This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on “The Double-Integration Method”.

1. Which of the following is correct boundary condition for a beam supported by pin at both ends?

a) Displacement at both ends is non-zero

b) Displacement at one of the end is non-zero

c) Displacement at both ends is zero

d) Can’t say

View Answer

Explanation: Since there will always be a vertical support reaction, displacement at both ends will be zero.

2. Which of the following is false for deflection of a point nearby a fixed support?

a) Displacement is zero

b) Slope is zero

c) Displacement and slope is zero

d) Displacement as well as slope is non-zero

View Answer

Explanation: Due to presence of vertical reaction and moment, there won’t be any displacement and slope will be zero.

3. The double integration method to calculate slope of deflected beam is applicable only when:-

a) Slope is very large

b) Slope is very small

c) Slope is -ve

d) Slope is +ve

View Answer

Explanation: During deriving the results, we have assumed that slope is zero once.

4. Which out of the following is true for x axis:-

a) It is parallel to undeflected beam

b) It is perpendicular to undeflected beam

c) It is at 450 to undeflected beam

d) Can’t say

View Answer

Explanation: During deriving, we have assumed x axis to be parallel to undeflected beam.

5. Where does origin lies?

a) At right of beam

b) At left of beam

c) At right of deflected beam

d) At centre of beam

View Answer

Explanation: Origin is assumed to be at left of beam and rightward is positive.

6. Positive value of slope is clockwise.

State whether the above statement is true or false.

a) True

b) False

View Answer

Explanation: Positive value of slope is counter clockwise.

Following is a cantilever beam and its length is Z.

A moment M is applied at the end B.

E and I are given.

7. What is the degree of static indeterminacy of this question?

a) 3

b) 2

c) 1

d) 0

View Answer

Explanation: This has 3 unknown reactions and three equations which make it statically determinate.

8. What will be value of double differentiation of deflection in y direction wrt distance from point A at point A?

a) M/EI

b) –M/EI

c) 0

d) Can’t say

View Answer

Explanation: Since moment M is acting counterclockwise, moment at A will be clockwise and will be equal to M.

9. How many boundary conditions will be required to solve this question?

a) 0

b) 1

c) 2

d) 3

View Answer

Explanation: Since double differentiation of deflection in y direction wrt distance from point A is independent of distance from point A, there will be only two unknown constants which would require 2 equations/boundary conditions.

10. What will be the value of differentiation of deflection in y direction wrt distance from point A at point A?

a) EI

b) 1/EI

c) -EI

d) 0

View Answer

Explanation: Value will be zero as slope is zero due to fixed support.

11. Value of deflection in y direction at point B will be zero.

State whether the above statement is true or false.

a) True

b) False

View Answer

Explanation: We can’t predict deflection in y direction at point B as it is a free end.

12. What will be the value of first obtained constant?

a) 0

b) EI

c) -EI

d) 1/EI

View Answer

Explanation: By replacing value of double differentiation of deflection in y direction wrt distance from point A at point A will give this result.

13. What will be the value of second obtained constant?

a) 0

b) EI

c) -EI

d) 1/EI

View Answer

Explanation: By replacing value of differentiation of deflection in y direction wrt distance from point A at point A will give this result.

14. What is slope at point B?

a) MZ/EI

b) -MZ/EI

c) 2MZ/EI

d) 0

View Answer

Explanation: By solving after putting value of first constant will give this MZ/EI.

15. What is deflection in y direction at point B?

a) MZ^{2}/EI

b) – MZ^{2}/EI

c) 2 MZ^{2}/EI

d) 0

View Answer

Explanation: By solving after putting value of first and second constants will give this MZ

^{2}/EI.

**Sanfoundry Global Education & Learning Series – Structural Analysis.**

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