GATE ME topic:solid-mechanics PYQs & Answers — Page 8

Questions 71–80 of 90. Imported answers require independent review unless marked reviewed.

A hollow circular shaft of inner radius 10 mm, outer radius 20 mm and length 1 m is to be used as a torsional spring. If the shear modulus of the material of the shaft is 150 GPa, the torsional stiffness of the shaft (in kN-m/rad) is ______ (correct to two decimal places).

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The state of stress at a point, for a body in plane stress, is shown in the figure below. If the minimum principal stress is 10 kPa, then the normal stress

(in kPa) is

Diagram for Mechanical Engineering question 29

Your answerChoose one option.

9.45

18.88

37.78

75.50

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A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of

as shown in the figure.

Diagram for Mechanical Engineering question 31

The glue used at the interface fails if Criterion 1: the maximum normal stress exceeds 2.5 MPa. Criterion 2: the maximum shear stress exceeds 1.5 MPa. Assume that the interface fails before the logs fail. When a uniform tensile stress of 4 MPa is applied, the interface

Your answerChoose one option.

fails only because of criterion 1

fails only because of criterion 2

fails because of both criteria 1 and 2

does not fail

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A bar of circular cross section is clamped at ends P and Q as shown in the figure. A torsional moment

is applied at a distance of 100 mm from end P. The torsional reactions

in Nm at the ends P and Q respectively are

Your answerChoose one option.

(50, 100)

(75, 75)

(100, 50)

(120, 30)

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A bimetallic cylindrical bar of cross sectional area 1 m

is made by bonding Steel (Young’s modulus = 210 GPa) and Aluminium (Young’s modulus = 70 GPa) as shown in the figure. To maintain tensile axial strain of magnitude

in Steel bar and compressive axial strain of magnitude

in Aluminium bar, the magnitude of the required force P (in kN) along the indicated direction is

Diagram for Mechanical Engineering question 33

Your answerChoose one option.

140

210

280

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A thin-walled cylindrical can with rigid end caps has a mean radius R = 100 mm and a wall thickness of t = 5 mm. The can is pressurized and an additional tensile stress of 50 MPa is imposed along the axial direction as shown in the figure. Assume that the state of stress in the wall is uniform along its length. If the magnitudes of axial and circumferential components of stress in the can are equal, the pressure (in MPa) inside the can is ________ (correct to two decimal places).

Diagram for Mechanical Engineering question 37

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A simply supported beam of width 100 mm, height 200 mm and length 4 m is carrying a uniformly distributed load of intensity 10 kN/m. The maximum bending stress (in MPa) in the beam is __________ (correct to one decimal place).

Diagram for Mechanical Engineering question 39

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The true stress (σ) - true strain (ε) diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e., up to stress of 500 MPa and strain of 0.5. Then from point A, there is unloading up to point B, i.e., to stress of 100 MPa. Given that the Young’s modulus E = 200 GPa, the natural strain at point B (ε

) is ________ (correct to three decimal places).

Diagram for Mechanical Engineering question 48

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The state of stress at a point is

and

. The maximum normal stress (in MPa) at that point is __________

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For a loaded cantilever beam of uniform cross-section, the bending moment (in N·mm) along the length is

, where

is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at

is __________

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GATE ME topic:solid-mechanics PYQs

Question 20

Question 29

Question 31

Question 31

Question 33

Question 37

Question 39

Question 48

Question 7

Question 8