# Structural Analysis Questions and Answers – Moment-Area Theorems – 2

This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Moment-Area Theorems – 2”.

Point A is pin joint and B is roller. A load of 40KN is applied at point C.
Length of AC is 2m and d same goes for beam CB.

1. What is the shape for SFD of this diagram?
a) Linear
b) Parabolic
c) Linear with discontinuity
d) Arbitrary curve

2. What is the shape of BMD for this diagram?
a) Rectangular
b) Triangular
c) Parabolic
d) Arbitrary curve

Explanation: It will increase till point C and then will start decreasing and in both cases linearly.

3. Where is the peak point of SFD?
a) A
b) C
c) B
d) between A and C

Explanation: Value of shear force at point A is +20KN which is the maximum for this case.

4. What is the peak value of BMD of this figure (all options are in KN-m)?
a) 10/EI
b) 20/EI
c) 30/EI
d) 40/EI

Explanation: At point A BM will be 0 and hen will start increasing till point C where its value will be 40/EI i.e. the area between SFD till that point.
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5. What should be the area that should be considered if we want to find slope at point B wrt initial beam?
a) from A to C
b) from A to B
c) from C to B

Explanation: If we thee deflected diagram of this figure, we will find that slope at point C will be zero as from that point, BM starts decreasing. So we should consider area between point C and B for slope wrt initial beam.

6. What is the value of slope at point B wrt initial beam?
a) 10/EI
b) 20/EI
c) 30/EI
d) 40/EI

Explanation: Just calculate the area between point C and point B.

7. To calculate maximum deformation in the deflected beam, which part of the area should be considered?
a) from A to B
b) from A to C
c) from B to C
d) can’t say

Explanation: Maximum deformation happens at point C and slope of C is zero i.e. tangent is parallel to initial beam. This property of point C can be used to calculate maximum deformation.

8. To calculate maximum deformation in deflected beam, about which point should we take moment of the required part of area?
a) A
b) B
c) C
d) can’t say

Explanation: Tangent at point A is at point A as there is no vertical deflection there and tangent of point C is parallel to initial beam. So, the length at which it will cut point A vertically will be the maximum deformation.

9. What is the value of maximum deformation in this case?
a) 80/3EI
b) 120/3EI
c) 180/3EI
d) 40/3EI

Explanation: Just take area between point A and C and calculate moment about point A.

10. To calculate relative deflections of tangents at point A and B at point B, about which point should we moment of the required part of area?
a) A
b) B
c) C
d) can’t say

Explanation: This is the basic second theorem of moment-area theorem.

11. To calculate relative deflections of tangents at point A and B at point B, which part of area should be considered?
a) A to B
b) A to C
c) C to B
d) can’t say

Explanation: This is the basic first theorem of the moment-area theorem.

12. What will be the value of relative deflections of tangents at point A and B at point B?
a) 20/3EI
b) 40/3EI
c) 80/3EI
d) 160/3EI

Explanation: On doing the steps suggested in Q11 and Q10, we will get this result.

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