# Finite Element Method Questions and Answers – Shear Force & Bending Moment

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This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Shear Force & Bending Moment”.

1. Which of the following statements are correct about a cantilevered beam with point load acting on the extreme end of the beam?
a) Bending stresses induced in the beam are constant throughout the length of the beam
b) Bending stresses induced in the beam decreases linearly from fixed end to free end
c) Bending stresses induced in the beam increases linearly from fixed end to free end
d) Bending stresses induced in the beam decreases exponentially from fixed end to free end

Explanation: Bending stresses induced in the beam decreases linearly from fixed end to free end. The point load acting induces normal as well as shear stresses, but when length beam is large the shear stresses are negligible.

2. Shear stress acts parallel to the cross section of the beam.
a) True
b) False

Explanation: Shear stress acts parallel to the cross section causing distortion. Shear stress results in angular deformation which is measured in terms of angle.

3. Which of the following is the correct equation for bending moment (M) of an element given value of young’s modulus (E), moment of inertia (I), and radius of curvature (R)?
a) M= EIR
b) M= EI/R
c) M=(EI)2R
d) M=(EI)2/R

Explanation: The correct equation is given by M= EI/R. The value of bending moment (M) is directly proportional to young’s modulus (E) and moment of inertia (I). The value of bending moment (M) is inversely proportional to radius of curvature (R).
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4. Which of the following statements are correct about a cantilevered beam with point load acting on the extreme end of the beam?
a) Shear stress along the length of the beam increases linearly
b) Shear stress along the length of the beam deceases linearly
c) Shear stress along the length of the beam decreases exponentially
d) Shear stress along the length of the beam remains constant

Explanation: Shear stress along the length of the beam remains constant. There is no change in the magnitude of the shear stress acting on the beam along its length.

5. Which of the following statements are correct regarding shear stress distribution across the cross section in a cantilevered beam with point load acting on the extreme end of the beam?
a) Shear stress distribution across the cross section of beam is constant
b) Shear stress distribution across the cross section of beam is zero
c) Shear stress distribution across the cross section of beam is zero at center and maximum at extreme ends
d) Shear stress distribution across the cross section of beam is zero at extreme ends and maximum at center

Explanation: The shear stress distribution across the cross section of beam is zero at extreme ends and maximum at center.The variation in the magnitude of shear stress from center to the extreme ends follows a circular curve.

6. Torque acting on the face of a cylindrical body induces bending moment in the body.
a) True
b) False

Explanation: Torque acting on the face of a cylindrical body does not induce bending moment in the body. The torque acting on the body induces torsional shear stress in the body.

7. Which of the following equations is the correct expression for shear force (V) in an element, given the modulus of elasticity (E), moment of inertia (I), element length (le), displacement (q) in a uniformly distributed load on a simply supported beam?
a) V=$$\frac{EI}{(le)^3}$$(2q1+leq2-2q3+leq4)
b) V=$$\frac{EI}{(le)^2}$$(2q1+leq2-2q3+leq4)
c) V=$$\frac{EI}{(le)^2}$$(2q1+leq2+2q3+leq4)
d) V=$$\frac{EI}{(le)^3}$$(2q1+leq2+2q3+leq4)

Explanation: The correct expression is given by
V=$$\frac{EI}{(le)^3}$$(2q1+leq2-2q3+leq4)
Here E is the ratio of normal stress to normal strain. Here q1, q2, q3, q4 are the four displacements at the two supported nodes of the simply supported beam.

8. Which of the following equations is the correct expression for bending moment (M) in an element, given the modulus of elasticity (E), moment of inertia (I), element length (le), shape function (ξ) and displacement (q) in a uniformly distributed load on a simply supported beam?
a) M=$$\frac{EI}{(le)^2}$$[6ξq1+(3ξ-1)leq2-6ξq3+(3ξ+1)leq4]
b) M=$$\frac{EI}{(le)^3}$$[6ξq1-(3ξ-1)leq2-6ξq3-(3ξ+1)leq4]
c) M=$$\frac{EI}{(le)^2}$$[6ξq1+(3ξ-1)leq2-6ξq3-(3ξ+1)leq4]
d) M=$$\frac{EI}{(le)^3}$$[6ξq1+(3ξ-1)leq2-6ξq3+(3ξ+1)leq4]

Explanation: The correct expression is given by
M=$$\frac{EI}{(le)^2}$$[6ξq1+(3ξ-1)leq2-6ξq3+(3ξ+1)leq4]
Here E is the ratio of normal stress to normal strain. Here q1, q2, q3, q4 are the four displacements at the two supported nodes of the simply supported beam. The value of shape function (ξ) varies between -1 to +1.

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