Structural Analysis Questions and Answers – Elastic-Beam Theory

This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Elastic-Beam Theory”.

1. Which of the following is correct?
a) 1/M = EI/p
b) 1/M = E/pI
c) 1/M = p/EI
d) 1/p = EI/m

Explanation: It can be derived by taking small elements and using Hooke’s law and flexural formula.
1/M = p/EI
Here, p = the radius of curvature at a specific point on the elastic curve
M = the internal moment in the beam at a point
E = material’s modulus of elasticity
I = the beam’s moment of inertia computed about the neutral axis

2. Elastic-Beam theory can be applied on a non-linear elastic material.[/expand] State whether the above statement is true or false.
a) True
b) False

Explanation: For elastic-beam theory to be applicable Hooke’s law must be applicable and for that material must behave in a linear-elastic manner.

3. From where is radius of curvature measured?
a) From centre of bar
b) From one of the ends of bar
c) From any internal point
d) From an external point.

Explanation: It is measured from centre of curvature and it lies at an external point.

4. Which of the following can be a possible value of EI?
a) 1
b) -1
c) -2
d) -3

Explanation: It is referred to EI and it is always positive.

5. What is the general form of elastic curve of a beam?
a) Linear first-order differential equation
b) Linear second-order differential equation
c) Non-linear first-order differential equation
d) Non-linear second-order differential equation

Explanation: On expressing 1/p in terms of x and y, we can reach to the curve equation.
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6. What is the assumption for deriving above mentioned equation?
a) Deflection is only due to shear force
b) Deflection is only due to bending
c) Deflection is due to both shear and bending
d) Axial forces caused bending

Explanation: While deriving, we have only considered bending forces by assuming that length is much greater than thickness.

7. Slope of a deflected curve is generally:-
a) Very large
b) Very small
c) In between
d) Can’t say

Explanation: Slope is very small and is generally assumed to be zero to predict the curve more properly.

8. On the elastic curve, points will be only displaced vertically not horizontally.
State whether the above statement is true or false.
a) True
b) False

Explanation: Since we have assumed slope to be zero, there won’t be any horizontal displacement.

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