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# MCQs on Section Modulus

What is the section modulus (Z) for a rectangular section?

a) bd^{2}/6

b) a^{3}/6

c) BD^{3}-bd^{3}

d) D^{4}-d^{4}

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Answer: a

Explanation: The modulus of section may be defined as the ratio of moment of inertia to the distance to the extreme fibre. It is denoted by Z.

Z= I/y ; For rectangular section, I = bd^{3}/12 & y = d/2.

Z= bd^{2}/6.

Find the modulus of section of square beam of size 300×300 mm.

a) 4.8 × 10^{6} mm^{3}

b) 4.5 × 10^{6} mm^{3}

c) 5.6 × 10^{6} mm^{3}

d) 4.2 × 10^{6} mm^{3}

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Answer: b

Explanation: Here, a = side of square section = 300 mm.

I = a^{4}/12. y= a/2.

Z = I/y = a^{3}/6

= 300^{3}/6

= 4.5 × 10^{6} mm^{3}.

_________ of a beam is a measure of its resistance against deflection.

a) Strength

b) Stiffness

c) Deflection

d) Slope

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Answer: b

Explanation: A beam is said to be a strength when the maximum induced bending and shear stresses are within the safe permissible stresses stiffness of a beam is a measure of its resistance against deflection.

To what radius an Aluminium strip 300 mm wide and 40mm thick can be bent, if the maximum stress in a strip is not to exceed 40 N/mm^{2}. Take young’s modulus for Aluminium is 7×105 N/mm^{2}.

a) 45m

b) 52m

c) 35m

d) 65m

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Answer: c

Explanation: Here, b = 300mm

d= 40mm. y= 20mm.

From the relation; E/R = f/y

R= E×y/f

=70×10^{3} × 20 / 40

= 35m.

The bending stress in a beam is ______ to bending moment.

a) Less than

b) Directly proportionate

c) More than

d) Equal

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Explanation: As we know, the bending stress is equal to bending moment per area. Hence, as the bending (flexure) moment increases/decreases the same is noticed in the bending stress too.

The Poisson’s ratio for concrete is __________

a) 0.4

b) 0.35

c) 0.12

d) 0.2

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Explanation: The ratio of lateral strain to the corresponding longitudinal strain is called Poisson’s ratio. The value of poisons ratio for elastic materials usually lies between 0.25 and 0.33 and in no case exceeds 0.5. The Poisson’s ratio for concrete is 0.20.

The term “Tenacity” means __________

a) Working stress

b) Ultimate stress

c) Bulk modulus

d) Shear modulus

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Answer: b

Explanation: The ultimate stress of a material is the greatest load required to fracture the material divided by the area of the original cross section in the point of fracture The ultimate stress is also known as tenacity.

A steel rod of 25 mm diameter and 600 mm long is subjected to an axial pull of 40000. The intensity of stress is?

a) 34.64 N/mm^{2}

b) 46.22 N/mm^{2}

c) 76.54 N/mm^{2}

d) 81.49 N/mm^{2}

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Answer: d

Explanation: Cross sectional area of steel rod [Circular]be 490.87 mm^{2}.

The intensity of stress = P/A = 40000/490.87

= 81.49 N/mm^{2}.

The bending strain is zero at _______

a) Point of contraflexure

b) Neutral axis

c) Curvature

d) Line of action of loading

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Answer: b

Explanation: The neutral axis is a line of intersection of neutral plane or neutral layer on a cross section. The neutral axis of a beam passes through the centroid of the section. At the neutral axis bending stress and bending strain is zero.

Strength of the beam depends only on the cross section.

a) True

b) False

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Answer: b

Explanation: The strength of two beams of the same material can be compared by the section modulus values. The strength of beam depends on the material, size and shape of cross section. The beam is stronger when section modulus is more, strength of the beam depends on Z.