Assemble the total stiffness matrix S, the force vectors P, PFEF and the displacement vector Dfor the whole structure needed to analyze the beam shown below.Use the shown numbering system and El=constant.1k₁25 kN/m=1200600-200 600600k22 -600 1200-200-600 200 -600600 1200 -600 2400Answer the following questions(16-22):6 m17. The Value of EI= .... in (kN.m²) is:a) 200b) 600(2)26 m{P} =[S]{D} + PFEFd) 3600c) 240018. For member 1, the value of K₂2 =.... in (kN.m²) is:a) -200b) -600c) 240019. For member 2, the value of k23 = .... in (kN.m²) is:a) -200b) -600c) 240020. For the whole structure, the value of S11in (kN.m²) is:b) 3600c) 2400a) 20021. The rotational displacements (0₂) of node (joint) 2 = .... in (radians) is:c) -0.03245a) 0.0b) 0.01562522. The value of the moment at node 3 (M32) on the bending moment diagram =a) 0.0b) +18.75c) -93.7523. The value of the total vertical reaction at node 2 (R₂) = .... in (kN) is:a) 85.5b) 175c) 93.75d) 3600d) 3600d) 4800d) 75.03d) 0.04532in (kN.m) is:d) -20.50

Local stiffness matrix for member-1 is given as

Assemble the total stiffness matrix S, the force vectors P, PFEF and the displacement vector D for the whole structure needed to analyze the beam shown below. Use the shown numbering system and EI=constant. 25 kN/m 1 6 m 2 6 m (3)

Assemble the total stiffness matrix S, the force vectors P, PFEF and the displacement vector D for the whole structure needed to analyze the beam shown below. Use the shown numbering system and EI=constant. 25 kN/m 1 6 m 2 6 m (3)

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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Question

Assemble the total stiffness matrix S, the force vectors P, PFEF and the displacement vector D
for the whole structure needed to analyze the beam shown below.
Use the shown numbering system and El=constant.
1
k₁
25 kN/m
=
1
200
600
-200 600
600
k22 -600 1200
-200
-600 200 -600
600 1200 -600 2400
Answer the following questions(16-22):
6 m
17. The Value of EI= .... in (kN.m²) is:
a) 200
b) 600
(2)
2
6 m
{P} =[S]{D} + PFEF
d) 3600
c) 2400
18. For member 1, the value of K₂2 =.... in (kN.m²) is:
a) -200
b) -600
c) 2400
19. For member 2, the value of k23 = .... in (kN.m²) is:
a) -200
b) -600
c) 2400
20. For the whole structure, the value of S11
in (kN.m²) is:
b) 3600
c) 2400
a) 200
21. The rotational displacements (0₂) of node (joint) 2 = .... in (radians) is:
c) -0.03245
a) 0.0
b) 0.015625
22. The value of the moment at node 3 (M32) on the bending moment diagram =
a) 0.0
b) +18.75
c) -93.75
23. The value of the total vertical reaction at node 2 (R₂) = .... in (kN) is:
a) 85.5
b) 175
c) 93.75
d) 3600
d) 3600
d) 4800
d) 75.0
3
d) 0.04532
in (kN.m) is:
d) -20.50

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Step 1: Introducing the problem statement

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Step 2: To determine flexural rigidity (EI) for beam-1

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Step 3: Determining k22 and k23

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Step 4: Assembling global stiffness matrix

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Step 5: Applying the boundary conditions

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Step 6: Determining the load vector

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Step 7: Applying the stiffness definition for determining joint displacement

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Step 8: Determining member end actions

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Solution

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