CHAPTER 2 Question 1 Beam 1 50 kN 50 kN 50 kN 50 kN Beam 2
CHAPTER 2
Question 1 50 kN
Beam 1
20 kNm-1
21.25 kNm
37.5 kNm
48.75 kNm
3m
Beam 1: (a) bending moment and (b) shear force diagrams
(a)
32.5 A
B -17.5 -47.5 kN
(b)
50 kN
50 kN
50 kN
50 kN
Beam 2
25 kNm
50 kNm
3m
(a)
Beam 2: (a) bending moment and (b) shear force diagrams
50 kN A
B
(b)
-50 kN
30 kN
30 kN
10 kNm-1
Beam 3
-106.25 kNm
-56.25 kNm
2.5 m
-16.25 kNm
5m
A (a)
B 55 kN 30 kN
A
Beam 3: (a) bending moment and (b) shear force diagrams
B -30 kN -55 kN (b)
100 kN -1
100 kN -1
20 kNm
20 kNm
Beam 4 x
B
A
2m
4m
2m -200 kNm
-40 kNm Beam 4: (a) bending moment and (b) shear force diagrams
(a) 100 kN 20 kN
B
-40 kN -80 kN (b)
-120 kN
Question 2 Dead, gk = 20 kNm-1 Imposed load, qk = 10 kNm-1 A ℓ1 = 6 m
ℓ2 = 2 m
Load Case 1
ωmax =1.4gk + 1.6qk x 88 kNm A
C B 156.4 kNm (x = 2.666 m) (a) Load case 1: (a) bending moment and (b) shear force diagrams
Vx=0 =117.3 kN Vx=6 = 88 kN
A
(b)
Vx=6 = –146.7 kN
Load Case 2 ωmin = 1.0gk 1.4gk + 1.6qk
RA
RB 40 kNm C
A
B 178.4 kNm (x = 2.848m)
Load case 2: (a) bending moment and (b) shear force diagrams
(a)
125.3 kN
40 kN
A (b)
-138.7 kN
Load Case 3 1.0gk
1.4gk + 1.6qk
88 kNm B
C (a)
51.3 kNm (x = 2.26665m )
45.3 kN
(b)
B
Load case 3: (a) bending moment and (b) shear force diagrams
88 kN
-74.7 kN
By inspection, design sagging moment = 178.4 kNm (Load Case 2) design hogging moment = 88.0 kNm (Load Cases 1 & 3) design shear force at A = 125.3 kN (Load Case 2) design shear force at B (towards A) = 146.7 kN (Load Case 1) design shear force at B (towards C) = 88 kN (Load Cases 1 & 3)
Question 3 B = 170 mm
D = 360 mm
x
T = 12 mm
x t = 7 mm
(a)
Cross-sectional area, A = 6432 mm2 Moment of inertia about major axis, Ixx = 14 570 ´ 106 mm4 Elastic section modulus about major axis, Zxx = 808 459 mm3 Plastic section modulus about major axis, Sxx = 907 488 mm3 Radius of gyration about major axis, rx = 150.5 mm
(b)
Working load, ωwl = 49.4 kNm-1 Collapse load, ωcl = 55.5 kNm-1
Question 5
Gk, Qk
Wk
1.2
m Load Case 1 Gk = 200 kN, Qk = 100 kN Wk = 50 kN
5m
Leg L 2m
Leg R
Load Case 1 - Maximum tensile force (in leg L) = 96 kN Maximum compression force (in leg R) = 348 kN Load Case 2 - Maximum tensile force (in leg L) = 194 kN Maximum compressive force (in leg R) = 434 kN
Load Case 2 Gk = 200 kN, Qk = 100 kN Wk = 75 kN
Question 1 50 kN
Beam 1
20 kNm-1
21.25 kNm
37.5 kNm
48.75 kNm
3m
Beam 1: (a) bending moment and (b) shear force diagrams
(a)
32.5 A
B -17.5 -47.5 kN
(b)
50 kN
50 kN
50 kN
50 kN
Beam 2
25 kNm
50 kNm
3m
(a)
Beam 2: (a) bending moment and (b) shear force diagrams
50 kN A
B
(b)
-50 kN
30 kN
30 kN
10 kNm-1
Beam 3
-106.25 kNm
-56.25 kNm
2.5 m
-16.25 kNm
5m
A (a)
B 55 kN 30 kN
A
Beam 3: (a) bending moment and (b) shear force diagrams
B -30 kN -55 kN (b)
100 kN -1
100 kN -1
20 kNm
20 kNm
Beam 4 x
B
A
2m
4m
2m -200 kNm
-40 kNm Beam 4: (a) bending moment and (b) shear force diagrams
(a) 100 kN 20 kN
B
-40 kN -80 kN (b)
-120 kN
Question 2 Dead, gk = 20 kNm-1 Imposed load, qk = 10 kNm-1 A ℓ1 = 6 m
ℓ2 = 2 m
Load Case 1
ωmax =1.4gk + 1.6qk x 88 kNm A
C B 156.4 kNm (x = 2.666 m) (a) Load case 1: (a) bending moment and (b) shear force diagrams
Vx=0 =117.3 kN Vx=6 = 88 kN
A
(b)
Vx=6 = –146.7 kN
Load Case 2 ωmin = 1.0gk 1.4gk + 1.6qk
RA
RB 40 kNm C
A
B 178.4 kNm (x = 2.848m)
Load case 2: (a) bending moment and (b) shear force diagrams
(a)
125.3 kN
40 kN
A (b)
-138.7 kN
Load Case 3 1.0gk
1.4gk + 1.6qk
88 kNm B
C (a)
51.3 kNm (x = 2.26665m )
45.3 kN
(b)
B
Load case 3: (a) bending moment and (b) shear force diagrams
88 kN
-74.7 kN
By inspection, design sagging moment = 178.4 kNm (Load Case 2) design hogging moment = 88.0 kNm (Load Cases 1 & 3) design shear force at A = 125.3 kN (Load Case 2) design shear force at B (towards A) = 146.7 kN (Load Case 1) design shear force at B (towards C) = 88 kN (Load Cases 1 & 3)
Question 3 B = 170 mm
D = 360 mm
x
T = 12 mm
x t = 7 mm
(a)
Cross-sectional area, A = 6432 mm2 Moment of inertia about major axis, Ixx = 14 570 ´ 106 mm4 Elastic section modulus about major axis, Zxx = 808 459 mm3 Plastic section modulus about major axis, Sxx = 907 488 mm3 Radius of gyration about major axis, rx = 150.5 mm
(b)
Working load, ωwl = 49.4 kNm-1 Collapse load, ωcl = 55.5 kNm-1
Question 5
Gk, Qk
Wk
1.2
m Load Case 1 Gk = 200 kN, Qk = 100 kN Wk = 50 kN
5m
Leg L 2m
Leg R
Load Case 1 - Maximum tensile force (in leg L) = 96 kN Maximum compression force (in leg R) = 348 kN Load Case 2 - Maximum tensile force (in leg L) = 194 kN Maximum compressive force (in leg R) = 434 kN
Load Case 2 Gk = 200 kN, Qk = 100 kN Wk = 75 kN
