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

View Answer

Explanation: Since loads are not uniform, SFD will be linear and loading at point C will lead to discontinuity.

2. What is the shape of BMD for this diagram?

a) Rectangular

b) Triangular

c) Parabolic

d) Arbitrary curve

View Answer

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

View Answer

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

View Answer

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.

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

d) depends upon the loading condition

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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

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