GATE ME topic:solid-mechanics PYQs & Answers — Page 9

Questions 81–90 of 90. Imported answers require independent review unless marked reviewed.

A cantilever beam of length

and flexural modulus

is subjected to a point load

at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) is

Your answerChoose one option.

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A steel bar is held by two fixed supports as shown in the figure

Diagram for Mechanical Engineering question 10

and is subjected to an increase of temperature

. If the coefficient of thermal expansion and Young’s modulus of elasticity of steel are

and

, respectively, the magnitude of thermal stress (in MPa) induced in the bar is __________

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The Poisson’s ratio for a perfectly incompressible linear elastic material is

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0.5

infinity

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A motor driving a solid circular steel shaft transmits 40 kW of power at 500 rpm. If the diameter of the shaft is 40 mm, the maximum shear stress in the shaft is ______ MPa.

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Consider a beam with circular cross-section of diameter

. The ratio of the second moment of area about the neutral axis to the section modulus of the area is

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An initially stress-free massless elastic beam of length

and circular cross-section with diameter

(

) is held fixed between two walls as shown. The beam material has Young’s modulus

and coefficient of thermal expansion

Diagram for Mechanical Engineering question 39

If the beam is slowly and uniformly heated, the temperature rise required to cause the beam to buckle is proportional to

Your answerChoose one option.

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A point mass of 100 kg is dropped onto a massless elastic bar (cross-sectional area = 100 mm², length = 1 m, Young’s modulus = 100 GPa) from a height

of 10 mm as shown (Figure is not to scale). If

m/s², the maximum compression of the elastic bar is __________ mm.

Diagram for Mechanical Engineering question 40

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A rectangular region in a solid is in a state of plane strain. The

coordinates of the corners of the undeformed rectangle are given by P(0,0), Q(4,0), R(4,3), S(0,3). The rectangle is subjected to uniform strains,

. The deformed length of the elongated diagonal, up to three decimal places, is __________ units.

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A horizontal bar, fixed at one end (

), has a length of 1 m, and cross-sectional area of 100 mm². Its elastic modulus varies along its length as given by

GPa, where

is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (

). The axial displacement of the free end is __________ mm.

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A rod of length 20 mm is stretched to make a rod of length 40 mm. Subsequently, it is compressed to make a rod of final length 10 mm. Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is

Your answerChoose one option.

−0.5

−0.69

−0.75

−1.0

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GATE ME topic:solid-mechanics PYQs

Question 9

Question 10

Question 13

Question 15

Question 16

Question 39

Question 40

Question 42

Question 44

Question 50