This set of Design of Steel Structures Multiple Choice Questions & Answers (MCQs) focuses on “Shear Strength of Beams”.

1. A beam can be subjected to which of the following shear?

a) longitudinal shear only

b) transverse shear only

c) longitudinal or transverse shear

d) beam is not subjected to shear

View Answer

Explanation: A beam is subjected to two types of shear: transverse (vertical) shear and longitudinal shear.

2. Shear forces will govern the design of beam if

a) beam is short

b) beam is long

c) beam carry light loads

d) shear forces will never act in beam

View Answer

Explanation: Shear forces will govern the design of beam if beams are short and are heavily loaded (heavy concentrated load) or deeply coped.

3. Longitudinal shear occurs due to

a) light load on beam

b) bending of beam

c) twisting of beam

d) does not occur

View Answer

Explanation: Longitudinal or horizontal shear occurs due to bending of beam. The fibers above shorten in length and those below neutral axis elongate under sagging bending moments. Therefore, the fibers tend to slip over each other and the effect is maximum at the neutral axis. The tendency to slip is resisted by shear strength of the material.

4. The shear stress distribution of I-section varies

a) cubically with depth

b) as straight line with depth

c) as horizontally with depth

d) parabolically with depth

View Answer

Explanation: The shear stress distribution of I-section varies parabolically with depth with maximum occurring at the neutral axis.

5. The longitudinal shear is given by

a) τ = VAyI_{z}t

b) τ = VAy/I_{z}t

c) τ = VAy/I_{z}

d) τ = Vy/I_{z}t

View Answer

Explanation: The longitudinal shear is given by τ = VAy/I

_{z}t, where V is vertical shear force at section under consideration, I

_{z}is moment of inertia of entire section about zz-axis, neutral axis, Ay is static moment of area of cross section, t is thickness of portion of cross section at which longitudinal shear is obtained.

6. In which of the following cases shear does not govern design of beam?

a) when web thickness is large in plate girders

b) when depth of beam section is small and loaded uniformly

c) when large concentrated loads are placed near support

d) when two members are rigidly connected together with their webs lying in same plane

View Answer

Explanation: Shear determines design of beam when depth of beam section is small and loaded uniformly, when large concentrated loads are placed near beam supports, when two members are rigidly connected together with their webs lying in same plane, when web thickness is small in plate girders.

7. Which of the following is true regarding I-section?

a) average shear is very larger than maximum shear

b) maximum shear is very larger than average shear

c) flanges resist very small portion of shear

d) webs resist very small portion of shear

View Answer

Explanation: For an I-section, flanges resist very small portion of shear and a significant portion is resisted by web. The maximum and average shear for I-section are almost same.

8. A_{v}erage stress is given by

a) τ_{av} = V/d

b) τ_{av} = Vdt_{w}

c) τ_{av} = V/t_{w}

d) τ_{av} = V/dt_{w}

View Answer

Explanation: for practical purposes, average shear stress is used and is given by τ

_{av}= V/A

_{v}= /dt

_{w}, where d = depth of web, t

_{w}= thickness of web, A

_{v}is shear area.

9. Nominal shear strength based on Von-Mises yield criterion is given by

a) V_{n} = A_{v}f_{yv}

b) V_{n} = A_{v}f_{yv}/√3

c) V_{n} = f_{yv}/√3

d) V_{n} = A_{v}f_{yv}/3

View Answer

Explanation: Nominal shear strength based on Von-Mises yield criterion is given by V

_{n}= A

_{v}f

_{yv}/√3, where f

_{yv}is yield strength of web, V

_{n}is nominal shear resistance.

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