Problem 1Determine the vertical displacement at joint H of the truss below using the method of virtual work. Each steelmember has a cross-sectional area of 4.5 in², and E = 29(10³) ksi. Hint: For more efficient computation of internalaxial forces, consider the concept of zero-force members and use the symmetry of the structure and the givenloading.AJ—12 ftB6 k12 ftHC8 k12 ftGD6 k- 12 ftFT9 ftE Table for:MMRectangleMTriangleMLTriangleMLTrapezoidLTriangle-α** ·b·LParabolaslope-0Lslope-0Parabolaslope = 0LParabolaSMQdxLParabolaLMMM₁MMslope - 0www.QRectangleLLMQLMQ2LMQLMQ(M,+M)The values in the table represent the integration of theproduct of the two shapes with a common length L.TriangleTriangleTrapezoid Q2LMQ2LMQ3LMQLMQLLMQ2LMQLMQ6MQ (L + a)6LO (M,+2M)SLMQ12LMQQQIMQ4LMQ12LLMQNELMQ6LMQ3(2M, + M)LMQSLMQ12Ι.ΜΟLMQLLM(Q+Q)IM(Q+20)LM (2Q+Q)[Q(+b)+Q₂(l+a)]Q(2M,+ M)1, +2M)]+Q₂ (M₂+IM (3Q+5Q)12[MsQ+3Q)IM(Q+30)(3Q+Q)

Given: Area of the member, A = 4.5 in2 Modulus of elasticity, E = 29000 ksi To find: Vertical…

Problem 1 Determine the vertical displacement at joint H of the truss below using the method of virtual work. Each steel member has a cross-sectional area of 4.5 in², and E = 29(10³) ksi. Hint: For more efficient computation of internal axial forces, consider the concept of zero-force members and use the symmetry of the structure and the given loading. 12 ft- B 6 k -12 ft- H 8 k 12 ft- G D 6 k 12 ft- 9 ft

Problem 1 Determine the vertical displacement at joint H of the truss below using the method of virtual work. Each steel member has a cross-sectional area of 4.5 in², and E = 29(10³) ksi. Hint: For more efficient computation of internal axial forces, consider the concept of zero-force members and use the symmetry of the structure and the given loading. 12 ft- B 6 k -12 ft- H 8 k 12 ft- G D 6 k 12 ft- 9 ft

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

Problem 1
Determine the vertical displacement at joint H of the truss below using the method of virtual work. Each steel
member has a cross-sectional area of 4.5 in², and E = 29(10³) ksi. Hint: For more efficient computation of internal
axial forces, consider the concept of zero-force members and use the symmetry of the structure and the given
loading.
A
J
—12 ft
B
6 k
12 ft
H
C
8 k
12 ft
G
D
6 k
- 12 ft
F
T
9 ft
E

Table for:
M
M
Rectangle
M
Triangle
M
L
Triangle
M
L
Trapezoid
L
Triangle
-α** ·b·
L
Parabola
slope-0
L
slope-0
Parabola
slope = 0
L
Parabola
SMQdx
L
Parabola
L
M
M
M₁
M
M
slope - 0
www.
Q
Rectangle
L
LMQ
LMQ
2
LMQ
LMQ
(M,+M)
The values in the table represent the integration of the
product of the two shapes with a common length L.
Triangle
Triangle
Trapezoid Q
2LMQ
2LMQ
3
LMQ
LMQ
L
LMQ
2
LMQ
LMQ
6
MQ (L + a)
6
LO (M,+2M)
SLMQ
12
LMQ
QQ
IMQ
4
LMQ
12
L
LMQ
NE
LMQ
6
LMQ
3
(2M, + M)
LMQ
SLMQ
12
Ι.ΜΟ
LMQ
L
LM(Q+Q)
IM(Q+20)
LM (2Q+Q)
[Q(+b)
+Q₂(l+a)]
Q(2M,+ M)
1, +2M)]
+Q₂ (M₂+
IM (3Q+5Q)
12
[MsQ+3Q)
IM(Q+30)
(3Q+Q)

Expert Solution

Step 1

Given:

Area of the member, A = 4.5 in²

Modulus of elasticity, E = 29000 ksi

To find:

Vertical displacement at H

Step by step

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