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

1. 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

View Answer

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.

2. Plane sections remain perpendicular to the deformed reference line of the beam.

a) False

b) True

View Answer

Explanation: The Timoshenko beam theory believes that after deformation, even though the plane sections might remain plane; it is highly unlikely for them to be perpendicular to the deformed reference line of the beam. This implies that slope of the reference line differs from rotation of cross section, leading to the formation of non zero shear strains.

3. Why is the Timoshenko beam theory more suited for squat beam members?

a) Significant axial deformations may develop

b) Significant shear deformations may not develop

c) Significant shear deformations may develop

d) Significant bending deformations may develop

View Answer

Explanation: Timoshenko beam theory gives provisions for existence of shear deformations. One of its major advantages is the presence of non zero shear deformations. In slender beams, this deformation is minimal. Whereas in squat beams, this deformation is quantifiable and thus suited for the Timoshenko beam theory.

4. Which of the following is the expression for finding shear force using the Timoshenko beam theory?

a) V = K*A*G/γ_{xy}

b) V = K*A*G-γ_{xy}

c) V = K*A*G+γ_{xy}

d) V = K*A*G*γ_{xy}

View Answer

Explanation: The expression for finding shear force using the Timoshenko beam theory is given by

V = K*A*G*γ

_{xy}

where,

V = shear force

K = shear factor

A = area of cross section

G = shear modulus

γ

_{xy}= shear strain

5. Which of the following defines a shear factor?

a) Ratio of shear area to area of cross section

b) Ratio of shear volume to area of cross section

c) Ratio of shear area to curved surface area

d) Ratio of shear area to lateral surface area

View Answer

Explanation: Shear factor is defined as the ratio of shear area to area of cross section. It is used to improve the accuracy of problems solved using the Timoshenko beam theory. For rectangular cross sections, a shear factor of 5/6 has proven to give desirable and accurate results.

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