Structural Analysis Questions and Answers - Elastic Beam Theory

1. A positive moment by standard sign convention would bend a horizontal beam:-
a) Concave upward
b) Concave downward
c) Convex upward
d) Can’t say

Answer: a
Explanation: Concave upward

2. 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

Answer: c
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

3. Elastic-Beam theory can be applied on a non-linear elastic material.
a) True
b) False

Answer: b
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.

4. 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.

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

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

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

6.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

Answer: d
Explanation: On expressing 1/p in terms of x and y, we can reach to the curve equation.

7. 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

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

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

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

9. On the elastic curve, points will be only displaced vertically not horizontally.
a) True
b) False

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

10. The change in slope between any two points on the elastic curve equals the area of M/EI diagram between both end points of beam.
a) True
b) False

Answer: b
Explanation: Change in slope will be equal to area of M/EI diagram between those two points.