# Finite Element Method Questions and Answers – Timoshenko Beam Element

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Timoshenko Beam Element”.

1. What is the main difference between the Timoshenko Beam Theory and Euler-Bernoulli Beam Theory?
a) Both are the same
b) Shear deformations in Timoshenko Beam Theory are zero values
c) Shear deformations in Euler-Bernoulli Beam Theory are nonzero values
d) Shear deformations in Timoshenko Beam Theory are nonzero values

Explanation: The two beam theories under consideration are given utmost importance while solving any beam related problems. In Euler-Bernoulli Beam Theory, the shear deformations are zero values; whereas in the Timoshenko Beam Theory, shear deformations are nonzero values.

2. Which of the following is not an assumption of Timoshenko Beam Theory?
a) Shear stress at a specific cross section is constant
b) Normal stress parallel to cross sectional plane is not equal to zero
c) Change of depth of cross section is neglected while determining axial displacement
d) Normal stress parallel to cross sectional plane is equal to zero

Explanation: According to the Timoshenko Beam Theory, Normal stress parallel to cross sectional plane is equal to zero. Hence, the statement is false and fails to satisfy the assumptions of the Timoshenko Beam Theory.

3. Timoshenko Beam Theory recognizes that the action of shear force causes a shear strain.
a) True
b) False

Explanation: The given statement is true. Timoshenko Beam theory takes into consideration the warping of beam elements that occur due to shear forces. Other beam theories don’t consider shear strain and assume the member to be free of the same.

4. Shear locking is applicable for which of the following beams?
a) Moderately thick beams
b) Thick beams
c) Thin beams
d) Moderately thin beams

Explanation: Shear locking is applicable only in the case of thin beams. In the scenario of thin beams, ratio (le/h) is very large; hence the results obtained by the normal convention are not correct. Under an ideal scenario, the shear term must tend to zero; in the case of thin beams, this is not true.

5. What is the phenomenon of increasing constraints of shear stiffness referred to as?
a) Spurious constraint
b) Authentic constraint
c) True constraint
d) Real constraint

Explanation: The phenomenon of increasing constraints of shear stiffness is referred to as spurious constraint. This type of error occurs explicitly in the case of thin beams alone. This error arises when the general formulae used for moderately thick beams is applied in the case of thin beams also.
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6. What are the two methods used for elimination of errors arising in the case of thin beams?
a) Implied integration technique, Field deformation element
b) Applied integration technique, Nodal deformation method
c) Incremented integration technique, Global deformation method
d) Reduced Integration technique, Field Consistency element

Explanation: Reduced Integration technique and Field consistency element are the two popular remedies used for eradication of errors arising in the case of thin beams. In reduced integration technique, the shear stiffness equation is integrated using one point Gaussian technique. In the Field Consistency element method, the function undergoes smoothening in order to give better results.

7. Timoshenko beam theory includes both shear and rotary corrections.
a) False
b) True

Explanation: Timoshenko beam theory is widely accepted because it takes into consideration the stresses arising due to rotary motion and shear stresses as well. Euler Bernoulli beam theory did not take into consideration these two effects, and is applicable only under certain ideal conditions.

8. Which of the following is a limitation of Timoshenko beam theory?
a) Cross sectional surface of shaft is curved
b) Cross sectional surface of shaft is parallel to the central axis
c) Cross sectional surface of shaft is not curved
d) Cross sectional surface of shaft is perpendicular to the central axis

Explanation: For calculation of shaft deformation, Timoshenko beam theory is used. In this, the bending and shear deformation are considered. But, in Timoshenko beam theory the cross sectional surface of shaft is not curved; thus giving rise to errors in theoretical and experimental values.

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