GATE AE topic:solid-mechanics PYQs & Answers — Page 5

Questions 41–50 of 68. Imported answers require independent review unless marked reviewed.

The deflection

of a certain beam of length

and uniform weight per unit length

, is given as

, where

is the distance from the point of support and

is a constant. The non-dimensional location

, where the deflection of the beam is maximum, is ______ (round off to two decimal places).

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A rigid horizontal bar ABC, with roller support at A, is pinned to the columns BD and CE at points B and C, respectively as shown in figure. The other end of the column BD is fixed at D, whereas the column CE is pinned at E. A vertical load P is applied on the bar at a distance ‘a’ from point B. The two columns are made of steel with elastic modulus 200 GPa and have a cross section of 1.5 cm x 1.5 cm. The value of ‘a’ for which both columns buckle simultaneously, is __________ cm (round off to one decimal place).

Diagram for Aerospace Engineering question 49

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Two cantilever beams AB and DC are in contact with each other at their free ends through a roller as shown in the figure. Both beams have a square cross section of 50 mm x 50 mm, and the elastic modulus E = 70 GPa. If beam AB is subjected to a uniformly distributed load of 20 kN/m, then the compressive force experienced by the roller is __________ kN (round off to one decimal place).

Diagram for Aerospace Engineering question 51

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Three long and slender aluminum bars of identical length are subjected to an axial tensile force. These bars have circular, triangular and rectangular cross sections, with same cross sectional area. If they yield at

and

, respectively, which one of the following is true?

Your answerChoose one option.

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The value of Poisson’s ratio at which the shear modulus of an isotropic material is equal to the bulk modulus is

Your answerChoose one option.

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A load

is applied to the free end of a stepped cantilever beam as shown in the figure. The Young’s modulus of the material is

, and the moments of inertia of the two sections of length 2 m and 1 m are

and

, respectively. Ignoring transverse shear and stress concentration effects, the deflection at the point where the load is applied at the free end of the cantilever is

Diagram for Aerospace Engineering question 29

Your answerChoose one option.

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The three dimensional strain-stress relation for an isotropic material, written in a general matrix form, is

and

are compliances which depend on the elastic properties of the material. Which one of the following is correct?

Your answerChoose one option.

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For the state of stress shown in the figure, which one of the following represents the correct free body diagram showing the maximum shear stress and the associated normal stresses?

Diagram for Aerospace Engineering question 34

Your answerChoose one option.

Diagram for Aerospace Engineering question 34 (figure 2)

Diagram for Aerospace Engineering question 34 (figure 3)

Diagram for Aerospace Engineering question 34 (figure 4)

Diagram for Aerospace Engineering question 34 (figure 5)

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A solid circular shaft, made of ductile material with yield stress

MPa, is subjected to a torque of 10 kNm. Using the Tresca failure theory, the smallest radius of the shaft to avoid failure is ______ cm (round off to two decimal places).

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As shown in the figure, a beam of length 1 m is rigidly supported at one end and simply supported at the other. Under the action of a uniformly distributed load of 10 N/m, the magnitude of the normal reaction force at the simply supported end is ______ N (round off to two decimal places).

Diagram for Aerospace Engineering question 53

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GATE AE topic:solid-mechanics PYQs

Question 39

Question 49

Question 51

Question 16

Question 28

Question 29

Question 30

Question 34

Question 42

Question 53