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

Questions 81–90 of 133. Imported answers require independent review unless marked reviewed.

The cantilever beam AC is composed of two segments AB and BC that are rigidly connected at B. The flexural rigidity of the segment AB is

, whereas the flexural rigidity of the segment BC is assumed to be infinite. Determine the magnitude of slope at B due to a force

applied at C.

Diagram for Engineering Sciences question 10

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Determine the correctness or otherwise of the following Assertion [a] and Reason [r].

Assertion [a]: Efficient columns are designed so that most of the column’s cross-sectional area is located as far away as possible from the principal centroidal axes of the section.

Reason [r]: Load carrying capacity of columns will increase as the moment of inertia of the cross-section increases.

Your answerChoose one option.

Both [a] and [r] are true and [r] is the correct reason for [a].

Both [a] and [r] are true but [r] is not the correct reason for [a].

Both [a] and [r] are false.

[a] is true but [r] is false.

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Consider the structure consisting of two massless elastic bars AB and BC, each of length

, cross-sectional area

, and Young’s modulus

. Connections at A, B, C are all pinned. A horizontal force

acts on the joint B as shown. Calculate the horizontal deflection of the joint B.

Diagram for Engineering Sciences question 12

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A beam of flexural rigidity

is fixed at A and supported by a linear spring of stiffness

at B. Determine the compressive force developed in the spring, when the beam is subjected to a uniformly distributed load of

per unit length.

Diagram for Engineering Sciences question 14

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The bar AB is fixed at A and is separated by a gap of 0.005 mm from wall at C as shown. The temperature of the bar is increased by

C. If the Young’s modulus of the bar is

GPa and the coefficient of thermal expansion is

C, then the magnitude of the compressive stress (in MPa) developed in the bar is _____.

Diagram for Engineering Sciences question 15

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A thin walled spherical pressure vessel has mean radius 100 mm and wall thickness 10 mm. The material has Young’s modulus 200 GPa and Poisson’s ratio 0.25. If the internal pressure is 100 MPa, the radial displacement (in mm) of the spherical pressure vessel (rounded off to two decimal places) is_____.

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A particle of mass

kg is released from rest and falls under gravity through a height of

m directly onto an upright massless elastic bar of length

mm, Young’s modulus 200 GPa, and cross-sectional area 100 mm

. Assume the following during impact: (a) particle mass sticks to the bar, (b) the bar does not buckle, and (c) no energy is lost. Use gravitational acceleration

m/s

. The maximum axial compression (in mm) of the bar due to the impact (rounded off to two decimal places) is _____.

Diagram for Engineering Sciences question 17

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Two beams AB and BC having diameter of 100 mm are connected by an internal hinge at B. The structure is fixed at A and roller supported at C. Load of

kN is applied at B. Ignoring the effect of any transverse shear stress, the tensile stress (in MPa) developed at A due to bending (rounded off to three decimal places) is _____.

Diagram for Engineering Sciences question 19

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The shear force diagram for a beam AD, which is simply supported at A and D, is shown. The magnitude of the maximum bending moment (in kN.m) is _____ (rounded off to three decimal places).

Diagram for Engineering Sciences question 20

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A rectangular thin plate with Young’s modulus 200 GPa and Poisson’s ratio 0.30 is subjected to uniform stress distribution at its edges as shown. However, it is stated that the dimension

of the plate does not change under the action of the stress components

and

. Considering micro-strains (in

), the change in the length of dimension

(in mm) is_____(rounded off to three decimal places).

Diagram for Engineering Sciences question 21

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GATE XE topic:solid-mechanics PYQs

Question 10

Question 11

Question 12

Question 14

Question 15

Question 16

Question 17

Question 19

Question 20

Question 21