This document provides the analysis and design of a roof truss system subjected to wind loads. It includes: 1) Calculation of wind loads on the truss members based on their location as windward or leeward. 2) Equilibrium equations to solve for member forces based on the applied wind loads and joint reactions. 3) The member forces are calculated as tension (T) or compression (C) values. 4) A diagram of the truss with member forces labeled is presented.

1. CEE-312
Structural Analysis and Design
Sessional-I
(1.0 credit)
Lecture: 4
Bijit Kumar Banik
Assistant Professor, CEE, SUST
Room No.: 115 (“C” building)
bijit_sustbd@yahoo.com
Department of Civil and Environmental Engineering

2. Analysis and design of an Industrial roof truss system
(4.41) (4.41) (3.53) (3.53) (4.41) (4.41)
(- 5.05)
(- 4.04)
(- 3.03) (- 3.03)
(- 4.04)
(- 5.05)
6@6 ft = 36 ft
L0
L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
2.94 k2.94 k
(.18)
(0.67)
(0.67)
(.18)
(2.14)
(-1.32)
(- 1.01)
(-1.32)
(- 1.01)

3. Analysis and design of an Industrial roof truss system
P = (0.07*29.05-2.1)*25.6 = -1.7 psf
For windward surface
For leeward surface
P = -0.7*25.6 = -17.92 psf
We already calculated in lecture-2
Once again what –ve sign means? Suction/Uplift
Wind load calculations

4. Wind Load Analysis
6@6 ft = 36 ft
10 ft
L0
L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
R1
R2
H
3@6.86 ft
Wind blows from left to right
Windward side joint loads (U1 & U2)= 1.7*20*6.86 = 0.23k
End joint loads [ L0 & (U3)left ] = 0.23/2 = 0.12k
Leeward side joint loads (U4 & U5)=17.92*20*6.86 = 2.46k
End joint loads [ L6 & (U3)right ] = 2.46/2 = 1.23k
0.23k
0.23k
0.12k
0.12k
2.46k
2.46k
1.23k
1.23k

5. 6@6 ft = 36 ft
10 ft
L0 L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
R1
R2
H
3@6.86 ft
–0.23*6.86 –0.23*2*6.86 –0.12*3*6.86 –1.23*(9/10.3)*18 +1.23*(5/10.3)*10
–2.46*(9/10.3)*24 +2.46*(5/10.3)*2*(10/3) – 2.46*(9/10.3)*30
+2.46*(5/10.3)*(10/3) – 1.23*(9/10.3)*36 + R1*36 = 0
0.23k
0.23k
0.12k
0.12k
2.46k
2.46k
1.23k
1.23k
∑ML0= 0 +ve
5
9
10.3
9
5
10.3
R1 = 4.54k
= 4.54k
Wind Load Analysis

6. 6@6 ft = 36 ft
10 ft
L0 L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
R1
R2
H
3@6.86 ft
R2 = (9/10.3)*(2*0.12+2*0.23+2*1.23+2*2.46) – 4.54
0.23k
0.23k
0.12k
0.12k
2.46k
2.46k
1.23k
1.23k
∑V= 0
5
9
10.3
9
5
10.3
R2 = 2.60k
H = (5/10.3)*(2*1.23+2*2.46) – (5/10.3)*(2*0.12+2*0.23)
∑H= 0
H = 3.24k
= 3.24k
= 2.60k
= 4.54k
Wind Load Analysis

7. 6@6 ft = 36 ft
10 ft
L0 L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
R1
R2
H
3@6.86 ft
0.23k
0.23k
0.12k
0.12k
2.46k
2.46k
1.23k
1.23k
5
9
10.3
9
5
10.3
= 3.24k
= 4.54k
= 2.60k
1
1
∑V = 0
(5/10.3)*L0U1+(9/10.3)*0.12 – 2.6 = 0
L0U1= 5.14 k (T) 5
9
10.3
∑H = 0
L0L1 +(9/10.3)*5.14 – (5/10.3)*0.12 – 3.24 =0
L0L1= 1.19 k (C)
2.60 k
0.12k
L0L1
L0U1
1-1
3.24 k
9
5
10.3
Wind Load Analysis

8. ∑V= 0
L1U1 = 0
L1L2 = L0L1 = 1.19k (C)
∑H= 0
6@6 ft = 36 ft
10 ft
L0 L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
R1
R2
H
3@6.86 ft
0.23k
0.23k
0.12k
0.12k
2.46k
2.46k
1.23k
1.23k
5
9
10.3
9
5
10.3
= 3.24k
= 4.54k
= 2.60k
2 2
L1L2
2-2
L0L1=1.19k
L1U1
Wind Load Analysis

9. 6@6 ft = 36 ft
10 ft
L0 L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
R1
R2
H
3@6.86 ft
0.23k
0.23k
0.12k
0.12k
2.46k
2.46k
1.23k
1.23k
5
9
10.3
9
5
10.3
= 3.24k
= 4.54k
= 2.60k
3
3
9
510.3
9
5
10.3
9
5
10.3
∑ML0 = 0
– 0.23*6.86 + (5/10.3)*U1L2*6 + (9/10.3)*U1L2*(10/3)= 0
U1L2= 0.27 k (T)
∑V = 0
(9/10.3)*0.12+(9/10.3)*0.23 + (5/10.3)*U1U2
– (5/10.3)*0.27 – 2.60= 0
U1U2= 5.0 k (T)
+ve 3-3
U1
L0 L1 L2
U2
0.23 k
0.12 k
2.60 k
(10/3)’
1.19k3.24k
Wind Load Analysis

10. 6@6 ft = 36 ft
10 ft
L0 L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
R1
R2
H
3@6.86 ft
0.23k
0.23k
0.12k
0.12k
2.46k
2.46k
1.23k
1.23k
5
9
10.3
9
5
10.3
= 3.24k
= 4.54k
= 2.60k
4 4
∑H = 0
L2L3= 0.95 k (C)
5
9
10.3
L2L3
4-4
1.19k
L2U2
0.27k
∑V = 0
L2U2 = (5/10.3)*0.27
L2U2= 0.13 k (C)
L2L3 +1.19 – (9/10.3)*0.27 = 0
Wind Load Analysis

11. 6@6 ft = 36 ft
10 ft
L0 L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
R1
R2
H
3@6.86 ft
0.23k
0.23k
0.12k
0.12k
2.46k
2.46k
1.23k
1.23k
5
9
10.3
9
5
10.3
= 3.24k
= 4.54k
= 2.60k
5
5
10
9
13.45
5
9
10.3
∑ML0 = 0
(9/13.45)*U2L3*(20/3)+ (10/13.45)*U2L3*12
– 0.23*6.86 – 0.23*2*6.86 = 0
U2L3= 0.35 k (T)
∑V = 0
(5/10.3)*U2U3+ (9/10.3)*(0.12+0.23+0.23)
– (10/13.45)*0.35 – 2.60 = 0
U2U3= 4.85 k (T)
+ve
9
5
10.3
5-5
L0 L1 L2 L3
U1
U2
U3
0.12 k
2.60 k
0.23 k
0.95 k
2*(10/3)
0.23 k
3.24 k
Wind Load Analysis

12. (5/10.3)*U5L6+(9/10.3)*1.23 – 4.54 = 0
∑V= 0
U5L6 = 7.14k (T)
∑H= 0
L5L6 = 5.64k (C)
6@6 ft = 36 ft
10 ft
L0 L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
R1
R2
H
3@6.86 ft
0.23k
0.23k
0.12k
0.12k
2.46k
2.46k
1.23k
1.23k
5
9
10.3
9
5
10.3
= 3.24k
= 4.54k
= 2.60k
6
6
5
9
10.3
5
9
10.3
4.54 k
U5L6 1.23k
6-6
L5L6(5/10.3)*1.23 – (9/10.3)*7.14 – L5L6= 0
Wind Load Analysis

13. 6@6 ft = 36 ft
10 ft
L0 L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
R1
R2
H
3@6.86 ft
0.23k
0.23k
0.12k
0.12k
2.46k
2.46k
1.23k
1.23k
5
9
10.3
9
5
10.3
= 3.24k
= 4.54k
= 2.60k
7 7
∑H = 0
5.64k
7 – 7
L4L5
L5U5
∑V = 0
L5U5= 0
L4L5 = 1.19k (C)
Wind Load Analysis

14. 6@6 ft = 36 ft
10 ft
L0 L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
R1
R2
H
3@6.86 ft
0.23k
0.23k
0.12k
0.12k
2.46k
2.46k
1.23k
1.23k
5
9
10.3
9
5
10.3
= 3.24k
= 4.54k
= 2.60k
8
8
5
9
10.3
9
510.3
9
5
10.3
L6
U5
L5L4
U4
2.46k
1.23k
4.54k
8-8
∑ML6 = 0
2.46*6.86 – (5/10.3)*U5L4*6
– (9/10.3)*U5L4*(10/3)= 0
U5L4= 2.90 k (T)
∑V = 0
(9/10.3)*2.46+(9/10.3)*1.23 + (5/10.3)*U4U5
– (5/10.3)*2.90 – 4.54= 0
U4U5= 5.61 k (T)
+ve
Wind Load Analysis

15. 6@6 ft = 36 ft
10 ft
L0 L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
R1
R2
H
3@6.86 ft
0.23k
0.23k
0.12k
0.12k
2.46k
2.46k
1.23k
1.23k
5
9
10.3
9
5
10.3
= 3.24k
= 4.54k
= 2.60k
9 9
∑H = 0
L3L4= 3.11 k (C)
∑V = 0
L4U4 = (5/10.3)*2.90
L4U4= 1.41 k (C)
L3L4+ (9/10.3)*2.90 – 5.64 = 0
9
510.3
5.64k
9-9
L4U4
2.90k
L3U4
Wind Load Analysis

16. 6@6 ft = 36 ft
10 ft
L0 L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
R1
R2
H
3@6.86 ft
0.23k
0.23k
0.12k
0.12k
2.46k
2.46k
1.23k
1.23k
5
9
10.3
9
5
10.3
= 3.24k
= 4.54k
= 2.60k
10
10
9
5
10.3
9
10
13.45
9
5
10.3
2.46k
2.46k
1.23k
4.54k
L6L5L4L3
U3
U5
U4
3.11k
10 -10∑ML6 = 0
–(9/13.45)*U4L3*(20/3) – (10/13.45)*U4L3*12
+ 2.46*6.86 +2.46*2*6.86 = 0
U4L3= 3.78 k (T)
∑V = 0
(5/10.3)*U3U4 + (9/10.3)*(1.23+2*2.46)
– (10/13.45)*3.78 – 4.54 = 0
U3U4= 4.07 k (T)
+ve
Wind Load Analysis

17. 6@6 ft = 36 ft
10 ft
L0 L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
R1
R2
H
3@6.86 ft
0.23k
0.23k
0.12k
0.12k
2.46k
2.46k
1.23k
1.23k
5
9
10.3
9
5
10.3
= 3.24k
= 4.54k
= 2.60k
11 11
∑V = 0
9
10
13.45
9
10
13.45
3.11k
11 – 11
0.95k
L3U3
L3
0.35k 3.78k(10/13.45)*3.78 + (10/13.45)*0.35 – L3U3= 0
L3U3= 3.07 k (C)
Wind Load Analysis

18. (- 1.19) (-1.19) (-0.95) (-3.11) (-5.64) (-5.64)
(5.14)
(5.00)
(4.85) (4.07)
(5.61)
(7.14)
6@6 ft = 36 ft
L0
L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
4.54 k2.60 k
(0)
(-0.13)
(-1.41)
(0)
(-3.07)
(0.35)
(0.27)
(3.78)
(2.90)
3.24k
L R
Wind Load Analysis