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# MCQs on Introduction to Shear Stress

At ________ the shearing stress in a beam are maximum.

a) Extreme fibres

b) Modulus of section

c) Neutral axis

d) Along the cross-sectional area

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Explanation: Shearing stress in a beam is maximum at the neutral axis. Shearing stress is defined as the resistance offered by the internal stress to the shear force.

Determine the shear stress at the level of neutral axis, if a beam has a triangle cross section having base “b” and altitude “h”. Let the shear force be subjected is F.

a) 3F/8bh

b) 4F/3bh

c) 8F/3bh

d) 3F/6bh

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Explanation: For a triangular section subjected to shear force the shear stress in neutral axis is

Shear stress at NA = 4/3 [Average shear stress].

= 4/3 [F/0.5 bh] = 8F / 3bh.

The maximum shear stress is ______ times the average shear stress [For rectangular beams].

a) 2.5

b) 3

c) 1.2

d) 1.5

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Answer: d

Explanation: The maximum shear stress occurs at neutral axis. Then y = 0.

Max shear stress = 3F/2bd = 3/2 [F/bd].

= 1.5 Average shear stress.

Shear stress in a beam is zero at ______

a) Neutral axis

b) Extreme fibres

c) Cross section

d) Junctions

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Explanation: The resistance offered by the internal stress to shear is known as shearing stress. Shearing stress is zero at extreme fibres of the beam. The bending stresses are maximum at extreme fibres of the beam cross section.

Shear stress distribution over rectangular section will be _________

a) parabolic

b) elliptical

c) triangular

d) trapezoidal

A round Steel rod of 100 mm diameter is bent into an arc of radius 100m. What is the maximum stress in the rod? Take E = 2×10^{5} N/mm^{2}.

a) 150 N/mm^{2}

b) 200 N/mm^{2}

c) 100 N/mm^{2}

d) 300 N/mm^{2}

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Answer: c

Explanation: D = 100m

y = 50 mm

R = 10 × 10^{3}mm

By equation of flexure; E/R = f/y

f=E/R ×y

= 2×10^{5}/ 100 × 10^{3}× 50

= 100 N/mm^{2}.

For circular section, the maximum shear stress is equal to ____________ times of average shear stress.

a) 2/3

b) 3/2

c) 4/3

d) 3/4

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Answer: c

Explanation: Maximum shear stress occurs at neutral axis & y = 0.

Max. Shear stress = 4/3 [ F/A ].

F/A is average shear stress.

The maximum shear stress distribution is 33% more than average shear stress.

A steel beam is 200 mm wide and 300 mm deep. The beam is simply supported and carries a concentrated load w. If the maximum stress are 2 N/mm^{2}. What will be the corresponding load?

a) 50 kN

b) 80 kN

c) 40 kN

d) 85 kN

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Answer: b

Explanation: For a rectangular cross section

Max. Shear stress = 3/2 [F/A ] 2 = 3/2 [w/200 × 300].

w = 80 kN.

Maximum shear stress in thin cylindrical shell be ___________

a) pr/2t

b) pr/3t

c) pr/4t

d) pr/ 5t

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Explanation: Hoop stress P(h) = pr/t

Longitudinal stress P(l) = pr/2t

Thus, hoop stress is twice the longitudinal stress

Max. Shear stress = P(h) – P(l) / 2

= pr/4t.

Circumferential stress is same as of _________

a) Hoop stress

b) Longitudinal stress

c) Transverse stress

d) Phreatic stress

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Answer: a

Explanation: In a thin cylindrical shell of internal radius r thickness t when subjected to internal fluid pressure P, the stress developed in the internal walls can be termed as circumferential stress or hoop stress.

P(h) = pr/t.