Structural Analysis Questions and Answers – Kinematic Indeterminacy of Trusses

This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Kinematic Indeterminacy of Trusses”.

1. The degree of freedom for a pin jointed plane frame is given by 3j – m – r.
a) True
b) False

Explanation: The degree of freedom for a pin jointed plane frame is given by 2j–r, where j is the number of joint and r is the number of reactions.

2. The degree of freedom for a pin jointed space frame is given by ____
a) 2j – r
b) 3j – r
c) 3j – m – r
d) 6j – r

Explanation: The degree of freedom for a pin jointed space frame is given by 3j – r, where j is the number of joints and r is the number of reactions.

3. In case of pin jointed plane frame, rotational displacement of the nodes are not considered.
a) True
b) False

Explanation: In case of pin jointed plane frame, rotational displacement of the nodes are not considered because member are not subjected to bending. Members are subjected to axial forces only.

4. Identify the correct statements of the followings.
a) Two degrees of freedom are available at each joint of pin jointed plane frame
b) Six degrees of freedom are available at each joint of pin jointed space frame
c) Four degrees of freedom are available at each joint of rigid jointed plane frame
d) Three degrees of freedom are available at each joint of pin jointed space frame

Explanation: Each joint of pin jointed plane frame, allows horizontal and vertical sway of the joint. Therefore, degree of freedom is two at a joint of pin jointed plane frame.

5. Calculate the kinematic indeterminacy of the following pin jointed plane frame.

a) 2
b) 6
c) 12
d) 18

Explanation: The truss is supported by hinged support at both ends. Hinged support in a pin jointed plane frame does not offers any degree of freedom as rotation is not considered. For the given truss, it consists of six pin joint offering two degree of freedom each. Therefore, the degree of freedom is 12.

6. Calculate the kinematic indeterminacy of the following pin jointed plane frame.

a) 12
b) 13
c) 14
d) 15

Explanation: The truss is supported by hinged support at one end and roller support at other end. Hinged support in a pin jointed plane frame does not offers any degree of freedom as rotation is not considered. But roller support offers horizontal movement and hence degree of freedom is 1. For the given truss, it consists of six pin joint offering two degree of freedom each. Therefore, the degree of freedom is 12 + 1 = 13.

7. Calculate the kinematic indeterminacy of the following pin jointed plane frame.

a) 8
b) 9
c) 10
d) 12

Explanation: The truss is supported by hinged support at one end and roller support at other end. Hinged support in a pin jointed plane frame does not offers any degree of freedom as rotation is not considered. But roller support offers horizontal movement and hence degree of freedom is 1. For the given truss, it consists of four pin joint offering two degree of freedom each. Therefore, the degree of freedom is 8 + 1 = 9.

8. Calculate the kinematic indeterminacy of the following pin jointed plane frame.

a) 8
b) 10
c) 12
d) 14

Explanation: The truss is supported by hinged support at both ends. Hinged support in a pin jointed plane frame does not offers any degree of freedom as rotation is not considered. For the given truss, it consists of four pin joint offering two degree of freedom each. Therefore, the degree of freedom is 8.

9. Calculate the kinematic indeterminacy of the following pin jointed plane frame.

a) 4
b) 5
c) 6
d) 8

Explanation: The truss is supported by hinged support at both ends. Hinged support in a pin jointed plane frame does not offers any degree of freedom as rotation is not considered. For the given truss, it consists of two pin joint offering two degree of freedom each. Therefore, the degree of freedom is 4.

10. Calculate the kinematic indeterminacy of the following pin jointed plane frame.

a) 4
b) 6
c) 8
d) 10

Explanation: The truss is supported by hinged support at both ends. Hinged support in a pin jointed plane frame does not offers any degree of freedom as rotation is not considered. For the given truss, it consists of four pin joint offering two degree of freedom each. Therefore, the degree of freedom is 8.

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