 19.2 (1.4) = 26.88kN/m
Live Load
A-A1 = 5.08(1.6) = 8.13 kN/m
A1-C = 3.84(1.6) = 6.14kN/m
Total Ultimate Load
A-A1 = 28.77 + 8.13 = 36.9kN/m
A1-C = 26.88 + 6.14 = 33.02kN/m
Adding Beam A1/4-5 (38.69kN) to beam A-C/4
Reaction Force
Calculate Moment at Point C
M(C) = 0
4.75Ray – 3.35 (103.32) – 1.95(38.69) – 0.975(64.39) = 0
4.75Ray -346.12 – 75.45 – 62.78 = 0
4.75Ray= 484.35
RAy = 101.97 kN
Calculate Vertical Forces = 0
ΣFy = 0
-103.32kN – 38.69kN – 64.39kN + 101.97kN + R(Cy) = 0
R(Cy) = 104.43 kN
Shear Force Diagram
From Uniform Distribution Load,
0 + 101.97 = 101.97 101.97-103.32kN = - 1.35 -1.35 - 38.69 = -40.04 -40.04 – 64.39 = -104.43 -104.43 + 104.43 = 0
Bending Moment Diagram
Positive area
1.35/(101.97+1.35) = X/ 2800 X= 36.59mm (0.037m)
½ (101.97 x (2.8 – 0.0370) = 140.87kNm (140.9kNm)
Negative area ½ (1.35 x 0.037) = 0.025 – small triangle ½ (40.04 + 104.43) x 1.95 = 140.86
Total Negative = 140.86 + 0.025 = 140.885 (140.9kNm)
First Floor Beam (1-5/C)
Dead Load Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab Self Weight = 0.15m x 24kN/m
= 3.6 kN/m²
Slab 1-4/A-C = 3.6kN/m² x (4.75/2)m
= 8.55kN/m
Slab 1-4/C-C1 = 3.6kN/m² x (2.325/2)m
= 4.19kN/m
Slab 4-5/A1-C = 3.6kN/m² x (1.95/2)m
= 3.51kN/m
Slab 4-5/C-D = 3.6kN/m² x (2.7/2)m
= 4.86kN/m
Brick Wall Self-Weight = (3x0.15)m² x 19kN/m³
= 8.55 kN/m
Total Dead Load
Slab 1-4 = 8.55 + 4.185 = 12.74kN/m
Slab 4-5 = 3.51 + 4.86 = 8.37kN/m
Slab 1‐4/A‐C = 6000/4750
= 1.26 < 2 (Two Way Slab)
Slab 4‐5/A‐A1 = 2800/2700
= 1.04 < 2 (Two Way Slab)
Slab 3‐4/A1‐C = 2700/1950
= 1.38 < 2 (Two Way Slab)
Reinforced Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Live Load
Slab 1-4/A-C = 1.5kN/m² x (4.75/2)m
= 3.56kN/m
Slab 1-4/C-C1 = 1.5kN/m² x (2.325/2)m
= 1.74 kN/m
Slab 4-5/A1-C = 1.5kN/m² x (1.95/2)m
= 1.46 kN/m
Slab 4-5/C-D = 1.5kN/m² x (2.7/2)m
= 2.03kN/m
Total Live Load
Slab 1-4 = 3.56 + 1.74 = 5.3 kN/m
Slab 4-5 = 1.46 + 2.03 = 3.49kN/m
Ultimate Load
DL Slab 1-4 : 12.74kN/m(1.4) = 17.84 kN/m LL Slab 1-4 : 5.3kN.m (1.6) = 8.48kN/m Total = 26.32 kN/m DL Slab 4-5 : 8.37 kN/m(1.4) = 11.7kN/m LL Slab 4-5 : 3.49 kN/m (1.6) = 5.58kN/m Total = 17.28kN/m
Adding Beam A-C/4 (104.43kN) to beam A-C/1-5
26.32 kN/m x 6m = 157.92kN 17.28kN/m x 2.7 = 46.66kN
Reaction Force
Calculate Moment at Point 5
M(5) = 0
8.7R1y- 5.7(157.92) – 2.7(104.43) – 1.35(46.66) = 0
8.7R1y = 900.14 + 281.96 + 62.99
8.7R1y = 1245.09
R1y = 143.11 kN
Calculate Vertical Forces = 0
ΣFy = 0
-157.92 – 104.43 – 46.66 + 143.11 + R(5y) = 0
R(5y) = 165.9 kN
Shear Force Diagram
From Uniform Distribution Load,
0 + 143.11 = 143.11kN
143.11 – 157.92 = -14.81
-14.81 – 104.43 = -119.24
-119.24 – 46.66 = -165.9
-165.9 + 165.9 = 0
Bending Moment Diagram
14.81/(14.81+143.11) = X / 6 X = 0.56m
Positive Area ½ [(6-0.56) x 143.11] = 389.26 (389kNm)
Negative Area ½ [(0.56x14.81) = 4.15 – mini triangle ½ (119.24+165.9) x 2.7 = 389.1 (389kNm)
Column D1
Dead Load
Ground Floor
Total wall length = 3.15 + 3.15 + 3.15 + 4.38 = 13.83m
Wall = 13.83m x 8.55 = 118.25 kN
Slab = 3.15 x 4.38 x 3.6kN/m2 = 49.67kN
Beam length = 3.15 +3.15 + 3.15 +4.38 = 13.83m
Beam = 13.83 x 1.44 = 19.92 kN
Column = 6.48kN
Total = 118.25 + 49.67 + 19.92 + 6.48 = 194.32 kN
Brick Wall (150mm) = 0.15 x 3 x 19kN/m3
= 8.55 kN/m
Beam = 0.2 x 0.3 x 24kN/m3
= 1.44kN/m
Slab = 0.15 x 24kN/m3
= 3.6kN/m2
Column = 0.3x 0.3 x 3m x 24kN/m3
= 6.48kN
First Floor
Total wall length = 6.48+ 3.15 + 0.98 = 10.61m
Wall = 10.61m x 8.55 = 90.72 kN
Slab = (3.15 x 6.48) x 3.6kN/m2 = 73.48kN
Beam length = 6.48+ 3.15 + 0.9 = 10.61m
Beam = 10.61m x 1.44 = 15.28 kN
Column = 6.48kN
Total = 90.72 + 73.48 + 15.28 + 6.48 = 185.96 kN
Roof Level
Slab = (6.48 x 3.15 ) x 1kN/m2 = 20.41kN
Roof beam = 10.61 x 1kN/m2
= 10.61 kN
Total dead load = 194.32 + 185.96 + 20.41 + 10.61 = 411.3 kN
Total ultimate dead load = 411.3 x 1.4 = 575.82kN
Live Load
Ground
Storage (3 x 2.65) x 2kN/m2 = 15.9kN
Maid’s room (1.38 x 3.15) x 1.5 kN/m2 = 6.52kN
Corridor (0.5 x 3) x 1.5kN/m2 =2.25 kN
Total 15.9 + 6.52 + 2.25 = 24.67 kN
First
Master Bedroom (5.35 x 3.15m) x 1.5 kN/m2 = 25.28kN
Changing room (1.13 x 3.15m) x 1.5 kN/m2 = 5.34kN
Total 25.28kN + 5.34kN = 30.62kN
Roof
(3.15 x 6.48 ) x 0.5 kN/m2 = 10.21kN
Total live load 24.67kN + 30.62kN + 10.21kN = 65.5kN
Total ultimate live load 65.5 x 1.6 = 104.8kN
Total Ultimate load acting on column D1 is 575.82 + 104.8 kN = 680.62kN
Column F1
Dead Load
Ground Floor
Total wall length = 2.63 + 3.15 = 5.78m
Wall = 5.78m x 8.55kN/m2 = 49.42 kN
Slab = (2.63 x 3.15) x 3.6kN/m2 = 29.82kN
Beam length = 2.63 + 3.15 = 5.78m
Beam = 5.78 x 1.44 = 8.32 kN
Column = 6.48kN
Total = 49.42 + 29.82 + 8.32+ 6.48 kN = 94.04kN
Brick Wall (150mm) = 0.15 x 3 x 19kN/m3
= 8.55 kN/m
Beam = 0.2 x 0.3 x 24kN/m3
= 1.44kN/m
Slab = 0.15 x 24kN/m3
= 3.6kN/m2
Column = 0.3x 0.3 x 3m x 24kN/m3
= 6.48kN
First Floor
Total wall length = 2.63+ 2.63 + 3.15 = 8.41m
Wall = 8.41m x 8.55kN/m2 = 71.91 kN
Slab = (3.15 x 2.63) x 3.6kN/m2 = 29.82kN
Beam length = 2.63 + 2.63 + 3.15 = 8.41m
Beam = 8.41m x 1.44 = 12.11kN
Column = 6.48kN
Total = 71.91 + 29.82 + 12.11 + 6.48 = 120.32 kN
Roof Level
Slab = (2.63 x 3.15 ) x 1kN/m2 = 8.28 kN
Beam Length = 2.63 + 2.63 + 3.15 = 8.41m
Roof beam = 8.41 x 1kN/m2
= 8.41 kN
Total dead load = 94.04 + 120.32 + 8.41 + 8.28kN = 231.05 kN
Total ultimate dead load = 231.05 x 1.4 = 323.47kN
Live Load
Ground
Guess Room (3.15 x 2.63) x 1.5kN/m2 = 12.43kN
First
Changing Bedroom (2.63 x 3.15m) x 1.5 kN/m2 = 12.43kN
Roof
(3.15 x 2.63 ) x 0.5 kN/m2 = 4.14kN
Total live load 12.43kN + 12.43kN + 4.14kN = 29kN
Total ultimate live load 29 x 1.6 = 46.4kN
Total ultimate load acting on column F1 is 323.47 + 46.4 kN = 369.87kN
Column A2
Dead Load
Ground Floor
Total wall length = 1.83 + 3.5 = 5.33m
Wall = 5.33m x 8.55kN/m2 = 45.57 kN
Slab = (1.83 x 3.5) x 3.6kN/m2 = 23.06kN
Beam length = 1.83+3.5 = 5.33m
Beam = 5.33 x 1.44 = 7.68kN
Column = 6.48kN
Total = 45.57 + 23.06 +7.68 + 6.48 kN = 82.79kN
Brick Wall (150mm) = 0.15 x 3 x 19kN/m3
= 8.55 kN/m
Beam = 0.2 x 0.3 x 24kN/m3
= 1.44kN/m
Slab = 0.15 x 24kN/m3
= 3.6kN/m2
Column = 0.3x 0.3 x 3m x 24kN/m3
= 6.48kN
First Floor
Total wall length = 4.52 + 5.13 + 1.37 + 4.52 = 15.54m
Wall = 15.54m x 8.55kN/m2 = 132.87 kN
Slab = (4.52 x 5.13) x 3.6kN/m2 = 83.48kN
Beam length = 4.52 + 1.37 + 4.52 + 5.13 = 15.54m
Beam = 15.54 x 1.44 = 22.38kN
Column = 6.48kN
Total = 132.87 + 83.48 + 22.38 + 6.48 = 245.21 kN
Roof Level
Slab = (4.52 x 5.13 ) x 1kN/m2 = 23.19kN
Beam Length = 4.52 + 4.52 + 5.13 = 14.17m
Roof beam = 14.17 x 1kN/m2
= 14.17 kN
Total dead load = 82.79 + 245.21 + 14.17 + 23.19 = 365.36 kN
Total ultimate dead load = 365.36 x 1.4 = 511.5kN
Live Load
Ground
Kitchen (1.83x3.5) x 2.0kN/m2 = 12.81kN
First
Bedroom (3x4.9m) x 1.5 kN/m2 = 22.05kN
Bathroom (2.95 x 1.52) x 2.0kN/m2 = 8.97kN
Study Room (0.23 x 3) x 1.5kN/ m2 = 1.04kN
Corridor (1.52 x 0.23) 1.5kN/ m2 = 0.52kN
Total first floor live load 22.05+8.97+1.04+0.52 = 32.58kN
Roof
(4.52 x 5.13 ) x 0.5 kN/m2 = 11.59kN
Total live load 12.81kN + 32.58kN + 11.59kN = 56.98kN
Total ultimate live load 56.98 x 1.6 kN = 91.17 kN
Total ultimate load acting on column A2 is 511.5 + 91.17 kN = 602.67kN
YEOH XIANG ANN
BEAM AND COLUMN ANALYSIS
Ground Floor Beam (4-5/A1)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab 1-2/C1-D = (0.15m x 24kN/m³)kN/m² x (1.95/2)m
= 3.51 kN/m
Slab 2-4/C1-D = (0.15m x 24kN/m³)kN/m² x (2.7/2)m
= 3.24 kN/m
Brick Wall Self-Weight = (3 x 0.15)m² x 19kN/m³
= 8.55 kN/m
Total Dead Load = (1.44 + 3.51 + 3.24 + 8.55)kN/m
= 16.74 kN/m
Slab 1‐2/C1‐D = 2950/2500
= 1.18 < 2 (Two Way Slab)
Slab 2‐4/C1‐D = 3500/2950
= 1.19 < 2 (Two Way Slab)
Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Live Load
Slab 1-2/C1-D = 2.0kN/m² x (2.7 x 2/3)m
= 2.21 kN/m
Slab 2-4/C1-D = 1.5kN/m² x (1.95/2)m
= 1.46 kN/m
Total Live Load = (2.21 + 1.46) kN/m
= 3.26 kN/m
Ultimate Load
Total Dead Load (1.4) + Total Live Load (1.6)
= 16.74kN/m(1.4) + 3.26kN/m(1.6)
= (23.44 + 5.22) kN/m
= 28.66 kN/m
Reaction Force
Calculate Moment at Point A
M(A) = 0
R(B) = 38.69 kN
Calculate Vertical Forces = 0
ΣFy = 0
R(A) = 38.69kN
Load Diagram
Shear Force Diagram
Bending Moment Diagram
Ground Floor Beam (5-5A/B)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab 3-4/B1-C1 = (0.15m x 24kN/m³)kN/m² x (3.87x2/3)m
= 2.58 kN/m
Slab 3-4/B1-C1 = (0.15m x 24kN/m³)kN/m² x (1.45/2)m
= 2.61 kN/m
Brick Wall Self-Weight = (3 x 0.15)m² x 19kN/m³
= 8.55 kN/m
Total Dead Load = (3.87+2.58+2.61)kN/m
= 15.18 kN/m
Live Load
Slab 1-3/B1-C1 = 1.5kN/m² x (3.87x2/3)m
= 1.08 kN/m
Slab 3-4/B1-C1 = 1.5kN/m² x (1.45/2)m
= 1.08 kN/m
Total Live Load = (1.08 + 1.08) kN/m
= 2.16 kN/m
Slab 1‐3/B1‐C1 = 3825/3000
= 1.28 < 2 (Two Way Slab)
Slab 3‐4/B1‐C1 = 3000/2175
= 1.38 < 2 (Two Way Slab)
Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Ultimate Load
Total Dead Load (1.4) + Total Live Load (1.6)
= 15.18kN/m(1.4) + 2.16kN/m(1.6)
= (21.25 + 3.46) kN/m
= 24.71 kN/m
Reaction Force
Calculate Moment at Point A
M(A) = 0
R(B) = 26.57 kN
Calculate Vertical Forces = 0
ΣFy = 0
R(A) = 26.57kN
Load Diagram
Shear Force Diagram
Bending Moment Diagram
Ground Floor Beam (5/A-C)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab 1-3/B1-C1 = (0.15m x 24kN/m³)kN/m² x (2.7/2)m
= 4.86 kN/m
Slab 3-4/B1-C1 = (0.15m x 24kN/m³)kN/m² x (3.51x2/3)m
= 2.34 kN/m
Slab 1-2/C1-D = (0.15m x 24kN/m³)kN/m² x (2.15/2)m
= 3.87 kN/m
Slab 2-4/C1-D = (0.15m x 24kN/m³)kN/m² x (2.61x2/3)m
= 1.74 kN/m
Brick Wall Self-Weight = (3 x 0.15)m² x 19kN/m³
= 8.55 kN/m
Total Dead Load
Beam (1 – 2) = (1.44+4.86+3.87+8.55)kN/m
= 18.72 kN/m
Slab 1‐3/B1‐C1 = 3825/3000
= 1.28 < 2 (Two Way Slab)
Slab 3‐4/B1‐C1 = 3000/2175
= 1.38 < 2 (Two Way Slab)
Slab 1‐2/C1‐D = 2950/2500
= 1.18 < 2 (Two Way Slab)
Slab 2‐4/C1‐D = 3500/2950
= 1.19 < 2 (Two Way Slab)
Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Beam (2 – 3) = (1.44+2.34+3.87+8.55)kN/m
= 16.2 kN/m
Beam (3 – 4) = (1.44+2.34+1.74+8.55)kN/m
= 17.94 kN/m
Live Load
Slab 1-3/B1-C1 = 2.0kN/m² x (2.7/2)m
= 2.7 kN/m
Slab 3-4/B1-C1 = 1.5kN/m² x (1.45 x 2/3)m
= 0.98 kN/m
Slab 1-2/C1-D = 1.5kN/m² x (2.15/2)m
= 1.61 kN/m
Slab 2-4/C1-D = 1.5kN/m² x (1.09/2)m
= 0.725 kN/m
Total Live Load
Beam (1 – 2) = (2.7+1.61)kN/m
= 4.31 kN/m
Beam (2 – 3) = (0.98 + 1.61)kN/m
= 2.59 kN/m
Beam (3 – 4) = (0.98+ 0.725)kN/m
= 1.7 kN/m
Ultimate Load
Total Dead Load (1.4) + Total Live Load (1.6)
Beam (1 – 2) = 18.72kN/m(1.4) + 4.31kN/m(1.6)
= 26.21 kN/m
Beam (2 – 3) = 16.2kN/m(1.4) + 2.59kN/m(1.6)
= 26.82 kN/m
Beam (3 – 4) = 17.94kN/m(1.4) + 1.7kN/m(1.6)
= 27.84 kN/m
Reaction Force
Calculate Moment at Point A
M(A) = 0
(-90.7kN x 1.4m) + (-13.41kN x 3.05m) + (-40.36kN x 4.025m)
+ (-38.69kN x 2.8m) + (-26.57kN x 3.3m) + R(BC) x (4.75m) = 0
R(C) = 111.4 kN
Calculate Vertical Forces = 0
ΣFy = 0
111.4kN + (-92.7kN) + (-13.4kN) + (-40.36kN)
+ (-38.69kN) + (-26.57kN) + R(A) = 0
R(A) = 100.33kN
Load Diagram
Shear Force Diagram
Bending Moment Diagram
Calculate Area in Sheer Force Diagram
= ½ x (100.33+7.63)(2.8)
= 151.14 kNm
Calculate Area in Sheer Force Diagram
= ½ x (111.4+71.03)(1.45)
= 151.14 kNm
x/4.89 = 0.5/13.41
x=0.18
First Floor Beam (5-6/B)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab 1-2/E-F = (0.15m x 24kN/m³)kN/m² x (7.2x2/3)m
= 4.8 kN/m
Slab 2a-4/E-F = (0.15m x 24kN/m³)kN/m² x (2.65/2)m
= 4.77 kN/m
Brick Wall Self-Weight = (3 x 0.15)m² x 19kN/m³
= 8.55 kN/m
Total Dead Load = (1.44 + 4.8 + 4.77 + 8.55)kN/m
= 19.56 kN/m
Live Load
Slab 1-2/C1-D = 1.5kN/m² x (3x2/3)m
= 2.0 kN/m
Slab 2-4/C1-D = 1.5kN/m² x (2.65/2)m
= 1.99 kN/m
Total Live Load = (2+1.99) kN/m
= 3.99 kN/m
Slab 1‐2a/E‐F = 5000/2875
= 1.74 < 2 (Two Way Slab)
Slab 2a‐4/E‐F = 5000/3125
= 1.6 < 2 (Two Way Slab)
Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Ultimate Load
Total Dead Load (1.4) + Total Live Load (1.6)
= 19.56kN/m(1.4) + 3.99kN/m(1.6)
= (27.38 + 6.38) kN/m
= 33.764 kN/m
Reaction Force
Calculate Moment at Point A
M(A) = 0
R(B) = 127.98 kN
Calculate Vertical Forces = 0
ΣFy = 0
R(A) = 127.97kN
Load Diagram
Shear Force Diagram
Bending Moment Diagram
First Floor Beam (5/A-C)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab 1-4/C1-E = (0.15m x 24kN/m³)kN/m² x (2.7/2)m
= 4.86 kN/m
Slab 1-2a/E-F = (0.15m x 24kN/m³)kN/m² x (4/2)m
= 7.2 kN/m
Slab 2a-4/E-F = (0.15m x 24kN/m³)kN/m² x (4.77 x 2/3)m
= 3.18 kN/m
Brick Wall Self-Weight = (3 x 0.15)m² x 19kN/m³
= 8.55 kN/m
Total Dead Load
Beam (1 – 2a) = (1.44+4.86+7.2+8.55)kN/m
= 22.05 kN/m
Beam (2a – 4) = (1.44+4.86+3.18+8.55)kN/m
= 18.03 kN/m
Slab 1‐4/C1‐E = 6000/5850
= 1.28 < 2 (Two Way Slab)
Slab 1‐2a/E‐F = 5000/2875
= 1.74 < 2 (Two Way Slab)
Slab 2a‐4/E‐F = 5000/3125
= 1.6 < 2 (Two Way Slab)
Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Live Load
Slab 1-4/C1-E = 1.5kN/m² x (2.7/2)m
= 2.025 kN/m
Slab 1-2a/E-F = 1.5kN/m² x (4/2)m
= 3.0 kN/m
Slab 2a-4/E-F = 1.5kN/m² x (2.65/2)m
= 1.33 kN/m
Total Live Load
Beam (1 – 2a) = (2.03+3)kN/m
= 5.03 kN/m
Beam (2a – 4) = (2.03+1.33)kN/m
= 3.35 kN/m
Ultimate Load
Total Dead Load (1.4) + Total Live Load (1.6)
Beam (1 – 2a) = 22.05kN/m(1.4) + 5.03kN/m(1.6)
= 38.91 kN/m
Beam (2a – 4) = 25.24kN/m(1.4) + 5.36kN/m(1.6)
= 13.4 kN/m
Reaction Force
Calculate Moment at Point A
M(A) = 0
(-67.53kN x 5.1 m) + (-198.44kN x 2.55m)
+ (-35.51kN x 6.425m) + R(F) x (7.75m) = 0
R(F) = 139.17 kN
Calculate Vertical Forces = 0
ΣFy = 0
(-67.53kN) + (-198.44kN) + (-35.51kN)
+ 139.17kN + R(D) = 0
R(D) = 162.31kN
Load Diagram
Shear Force Diagram
Bending Moment Diagram
First Floor Beam (6/A-C)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab 1-4/C1-E = (0.15m x 24kN/m³)kN/m² x (7.2x2.35/5.1)m
= 3.32 kN/m
Slab 2a-4/E-F = (0.15m x 24kN/m³)kN/m² x (4.77x2/3)m
= 3.18 kN/m
Brick Wall Self-Weight = (3 x 0.15)m² x 19kN/m³
= 8.55 kN/m
Total Dead Load
Beam (D – E) = (1.44+3.32+8.55)kN/m
= 13.17 kN/m
Beam (E – F) = (1.44+3.18+8.55)kN/m
= 13.31 kN/m
Slab 1‐4/C1‐E = 6000/5850
= 1.28 < 2 (Two Way Slab)
Slab 2a‐4/E‐F = 5000/3125
= 1.6 < 2 (Two Way Slab)
Slab 4‐5/D‐F = 7775/2700
= 2.88 > 2 (One Way Slab)
Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Live Load
Slab 1-4/C1-E = 1.5kN/m² x (3x2.35/5.1)m
= 1.38 kN/m
Slab 2a-4/E-F = 1.5kN/m² x (1.98x2/3)m
= 1.33 kN/m
Ultimate Load
Total Dead Load (1.4) + Total Live Load (1.6)
Beam (D – E) = 13.17kN/m(1.4) + 1.33kN/m(1.6)
= 20.56 kN/m
Beam (E – F) = 13.31kN/m(1.4) + 1.325kN/m(1.6)
= 20.84 kN/m
Reaction Force
Calculate Moment at Point A
M(F) = 0
(-54.48kN x 1.33m) + (-48.98kN x 3.83m)
+ (-67.53kN x 2.65m) + R(E) x (5m) = 0
R(E) = 87.7 kN
Calculate Vertical Forces = 0
ΣFy = 0
(-54.48kN) + (-48.98kN) + (-67.53kN)
+ 87.7kN + R(A) = 0
R(A) = 83.29kN
Load Diagram
Shear Force Diagram
Bending Moment Diagram
Column (D/4)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m x 24kN/m³
= 1.44 kN/m²
Brick Wall Self-Weight = (3x0.15)m x 19kN/m³
= 8.55 kN/m²
Slab Self-Weight = 0.15m x 24kN/m³
= 3.6 kN/m²
Column = (0.3x0.3x0.3)m³ x 24kN/m³
= 6.48kN
Roof Level (assume flat roof)
Slab = 3.6kN/m² x (4.35x6.475)m
= 101.3985kN
Beam = 1.44kN/m² x (6.475+1.2+2.85)m
= 15.156kN
Live Load = 0.5kN/m² x (4.35x6.475)m
= 14.08kN
First Level (Dead Load)
Walls = (6.475+2.85)m x 8.55kN/m²
= 79.721kN
Slab = (4.35x6.475)m x 3.6kN/m²
= 28.166kN
Beam = (6.475+1.2+2.85)m x 1.44kN/m²
= 15.156kN
Total Dead Load = (79.728+28.17+15.156+6.48)kN
= 129.53kN
First Level (Live Load)
Master Bedroom = (2.85x5.2)m x 1.5kN/m²
= 22.23kN
Slab = (0.975x2.85)m x 2.0kN/m²
= 5.56kN
Beam = (1.2x6.475)m x 4.0kN/m²
= 31.08kN
Total Live Load = (22.23+5.56+31.08)kN
= 58.87kN
Ground Level (Dead Load)
Walls = (2.85+2.6+2.7+3)m x 8.55kN/m²
= 95.33kN
Slab = (4.35x6.475)m x 3.6kN/m²
= 101.4kN
Beam = (6.475+4.35+2.433+1.125+2.85)m x 1.44kN/m²
= 24.82kN
Total Dead Load = (5.33+101.4+24.82+6.48)kN
= 228.03kN
Ground Level (Live Load)
Corridor = [(4.35x2.3)m + (1.2x6.475)m] x 4.0kN/m²
= 71.1kN
Bathroom = (2.45x2)m x 2.0kN/m²
= 9.8kN
Guest Room = (2.85x1.125)m x 1.5kN/m²
= 4.81kN
Bedroom = (0.55x2.43)m x 1.5kN/m²
= 2kN
Total Live Load = (71.1+9.8+4.81+2)kN
= 87.71kN
Total Dead Load = (101.3985+15.156+129.53+228.03)kN
= 474.11kN
Apply 1.4 factor = 663.76kN
Total Live Load = (14.08+58.87+87.71)kN
= 160.66kN
Apply 1.6 factor = 257.061kN
*So Ultimate Load acting on column D/4 = 920.822kN
Column (A/1)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m x 24kN/m³
= 1.44 kN/m²
Brick Wall Self-Weight = (3x0.15)m x 19kN/m³
= 8.55 kN/m²
Slab Self-Weight = 0.15m x 24kN/m³
= 3.6 kN/m²
Column = (0.3x0.3x0.3)m³ x 24kN/m³
= 6.48kN
Roof Level (assume flat roof)
Slab = 3.6kN/m² x (3.15x2.525)m
= 28.6335kN
Beam = 1.44kN/m² x (3.15+2.525)m
= 8.172kN
Live Load = 0.5kN/m² x (3.15x2.525)m
= 3.98kN
First Level (Dead Load)
Walls = (3.15+2.525)m x 8.55kN/m²
= 48.52kN
Slab = (3.15x2.525)m x 3.6kN/m²
= 28.63kN
Beam = (3.15+2.525)m x 1.44kN/m²
= 8.172kN
Total Dead Load = (48.52+28.63+8.172+6.48)kN
= 91.8kN
First Level (Live Load)
Bedroom = (3.15x2.552)m x 1.5kN/m²
= 11.931kN
Total Live Load = 11.931kN
Ground Level (Dead Load)
Total Dead Load = 6.48kN
Ground Level (Live Load)
Total Live Load = 0kN
Total Dead Load = (28.6335+8.172+91.8+6.48)kN
= 135.09kN
Apply 1.4 factor = 189.12kN
Total Live Load = (3.98+11.931)kN
= 15.91kN
Apply 1.6 factor = 25.46kN
*So Ultimate Load acting on column A/1 = 214.58kN
Column (E/6)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m x 24kN/m³
= 1.44 kN/m²
Brick Wall Self-Weight = (3x0.15)m x 19kN/m³
= 8.55 kN/m²
Slab Self-Weight = 0.15m x 24kN/m³
= 3.6 kN/m²
Column = (0.3x0.3x0.3)m³ x 24kN/m³
= 6.48kN
Roof Level (assume flat roof)
Slab = 3.6kN/m² x (5x3.875)m
= 69.75kN
Beam = 1.44kN/m² x (5+3.875+1.85)m
= 15.444kN
Live Load = 0.5kN/m² x (5x3.875)m
= 9.6875kN
First Level (Dead Load)
Walls = (3.875+1.85+1.85)m x 8.55kN/m²
= 64.77kN
Slab = [(5x1.525)m + (2.35x2.15)m] x 3.6kN/m²
= 45.639kN
Beam = (3.875+5+1.85)m x 1.44kN/m²
= 15.4kN
Total Dead Load = (64.77+45.639+15.4+6.48)kN
= 132.3kN
First Level (Live Load)
Storage = (2x2.5)m x 2.5kN/m²
= 12.5kN
Gathering Space = (2x1.375)m x 4.0kN/m²
= 11kN
Total Live Load = (12.5+11)kN
= 23.5kN
Ground Level (Dead Load)
Walls = (2.85+2.35)m x 8.55kN/m²
= 44.46kN
Slab = [(5x1.525)m + (2.35x2.15)m] x 3.6kN/m²
= 45.639kN
Beam = (3.875+1.85+2.85)m x 1.44kN/m²
= 12.348kN
Total Dead Load = (44.46+45.639+12.348+6.48)kN
= 108.93kN
Ground Level (Live Load)
Entrance = (3.725x2)m x 4.0kN/m²
= 29.8kN
Living Room = (3x1.375)m x 4.0kN/m²
= 16.5kN
Total Live Load = (29.8+16.5)kN
= 46.3kN
Total Dead Load = (69.75+15.4+132.3+108.927)kN
= 326.454kN
Apply 1.4 factor = 457.04kN
Total Live Load = (9.6875+23.5+46.3)kN
= 79.4875kN
Apply 1.6 factor = 127.18kN
*So Ultimate Load acting on column E/6 = 584.22kN
LEONG YU SHI
BEAM AND COLUMN ANALYSIS
Ground Floor Beam (2/C1-D)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Brick Wall Self-Weight = (3 x 0.15)m² x 19kN/m³
= 8.55 kN/m
Slab 1-2/C1-D = (0.15m x 24kN/m³)kN/m² x (2.95/2)m
= 5.31 kN/m
Slab 2-4/C1-D = (0.15m x 24kN/m³)kN/m² x (2.95/2 x 2/3)m
= 3.54 kN/m
Total Dead Load = (1.44 + 5.31 + 3.54 + 8.55)kN/m
= 13.84 kN/m
Live Load
Slab 1-2/C1-D = 1.5kN/m² x (2.95/2)m
= 2.21 kN/m
Slab 2-4/C1-D = 1.5kN/m² x (2.95/2 x 2/3)m
= 1.48 kN/m
Total Live Load = (2.21 + 1.475) kN/m
= 3.685 kN/m
Slab 1‐2/C1‐D = 2950/2500
= 1.18 < 2 (Two Way Slab)
Slab 2‐4/C1‐D = 3500/2950
= 1.19 < 2 (Two Way Slab)
Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Ultimate Load
Total Dead Load (1.4) + Total Live Load (1.6)
= 13.84kN/m(1.4) + 3.685kN/m(1.6)
= (19.38 + 5.896) kN/m
= 25.27 kN/m
Total Load
= 25.27kN/m x 2.95m
= 74.55 kN
Reaction Force
Calculate Moment at Point A
M(A) = 0
(-25.27kN/m x 2.95m x 1.475m) + R(B) x (2.95m) = 0
R(B) = 37.27 kN
Calculate Vertical Forces = 0
ΣFy = 0
-74.55kN + 37.27kN + R(A) = 0
R(A) = 37.28kN
Load Diagram
Shear Force Diagram
Bending Moment Diagram
Ground Floor Beam (3/B1-C1)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Brick Wall Self-Weight = (3 x 0.15)m² x 19kN/m³
= 8.55 kN/m
Slab 1-3/B1-C1 = (0.15m x 24kN/m³)kN/m² x (3/2 x 2/3)m
= 3.6 kN/m
Slab 3-4/B1-C1 = (0.15m x 24kN/m³)kN/m² x (3.0/2)m
= 5.4 kN/m
Total Dead Load = (1.44 + 3.6 + 5.4 + 8.55)kN/m
= 18.99 kN/m
Live Load
Slab 1-3/B1-C1 = 1.5kN/m² x (3/2 x 2/3)m
= 1.5 kN/m
Slab 3-4/B1-C1 = 1.5kN/m² x (3.0/2)m
= 2.25 kN/m
Total Live Load = (1.5 + 2.25) kN/m
= 3.75 kN/m
Slab 1‐3/B1‐C1 = 3825/3000
= 1.28 < 2 (Two Way Slab)
Slab 3‐4/B1‐C1 = 3000/2175
= 1.38 < 2 (Two Way Slab)
Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Ultimate Load
Total Dead Load (1.4) + Total Live Load (1.6)
= 18.99kN/m(1.4) + 3.75kN/m(1.6)
= (26.59 + 6.0) kN/m
= 32.59 kN/m
Total Load
= 32.59kN/m x 3.0m
= 97.77 kN
Reaction Force
Calculate Moment at Point A
M(A) = 0
(-32.59kN/m x 2.95m x 1.5m ) + R(B) x (3.0m) = 0
R(B) = 48.07 kN
Calculate Vertical Forces = 0
ΣFy = 0
-97.77kN + 48.07kN + R(A) = 0
R(A) = 49.7kN
Load Diagram
Shear Force Diagram
Uniform Distribution Load
49.7kN – (32.59 x 3.0)kN = - 48.07kN
Bending Moment Diagram
Calculate Area in Sheer Force Diagram
= ½ x 49.7kN x 1.5m
= 37.28 kNm
Ground Floor Beam (1-4/C1)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab 1-3/B1-C1 = (0.15m x 24kN/m³)kN/m² x (3.825/2)m
= 6.89 kN/m
Slab 3-4/B1-C1 = (0.15m x 24kN/m³)kN/m² x (2.175/2 x 2/3)m
= 2.61 kN/m
Slab 1-2/C1-D = (0.15m x 24kN/m³)kN/m² x (2.5/2 x 2/3)m
= 3.00 kN/m
Slab 2-4/C1-D = (0.15m x 24kN/m³)kN/m² x (3.5/2)m
= 6.30 kN/m
Brick Wall Self-Weight = (3 x 0.15)m² x 19kN/m³
= 8.55 kN/m
Total Dead Load
Beam (1 – 2) = (1.44 + 6.89 + 3.00 + 8.55)kN/m
= 19.88 kN/m
Beam (2 – 3) = (1.44 + 6.89 + 6.3 + 8.55)kN/m
= 23.18 kN/m
Slab 1‐3/B1‐C1 = 3825/3000
= 1.28 < 2 (Two Way Slab)
Slab 3‐4/B1‐C1 = 3000/2175
= 1.38 < 2 (Two Way Slab)
Slab 1‐2/C1‐D = 2950/2500
= 1.18 < 2 (Two Way Slab)
Slab 2‐4/C1‐D = 3500/2950
= 1.19 < 2 (Two Way Slab)
Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Beam (3 – 4) = (1.44 + 2.61 + 6.3 + 8.55)kN/m
= 18.9 kN/m
Live Load
Slab 1-3/B1-C1 = 1.5kN/m² x (3.825/2)m
= 2.87 kN/m
Slab 3-4/B1-C1 = 1.5kN/m² x (2.175/2 x 2/3)m
= 1.09 kN/m
Slab 1-2/C1-D = 1.5kN/m² x (2.5/2 x 2/3)m
= 1.25 kN/m
Slab 2-4/C1-D = 1.5kN/m² x (3.5/2)m
= 2.63 kN/m
Total Live Load
Beam (1 – 2) = (2.87 + 1.25)kN/m
= 4.12 kN/m
Beam (2 – 3) = (2.87 + 2.63)kN/m
= 5.5 kN/m
Beam (3 – 4) = (1.09 + 2.25)kN/m
= 2.45 kN/m
Ultimate Load
Total Dead Load (1.4) + Total Live Load (1.6)
Beam (1 – 2) = 19.88kN/m(1.4) + 4.12kN/m(1.6)
= 34.42 kN/m
Beam (2 – 3) = 23.18kN/m(1.4) + 5.5kN/m(1.6)
= 41.25 kN/m
Beam (3 – 4) = 18.9kN/m(1.4) + 2.45kN/m(1.6)
= 30.38 kN/m
Reaction Force
Calculate Moment at Point A
M(A) = 0
(-34.42kN/m x 1.25m x 2.5m) + (-41.25kN/m x 1.325m x 3.825m)
+ (-30.38kN x 2.175m x 1.25m) + (-49.7kN x 1.91m)
+ (-37.27kN x 4.91m) + R(B) x (6.0m) = 0
R(B) = 112.86 kN
Calculate Vertical Forces = 0
ΣFy = 0
-86.05kN + (-157.78kN) + (-66.08kN) + (-40.52kN)
+ (-37.27kN) + 112.86kN+ R(A) = 0
R(A) = 102.71kN
Load Diagram
Shear Force Diagram
Bending Moment Diagram
First Floor Beam (2a/E-F)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab 1-2/E-F = (0.15m x 24kN/m³)kN/m² x (5.0/2)m
= 9.0 kN/m
Slab 2a-4/E-F = (0.15m x 24kN/m³)kN/m² x (5.0/2)m
= 9.0 kN/m
Brick Wall Self-Weight = (3 x 0.15)m² x 19kN/m³
= 8.55 kN/m
Total Dead Load = (1.44 + 9.00 + 9.00 + 8.55)kN/m
= 27.99 kN/m
Live Load
Slab 1-2/C1-D = 1.5kN/m² x (5.0/2)m
= 3.75 kN/m
Slab 2-4/C1-D = 1.5kN/m² x (5.0/2)m
= 3.75 kN/m
Total Live Load = (3.75 + 3.75) kN/m
= 7.50 kN/m
Slab 1‐2a/E‐F = 5000/2875
= 1.74 < 2 (Two Way Slab)
Slab 2a‐4/E‐F = 5000/3125
= 1.6 < 2 (Two Way Slab)
Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Ultimate Load
Total Dead Load (1.4) + Total Live Load (1.6)
= 27.99kN/m(1.4) + 7.50kN/m(1.6)
= (39.19 + 12.0) kN/m
= 51.19 kN/m
Total Load
= 51.19kN/m x 5.0m
= 255.95 kN
Reaction Force
Calculate Moment at Point A
M(A) = 0
-51.19kN/m x 5m x 2.5m + R(B) x (5.0m) = 0
R(B) = 127.98 kN
Calculate Vertical Forces = 0
ΣFy = 0
-255.95kN + 127.98kN + R(A) = 0
R(A) = 127.97kN
Load Diagram
Shear Force Diagram
Uniform Distribution Load
127.97kN – (51.19 x 5.0)kN = - 127.98kN
Bending Moment Diagram
Calculate Area in Sheer Force Diagram
= ½ x 127.97kN x 2.5m
= 159.96 kNm
First Floor Beam (1-4/C1-F)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab 1-4/C1-E = (0.15m x 24kN/m³)kN/m² x (5.85/2)m
= 10.53 kN/m
Slab 1-2a/E-F = (0.15m x 24kN/m³)kN/m² x (2.88/2x2/3)m
= 5.18 kN/m
Slab 2a-4//E-F = (0.15m x 24kN/m³)kN/m² x (3.13/2x2/3)m
= 5.63 kN/m
Brick Wall Self-Weight = (3 x 0.15)m² x 19kN/m³
= 8.55 kN/m
Total Dead Load
Beam (1 – 2a) = (1.44+8.55+5.18+10.53)kN/m
= 25.7 kN/m
Beam (2a – 4) = (1.44+10.53+5.63+8.55)kN/m
= 26.15 kN/m
Slab 1‐4/C1‐E = 6000/5850
= 1.28 < 2 (Two Way Slab)
Slab 1‐2a/E‐F = 5000/2875
= 1.74 < 2 (Two Way Slab)
Slab 2a‐4/E‐F = 5000/3125
= 1.6 < 2 (Two Way Slab)
Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Live Load
Slab 1-4/C1-E = 1.5kN/m² x (5.85/2)m
= 4.39 kN/m
Slab 1-2a/E-F = 1.5kN/m² x (2.88/2x2/3)m
= 2.16 kN/m
Slab 2a-4//E-F = 1.5kN/m² x (3.13/2x2/3)m
= 2.35 kN/m
Total Live Load
Beam (1 – 2a) = (2.16+4.39)kN/m
= 6.55 kN/m
Beam (2a – 4) = (4.39+2.35)kN/m
= 6.74 kN/m
Ultimate Load
Total Dead Load (1.4) + Total Live Load (1.6)
Beam (1 – 2a) = 25.7kN/m(1.4) + 6.55kN/m(1.6)
= 35.98 kN/m
Beam (2a – 4) = 26.15kN/m(1.4) + 6.74kN/m(1.6)
= 36.61 kN/m
Reaction Force
Calculate Moment at Point A
M(A) = 0
= 6Ra - ( 133.8 x 4.57 ) - ( 116.67 ) - ( 148.36 x 1.57)
= 6Ra – 611.47 – 116.67 – 232.93
= 6Ra – 961.07
Ra = 160.18kN
Calculate Vertical Forces = 0
ΣFy = 0
= Ra + Rb – (133.8) – ( 37.28 ) – (148.36)
= 160.18 + Rb – 319.44
Rb = 159. 26
Load Diagram
Shear Force Diagram
Bending Moment Diagram
First Floor Beam (4/D-F)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m² x 24kN/m³
= 1.44 kN/m
Slab 1-4/C1-E = (0.15m x 24kN/m³)kN/m² x (6/2 x 2/3)m
= 14.4 kN/m
Slab 2a-4/E-F = (0.15m x 24kN/m³)kN/m² x (6.0/2)m
= 10.8 kN/m
Slab 4-5/D-F = (0.15m x 24kN/m³)kN/m² x (7.775/2)m
= 14.0 kN/m
Brick Wall Self-Weight = (3 x 0.15)m² x 19kN/m³
= 8.55 kN/m
Total Dead Load
Beam (D – E) = (1.44+14.4+14.0+8.55)kN/m
= 38.39 kN/m
Beam (E – F) = (1.44+10.8+14.0+8.55)kN/m
= 35.19 kN/m
Slab 1‐4/C1‐E = 6000/5850
= 1.28 < 2 (Two Way Slab)
Slab 2a‐4/E‐F = 5000/3125
= 1.6 < 2 (Two Way Slab)
Slab 4‐5/D‐F = 7775/2700
= 2.88 > 2 (One Way Slab)
Concrete Density = 24kN/m³
Brick Density = 19kN/m³
Live Load
Slab 1-4/C1-E = 1.5kN/m² x (6/2 x 2/3)m
= 3.0 kN/m
Slab 2a-4/E-F = 1.5kN/m² x (6.0/2)m
= 4.5 kN/m
Slab 4-5/D-F = 1.5kN/m² x (7.775/2)m
= 5.83 kN/m
Total Live Load
Beam (D – E) = (3 + 5.83)kN/m
= 8.83 kN/m
Beam (E – F) = (4.5 + 5.83)kN/m
= 10.33 kN/m
Ultimate Load
Total Dead Load (1.4) + Total Live Load (1.6)
Beam (D – E) = 38.39kN/m(1.4) + 8.83kN/m(1.6)
= 67.85 kN/m
Beam (E – F) = 35.19kN/m(1.4) + 10.33kN/m(1.6)
= 65.79 kN/m
Reaction Force
Calculate Moment at Point A
M(A) = 0
(-72.67kN x 2.5m) + (-126.01kN)
+ (-65.79kN x 6.39m) + R(B) x (7.775m) = 0
R(B) = 61.23 kN
Calculate Vertical Forces = 0
ΣFy = 0
(-67.85) + (-182.57kN) + (-126.01kN)
+ 61.23kN + R(A) = 0
R(A) = 64.5kN
Load Diagram
Shear Force Diagram
Bending Moment Diagram
Column (F/6)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m x 24kN/m³
= 1.44 kN/m²
Brick Wall Self-Weight = (3x0.15)m x 19kN/m³
= 8.55 kN/m²
Slab Self-Weight = 0.15m x 24kN/m³
= 3.6 kN/m²
Column = (0.3x0.3x0.3)m³ x 24kN/m³
= 6.48kN
Roof Level (assume flat roof)
Slab = 3.6kN/m² x (2.65x2.15)m
= 20.511kN
Beam = 1.44kN/m² x (2.65+2.15)m
= 6.912kN
Live Load = 0.5kN/m² x (2.65X2.15)m
= 2.85Kn
First Level (Dead Load)
Walls = (2.65+2.15)m x 8.55kN/m²
= 41.04kN
Slab = (2x2.5)m x 3.6kN/m²
= 18kN
Beam = (3.15+2.15)m x 1.44kN/m²
= 7.632kN
Total Dead Load = (41.04+18+7.632+6.48)kN
= 73.152kN
First Level (Live Load)
Stairs = (2x2.5)m x 1.5kN/m²
= 7.5kN
Ground Level (Dead Load)
Walls = (2.65+2.15)m x 8.55kN/m²
= 41.04kN
Slab = (2x2.5)m x 3.6kN/m²
= 18kN
Beam = (3.15+2.15)m x 1.44kN/m²
= 7.5kN
Total Dead Load = (41.04+18+7.5+6.48)kN
= 73.152kN
Ground Level (Live Load)
Corridor = (2x2.5)m x 1.5kN/m²
= 71.1kN
Total Dead Load = (20.511+6.912+73.152+73.152)kN
= 173.727kN
Apply 1.4 factor = 243.22kN
Total Live Load = (2.85+7.5+7.5)kN
= 17.85kN
Apply 1.6 factor = 28.56kN
*So Ultimate Load acting on column F/6 = 271.78kN
Column (D/5)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m x 24kN/m³
= 1.44 kN/m²
Brick Wall Self-Weight = (3x0.15)m x 19kN/m³
= 8.55 kN/m²
Slab Self-Weight = 0.15m x 24kN/m³
= 3.6 kN/m²
Column = (0.3x0.3x0.3)m³ x 24kN/m³
= 6.48kN
Roof Level (assume flat roof)
Slab = 3.6kN/m² x (3.375X6.475)m
= 78.67kN
Beam = 1.44kN/m² x (6.475+1.85+1.85)m
= 14.652kN
Live Load = 0.5kN/m² x (3.375X6.475)m
= 10.97kN
First Level (Dead Load)
Walls = (6.475+1.875+1.875)m x 8.55kN/m²
= 87.424kN
Slab = [(2.025x2.6)m + (2.025x1.35)m + (3.875x1.35)m +
(2.025x2.75)m + (2.025x1.125)m] 3.6kN/m²
= 80.22kN
Beam = (6.475+1.85+1.85)m x 1.44kN/m²
= 14.652kN
Total Dead Load = (87.424+80.22+14.652+6.48)kN
= 188.776kN
First Level (Live Load)
Corridor = (6.475x1.35)m x 4.0kN/m²
= 34.965kN
Storage = (2.025x1.125)m x 2.5kN/m²
= 5.7kN
Gathering Space = (2.025x2.75)m x 4.0kN/m²
= 22.275kN
Total Live Load = (34.965+5.7+22.275)kN
= 62.94kN
Ground Level (Dead Load)
Walls = (2.45+1.875+0.975)m x 8.55kN/m²
= 47.61kN
Slab = [(2.6x1.35)m + (2.025x2.6)m + (3.875x1.35)m +
(2.025x3.895)m] 3.6kN/m²
= 78.67kN
Beam = (6.475+3.375)m x 1.44kN/m²
= 14.18kN
Total Dead Load = (47.61+78.67+14.184+6.48)kN
= 146.94kN
Ground Level (Live Load)
Corridor = [(16.475x1.35)m + (2.025x3.875)m] x 4.0kN/m²
= 429.04kN
Total Dead Load = (78.67+14.652+188.776+146.944)kN
= 429.042N
Apply 1.4 factor = 600.66kN
Total Live Load = (10.97+62.94+120.35)kN
= 194.26kN
Apply 1.6 factor = 310.82kN
*So Ultimate Load acting on column D/5 = 911.479kN
Column (F/4)
Dead Load
Concrete Beam Self-Weight = (0.3 x 0.2)m x 24kN/m³
= 1.44 kN/m²
Brick Wall Self-Weight = (3x0.15)m x 19kN/m³
= 8.55 kN/m²
Slab Self-Weight = 0.15m x 24kN/m³
= 3.6 kN/m²
Column = (0.3x0.3x0.3)m³ x 24kN/m³
= 6.48kN
Roof Level (assume flat roof)
Slab = 3.6kN/m² x (4.35x4.025)m
= 63.0315kN
Beam = 1.44kN/m² x (4.35+4.025)m
= 12.06kN
Live Load = 0.5kN/m² x (4.35x4.025)m
= 8.754kN
First Level (Dead Load)
Walls = (3.725+4.35)m x 8.55kN/m²
= 69.041kN
Slab = [(1.35x3.875)m + (3.875x3m] x 3.6kN/m²
= 60.68kN
Beam = (4.35+4.025)m x 1.44kN/m²
= 12.06kN
Total Dead Load = (69.041+60.68+12.06+6.48)kN
= 148.261kN
First Level (Live Load)
Bathroom = (3x3.875)m x 2.0kN/m²
= 23.25kN
Corridor = (3.875x1.35)m x 4.0kN/m²
= 20.925kN
Total Live Load = (23.25+20.925)kN
= 44.175kN
Ground Level (Dead Load)
Walls = (3.725+2.85+0.9+2.35)m x 8.55kN/m²
= 84kN
Slab = [(1.675x2.05)m + (2.05x2.2)m + (0.95x3.875)m +
(1.35x3.875)] x 3.6kN/m²
= 60.68kN
Beam = (3.875+3.875+2.05+4.35)m x 1.44kN/m²
= 20.376kN
Total Dead Load = (84+60.68+20.376)kN
= 165.1kN
Ground Level (Live Load)
Entrance = (3.009x3.875)m x 1.5kN/m²
= 17.49kN
Living Room = (1.35x3.875)m x 4.0kN/m²
= 20.925kN
Total Live Load = (17.49 + 20.925)kN
= 38.415kN
Total Dead Load = (63.0315+12.06+148.261+165.1)kN
= 388.45kN
Apply 1.4 factor = 543.83kN
Total Live Load = (8..754+44.175+38.415)kN
= 91.344kN
Apply 1.6 factor = 146.15kN
*So Ultimate Load acting on column F/4 = 690kN
7. Conclusion
At the end of this project, we have learnt about the proper method of calculation
for the analysis of load distribution in building structure. The analysis has helped us
in basic understanding on the design based on the placement of columns and the
load distribution of the structural system. Upon completing this project, we are able
to gain basic knowledge about the formulas used in calculating the load distribution
of a structure.