# Finite Element Method Questions and Answers – Beams and Frames – Load Vector

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Beams and Frames – Load Vector”.

1. On a simply supported beam with uniformly distributed load (p) over length (l) the value of reaction force at one support is _______
a) p*l
b) (p*l)/2
c) (p*l)2
d) (p*l)/3

Explanation: Overall force acting on the beam=p*l
The reaction force at one of the two supports=(p*l)/2.

2. In Galerkin method we convert a continuous operator problem into a discrete problem.
a) True
b) False

Explanation: In Galerkin method we convert a continuous operator problem into a discrete problem. In beams the problem is formulated into finite elements using Galerkin Method.

3. Which of the following is not a one dimensional element?
a) bar
b) brick
c) beam
d) rod

Explanation: Brick is not a one dimensional element. One dimensional element is used when one dimension of the model geometry is significantly greater than the other two dimensions.

4. Three geometrically identical beams made out of steel, aluminum, and titanium are axially loaded. Which of the following statements is correct?
a) Stress in titanium is the least
b) Stress in cast iron is the highest
c) Stress in steel is the least
d) Stress in all three beams is the same

Explanation: The stress in all three beams will be induced equally. Stress in not dependent on the material, but the geometry and cross section of the element.

5. The application of force at which of the following point on a beam will nullify the effect of torsion?
a) Centroid
b) Center of mass
c) Extreme fiber
d) Shear centre

Explanation: The application of force on shear centre nullifies the effect of torsion on a beam element. This is useful when the cross section of beam is asymmetric and creates a twisting effect on application of force.

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6. For a taper beam element two cross sections are necessary to define the geometry.
a) True
b) False

Explanation: A taper beam element requires two cross sections to define the geometry. Regular beam element cannot take into account the variation in cross section required to define the geometry.

7. Which of the following statements is correct?
a) Beam elements are recommended for unsymmetrical cross sections
b) Bar elements are recommended for unsymmetrical cross sections
c) Beam and bar elements can both be used for unsymmetrical cross sections
d) Neither beam nor bar elements can be used for unsymmetrical cross sections

Explanation: Beam elements are recommended for unsymmetrical cross sections due to their ability to take into account the shear centre. Thus shear centre can nullify effects of torsion acting on unsymmetrical cross section which is limited in case of bar elements.

8. The equivalent load (f) acting on a simply supported beam element loaded with uniformly distributed load (p) over an element of length (l) is given by which of the following expressions?
a) f=$$[\frac{pl}{2},\frac{pl^2}{12},\frac{pl}{2},-\frac{pl^2}{12}]$$
b) f=$$[\frac{pl}{2},\frac{pl^2}{12},\frac{pl}{2},\frac{pl^2}{12}]$$
c) f=$$[\frac{pl}{2},-\frac{pl^2}{12},\frac{pl}{2},-\frac{pl^2}{12}]$$
d) f=$$[\frac{pl}{2},\frac{pl^2}{12},\frac{-pl}{2},-\frac{pl^2}{12}]$$

Explanation: The value of equivalent load is given by
f=$$[\frac{pl}{2},\frac{pl^2}{12},\frac{pl}{2},-\frac{pl^2}{12}]$$
Here l is length of beam element, and p is the uniformly distributed load. Here $$\frac{pl}{2}$$ represents the reaction force on the supports, and $$\frac{pl^2}{12}$$ represents the moment acting on the supports.

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