GATE XE Mechanics of deformable bodies PYQs & Answers — Page 7

Questions 61–70 of 133. Imported answers require independent review unless marked reviewed.

A cantilever beam has a span of 1 m and carries a uniformly distributed load of

N/m over a portion as shown. A force

N acts at a distance

from the fixed end. The distance

is such that the bending moment at the fixed end is zero. The beam has a rectangular cross-section of depth 20 mm and width 24 mm. For this loading, the magnitude of the maximum bending stress in the beam in MPa is

Diagram for Engineering Sciences question 86

______________ (round off to the nearest integer)

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The figure shows two identical mass-less beams AB and CD, each clamped at one of their ends. The left end of beam CD rests on the right end of beam AB such that the ends of the beams are just in contact. The beams are unstressed before the application of load. Assume no friction at the contact. Now, if a uniformly distributed load of 800 N/m is applied on beam CD, the bending moment at the end B of beam AB in N.m is __________ (rounded off to the nearest integer)

Diagram for Engineering Sciences question 87

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If the yield point shear stress obtained from the torsion test of a cylindrical specimen is τᵧ, then what is the maximum value of principal strain at yielding? (μ is Poisson’s ratio and E is Young’s modulus)

Your answerChoose one option.

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If the ratio of Young’s modulus to bulk modulus of a material is 3/2, then the ratio of shear modulus to the Young’s modulus of the material is

Your answerChoose one option.

2/5

1/3

3/5

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With respect to the plane of maximum shear stress, which of the following statements is INCORRECT?

Your answerChoose one option.

The normal stress on the plane is zero.

The maximum shear stress is equal to the largest of the one half the difference of principal stresses

The plane of maximum shear stress occurs at 45° to the principal planes.

The magnitude of the maximum shear stress is equal to the largest of the radius of the Mohr’s circles.

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A simply supported beam of length L is loaded by two symmetrically applied point loads P at L/3 from each support. Both the loads are then shifted to new points which are at a distance L/4 from each support. The bending moments at the mid-section of the beam in both the cases are same. The magnitude of P1 in terms of P is

Diagram for Engineering Sciences question 7

Your answerChoose one option.

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A beam having rectangular cross section is subjected to transverse loading. The ratio of maximum shear stress developed in the beam to the average shear stress is

Your answerChoose one option.

1.50

1.25

1.33

1.66

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For the state of plane stress shown, the components of normal and shear stresses are given in terms of stress

and unknown constants

and

. If the normal and shear components of stress on a 45° plane are

and zero, the values of

and

would be:

Diagram for Engineering Sciences question 10

Your answerChoose one option.

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For a state of plane strain, the normal strains are given by

and the maximum shear strain is

. The value of shear strain

for this strain state is

Your answerChoose one option.

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A thin cylinder (closed at its ends) of radius r and thickness t (r ≫ t) is subjected to internal pressure p. The maximum shear stress in the wall of the cylinder is

Your answerChoose one option.

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GATE XE Mechanics of deformable bodies PYQs

Question 86

Question 87

Question 4

Question 5

Question 6

Question 7

Question 8

Question 10

Question 11

Question 12