GATE XE Mechanics of deformable bodies PYQs & Answers — Page 10

Questions 91–100 of 133. Imported answers require independent review unless marked reviewed.

A solid transmission shaft has length 10 m and diameter 100 mm. The shaft is supported by frictionless bearings at ends that act as simple supports. In addition to its self-weight acting as a uniformly distributed load per unit length, an operational torque of

kN.m is applied. The density and yield strength of the material are 800 kg/m

and 350 MPa, respectively. Use gravitational acceleration as 10 m/s

and ignore the effect of transverse shear stress. The factor of safety of the shaft as per maximum shear stress failure theory (Tresca criterion) is ________ (rounded off to two decimal places).

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For a pinned-pinned slender column of length L, with uniform circular cross section, and with second moment of cross sectional area I, the critical buckling load is P_cr. For a similar column, made of same material, having length 2L and second moment of cross sectional area 4I, the critical buckling load is

Your answerChoose one option.

4P_cr

2P_cr

P_cr

0.5P_cr

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Two rods P and Q of uniform circular cross section are made of same material and are subjected to identical uniaxial tensile load. The length of rod P is twice the length of rod Q and the diameter of rod P is also twice the diameter of rod Q. The ratio of elastic strain energy stored in rod P to that stored in rod Q is

Your answerChoose one option.

4:1

2:1

1:1

1:2

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In a bending moment diagram of a simply supported beam, discontinuity in the bending moment occurs

Your answerChoose one option.

at the point of application of a couple

at the point of application of a concentrated force

at a point where the cross section of the beam changes abruptly

at a point where shear force is zero

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For a solid circular shaft fixed at one end and a torque applied at the other end, which one of the following is TRUE?

Your answerChoose one option.

Every cross section of the shaft is subjected to the same internal torque

The internal torque gradually increases from one end of the shaft to the other end

Every cross section of the shaft is subjected to the same bending moment

No cross section of the shaft rotates relative to another cross section

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Flexural stress occurs in a straight beam when

Your answerChoose one option.

it is subjected to pure torsion

it is subjected to axial loads

it is subjected to transverse loads

it is subjected to combined axial and torsional loads

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The bending moment at a point in a beam changes its sign. Which one of the following is ALWAYS TRUE?

Your answerChoose one option.

The slope of the beam changes its sign at that point

The deflection of the beam changes its sign at that point

The shear force of the beam changes its sign at that point

The curvature of the beam changes its sign at that point

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The state of stress at a point in a body under plane stress condition is given as σ_x = 5 MPa, σ_y = −1 MPa and τ_xy = 4 MPa. If one of the principal stresses at that point is 7 MPa, then the other non-zero principal stress (in MPa) is _____

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A cantilever beam of constant cross section is subjected to a positive moment

and a positive axial force

as shown. The normal stress due to the axial force

is 200 MPa and the maximum compressive stress due to the moment

is 100 MPa. If the point A is located on the top surface and the point B is located on the centroidal axis of the beam, the stress elements at these points are (with stresses shown in MPa)

Diagram for Engineering Sciences question 11

Your answerChoose one option.

Diagram for Engineering Sciences question 11 (figure 2)

Diagram for Engineering Sciences question 11 (figure 3)

Diagram for Engineering Sciences question 11 (figure 4)

Diagram for Engineering Sciences question 11 (figure 5)

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A simply supported beam is subjected to a concentrated force P = 4800 N at the mid-span as shown. The flexural rigidity of the beam is EI = 11 × 10⁶ N·m². The curvature of the beam between points Q and R is given as κ = (Px/2EI). The magnitude of deflection (in mm) of the beam at x = 0.5 m is

Diagram for Engineering Sciences question 14

Your answerChoose one option.

0.5

1.0

1.5

2.0

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GATE XE Mechanics of deformable bodies PYQs

Question 22

Question 1

Question 2

Question 5

Question 6

Question 7

Question 8

Question 9

Question 11

Question 14