JUNE / 2019
BUILDING STRUCTURES (BLD61003)
Structural Analysis of a Bungalow
KAYU KAYU RESTAURANT
Daren Lai Kam Fei
0332570
Esther Wong Jia En
0332188
Gavin Tio Kang Hui
0333373
Priscilla Huong Yunn
0332599
Wendy Lau Jia Yee
0333538
Yong Ping Ping
0332585
Tutor : Mr. Mohd Adib Ramli
Content
CONTENT 1.0
Abstract
Page 1 - 2
2.0
Architectural Plans
Page 3 - 6
2.1
Ground Floor Plan
2.2
First Floor Plan
2.3
Roof Plan
3.0
Structural Brief
3.1
Dimension of Structure
3.2
Standard Weight of Materials
3.3
Dead Load Self Weight
3.4
Live Load Self Weight
3.5
Load Factor
4.0
Structural Plans
4.1
Foundation Structural Plan
4.2
Ground Floor Structural Plan
4.3
First Floor Structural Plan
4.4
Roof Structural Plan
5.0
Load Distribution Diagrams
5.1
Ground Floor Load Distribution
5.2
First Floor Load Distribution
5.3
Roof Load Distribution
6.0
Tributary Area Diagrams
6.1
Ground Floor Tributary Area
6.2
First Floor Tributary Area
6.3
Roof Tributary Area
7.0
Structural Analysis
Page 23
7.1
Daren Lai Kam Fei
Page 24 - 42
Page 7 - 9
Page 10 - 14
Page 15 - 18
Page 19 - 22
7.1.1
Uniformly Distributed Load
7.1.2
Pointed Load and Uniformly Distributed Load
7.1.3
Perimeter Column
7.1.4
Internal Column i
Content
Content List
7.2
7.3
7.4
7.5
7.6
Esther Wong Jia En
Page 43 - 62
7.2.1
Uniformly Distributed Load
7.2.2
Pointed Load and Uniformly Distributed Load
7.2.3
Perimeter Column
7.2.4
Internal Column
Page 63 - 81
Gavin Tio Kang Hui 7.3.1
Uniformly Distributed Load
7.3.2
Pointed Load and Uniformly Distributed Load
7.3.3
Perimeter Column
7.3.4
Internal Column
Page 82 - 100
Priscilla Houng Yunn 7.4.1
Uniformly Distributed Load
7.4.2
Pointed Load and Uniformly Distributed Load
7.4.3
Perimeter Column
7.4.4
Internal Column
Page 101 - 119
Wendy Lau Jia Yee 7.5.1
Uniformly Distributed Load
7.5.2
Pointed Load and Uniformly Distributed Load
7.5.3
Perimeter Column
7.5.4
Internal Column
Page 120 - 138
Yong Ping Ping 7.6.1
Uniformly Distributed Load
7.6.2
Pointed Load and Uniformly Distributed Load
7.6.3
Perimeter Column
7.6.4
Internal Column
ii
01 / ABSTRACT
Abstract
1.0
Abstract
The objectives of this project is to introduce the basic process of a structural design of a building to gain holistic structural design experience including the basic concepts in structural design, engineering considerations in building structure, quantification of loads and stresses, as well as the estimation of the sizes of structural members.The assignment is designed to gauge the students’ knowledge and understand the main topics in this module by carrying out structural analysis for the columns and beams. We are to obtain a set of architectural drawings of a two or three-storey building, which includes ground floor plan, first floor plan and roof plan.
1.1
Case Study Building Overview
Name
: Kayu Kayu Restaurant
Architect
: W Office
Location
: North Serpong, South Tangerang City, Banten, Indonesia
Area
: 860.0 m2
Project Year : 2017
Kayu-Kayu is a restaurant for family gathering and corporate events. The open floor plans are organized by a structural
grid
of
6
meters
for
efficiency with a void in the middle for vertical
circulation
with
operable
skylight above. The double spiral staircase is wrapping around a giant Alstonia tree with koi fish pond below. The first floor is mainly used for restaurant and cafe while the second floor is a event space with bar and terrace overlooking the garden area.
Page 2
02 / ARCHITECTURAL PLANS
03 / STRUCTURAL BRIEF
Structural Brief
Structural Analysis
3.0
Structural Brief
3.1
Dimension of Structure
Structure
Dimension
Slab
Thickness / m 0.150
Wall
Beam
Column
3.2
Thickness / m
Height / m
0.150
3.000
Width / m
Depth / m
0.225
0.300
Width / m
Length / m
Height / m
0.225
0.225
3.450
Standard Weight of Materials
Material
Standard Weight (kN/m3)
Reinforced concrete
24
Brick wall
19
3.3
Dead Load Self Weight
Structure
Calculation
Self-weight
Concrete slab
24kN/m3 x 0.15m
3.6kN/m2
Brick wall
19kN/m3 x 0.15m
x 3.0m
8.55kN/m
Beam
24kN/m3 x 0.225m x 0.3m
1.62kN/m
Column
24kN/m3 x 0.225m x 0.225m x 3.45m
4.192kN
Roof
-
1.0 kN/m2
Page 8
Structural Brief
3.4
Structural Analysis
Live Load Self Weight
Structure
Self-weight
Slab
1.5 kN/m2
Roof
0.5 kN/m2
3.5
Load Factor
Types of Load
Load Factor
Dead Load
1.4
Live Load
1.6
Page 9
04 / STRUCTURAL PLANS
05 / LOAD DISTRIBUTION DIAGRAMS
Ground Floor Load Distribution Diagram
Load Distribution Diagrams
Ground Floor Load Distribution Diagram
Two-way Slab
One-way Slab Page 16
Cantilevered Slab
Load Distribution Diagram - First Floor
Load Distribution Diagrams
First Floor Load Distribution Diagram
Two-way Slab
One-way Slab Page 17
Cantilevered Slab
Load Distribution Diagram - Roof
Load Distribution Diagrams
Roof Floor Load Distribution Diagram
Two-way Slab
One-way Slab Page 18
Cantilevered Slab
06 / TRIBUTARY AREA DIAGRAMS
Ground Floor Tributary Area Diagram
Tributary Area Diagrams
Ground Floor Tributary Area Diagram
Page 20
First Floor Tributary Area Diagram
Tributary Area Diagrams
First Floor Tributary Area Diagram
Page 21
Roof Tributary Area Diagram
Tributary Area Diagrams
Roof Tributary Area Diagram
Page 22
07 / STRUCTURAL ANALYSIS
DAREN LAI KAM FEI 0332570
Beam Analysis
Location of Beam
Structural Analysis
: 1. Beam C / 4-7 2. Beam B-D / 7
2
1
Page 25
Beam Analysis - UDL
Structural Analysis
Beam C / 4-7
4
5 6
DEAD LOAD
7 6000
1100
Beam self weight
800
4100
1.62kN/m
= length x depth x density of material = (0.225 x 0.3)m2 x 24kN/m3 = 1.620kN/m
8.55kN/m
Brick wall weight = length x depth x density of material = (3.0 x 0.15)m2 x 19kN/m3 = 8.550kN/m Dead load on Slab B-C / 4-7
3.600kN/m
= 3.6kN/m2 x (2/2)m = 3.600kN/m
Dead load on Slab C-D / 4-7 3.600kN/m
= 3.6kN/m2 x (2/2)m = 3.600kN/m
17.370kN/m
TOTAL Dead Load on Beam C / 4-7 = (1.620 + 8.550 + 3.600 + 3.600)kN/m = 17.370kN/m
Page 26
Beam Analysis - UDL
Structural Analysis
Beam C / 4-7
4
5 6
LIVE LOAD
7 6000
1100
800
4100
Live load on Slab B-C / 4-7 1.500kN/m
= 1.5kN/m2 x (2/2)m = 1.500kN/m
Live load on Slab C-D / 4-7 = 1.5kN/m2 x (2/2)m 1.500kN/m
= 1.500kN/m
3.000 kN/m
TOTAL Live load on Beam C / 4-7 = (1.500 + 1.500)kN/m = 3.000kN/m
Page 27
Beam Analysis - UDL
Structural Analysis
Beam C / 4-7
4
5 6
ULTIMATE LOAD
7 6000
1100
Ultimate dead load
800
4100
24.318kN/m
= Total dead load x 1.4 = 17.370kN/m x 1.4 = 24.318kN/m
4.800 kN/m
Ultimate live load = Total live load x 1.6 = 3.000kN/m x 1.6 = 4.800kN/m
29.12kN/m
Ultimate load on Beam C / 4-7 = Ultimate dead load + ultimate live load = (24.318 + 4.800)kN/m = 29.118kN/m ≈ 29.12kN/m
Page 28
Beam Analysis - UDL
Structural Analysis
Beam C / 4-7
4
5 6
REACTION FORCE
7 6000
1100
800
4100
29.12 kN/m
Pointed load on Beam C / 4-7 = 29.118kN/m x 6m = 174.708kN Let R7 be the reference point
ΣM = MA + (-MB)= 0
174.71 kN
M4 = M7 6m x R4 = (6/2)m x 174.708kN R4 = 87.354kN ≈ 87.35kN ΣF = 0, ΣFUP = ΣFDOWN R4
R4 + R7 = 174.708kN 87.354 + R7 = 174.708kN R7 = 87.354kN ≈ 87.35kN
Page 29
R7
Beam Analysis - UDL
Structural Analysis
Beam C / 4-7 BENDING MOMENT DIAGRAM SHEAR FORCE DIAGRAM Positive area
6000
= (1/2 x 3x 87.354) kN/m = 131.031kN/m
3000
3000
≈ 131.03kN/m 87.354kN
Negative area = (1/2 x 3x 87.354) kN/m = 131.031kN/m
(+)
-87.354kN + 87.354kN = 0kN
≈ 131.03kN/m 0 kN
∴ Positive area = Negative area Beam C / 4-7 is in equilibrium and structurally stable
(-)
87.354kN - 174.708kN = -87.354kN
BENDING MOMENT DIAGRAM 6000
3000
3000
131.03 kN
0 kN
Page 30
0 kN
Beam Analysis - UDL & Point load
Structural Analysis
Beam B-D / 7
B
C
DEAD LOAD
D
4000 2000
Beam self weight
2000
1.620 kN/m
= length x depth x density of material = (0.225 x 0.3)m2 x 24kN/m3 = 1.620kN/m
8.550 kN/m
Brick wall weight = length x depth x density of material = (3.0 x 0.15)m2 x 19kN/m3 = 8.550kN/m
4.800 kN/m
Dead load on Slab B-D/ 7-8 = 3.6kN/m2 x (4/2)m x (2/3) = 4.800kN/m
TOTAL Dead Load on Beam B-D/ 7 = (1.620 + 8.550 + 4.800)kN/m = 14.970kN/m
14.970 kN/m
Page 31
Beam Analysis - UDL & Point load
Structural Analysis
Beam B-D / 7
B
C
LIVE LOAD
D
4000 2000
Live load on Slab B-D / 7-8
2000
2.000 kN/m
= 1.5kN/m2 x (4/2)m x (2/3) = 2.000kN/m
TOTAL Live load on Beam B-D / 7 = 1.5kN/m2 x (4/2)m x (2/3) = 2.000kN/m 2.000 kN/m
Page 32
Beam Analysis - UDL & Point load
Structural Analysis
Beam B-D / 7
B
C
ULTIMATE LOAD
D
4000 2000
Ultimate dead load on Beam B-D / 7
2000
20.958 kN/m
= Total dead load x 1.4 = 14.970kN/m x 1.4 = 20.958kN/m
3.200 kN/m
Ultimate live load on Beam B-D / 7 = Total live load x 16 = 2.000kN/m x 1.6 = 3.200kN/m
24.158 kN/m
Total ultimate load on Beam B-D / 7 = Total dead load + total live load = (20.958 + 3.200)kN/m = 24.158kN/m
Page 33
Beam Analysis - UDL & Point load
Structural Analysis
Beam B-D / 7
B
C
REACTION FORCE
D
4000 2000
2000
Pointed load on Beam C / 7 24.158 kN/m
= 87.354kN
Pointed load on Beam B-D / 7 = 24.158kN/m x 4m = 96.632kN
87.354kN
Let RD be the reference point
96.632 kN
ΣM = MA + (-MB)= 0 MB = MD 4m x RB = [ ( 96.632 x 2.0) + (87.354 x 2.0] kN 4RB = 367.972kN RB
RB = 91.993kN ≈ 91.99kN ΣF = 0, ΣFUP = ΣFDOWN RB + RD = (96.632 + 87.354)kN 91.993 + RD = 183.986kN RD = 91.993kN
Page 34
RD
Beam Analysis - UDL & Point load
Structural Analysis
Beam B-D / 7 BENDING MOMENT DIAGRAM SHEAR FORCE DIAGRAM Positive area
4000
= (43.677 + 91.993) x 2.0 x 1/2 kN/m = 135.67kN/m Negative area
2000
91.993kN
2000
91.993kN - (24.158 x 2)kN =43.677kN
= (43.677 + 91.993) x 2.0 x 1/2 kN/m = 135.67kN/m
(+)
∴ Positive area = Negative area Beam B-D / 7 is in equilibrium and structurally stable
-91.993kN +91.993kN = 0kN
0 kN
(-) 43.677kN - 87.354kN = -43.677kN -43.677kN - (24.158 x 2)kN = -91.993kN
BENDING MOMENT DIAGRAM 4000
2000
2000
135.67 kN
0 kN
Page 35
0 kN
Column Analysis
Location of Column
Structural Analysis
: 1. Column F / 2 2. Column I / 4
1
2
Page 36
Column Analysis - Perimeter Column
Structural Analysis
Column F / 2 Roof Level
Structure Roof Self Weight
(1.5 + 3.0)m x (1.55 + 1.5)m x 2
Roof Beam
Live Load
Dead Load
(1.5 + 3.0)m x (1.55 + 1.5)m x
1.0kN/m
0.5kN/m2
= 4.5m x 3.05m x 1.0kN/m2
= 4.5m x 3.05m x 0.5kN/m2
= 13.725kN
= 6.863kN
(1.5 + 3.0 + 1.55 + 1.5)m x
-
1.62kN/m = 12.231kN Total Load
13.725kN + 12.231kN
6.863kN
= 25.956kN Ultimate Load
25.956kN x 1.4
6.863kN x 1.6
= 36.338kN Total Ultimate Load
= 10.981kN
36.338kN + 10.981kN = 47.319kN ≈ 47.32kN
Page 37
Column Analysis - Perimeter Column
Structural Analysis
Column F / 2 First Floor Level
Structure Slab
(3.0 x 1.5)m2 x 3.6kN/m2 = 16.200kN
Roof Self Weight
Live Load
Dead Load
(3.0 x 1.5)m2 x 1.5kN/m2 = 6.750kN
[ 2.0 x (1.55 + 1.5) ]m2 x
[ 2.0 x (1.55 + 1.5) ] x 0.5kN/m2
1.0kN/m2
= 6.1m2 x 0.5kN/m2
= 6.1m2 x 1.0kN/m2
= 3.050kN
= 6.100kN Brick Wall
(3.0 + 1.5)m x 8.55kN/m
-
= 38.475kN Beam
(2.0 + 3.0 + 1.55 + 1.5)m x
-
1.62kN/m = 13.041kN Column Self Weight
4.192kN
-
Total Load
16.2kN + 6.1kN + 38.475kN + 13.041kN + 4.192kN
6.75kN + 3.05kN =9.800kN
= 78.008kN Ultimate Load
78.008kN x 1.4
9.800kN x 1.6
= 109.211kN Total Ultimate Load
= 15.680kN
109.211kN + 15.680kN = 124.891kN ≈ 124.89kN Page 38
Column Analysis - Perimeter Column
Structural Analysis
Column F / 2 Ground Floor Level
Structure Slab
Brick Wall
Dead Load
Live Load
(2.0 + 3.0)m x 1.5m x 3.6kN/m2
(2.0 + 3.0)m x 1.5m x 1.5kN/m2
= 5.0m x 1.5m x 3.6kN/m2
= 5.0m x 1.5m x 1.5kN/m2
= 27.000kN
= 11.250kN
(2.0 + 3.0 + 1.5)m x 8.55kN/m
-
= 55.575kN Beam
(2.0 + 3.0 + 1.5)m x 1.62kN/m
-
= 10.530kN Column Self Weight
4.192kN
-
Total Load
27.0kN + 55.575kN + 10.530kN
11.250kN
+ 4.192kN = 97.297kN Ultimate Load
97.297kN x 1.4
11.250kN x 1.6
= 136.216kN Total Ultimate Load
= 18.000kN
136.216kN + 18.000kN =154.216kN ≈154.21kN
∴ Total load on Column F2 = 47.319kN + 124.891kN + 154.216kN = 326.426kN ≈ 326.43kN Page 39
Column Analysis - Internal Column
Structural Analysis
Column I / 4 Roof Level
Structure Roof Self Weight
Live Load
Dead Load (3.0 + 3.0)m x (1.5 + 3.0)m x
(3.0 + 3.0)m x (1.5 + 3.0)m x
2
0.5kN/m2
1.0kN/m
Roof Beam
= 6.0m x 4.5m x 1.0kN/m2
= 6.0m x 4.5m x 0.5kN/m2
= 27.000kN
= 13.500kN
(3.0 + 3.0 + 1.5 + 3.0) x
-
1.62kN/m = 17.01kN Total Load
27.000kN + 17.01kN
13.500kN
= 44.010kN Ultimate Load
44.010kN x 1.4
13.500kN x 1.6
= 61.614kN Total Ultimate Load
= 21.600kN
61.614kN + 21.600kN = 83.214kN ≈ 83.21kN
Page 40
Column Analysis - Internal Column
Structural Analysis
Column I / 4 First Floor Level
Structure Slab
(3.0 + 3.0)m x (1.5 + 3.0)m x 3.6kN/m
Brick Wall
Live Load
Dead Load
(3.0 + 3.0)m x (1.5 + 3.0)m x
2
1.5kN/m2
= 6.0m x 4.5m x 3.6kN/m2
= 6.0m x 4.5m x 1.5kN/m2
= 97.200kN
= 40.500kN
(3.0 + 3.0)m x 8.55kN/m
-
= 51.300kN Beam
(3.0 + 3.0 +1.5 + 3.0)m x
-
1.62kN/m = 17.010kN Column Self Weight
4.192kN
-
Total Load
97.2kN + 51.3kN + 17.01kN +
40.500kN
4.192kN = 169.702kN Ultimate Load
169.702kN x 1.4
40.500kN x 1.6
= 237.583kN Total Ultimate Load
= 64.800kN
237.583kN + 64.800kN = 302.383kN ≈ 302.38kN
Page 41
Column Analysis - Internal Column
Structural Analysis
Column I / 4 Ground Floor Level
Structure Slab
Dead Load (3.0 + 3.0)m x (1.5 + 3.0)m x 3.6kN/m
Beam
Live Load (3.0 + 3.0)m x (1.5 + 3.0)m x
2
1.5kN/m2
= 6.0m x 4.5m x 3.6kN/m2
= 6.0m x 4.5m x 1.5kN/m2
= 97.200kN
= 40.500kN
(3.0 + 3.0 +1.5 + 3.0)m x
-
1.62kN/m = 17.010kN Column Self Weight
4.192kN
-
Total Load
97.2kN + 17.01kN + 4.192kN
40.500kN
= 118.402kN
Ultimate Load
118.402kN x 1.4
40.500kN x 1.6
= 165.763kN Total Ultimate Load
= 64.800kN
165.763kN + 64.800kN = 230.563kN ≈ 230.56kN
∴ Total load on Column I / 4 = 83.214kN + 302.383kN + 230.563kN = 616.16kN
Page 42
ESTHER WONG JIA EN 0332188
Beam Analysis
Location of Beam
Structural Analysis
: 1. Beam F-G / 5 2. Beam F / 4-7
2
1
Page 44
Beam Analysis - UDL
Structural Analysis
Beam F-G / 5
F
G
F1
DEAD LOAD
6000 4710
Beam self weight
1290
1.62 kN/m
= length x depth x density of material = (0.225 x 0.3)m2 x 24kN/m3 = 1.620kN/m
8.55 kN/m
Brick wall weight of F-F1 = length x depth x density of material = (3.0 x 0.15)m2 x 19kN/m3 = 8.550kN/m
1.98 kN/m
Dead load on Slab F-G / 4-5 = 3.6kN/m2 x (1.1/2)m = 1.980kN/m
8.82 kN/m
Dead load on Slab F-G / 5-7 = 3.6kN/m2 x (4.9/2)m = 8.820kN/m
TOTAL Dead Load on Beam F-F1 / 5 = (1.620 + 8.550 + 1.980 + 8.820)kN/m 20.97 kN/m
= 20.970kN/m TOTAL Dead Load on Beam F1-G / 5 = (1.620 + 1.980 + 8.820)kN/m = 12.420kN/m
Page 45
12.42 kN/m
Beam Analysis - UDL
Structural Analysis
Beam F-G / 5
F
G
F1
LIVE LOAD
6000 4710
0.825 kN/m
Live load on Slab F-G / 4-5 = 1.5kN/m2 x (1.1/2)m = 0.825kN/m
3.675 kN/m
Live load on Slab F-G / 5-7 = 1.5kN/m2 x (4.9/2)m = 3.675kN/m
TOTAL Live Load on Beam F-G / 5
4.50 kN/m
= (0.825 + 3.675)kN/m = 4.500kN/m
Page 46
1290
Beam Analysis - UDL
Structural Analysis
Beam F-G / 5
F
G
F1
ULTIMATE LOAD
6000 4710
1290
29.358 kN/m
17.388 kN/m
Ultimate dead load on Beam F-F1 / 5 = Total dead load x 1.4 = 20.97kN/m x 1.4 = 29.358kN/m
Ultimate dead load on Beam F1-G / 5 = Total dead load x 1.4 = 12.42kN/m x 1.4 = 17.388kN/m
Ultimate live load on Beam F-G / 5 7.20 kN/m
= Total live load x 1.6 = 4.50kN/m x 1.6 = 7.200kN/m
TOTAL Ultimate Load on Beam F-F1 / 5 = Ultimate dead load + ultimate live load = (29.358 + 7.2)kN/m = 36.558kN/m
36.558 kN/m
TOTAL Ultimate Load on Beam F1-G / 5 = Ultimate dead load + ultimate live load = (17.388 + 7.2)kN/m = 24.588kN/m
Page 47
24.588 kN/m
Beam Analysis - UDL
Structural Analysis
Beam F-G / 5
F
G
F1
REACTION FORCE
6000 4710
1290
36.558 kN/m
24.588 kN/m
Point load on beam F-F1 / 5 = 36.558kN/m x 4.71m = 172.188kN Point load on beam F1-G / 5 = 24.588kN/m x 1.29m = 31.719kN Let RA be the reference point
ΣM = MA + (-MB) = 0
2355
2355
645 645
M A = MB 6m x RB = [(172.188 x 2.355) + (31.719 x 5.355)]kN 172.188 kN
RB = 95.8929kN
31.719 kN
≈ 95.893kN ΣF = 0, ΣFUP = ΣFDOWN RA + RB = (172.188 + 31.719)kN RA
RA = 108.014kN ≈ 108.01kN
Page 48
RB
Beam Analysis - UDL
Structural Analysis
Beam F-G / 5
SHEAR FORCE DIAGRAM
SHEAR FORCE DIAGRAM
F
Using Triangular Ratio Proportion:
G
F1 6000 4710
108.014 172.188 x
= =
x
1290
108.014kN
4.710 2.955
0 kN 108.014kN - 172.188kN = -64.174kN
-64.174kN 31.719kN = -95.893kN
BENDING MOMENT DIAGRAM Positive area 108.014
= (1/2 x 108.014 x 2.955) kNm 172.188
= 159.591kNm ≈ 159.59kNm Negative area
x
= (1/2 x 64.174 x 1.755)kN/m + [1/2 x (64.174 4.71
+ 95.893) x 1.29]kNm = 159.556kNm
BENDING MOMENT DIAGRAM
≈ 159.56kNm Difference = 0.03 ≈0
F
G
F1 6000
∴ Positive area = Negative area Beam F-G / 5 is in equilibrium and structurally stable
2955
1755
1290
159.6 kN
103.2 kN
0 kN Page 49
0 kN
Beam Analysis - UDL & Point load
Structural Analysis
Beam F / 4-7
4
5
7
5A
DEAD LOAD
6000 1100
640
Beam self weight
4260
1.62 kN/m
= length x depth x density of material = (0.225 x 0.3)m2 x 24kN/m3 = 1.620kN/m
Brick wall weight of 4-5A
8.55 kN/m
= length x depth x density of material = (3.0 x 0.15)m2 x 19kN/m3 = 8.550kN/m
7.20 kN/m
Dead load on Slab D-F / 4-7 = 3.6kN/m2 x (4/2)m = 7.200kN/m
5.88 kN/m
Dead load on Slab F-G / 5-7 = 3.6kN/m2 x (4.9/2)m x (2/3) = 5.880kN/m
TOTAL Dead Load on Beam F / 4-5 = 17.370kN/m 17.37 kN/m
TOTAL Dead Load on Beam F / 5-5A = (1.620 + 8.550 + 7.200 + 5.880)kN/m = 23.250kN/m TOTAL Dead Load on Beam F / 5A-7 = (1.620 + 7.200 + 5.880)kN/m = 14.700kN/m
Page 50
23.25 kN/m
= (1.620 + 8.550 + 7.200)kN/m
14.70 kN/m
Beam Analysis - UDL & Point load
Structural Analysis
Beam F / 4-7
4
5
LIVE LOAD
7
5A 6000
1100
Live load on Slab D-F / 4-7
640
4260
3.00 kN/m
= 1.5kN/m2 x (4/2)m = 3.000kN/m
Live load on Slab F-G / 5-7
2.45 kN/m
= 1.5kN/m2 x (4.9/2)m x (2/3) = 2.450kN/m
TOTAL Live Load on Beam F / 4-5 = 3.000kN/m 3.00 kN/m
TOTAL Live Load on Beam F / 5-7 = (3.000 + 2.450)kN/m = 5.450kN/m
Page 51
5.45 kN/m
Beam Analysis - UDL & Point load
Structural Analysis
Beam F / 4-7
4
5
7
5A
ULTIMATE LOAD 1100
640
4260
24.32 kN/m
32.55 kN/m
6000
20.58 kN/m
Ultimate dead load on Beam F / 4-5 = Total dead load x 1.4 = 17.370kN/m x 1.4 = 24.318kN/m
Ultimate dead load on Beam F / 5-5A = Total dead load x 1.4 = 23.250kN/m x 1.4 = 32.550kN/m
Ultimate dead load on Beam F / 5A-7 = Total dead load x 1.4 = 14.700kN/m x 1.4 = 20.580kN/m
Ultimate live load on Beam F / 4-5 = Total live load x 1.6 = 3.000kN/m x 1.6 = 4.800kN/m
4.80 kN/m
Ultimate live load on Beam F / 5-7 = Total live load x 1.6 = 5.450kN/m x 1.6 = 8.720kN/m
Page 52
8.72 kN/m
Beam Analysis - UDL & Point load
Structural Analysis
Beam F / 4-7
4
5
7
5A
ULTIMATE LOAD 1100
640
4260
36.56 kN/m
41.27 kN/m
6000
29.30 kN/m
TOTAL Ultimate Load on Beam F / 4-5 = Ultimate dead load + ultimate live load = (24.318 + 4.800)kN/m = 36.558kN/m
TOTAL Ultimate Load on Beam F / 5-5A = Ultimate dead load + ultimate live load = (32.550 + 8.720)kN/m = 41.270kN/m
TOTAL Ultimate Load on Beam F / 5A-7 = Ultimate dead load + ultimate live load = (20.580 + 8.720)kN/m = 29.300kN/m
Page 53
Beam Analysis - UDL & Point load
Structural Analysis
Beam F / 4-7
4
5
7
5A
REACTION FORCE 1100
640
4260
36.56 kN/m
41.27 kN/m
6000
29.30 kN/m
Point load from beam F-G / 5 = 108.014kN Point load on beam F / 4-5 = 29.118kN/m x 1.10m = 32.030kN Point load on beam F / 5-5A
Point load on beam F / 5A-7
320 320
= 26.413kN
550
550
= 41.270kN/m x 0.64m 2130
2130
108.014kN
= 29.300kN/m x 4.26m
32.03 kN
= 124.818kN
26.413 kN
124.818kN
Let RC be the reference point
ΣM = MC + (-MD) = 0 M C = MD
RC
6m x RD = [(32.030 x 0.55) + (108.014 x 1.10) + (26.413 x 1.42) + (124.818 x 3.87)]kN RD = 109.497kN ≈ 109.50kN ΣF = 0, ΣFUP = ΣFDOWN RC + RD = (32.030 + 108.014 + 26.413 + 124.818)kN RC = 181.778kN ≈ 181.78kN
Page 54
RD
Beam Analysis - UDL & Point load
Structural Analysis
Beam F / 4-7
SHEAR FORCE DIAGRAM
SHEAR FORCE DIAGRAM
4
Using Triangular Ratio Proportion:
5
7
5A 6000
1100
15.321 124.818 x
= =
x
640
4260
181.778kN - 32.03kN 181.778 - 32.030kN = 149.748kN
181.778kN
4.260
149.748 - 108.014kN = 41.734kN
0.523 0 kN
41.734kN 26.413kN = 15.321kN
15.321kN 124.818kN = -109.497kN
BENDING MOMENT DIAGRAM Positive area
15.321
= [1/2 x (181.778 + 149.748) x 1.10]kNm + 124.818
[1/2 x (41.734 + 15.321) x 0.64]kNm + (1/2 x 15.321 x 0.523)kNm = 204.602kNm ≈ 204.60kNm
x 4.26
Negative area = (1/2 x 109.497 x 3.737)kNm
BENDING MOMENT DIAGRAM
= 204.595kNm ≈ 204.60kNm
4
5
7
5A
Difference = 0 6000
∴ Positive area = Negative area Beam F / 4-7 is in equilibrium and structurally stable
1100
640 523
3737
204.60 kN 200.60 kN 182.34 kN
0 kN Page 55
0 kN
Column Analysis
Location of Column
Structural Analysis
: 1. Column M / 7 2. Column J / 7
2
1
Page 56
Column Analysis - Perimeter Column
Structural Analysis
Column M / 7 Roof Level
Structure Roof Self Weight
Roof Beam
Live Load
Dead Load [(1.25 + 1.5) x (3.0 + 3.0)]m2 x
[(1.25 + 1.5) x (3.0 + 3.0)]m2 x
1.0kN/m2
0.5kN/m2
= (2.75 x 6.0)m2 x 1.0kN/m2
= (2.75 x 6.0)m2 x 0.5kN/m2
= 16.500kN
= 8.25kN
(6.0 + 1.5 + 1.25)m x 1.62kN/m
-
= 8.75m x 1.62kN/m = 14.175kN Total Load
16.5kN + 14.175kN
8.250kN
= 30.675kN Ultimate Load
30.675kN x 1.4
8.250kN x 1.6
= 42.945kN Total Ultimate Load
= 13.200kN
42.945kN + 13.20kN = 56.145kN ≈ 56.15kN
Page 57
Column Analysis - Perimeter Column
Structural Analysis
Column M / 7 First Floor Level
Structure Slab
Brick Wall
Live Load
Dead Load 1.25m x (3.0 + 3.0)m x 3.6kN/m2
1.25m x (3.0 + 3.0)m x 1.5kN/m2
= 1.25m x 6.0m x 3.6kN/m2
= 1.25m x 6.0m x 1.5kN/m2
= 27.000kN
= 11.250kN
(3.0 + 3.0)m x 8.55kN/m
-
= 51.300kN Beam
(3.0 + 3.0 + 1.25)m x 1.62kN/m
-
= 7.25m x 1.62kN/m = 11.745kN Column Self Weight
4.192kN
-
Total Load
27.0kN + 51.3kN + 11.745kN +
11.250kN
4.192kN = 94.235kN Ultimate Load
94.235kN x 1.4
11.25kN x 1.6
= 131.929kN Total Ultimate Load
= 18.000kN
131.929kN + 18.0kN = 149.929kN ≈ 149.93kN
Page 58
Column Analysis - Perimeter Column
Structural Analysis
Column M / 7 Ground Floor Level
Structure Slab
Beam
Dead Load
Live Load
1.25m x (3.0 + 3.0)m x 3.6kN/m2
1.25m x (3.0 + 3.0)m x 1.5kN/m2
= 1.25m x 6.0m x 3.6kN/m2
= 1.25m x 6.0m x 1.5kN/m2
= 27.000kN
= 11.250kN
(3.0 + 3.0 + 1.25)m x 1.62kN/m
-
= 7.25m x 1.62kN/m = 11.745kN Column Self Weight
4.192kN
-
Total Load
27.0kN + 11.745kN + 4.192kN
11.250kN
= 42.935kN Ultimate Load
42.935kN x 1.4
11.250kN x 1.6
= 60.109kN Total Ultimate Load
= 18.000kN
60.109kN + 18.0kN = 78.109kN ≈ 78.11kN
∴ Total load on Column L / 9 = 56.145kN + 149.929kN + 78.109kN = 284.183kN ≈ 284.18kN Page 59
Column Analysis - Internal Column
Structural Analysis
Column J / 7 Roof Level
Structure Roof Self Weight
Roof Beam
Dead Load
Live Load
3.0m x (3.0 + 3.0)m x 1.0kN/m2
3.0m x (3.0 + 3.0)m x 0.5kN/m2
= 3.0m x 6.0m x 1.0kN/m2
= 3.0m x 6.0m x 0.5kN/m2
= 18.000kN
= 9.000kN
(3.0 + 3.0 + 3.0)m x 1.62kN/m
-
= 14.580kN Total Load
18.0kN + 14.58kN
9.000kN
= 32.580kN Ultimate Load
32.58kN x 1.4
9.0kN x 1.6
= 45.612kN Total Ultimate Load
= 14.400kN
45.612kN + 14.4kN = 60.012kN ≈ 60.01kN
Page 60
Column Analysis - Internal Column
Structural Analysis
Column J / 7 First Floor Level
Structure Slab
Beam
Dead Load
Live Load
3.0m x (3.0 + 3.0)m x 3.6kN/m2
3.0m x (3.0 + 3.0)m x 1.5kN/m2
= 3.0m x 6.0m x 3.6kN/m2
= 3.0m x 6.0m x 1.5kN/m2
= 64.800kN
= 27.000kN
(3.0 + 3.0 + 3.0)m x 1.62kN/m
-
= 14.580kN Column Self Weight
4.192kN
-
Total Load
64.8kN + 14.58kN + 4.192kN
27.000kN
= 83.570kN Ultimate Load
83.57kN x 1.4
27.0kN x 1.6
= 116.998kN Total Ultimate Load
= 43.200kN
116.998kN + 43.2kN = 160.198kN ≈ 160.20kN
Page 61
Column Analysis - Internal Column
Structural Analysis
Column J / 7 Ground Floor Level
Structure Slab
Beam
Dead Load
Live Load
6.0m x (3.0 + 3.0)m x 3.6kN/m2
6.0m x (3.0 + 3.0)m x 1.5kN/m2
= 6.0m x 6.0m x 3.6kN/m2
= 6.0m x 6.0m x 1.5kN/m2
= 129.600kN
= 54.000kN
(3.0 + 3.0 + 6.0)m x 1.62kN/m
-
= 19.440kN Column Self Weight
4.192kN
-
Total Load
129.6kN + 19.44kN + 4.192kN
54.000kN
4.19kN = 153.230kN Ultimate Load
153.23kN x 1.4
54.0kN x 1.6
= 214.522kN Total Ultimate Load
= 86.400kN
214.522kN + 86.4kN = 300.922kN ≈ 300.92kN
∴ Total load on Column J / 7 = 60.012kN + 160.198kN + 300.922 kN = 512.132kN ≈ 512.13kN Page 62
GAVIN TIO KANG HUI 0333373
Beam Analysis
Location of Beam
Structural Analysis
: 1. Beam F-G / 6 2. Beam G / 4-7
1
2
Page 64
Beam Analysis - UDL
Structural Analysis
Beam F-G / 6
F
G 6000
DEAD LOAD
Beam self weight
1.62 kN/m
= length x depth x density of material = (0.225 x 0.3)m2 x 24kN/m3 = 1.620kN/m
8.55 kN/m
Brick wall weight = length x depth x density of material = (3.0 x 0.15)m2 x 19kN/m3 = 8.550kN/m
3.42 kN/m
Dead load on Slab F-G / 4-6 = 3.6kN/m2 x (1.9/2)m = 3.420kN/m
7.38 kN/m
Dead load on Slab F-G / 6-7 = 3.6kN/m2 x (4.1/2)m = 7.380kN/m
20.97 kN/m
TOTAL Dead Load on Beam F-G / 6 = (1.620 + 8.550 + 3.420 + 7.380)kN/m = 20.970kN/m
Page 65
Beam Analysis - UDL
Structural Analysis
Beam F-G / 6
F
G 6000
LIVE LOAD
1.425 kN/m
Live load on Slab F-G / 4-6 = 1.5kN/m2 x (1.9/2)m = 1.425kN/m
3.075 kN/m
Live load on Slab F-G / 6-7 = 1.5kN/m2 x (4.1/2)m = 3.075kN/m
4.5 kN/m
TOTAL Live load on Beam F-G / 6 = (1.425 + 3.075)kN/m = 4.500kN/m
Page 66
Beam Analysis - UDL
Structural Analysis
Beam F-G / 6
F
G 6000
ULTIMATE LOAD
Ultimate Dead Load
29.358 kN/m
= Total dead load x 1.4 = 20.970kN/m x 1.4 = 29.358kN/m
Ultimate Live Load
7.2 kN/m
= Total live load x 1.6 = 4.5kN/m x 1.6 = 7.200kN/m
Ultimate Load on Beam F-G / 6
36.558 kN/m
= Ultimate Dead Load + Ultimate Live Load = (29.358 + 7.200)kN/m = 36.558kN/m
Page 67
Beam Analysis - UDL
Structural Analysis
Beam F-G / 6
F
G 6000
REACTION FORCE
36.558 kN/m
Pointed Load on Beam F-G / 6 = 36.558N/m x 6.0m = 219.348kN ≈ 219.35kN
3000
3000
Let RF be Reference Point ΣM = MF + (-MG) = 0
219.35 kN
M F = MG 219.348kN x 3m = RG x 6m 6 RG = 658.044kN RG = 109.674kN ≈ 109.67kN RF
ΣF = 0,
ΣFUP = ΣFDOWN RF + RG = 219.35kN
RF + 109.674kN = 219.35kN RF = 219.35kN - 109.674kN RF = 109.674kN ≈ 109.67kN
Page 68
RG
Beam Analysis - UDL
Structural Analysis
Beam F-G / 6
BENDING MOMENT DIAGRAM
SHEAR FORCE DIAGRAM 6000
Positive area = (1/2 x 3.0 x 109.674) kNm
3000
3000
= 164.511kN/m ≈ 164.51kN/m
109.67kN
Negative area = (1/2 x 3.0 x 109.674) kNm
109.67kN + (-109.67kN) = 0kN
(+)
= 164.511kN/m ≈ 164.51kN/m
0 kN
(-)
∴ Positive area = Negative area Beam F-G / 6 is in equilibrium and structurally stable
109.67kN - 219.35kN = -109.67kN
BENDING MOMENT DIAGRAM 6000
3000
3000
164.51 kN
0 kN
Page 69
0 kN
Beam Analysis - UDL & Point load
Structural Analysis
Beam G / 4-7
6
4 DEAD LOAD
7 6000
1900
Beam self weight
4100
1.62 kN/m
= length x depth x density of material = (0.225 x 0.3)m2 x 24kN/m3 = 1.620kN/m
8.55 kN/m
Brick wall weight = length x depth x density of material = (3.0 x 0.15)m2 x 19kN/m3 = 8.550kN/m
4.92kN/m
Dead load on Slab F-G / 6-7 Triangular area formula on two way slab = dead load x (Lx/2)m x (2/3) = 3.6kN/m2 x (4.1/2)m x 2/3 = 4.920kN/m
7.2 kN/m
Dead load on Slab G-I / 4-7 Triangular area formula on two way slab = dead load x (Lx/2)m x (2/3) = 3.6kN/m2 x (6/2)m x 2/3 = 7.200kN/m
TOTAL Dead Load on Beam G / 4-6
17.37 kN/m
= (1.620 + 8.550 + 7.200)kN/m = 17.370kN/m TOTAL Dead Load on Beam G / 6-7 = (1.620 + 8.550 + 4.920 + 7.200)kN = 22.290kN/m Page 70
22.29 kN/m
Beam Analysis - UDL & Point load
Structural Analysis
Beam G / 4-7
6
4 LIVE LOAD
7 6000
1900
Live load on Slab F-G / 6-7
4100
2.05 kN/m
Triangular area formula on two way slab = live load x (Lx/2)m x (2/3) = 1.5kN/m2 x (4.1/2)m x 2/3 = 2.050kN/m 3.0 kN/m
Live load on Slab G-I / 4-7 Triangular area formula on two way slab = live load x (Lx/2)m x (2/3) = 1.5kN/m2 x (6/2)m x 2/3 = 3.000kN/m
TOTAL Live load on Beam G / 4-6
3.0 kN/m
= 3.000kN/m TOTAL Live load on Beam G / 6-7 = (2.05 + 3.0)kN/m = 5.050kN/m
Page 71
5.05 kN/m
Beam Analysis - UDL & Point load
Structural Analysis
Beam G / 4-7
6
4 ULTIMATE LOAD
7 6000
1900
Ultimate dead load on beam G / 4-6
4100
24.32 kN/m
= Total dead load x 1.4 = 17.37kN/m x 1.4 = 24.318kN/m Ultimate dead load on beam G / 6-7
31.21 kN/m
= Total dead load x 1.4 = 22.29kN/m x 1.4 = 31.206kN/m Ultimate live load on Beam G / 4-6
4.8 kN/m
= Total live load x 1.6 = 3.0kN/m X 1.6 = 4.800kN/m Ultimate live load on Beam G / 6-7
8.08 kN/m
= Total live load x 1.6 = 5.050kN/m X 1.6 = 8.080kN/m Total ultimate load on beam G / 4-6
29.12 kN/m
= Total dead load + total live load = (24.318 + 4.800)kN/m = 29.118kN/m Total ultimate load on beam G / 6-7
39.286 kN/m
= Total dead load + total live load = (31.206 + 8.08)kN/m = 39.286kN
Page 72
Beam Analysis - UDL & Point load
Structural Analysis
Beam G / 4-7
6
4 REACTION FORCE
7 6000
1900
Pointed load on beam G / 4-6
4100
29.12 kN/m
39.286 kN/m
1900
4100
= 29.118kN/m x 1.9m = 55.324kN Pointed load on beam G / 6-7 = 39.286kN/m x 4.1m = 161.073kN Let R4 be the reference point
109.67kN
ΣM = M4 + (-M7) = 0
950
950
2050
2050
M 4 = M7 55.32kN
6m x R7 = [(55.324 x 1.9/2) +
161.07kN
(109.67 x 1.9) + (161.073 x 3.95)]kNm R7 = 149.528kN ≈ 149.53kN R4
ΣF = 0, ΣFUP = ΣFDOWN R4 + R7 = (55.324 + 109.67 +161.073)kN R4 = (326.067 - 149.528)kN R4 = 176.539kN ≈ 176.54kN
Page 73
R7
Beam Analysis - UDL & Point load
Structural Analysis
Beam G / 4-7
SHEAR FORCE DIAGRAM
SHEAR FORCE DIAGRAM
4
Using triangular proportion,
6
7 6000
11.545 161.073 x
= =
1900
x
4100
4.1 0.294
176.539kN - 55.324kN = 121.215kN
176.539kN
121.215kN - 109.67kN = 11.545kN
(+) 0 kN
(-) 11.545kN - 161.073kN = -149.528kN
BENDING MOMENT DIAGRAM Positive area
11.545
= (1/2 x 0.294 x 11.545)kNm + [1/2 x (176.539 + 121.215) x 1.9]kNm
161.073
= 284.563kNm ≈ 284.56kN/m Negative area
x
= [1/2 x (4.1 - 0.294) x 149.528] kNm 4.1
= 284.552kN/m ≈ 284.55kN/m
BENDING MOMENT DIAGRAM Difference = 0.01 ≈0
4
6
7 6000
∴ Positive area = Negative area Beam G / 4-7 is in equilibrium and structurally stable
1900
Max 284.56kN
4100
282.87kN
0 kN
Page 74
0 kN
Column Analysis
Location of Column
Structural Analysis
: 1. Column J / 2 2. Column L / 9
1
2
Page 75
Column Analysis - Perimeter Column
Structural Analysis
Column J / 2 Roof Level
Structure Roof Self Weight
Roof Beam
Live Load
Dead Load 6.0m x (1.5 + 1.55)m x 1.0kN/m2
6.0m x (1.5 + 1.55)m x 0.5kN/m2
= 6.0m x 3.05m x 1.0kN/m2
= 6.0m x 3.05m x 0.5kN/m2
= 18.300kN
= 9.150kN
(6.0 + 1.5 + 1.55)m x 1.62kN/m
-
= 14.661kN Total Load
18.3kN + 14.661kN
9.150kN
= 32.961kN Ultimate Load
32.961kN x 1.4
9.15kN x 1.6
= 46.145kN Total Ultimate Load
= 14.640kN
46.145kN + 14.640kN = 60.785kN ≈ 60.79kN
Page 76
Column Analysis - Perimeter Column
Structural Analysis
Column J / 2 First Floor Level
Structure Slab
6.0m x 1.5m x 3.6kN/m2 = 32.400kN
Beam
Live Load
Dead Load
6.0m x 1.5m x 1.5kN/m2 = 13.500kN
(3.0 + 3.0 + 1.5)m x 1.62kN/m
-
= 12.150kN Column Self Weight
4.192kN
-
Total Load
32.4kN + 12.15kN + 4.192kN
13.500kN
= 48.742kN Ultimate Load
48.742kN x 1.4
13.5kN x 1.6
= 68.239kN Total Ultimate Load
= 21.600kN
68.239kN + 21.6kN = 89.839kN ≈ 89.84kN
Page 77
Column Analysis - Perimeter Column
Structural Analysis
Column J / 2 Ground Floor Level
Structure Slab
Dead Load 6.0m x 1.5m x 3.6kN/m2 = 32.400kN
Brick Wall
Live Load 6.0m x 1.5m x 1.5kN/m2 = 13.500kN
(3.0 + 3.0)m x 8.55kN/m
-
= 51.300kN Beam
(3.0 + 3.0 + 1.5)m x 1.62kN/m
-
= 12.150kN Column Self Weight
4.192kN
-
Total Load
32.4kN + 51.3kN + 12.15kN
13.500kN
4.192kN = 100.042kN Ultimate Load
100.042kN x 1.4
13.5kN x 1.6
= 140.059kN Total Ultimate Load
= 21.600kN
140.059kN + 21.6kN = 161.659kN ≈ 161.66kN
∴ Total load on Column J / 2 = 60.785kN + 89.839kN + 161.659kN = 312.283kN ≈ 312.28kN Page 78
Column Analysis - Internal Column
Structural Analysis
Column L / 9 Roof Level
Structure Roof Self Weight
Live Load
Dead Load [(1.25 x 6.0) + (3.0 x 3.0) + 2
[(1.25 x 6.0) + (3.0 x 3.0) +
2
(3.0 x 1.5)]m2 x 0.5kN/m2
(3.0 x 1.5)]m x 1.0kN/m
Roof Beam
= 21.0m2 x 1.0kN/m2
= 21.0m2 x 0.5kN/m2
= 21.000kN/m
= 10.500kN
[(3.0 x 3.0) + 1.25]m x 1.62kN/m
-
= 16.605kN Total Load
21.0kN + 16.605kN
10.500kN
= 37.605kN Ultimate Load
37.605kN x 1.4
10.5kN x 1.6
= 52.647kN Total Ultimate Load
= 16.800kN
52.647kN + 16.8kN = 69.447kN ≈ 69.45kN
Page 79
Column Analysis - Internal Column
Structural Analysis
Column L / 9 First Floor Level
Structure Slab
Live Load
Dead Load [(1.25 x 6.0) + (3.0 x 3.0) + 2
[(1.25 x 6.0) + (3.0 x 3.0) +
2
(3.0 x 1.5)]m2 x 1.5kN/m2
(3.0 x 1.5)]m x 3.6kN/m
Brick Wall
= 21m2 x 3.6kN/m2
= 21m2 x 1.5kN/m2
= 75.600kN
= 31.500kN
(3.0 + 3.0)m x 8.55kN/m
-
= 51.300kN Beam
(3.0 x 4.0 + 1.25)m x 1.62kN/m
-
= 21.465kN Column Self Weight
4.192kN
-
Total Load
75.6kN + 51.3kN + 21.465kN +
31.500kN
4.192kN = 152.557kN Ultimate Load
152.557kN x 1.4
31.5kN x 1.6
= 213.580kN Total Ultimate Load
= 50.400kN
213.580kN + 50.400kN = 263.98kN
Page 80
Column Analysis - Internal Column
Structural Analysis
Column L / 9 Ground Floor Level
Structure Slab
Brick Wall
Dead Load
Live Load
6.0m x (3.0 + 1.25)m x 3.6kN/m2
6.0m x (3.0 + 1.25)m x 1.5kN/m2
= 6m x 4.25m x 3.6kN/m2
= 6m x 4.25m x 1.5kN/m2
= 91.800kN
= 38.250kN
(3.0 + 3.0)m x 8.55kN/m
-
= 51.300kN Beam
[(3.0 x 3.0) + 1.25]m x 1.62kN/m
-
= 16.605kN Column Self Weight
4.192kN
-
Total Load
91.8kN + 51.3kN + 16.605kN
38.250kN
4.192kN = 163.897kN Ultimate Load
163.897kN x 1.4
38.25kN x 1.6
= 229.456kN Total Ultimate Load
= 61.200kN
229.456kN + 61.2kN = 290.656kN ≈ 290.66kN
∴ Total load on Column L / 9 = 69.447kN + 263.98kN + 290.656kN = 624.083kN ≈ 624.08kN Page 81
PRISCILLA HUONG YUNN 0332599
Beam Analysis
Location of Beam
Structural Analysis
: 1. Beam B-D / 10 2. Beam C / 8-10
1
2
Page 83
Beam Analysis - UDL
Structural Analysis
Beam B-D/ 10
A
C 4000
DEAD LOAD
1.62 kN/m
Beam self weight = length x depth x density of material = (0.225 x 0.3)m2 x 24kN/m3 = 1.620kN/m
8.55 kN/m
Brick wall weight = length x depth x density of material = (3.0 x 0.15)m2 x 19kN/m3 = 8.550kN/m Dead load on Slab A-C / 9-10
3.15kN/m
2
= 3.6kN/m x (1.75/2)m = 3.150kN/m
Dead load on Slab A-C / 10-11
4.80 kN/m
= 3.6kN/m2 x (4/2)m x (2/3) = 4.800kN/m
18.12 kN/m
TOTAL Dead Load on Beam 3 / G-F = (1.620 + 8.550 + 3.150 + 4.80)kN/m = 18.120kN/m
Page 84
Beam Analysis - UDL
Structural Analysis
Beam B-D/ 10
A LIVE LOAD
C 4000
Live load on Slab B-D / 9-10 1.313 kN/m
= 1.5kN/m2 x (1.75/2)m = 1.313kN/m Live load on Slab B-D / 10-11 = 1.5kN/m2 x (4/2)m x (2/3) = 2.000kN/m
2.000 kN/m
3.313 kN/m
TOTAL Live load on Beam B-D / 10 = (1.313+2.000)kN/m = 3.313kN/m
Page 85
Beam Analysis - UDL
Structural Analysis
Beam B-D/ 10
A ULTIMATE LOAD
C 4000
Ultimate dead load
25.37 kN/m
= Total dead load x 1.4 = 18.120kN/m x 1.4 = 25.368kN/m
5.30 kN/m
Ultimate live load = Total live load x 1.6 = 3.313kN/m x 1.6 = 5.301kN/m
30.67 kN/m
Ultimate load on Beam B-D / 10 = Ultimate dead load + ultimate live load = (25.368 + 5.301)kN/m = 30.669kN/m ≈ 30.67kN/m
Page 86
Beam Analysis - UDL
Structural Analysis
Beam B-D/ 10
C
B
REACTION FORCE
D
4000
Pointed load on beam B-D/ 10 = 30.669kN/m x 4m
30.669 kN/m
= 122.676kN Let RB be the reference point
ΣM = MA + (-MB) = 0 M A = MB 4m x RA = 2m x 122.676kN RA = 61.337kN
2000
2000
≈ 61.34kN 122.676 kN
ΣF = 0, ΣFUP = ΣFDOWN RA + RB = 122.67kN RB = 61.337kN ≈ 61.34kN RA
Page 87
RB
Beam Analysis - UDL
Structural Analysis
SHEAR FORCE DIAGRAM
Beam B-D/ 10
C
B
D
4000
REACTION FORCE
2000
2000
Pointed load on beam B-D / 10
61.34kN
= 30.669kN/m x 4m = 122.676kN 61.34kN + (-61.34kN) = 0kN
(+) Let RB be the reference point
ΣM = MA + (-MB) = 0
0 kN
(-)
M A = MB 4m x RA = 2m x 122.676kN RA = 61.337kN 38.1kN - 76.20kN = -61.34kN
≈ 61.34kN ΣF = 0, ΣFUP = ΣFDOWN RA + RB = 122.67kN RB = 61.337kN ≈ 61.34kN
BENDING MOMENT DIAGRAM 4000
BENDING MOMENT DIAGRAM
2000
2000
Positive area = (1/2 x 2x 61.337) kN/m
61.34 kN
= 61.337kN/m ≈ 61.34kN/m Negative area = (1/2 x 2x 61.337) kN/m
0 kN
= 61.337kN/m ≈ 61.34kN/m ∴ Positive area = Negative area Beam A-C / 9 is in equilibrium and structurally stable
Page 88
0 kN
Beam Analysis - UDL & Point load
Structural Analysis
Beam D / 9-11
9 DEAD LOAD
10 1750
Beam self weight
11 4250
1.62 kN/m
= length x depth x density of material = (0.225 x 0.3)m2 x 24kN/m3 = 1.620kN/m
8.55 kN/m
Brick wall weight = length x depth x density of material = (3.0 x 0.15)m2 x 19kN/m3 = 8.550kN/m
7.2kN/m
Dead load on Slab D / 9-10 = 3.6kN/m2 x (4/2)m = 7.200kN/m
7.20 kN/m
Dead load on Slab D / 10-11 = 3.6kN/m2 x (4/2)m = 7.200kN/m
17.37 kN/m
TOTAL Dead Load on Beam D / 9-10 = (1.620 + 8.550 + 7.200)kN/m = 17.370kN/m TOTAL Dead Load on Beam D / 10-11 = (1.620 + 8.550 + 7.200 + 7.200)kN = 24.570kN/m
Page 89
24.57 kN/m
Beam Analysis - UDL & Point load
Structural Analysis
Beam D / 9-11
9 LIVE LOAD
10
11 4250
1750
Live load on Slab B-D / 9-11
3.0kN/m
= 1.5kN/m2 x (4/2)m = 3.000kN/m Live load on Slab B-D / 10-11 = 1.5kN/m2 x (4/2)m 3.0 kN/m
= 3.000kN/m
3.0 kN/m
TOTAL Live load on Beam D / 9-10 = 1.5kN/m2 x (4/2)m = 3.000kN/m TOTAL Live load on Beam D / 10-11 = 3.0kN/m2 + 3.0 kN/m = 6.000kN/m
Page 90
6.0 kN/m
Beam Analysis - UDL & Point load
Structural Analysis
Beam D / 9-11
10
9 ULTIMATE LOAD
1750
Ultimate dead load on Beam D / 9-10
24.32kN/m
11 4250
34.40kN/m
= Total dead load x 1.4 = 17.37kN/m x 1.4 = 24.318kN/m
Ultimate dead load on Beam D / 10-11
0.48 kN/m
9.60kN/m
29.12 kN/m
44.0kN/m
= Total dead load x 1.4 = 24.570kN/m x 1.4 = 34.398kN/m
Ultimate live load on Beam D / 9-10 = Total live load x 1.6 = 3.0 X 1.6 = 4.800kN/m Ultimate live load on Beam C / 9-10 = Total live load x 1.6 = 6.0 X 1.6 = 9.600kN/m
Total ultimate load on Beam C / 8-9 = Total dead load + total live load = (24.318 + 4.800)kN/m = 29.118kN/m Total ultimate load on Beam C / 9-10 = Total dead load + total live load = (34.398 + 9.600)kN/m = 44.000kN/m Page 91
Beam Analysis - UDL & Point load
Structural Analysis
Beam D / 9-11
10
9 REACTION FORCE
11
1750
Pointed load on Beam D / 9-10
4250
29.12 kN/m
44.0kN/m
= 29.118kN/m x 1.750 = 50.956kN Pointed load on Beam D / 10-11 = 44.000kN/m x 4.250 = 187.000kN 875
Let RA be the reference point
875
2125
2125
ΣM = MA + (-MB) = 0 M A = MB 6m x RB = [(50.96 x 0.875) + 50.9kN
(73.1x 1.75) +
73.188 kN
187.0 kN
(187.0 x 3.875)]kN RB = 149.523kN ≈ 149.52kN RA = 161.537kN
ΣF = 0, ΣFUP = ΣFDOWN RA + RB = (50.96 + 73.1 +187.0)kN RA = ( 311.06 - 149.52 )kN ≈ 161.537kN
Page 92
RB = 149.543kN
Beam Analysis - UDL & Point load
Structural Analysis
Beam D / 9-11
Using triangular proportion, 37.477 187.0 x
= =
37.477
x
187.0
4.250 0.8517
x 4.25
BENDING MOMENT DIAGRAM
SHEAR FORCE DIAGRAM
8
Positive area
10
9
= [(1/2)(161.537 + 110.577)(1.75) + (1/2)(0.8517 x 37.477) ] kN/m = (238.099 + 15.959)kN/m
161.537kN
= 254.059kN/m
110.577kN 37.477kN
161.537kN - 50.96kN = 110.577kN
(+)
0
Negative area
37.477kN - 187kN = -149.523kN
= (1/2 x 149.523 x 3.398) = 254.040kN/m
(-)
-149.523
Difference = 0.019 ≈0 BENDING MOMENT DIAGRAM ∴ Positive area = Negative area Beam D / 9 -11 is in equilibrium and structurally stable
254.0kN 238.099kN
0 kN
Page 93
0 kN
Column Analysis
Location of Column
Structural Analysis
: 1. Column I / 11 2. Column I / 7
2
Page 94
1
Column Analysis - Perimeter Column
Structural Analysis
Column I / 11 Roof Level
Structure Roof Self Weight
(8.25 x 6.0)m2 x 1.0kN/m2 = 49.500kN
Roof Beam
Live Load
Dead Load
(8.25 x 6.0)m2 x 0.5kN/m2 = 24.750kN
(8.25 x 6.0)m2 x 1.62kN/m
-
= 80.190kN Total Load
49.5kN + 80.19kN
24.750kN
= 129.690kN Ultimate Load
129.69kN x 1.4
24.750kN x 1.6
= 181.566kN Total Ultimate Load
= 39.600kN
181.566kN + 39.600kN =221.166kN ≈ 221.17kN
Page 95
Column Analysis - Perimeter Column
Structural Analysis
Column I / 11 First Floor Level
Structure Slab
Live Load
Dead Load [(3 x 6) + (2.15 x 3)]m² x 3.6kN/m²
[(3.0 x 6.0) + (2.15 x 3.0)]m² x
= 24.45m² x 3.6kN/m²
1.5kN/m²
= 88.020kN
= 24.45m² x 1.5kN/m² = 36.675kN
Brick Wall
8.55kN/m x (3.2 + 2.15 + 3)m
-
= 69.683kN Beam
(3 + 2.15 + 6)m x 1.62 kN/m
-
= 11.15m x 1.62 kN/m = 18.063kN Total Load
88.02kN + 69.683kN + 18.063kN
36.675kN
= 175.766kN Ultimate Load
175.766 kN x 1.4
36.675kN x 1.6
= 246.072kN Total Ultimate Load
= 58.680kN
246.072kN + 58.680kN = 304.752kN ≈ 304.76kN
Page 96
Column Analysis - Perimeter Column
Structural Analysis
Column I / 11 Ground Floor Level
Structure Slab
Brick Wall
Live Load
Dead Load (3.0 x 6.0)m² x 3.6kN/m²
(3.0 x 6.0)m²x 1.5kN/m²
= 18.0m² x 3.6kN/m²
= 18.0m² x 1.5kN/m²
= 64.800kN
= 27.000kN
8.55kN/m x 6.0m
-
= 51.300kN Beam
(3.0 + 6.0)m² x 1.62 kN/m²
-
= 9m² x 1.62 kN/m² = 14.580kN Total Load
64.80kN + 51.30kN + 14.58kN
27.000kN
= 130.680kN Ultimate Load
130.68 kN x 1.4
27.000kN x 1.6
= 182.952kN Total Ultimate Load
= 43.200kN
182.952kN + 43.200kN = 226.152kN ≈ 226.15kN
∴ Total load on Column G/10 = 226.152kN + 304.752kN + 60.012kN = 590.916kN ≈ 590.92kN Page 97
Column Analysis - Internal Column
Structural Analysis
Column I / 7 Roof level
Structure Roof Self Weight
Live Load
Dead Load (3.0 + 3.0)m x 3m x 1.0kN/m² = 6.0m x 3.0m x 1.0kN/m
2
6.0m x 3.0m x 0.5kN/m² = 9.000kN
= 18.000kN Roof Beam
(3.0 + 3.0 + 3.0)m x 1.62kN/m
-
= 14.580kN Total Load
18.0kN + 14.58kN
9.000kN
= 32.580kN Ultimate Load
32.58kN x 1.4
9.0kN X 1.6
= 45.610kN Total Ultimate Load
=14.400kN
45.61kN + 14.4kN = 60.012kN ≈ 60.01kN
Page 98
Column Analysis - Internal Column
Structural Analysis
Column I / 7 First Floor Level
Structure Slab
Beam
Live Load
Dead Load 6.0m x 3.0m x 3.6kN/m²
6.0m x 3.0m x 1.5kN/m²
= 18.0m² x 3.6kN/m²
= 18.0m²x 1.5kN/m²
= 64.800kN
= 27.000kN
6.0m x 3.0m x 1.62kN/m
-
= 9.0m x 1.62kN/m = 14.580kN Column Self-Weight
4.190kN
-
Total Load
64.8kN + 14.58kN + 4.19kN
27.000kN
= 83.570kN Ultimate Load
83.57kN x 1.4 = 116.998kN
Total Ultimate Load
27.0kN x 1.6 = 43.200kN
116.998kN + 43.2kN = 160.198kN ≈ 160.20kN
Page 99
Column Analysis - Internal Column
Structural Analysis
Column I / 7 Ground Floor Level
Structure Slab
Beam
Dead Load
Live Load
(6.0 x 6.0)m² x 3.6kN/m
(6.0 x 6.0)m² x 1.5kN/m²
= 36.0m² x 3.6kN/m²
= 36.0m² x 1.51kN/m²
= 129.600kN
= 54.360kN
(6 + 6)m x 1.62 kN/m
-
=19.440kN
Column Self-Weight
4.192kN
-
Total Load
(129.6 + 19.44 + 4.192)kN
54.360kN
= 153.232kN Ultimate Load
153.232kN x 1.4
54.36kN x 1.6
= 214.523kN Total Ultimate Load
= 86.400kN
214.523kN + 86.4kN = 300.9248kN ≈ 300.92kN
∴ Total load on Column G/6 = 60.012kN + 160.198kN + 300.92kN = 521.132kN ≈ 521.13kN
Page 100
WENDY LAU JIA YEE 0333538
Beam Analysis
Structural Analysis
Location of Beam
: 1. Beam F-G / 3 2. Beam F / 2-4
2
1
Page 102
Beam Analysis - UDL
Structural Analysis
Beam F-G / 3
2
3
4
3000
DEAD LOAD
2350
Beam self weight
1.620 kN/m
= length x depth x density of material = (0.225 x 0.3)m x 24kN/m3 = 1.620kN/m
8.550 kN/m
Brick wall weight = length x depth x density of material = (3.0 x 0.15)m x 19kN/m3 = 8.550kN/m
4.230 kN/m
Dead load on Slab G-F / 2-3 = 3.6kN/m2 x (2.35/2)m = 4.230kN/m
1.170 kN/m
Dead load on Slab G-F / 3-4 = 3.6kN/m2 x (0.65/2)m = 1.170kN/m
15.57 kN/m
TOTAL Dead Load on Beam 3 / G-F = (1.620 + 8.550 + 4.230 + 1.170)kN/m = 15.57kN/m
Page 103
650
Beam Analysis - UDL
Structural Analysis
Beam F-G / 3
2
3
4
3000
LIVE LOAD
2350
Live load on Slab G-F / 2-3
1.763 kN/m
= 1.5kN/m2 x (2.35/2)m = 1.763kN/m
Live load on Slab G-F / 3-4
0.488 kN/m
= 1.5kN/m2 x (0.65/2)m = 0.488kN/m
2.251 kN/m
TOTAL Live load on Beam 3 / G-F = (1.763 + 0.488)kN/m = 2.251kN/m
Page 104
650
Beam Analysis - UDL
Structural Analysis
Beam F-G / 3
2
3
4
3000
ULTIMATE LOAD
2350
Ultimate Dead Load
21.798 kN/m
= Total dead load x 1.4 = 15.570kN/m x 1.4 = 21.798kN/m
3.602 kN/m
Ultimate Live Load = Total live load x 1.6 = 2.25kN/m x 1.6 = 3.602kN/m
25.40 kN/m
Ultimate Load on Beam 3 / G-F = Ultimate Dead Load + Ultimate Live Load = (21.798 + 3.602)kN/m = 25.40kN/m
Page 105
650
Beam Analysis - UDL
Structural Analysis
Beam F-G / 3
2
3
4
3000
REACTION FORCE
650
2350
25.40 kN/m
Pointed Load on Beam 3 / F-G = 25.40kN/m x (2.35 + 0.65)m = 25.40kN/m x 3m = 76.20kN
1500
1500
Let R2 be Reference Point ΣM = M2 + (-M4) = 0
76.62 kN
M 2 = M4 76.20kN x 3m = R4 x 6m 6 R4 = 228.6kN R4 = 38.10kN R2 = 38.10kN
ΣF = 0,
ΣFUP = ΣFDOWN R2 + R4 = 76.20kN
R2 + 38.10kN = 76.20kN R2 = 76.20kN - 38.10kN R2 = 38.10kN
Page 106
R4 = 38.10 kN
Beam Analysis - UDL
Structural Analysis
Beam F-G / 3
BENDING MOMENT DIAGRAM
SHEAR FORCE DIAGRAM
Positive area
2
4
= (1/2 x 1.5 x 38.1) kN/m
3000
= 28.575kN/m
1500
1500
≈ 28.58kN/m 38.1kN
Negative area = (1/2 x 1.5 x 38.1) kN/m = 28.575kN/m
(+)
38.1kN + (-38.1kN) = 0kN
≈ 28.58kN/m 0 kN
(-)
∴ Positive area = Negative area Beam 3 / F-G is in equilibrium and structurally stable
38.1kN - 76.20kN = -38.1kN
BENDING MOMENT DIAGRAM
2
4 3000 1500
1500
28.58 kN
0 kN
Page 107
0 kN
Beam Analysis - UDL & Point load
Structural Analysis
Beam F / 2-4
2
3
4
3000
DEAD LOAD
2350
Beam self weight
1.620 kN/m
= length x depth x density of material = (0.225 x 0.3)m x 24kN/m3 = 1.620kN/m
8.550 kN/m
Brick wall weight = length x depth x density of material = (3.0 x 0.15)m x 19kN/m3 = 8.550kN/m
3.600 kN/m
Dead load on Slab D-F / 2-4 Triangular area formula on two way slab = slab self-weight x (Lx/2)m x (2/3) = 3.6kN/m2 x (3/2)m x (2/3) = 3.600kN/m
13.770 kN/m
TOTAL Dead Load on Beam F / 2-4 = (1.620 + 8.550 + 3.600)kN/m = 13.770kN/m
Page 108
650
Beam Analysis - UDL & Point load
Structural Analysis
Beam F / 2-4
2
3
4
3000
LIVE LOAD
2350
Live load on Slab D-F / 2-4
1.500 kN/m
Triangular area formula on two way slab = live load x (Lx/2)m x (2/3) = 1.5kN/m2 x (3/2)m x (2/3) = 1.500kN/m
TOTAL Live load on Beam F / 2-4
1.500 kN/m
= 1.50kN/m
Page 109
650
Beam Analysis - UDL & Point load
Structural Analysis
Beam F / 2-4
2
3
4
3000
ULTIMATE LOAD
2350
Ultimate Dead Load
19.278 kN/m
= Total dead load x 1.4 = 13.770kN/m x 1.4 = 19.278kN/m
2.400 kN/m
Ultimate Live Load = Total live load x 1.6 = 1.500kN/m x 1.6 = 2.400kN/m
21.678 kN/m
Ultimate Load on Beam 3 / G-F = Ultimate Dead Load + Ultimate Live Load = (19.278 + 2.400)kN/m = 21.678kN/m ≈ 21.68kN/m
Page 110
650
Beam Analysis - UDL & Point load
Structural Analysis
Beam F / 2-4
2
3
4
3000
REACTION FORCE
650
2350
21.678 kN/m
Pointed Load on Beam F / 3 = 76.200kN Pointed Load on Beam F / 2-3 = 21.678kN/m x 2.35m = 50.943kN
1500
1500
Pointed Load on Beam F / 3-4
76.20kN
= 21.678kN/m x 0.65
2350
= 14.091kN
1175
650 1175
50.943kN
325
325
14.091kN
Let R2 be Reference Point ΣM = M2 + (-M4) = 0 M2 = M4 R4 x 3m = (50.943kN x 1.175m) + (76.200kN x 2.350m) +
R2 = 49.027kN
(14.091kN x 2.675m) 3 R4 = 276.621kN R4 = 92.207kN
ΣF = 0,
ΣFUP = ΣFDOWN R2 + R4 = (50.943 + 76.200 + 14.091)
R2 + 92.207kN = 141.234kN R2 = 141.234kN - 92.207kN R2 = 49.027kN R2 ≈ 49.03kN
Page 111
R4 = 92.207kN
Beam Analysis - UDL & Point load
Structural Analysis
Beam F / 2-4
SHEAR FORCE DIAGRAM
SHEAR FORCE DIAGRAM
2
Using Triangular Ratio Proportion:
3
4
3000 2350
2.35
x
=
50.943
650
49.03kN
1.918
49.03kN - 50.943kN = -1.919kN
(+) x
=
0.088
0 kN
(-)
-1.919kN - 76.2kN = -78.12kN
-78.12kN - 14.091kN = -92.21kN
BENDING MOMENT DIAGRAM Positive area
2.35
= (1/2 x 49.03 x 2.262) kN/m = 55.446kN/m
50.943
≈ 55.45kN/m Negative area x
= (1/2 x 0.088 x 1.918) + [1/2 x (78.108 + 92.20) x 0.65]kN/m
1.918
= 0.0844kN/m + 55.35kN/m BENDING MOMENT DIAGRAM
= 55.434kN/m ≈ 55.43kN/m
2
3
4
3000
Difference of 0.02 ≈ 0 ∴ Positive area = Negative area Beam F / 2-4 is in equilibrium and structurally stable
2350
650
55.43 kN
0 kN
Page 112
0 kN
Column Analysis
Location of Column
Structural Analysis
: 1. Column M / 11 2. Column J / 4
2
1
Page 113
Column Analysis - Perimeter Column
Structural Analysis
Column M / 11 Roof Level
Structure Roof Self Weight
Roof Beam
Live Load
Dead Load (2.75 x 8.25)m2 x 1.0kN/m2
(2.75 x 8.25)m2 x 0.5kN/m2
= 22.688m2 x 1.0kN/m2
= 22.688m2 x 0.5kN/m2
= 22.688kN/m
= 11.344kN
(2.75 + 8.25)m x 1.62kN/m
-
= 17.82kN Total Load
22.688kN + 17.82kN
11.344kN
= 40.508kN Ultimate Load
40.508kN x 1.4
11.344kN x 1.6
= 56.711kN Total Ultimate Load
= 18.15kN
56.711kN + 18.15kN = 74.861kN ≈ 74.86kN
Page 114
Column Analysis - Perimeter Column
Structural Analysis
Column M / 11 First Floor Level
Structure Slab
Brick Wall
Live Load
Dead Load 3.0m x 1.25m x 3.6kN/m2
3.0m x 1.25m x 1.5kN/m2
= 3.75m x 3.6kN/m2
= 3.75m x 1.5kN/m2
= 13.500kN
= 5.625kN
(3.0 + 1.25)m x 8.55kN/m
-
= 36.338kN Beam
(3.0 + 1.25)m x 1.62kN/m
-
= 6.885kN Column Self Weight
4.192kN
-
Total Load
13.500kN + 36.338kN + 6.885kN
5.625kN
+ 4.192kN = 60.915kN Ultimate Load
60.915kN x 1.4
5.625kN x 1.6
= 85.281kN Total Ultimate Load
= 9.000kN
85.281kN + 9.000kN = 94.281kN ≈ 94.28kN
Page 115
Column Analysis - Perimeter Column
Structural Analysis
Column M / 11 Ground Floor Level
Structure Slab
Beam
Dead Load
Live Load
3.0m x 1.25m x 3.6kN/m2
3.0m x 1.25m x 1.5kN/m2
= 3.75m x 3.6kN/m2
= 3.75m x 1.5kN/m2
= 13.500kN
= 5.625kN
(3.0 + 1.25)m x 1.62kN/m
-
= 6.885kN Column Self Weight
4.192kN
-
Total Load
13.5kN + 6.885kN + 4.192kN
5.625kN
= 24.577kN Ultimate Load
24.577kN x 1.4
5.625kN x 1.6
= 34.408kN Total Ultimate Load
= 9.000kN
34.408kN + 9.000kN = 43.408kN ≈ 43.41kN
∴ Total load on Column M /11 = 74.861kN + 94.281kN + 43.408kN =
Page 116
212.55kN
Column Analysis - Internal Column
Structural Analysis
Column J / 4 Roof Level
Structure Roof Self Weight
Roof Beam
Dead Load
Live Load
6.0m x (3.0 + 1.5)m x 1.0kN/m2
6.0m x (3.0 + 1.5)m x 0.5kN/m2
= 6m x 4.5m x 1.0kN/m2
= 6.0m x 4.5m x 0.5kN/m2
= 27.000kN
= 13.500kN
[(3.0m x 3) + 1.5m] x 1.62kN/m
-
= 17.010kN Total Load
27.0kN + 17.01kN
13.500kN
= 44.010kN Ultimate Load
44.010kN x 1.4
13.500kN x 1.6
= 61.614kN Total Ultimate Load
= 21.600kN
61.614kN + 21.600kN = 83.214kN ≈ 83.21kN
Page 117
Column Analysis - Internal Column
Structural Analysis
Column J / 4 First Floor Level
Structure Slab
Brick Wall
Dead Load
Live Load
6.0m x (1.5 + 3.0)m x 3.6kN/m2
6.0m x (1.5 + 3.0)m x 1.5kN/m2
= 6.0m x 4.5m x 3.6kN/m2
= 6m x 4.5m x 1.5kN/m2
= 97.200kN
= 40.500kN
(3.0 + 3.0)m x 8.55kN/m
-
= 51.300kN Beam
(6.0 + 3.0 + 1.5)m x 1.62kN/m
-
= 17.010kN Column Self Weight
4.192kN
-
Total Load
97.200kN + 51.300kN +
40.500kN
17.010kN + 4.192kN = 169.702kN Ultimate Load
169.702kN x 1.4
40.500kN x 1.6
= 237.583kN Total Ultimate Load
= 64.800kN
237.583kN + 64.800kN = 302.383kN ≈ 302.38kN
Page 118
Column Analysis - Internal Column
Structural Analysis
Column J / 4 Ground Floor Level
Structure Slab
Beam
Dead Load
Live Load
6.0m x (1.5 + 3.0)m x 3.6kN/m2
6.0m x (1.5 + 3.0)m x 1.5kN/m2
= 6m x 4.5m x 3.6kN/m2
= 6m x 4.50m x 1.5kN/m2
= 97.200kN
= 40.500kN
(6.0 + 1.5 + 3.0)m x 1.62kN/m
-
= 10.5m x 1.62kN/m = 17.010kN Column Self Weight
4.192kN
-
Total Load
97.200kN + 17.010kN + 4.192kN
40.500kN
= 118.402kN
Ultimate Load
118.402kN x 1.4
40.500kN x 1.6
= 165.763kN Total Ultimate Load
= 64.800kN
165.763kN + 64.800kN = 230.563kN ≈ 230.56kN
∴ Total load on Column J / 4 = 83.214kN + 302.383kN + 230.563kN = 616.16kN
Page 119
YONG PING PING 0332585
Beam Analysis
Location of Beam
Structural Analysis
: 1. Beam B-D / 8 2. Beam B / 7-9
2
1
Page 121
Beam Analysis - UDL
Structural Analysis
Beam B-D / 8
B
C
DEAD LOAD
D
4000 2000
Beam self weight
2000
1.62kN/m
= length x depth x density of material = (0.225 x 0.3)m2 x 24kN/m3 = 1.620kN/m
8.55kN/m
Brick wall weight = length x depth x density of material = (3.0 x 0.15)m2 x 19kN/m3 = 8.550kN/m Dead load on Slab B-D / 7-8
4.800kN/m
= 3.6kN/m2 x (4/2)m x (2/3) = 4.800kN/m
Dead load on Slab B-D / 8-9 3.150kN/m
= 3.6kN/m2 x (1.75/2)m = 3.150kN/m
18.120kN/m
TOTAL Dead Load on Beam B-D / 8 = (1.620 + 8.550 + 3.150 + 4.80)kN/m = 18.120kN/m
Page 122
Beam Analysis - UDL
Structural Analysis
Beam B-D / 8
B
C
LIVE LOAD
D
4000 2000
2000
Live load on Slab B-D / 7-8 2.000kN/m
= 1.5kN/m2 x (4/2)m x (2/3) = 2.000kN/m
Live load on Slab B-D / 8-9 = 1.5kN/m2 x (1.75/2)m 1.313kN/m
= 1.313kN/m
3.313 kN/m
TOTAL Live load on Beam A-C / 7 = (2.000 + 1.313)kN/m = 3.313kN/m
Page 123
Beam Analysis - UDL
Structural Analysis
Beam B-D / 8
B
C
ULTIMATE LOAD
D
4000 2000
Ultimate dead load
2000
25.368kN/m
= Total dead load x 1.4 = 18.120kN/m x 1.4 = 25.368kN/m
5.301 kN/m
Ultimate live load = Total live load x 1.6 = 3.313kN/m x 1.6 = 5.301kN/m
30.67kN/m
Ultimate load on Beam B-D / 8 = Ultimate dead load + ultimate live load = (25.368 + 5.301)kN/m = 30.669kN/m ≈ 30.67kN/m
Page 124
Beam Analysis - UDL
Structural Analysis
Beam B-D / 8
B
C
REACTION FORCE
D
4000 2000
2000
30.67 kN/m
Pointed load on Beam B-D /8 = 30.669kN/m x 4m = 122.676kN Let RD be the reference point
ΣM = MA + (-MB) = 0
122.68 kN
MB = MD 4m x RB = 2m x 122.676kN RB = 61.337kN ≈ 61.34kN ΣF = 0, ΣFUP = ΣFDOWN RB
RB + RD = 122.67kN RD = 61.337kN ≈ 61.34kN
Page 125
RD
Beam Analysis - UDL
Structural Analysis
Beam B-D / 8 BENDING MOMENT DIAGRAM SHEAR FORCE DIAGRAM Positive area
4000
= (1/2 x 2x 61.337) kN/m = 61.337kN/m
2000
2000
≈ 61.34kN/m 61.34kN
Negative area = (1/2 x 2x 61.337) kN/m = 61.337kN/m
61.34kN + (-61.34kN) = 0kN
(+)
≈ 61.34kN/m 0 kN
∴ Positive area = Negative area Beam B-D /8 is in equilibrium and structurally stable
(-)
61.34kN-122.68kN = -61.34kN
BENDING MOMENT DIAGRAM 4000
2000
2000
61.34 kN
0 kN
Page 126
0 kN
Beam Analysis - UDL & Point load
Structural Analysis
Beam B / 7-9
7
8
DEAD LOAD
9
6000 4250
Beam self weight
1750
1.620 kN/m
= length x depth x density of material = (0.225 x 0.3)m2 x 24kN/m3 = 1.620kN/m
8.550 kN/m
Brick wall weight = length x depth x density of material = (3.0 x 0.15)m2 x 19kN/m3 = 8.550kN/m
7.200 kN/m
Dead load on Slab B-D/ 7-8 = 3.6kN/m2 x (4/2)m = 7.200kN/m
TOTAL Dead Load on Beam B / 7- 8 = (1.620 + 8.550 + 7.200)kN/m = 17.370kN/m 17.370 kN/m
TOTAL Dead Load on Beam B / 8 - 9 = (1.620 + 8.550)kN = 10.170kN/m
Page 127
10.170 kN/m
Beam Analysis - UDL & Point load
Structural Analysis
Beam B / 7-9
7
8
LIVE LOAD
9
6000 4250
Live load on Slab B-D / 7-8
3.000 kN/m
= 1.5kN/m2 x (4/2)m = 3.000 kN/m
TOTAL Live load on Beam B / 7-9 = 1.5kN/m2 x (4/2)m = 3.000 kN/m 3.000 kN/m
Page 128
1750
Beam Analysis - UDL & Point load
Structural Analysis
Beam B / 7-9
7
8
ULTIMATE LOAD
9
6000 4250
Ultimate dead load on Beam B / 7- 8
1750
24.318 kN/m
= Total dead load x 1.4 = 17.37kN/m x 1.4 = 24.318kN/m
14.238kN/m
Ultimate dead load on Beam B / 8 - 9 = Total dead load x 1.4 = 10.17kN/m x 1.4 = 14.238kN/m
4.800 kN/m
Ultimate live load on Beam B / 7-8 = Total live load x 1.6 = 3.000kN/m x 1.6 = 4.800kN/m
29.118 kN/m
Total ultimate load on Beam B / 7- 8 = Total dead load + total live load = (24.318 + 4.800)kN/m = 29.118kN/m 14.238kN/m
Total ultimate load on Beam B / 8 - 9 = Total dead load + total live load = (14.238 + 0.000)kN/m = 14.238kN
Page 129
Beam Analysis - UDL & Point load
Structural Analysis
Beam B / 7-9
7
8
REACTION FORCE
9
6000
Pointed load on Beam B/ 7-8
4250
1750
29.118 kN/m
14.238 kN/m
4250
1750
= 29.118kN/m x 4.25 = 123.752kN Pointed load on Beam B / 8-9 = 14.238kN/m x 1.750 = 24.917kN
61.337 kN/m
Let R7 be the reference point
ΣM = M7 + (-M9) = 0
2125
2125
875
875
M 9 = M7 6m x R9 = [(123.715 x 2.125) +
123.752 kN/m
24.917kN/m
(61.337 x 4.25) + (24.917 x 5.125)]kN R9 = 108.554kN ≈ 108.55kN R7
ΣF = 0, ΣFUP = ΣFDOWN R7 + R9 = (123.715 + 61.337 + 24.917)kN R7 = 101.444kN ≈ 101.44kN
Page 130
R9
Beam Analysis - UDL & Point load
Structural Analysis
Beam B / 7-9
SHEAR FORCE DIAGRAM
SHEAR FORCE DIAGRAM
7
Using Triangular Ratio Proportion:
8
9
6000 4250
101.444kN
1750
x
22.31
=
123.752 x
=
0.766
101.444kN - 123.752kN = -22.308kN
(+)
4.250
(-)
0 kN
-22.308kN - 61.337kN = -83.646kN -83.646kN - 24.917kN = -108.554kN
BENDING MOMENT DIAGRAM Positive area
22.31
= (1/2 x 101.444 x 3.484) kN/m = 176.715kN/m
123.572
≈ 176.72kN/m Negative area x
= (1/2 x 0.766x 22.31)kN/m + [1/2 x (108.554+83.64) x 1.75]kN/m
4.25
= 176.714kN/m BENDING MOMENT DIAGRAM
≈ 176.71kN/m
8
7
Difference = 0.01 ≈0
9
6000 4250
∴ Positive area = Negative area Beam 7 / A-C is in equilibrium and structurally stable
1750
176.715 kN
0 kN
Page 131
0 kN
Column Analysis
Location of Column
Structural Analysis
: 1. Column F / 11 2. Column G / 9
2
1
Page 132
Column Analysis - Perimeter Column
Structural Analysis
Column F / 11 Roof Level
Structure Roof Self Weight
Roof Beam
Live Load
Dead Load 4.5m x (5.25 + 3.0)m x 1.0kN/m2
4.5m x (5.25 + 3.0)m x 0.5kN/m2
= 4.5m x 8.25m x 1.0kN/m2
= 4.5m x 8.25m x 0.5kN/m2
= 37.125kN
= 18.563kN
(6.0 + 5.25 + 1.5)m x 1.62kN/m
-
= 20.655kN Total Load
37.125kN + 20.655kN
18.563kN
= 57.780kN Ultimate Load
57.780kN x 1.4
18.563kN x 1.6
= 80.892kN Total Ultimate Load
= 29.701kN
80.892kN + 29.701kN = 110.593kN ≈ 110.59kN
Page 133
Column Analysis - Perimeter Column
Structural Analysis
Column F / 11 First Floor Level
Structure Slab
Roof Self Weight
Brick Wall
Live Load
Dead Load (3.0 x 3.0)m2 x 3.6kN/m2
(3.0 x 3.0)m2 x 1.5kN/m2
= 9.0m2 x 3.6kN/m2
= 9.0m2 x 1.5kN/m2
= 32.400kN
= 13.500kN
[9.0 + (8.25 x 1.5)]m2 x 1.0kN/m2
[9.0 + (8.25 x 1.5)]m2 x 0.5kN/m2
= 21.375m2 x 1.0kN/m2
= 21.375m2 x 0.5kN/m2
= 21.375kN
= 10.688kN
(3.0 + 3.0)m x 8.55kN/m
-
= 51.300kN Beam
(2.0 + 6.0 + 5.25)m x 1.62kN/m
-
= 21.465kN Column Self Weight
4.192kN
-
Total Load
(32.4 + 21.375 + 51.3 +
24.188kN
21.465 + 4.192)kN = 130.732kN Ultimate Load
130.732kN x 1.4
24.188kN x 1.6
= 183.025kN Total Ultimate Load
= 38.700kN
183.025kN + 38.700kN = 221.726kN ≈ 221.73kN
Page 134
Column Analysis - Perimeter Column
Structural Analysis
Column F / 11 Ground Floor Level
Structure Slab
Brick Wall
Dead Load
Live Load
3.0m x (3.0 + 2.0)m x 3.6kN/m2
3.0m x (3.0 + 2.0)m x 1.5kN/m2
= 3.0m x 5.0m x 3.6kN/m2
= 3.0m x 5.0m x 1.5kN/m2
= 54.000kN
= 22.500kN
(3.0 + 3.0 + 2.0)m x 8.55kN/m
-
= 68.400kN Beam
(3.0 + 3.0 + 2.0)m x 1.62kN/m
-
= 12.960kN Column Self Weight
4.192kN
-
Total Load
54kN + 68.4kN + 12.96kN +
22.500kN
4.192kN = 139.552kN Ultimate Load
139.552kN x 1.4
22.5kN x 1.6
= 195.373kN Total Ultimate Load
= 36.000kN
195.373kN + 36kN = 231.373kN ≈ 231.37kN
∴ Total load on Column F11 = 110.593kN + 221.726kN + 231.373kN = 563.692kN ≈ 563.69kN Page 135
Column Analysis - Internal Column
Structural Analysis
Column G / 9 Roof Level
Structure Roof Self Weight
Roof Beam
Live Load
Dead Load (6.0 x 3.0 x 1.0)m + (3.0 x 4.5x
[(3.0 x 6.0)m + (3.0 x 4.5)m] x
1.0)m
0.5kN/m2
= 18.0m + 13.5kN/m2
= 31.5 x 0.5kN/m2
= 31.500kN/m
= 15.75kN
[(3.0 x 2.0)m + (3.0 x 2.0)m] x
-
1.62kN/m = 19.440kN Total Load
31.500kN + 19.44kN
15.75kN
= 50.940kN Ultimate Load
50.940kN x 1.4
15.75kN x 1.6
= 71.316kN Total Ultimate Load
= 25.200kN
71.316kN + 25.200kN = 96.516kN ≈ 96.52kN
Page 136
Column Analysis - Internal Column
Structural Analysis
Column G / 9 First Floor Level
Structure Slab
Live Load
Dead Load
(4.5 + 18.0 + 9.0)m x 1.5kN/m2
[(1.5 x 3.0)m + (3.0 x 6.0)m + (3.0 x 3.0)m] x 3.6kN/m2 = (4.5 + 18 +9)m x 3.6kN/m2
= 31.5m x 1.5kN/m2 = 47.250kN
= 113.400kN Brick Wall
(3.0 + 3.0)m x 8.55kN/m
-
= 51.300kN Beam
[(3.0 x 2)m + (3.0 x 2)m + 3.0] x
-
1.62kN/m = 24.300kN Column Self Weight
4.192kN
-
Total Load
113.4kN + 51.3kN + 24.300kN +
47.250kN
4.192kN = 193.192kN Ultimate Load
193.192kN x 1.4
47.250kN x 1.6
= 270.469kN Total Ultimate Load
= 75.600kN
270.469kN + 75.600kN = 346.069kN ≈ 346.07N
Page 137
Column Analysis - Internal Column
Structural Analysis
Column G / 9 Ground Floor Level
Structure Slab
Brick Wall
Dead Load
Live Load
6.0m x 6.0m x 3.6kN/m2
6.0m x 6.0m x 1.5kN/m2
= 36.0m x 3.6kN/m2
= 36.0m x 1.5kN/m2
= 129.600kN
= 54.000kN
(3.0 x 2)m x 8.55kN/m
-
= 51.300kN Beam
(6.0m + 6.0m) x 1.62kN/m
-
= 19.440kN Column Self Weight
4.192kN
-
Total Load
129.6kN + 51.3kN + 19.44kN
54.000kN
4.192kN = 204.532kN Ultimate Load
204.532kN x 1.4
54.000kN x 1.6
= 286.345kN Total Ultimate Load
= 86.400kN
286.345kN + 86.400kN = 372.745kN ≈ 372.75kN
∴ Total load on Column L / 9 = 96.516kN + 346.096kN + 372.745kN = 815.357kN ≈ Page 138
815.36kN