GATE ME concept:stress PYQs & Answers — Page 2

Questions 11–20 of 49. Imported answers require independent review unless marked reviewed.

The principal stresses at a point P in a solid are 70 MPa, −70 MPa and 0. The yield stress of the material is 100 MPa. Which prediction(s) about material failure at P is/are CORRECT?

Your answerSelect all correct options. You can choose more than one.

Maximum normal stress theory predicts that the material fails

Maximum shear stress theory predicts that the material fails

Maximum normal stress theory predicts that the material does not fail

Maximum shear stress theory predicts that the material does not fail

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Which of the plot(s) shown is/are valid Mohr’s circle representations of a plane stress state in a material? (The center of each circle is indicated by O.)

Diagram for Mechanical Engineering question 27

Your answerSelect all correct options. You can choose more than one.

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The figure shows a thin-walled open-top cylindrical vessel of radius

and wall thickness

. The vessel is held along the brim and contains a constant-density liquid to height

from the base. Neglect atmospheric pressure, the weight of the vessel and bending stresses in the vessel walls.

Which one of the plots depicts qualitatively CORRECT dependence of the magnitudes of axial wall stress (

) and circumferential wall stress (

) on

Diagram for Mechanical Engineering question 40

Your answerChoose one option.

Diagram for Mechanical Engineering question 40 (figure 2)

Diagram for Mechanical Engineering question 40 (figure 3)

Diagram for Mechanical Engineering question 40 (figure 4)

Diagram for Mechanical Engineering question 40 (figure 5)

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Cylindrical bars P and Q have identical lengths and radii, but are composed of different linear elastic materials. The Young’s modulus and coefficient of thermal expansion of Q are twice the corresponding values of P. Assume the bars to be perfectly bonded at the interface, and their weights to be negligible.

The bars are held between rigid supports as shown in the figure and the temperature is raised by

. Assume that the stress in each bar is homogeneous and uniaxial. Denote the magnitudes of stress in P and Q by

and

, respectively.

Which of the statement(s) given is/are CORRECT?

Diagram for Mechanical Engineering question 46

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The interface between P and Q moves to the left after heating

The interface between P and Q moves to the right after heating

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Which one of the following is the definition of ultimate tensile strength (UTS) obtained from a stress-strain test on a metal specimen?

Your answerChoose one option.

Stress value where the stress-strain curve transitions from elastic to plastic behavior

The maximum load attained divided by the original cross-sectional area

The maximum load attained divided by the corresponding instantaneous cross-sectional area

Stress where the specimen fractures

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A structural member under loading has a uniform state of plane stress which in usual notations is given by

and

, where

. The yield strength of the material is 350 MPa. If the member is designed using the maximum distortion energy theory, then the value of

at which yielding starts (according to the maximum distortion energy theory) is

Your answerChoose one option.

70 MPa

90 MPa

120 MPa

75 MPa

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Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the following statement(s) is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

A body subjected to hydrostatic pressure has no shear stress.

If a long solid steel rod is subjected to tensile load, then its volume increases.

Maximum shear stress theory is suitable for failure analysis of brittle materials.

If a portion of a beam has zero shear force, then the corresponding portion of the elastic curve of the beam is always straight.

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A linear elastic structure under plane stress condition is subjected to two sets of loading, I and II. The resulting states of stress at a point corresponding to the two loads are shown in the figure below. If these two sets of loading are applied simultaneously, then the net normal component of stress

is ______.

Diagram for Mechanical Engineering question 38

Your answerChoose one option.

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A shaft of length

is made of two materials, one in the inner core and the other in the outer rim, and the two are perfectly joined together (no slip at the interface) along the entire length of the shaft. The diameter of the inner core is

and the external diameter of the rim is

, as shown in the figure. The modulus of rigidity of the core and rim materials are

and

, respectively. It is given that

and

. When the shaft is twisted by application of a torque along the shaft axis, the maximum shear stress developed in the outer rim and the inner core turn out to be

and

, respectively. All the deformations are in the elastic range and stress-strain relations are linear. Then the ratio

is _____ (round off to 2 decimal places).

Diagram for Mechanical Engineering question 50

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A rigid beam AD of length

m is hinged at frictionless pin joint A and supported by two strings as shown in the figure. String BC passes over two small frictionless pulleys of negligible radii. All the strings are made of the same material and have equal cross-sectional area. A force

kN is applied at C and the resulting stresses in the strings are within linear elastic limit. The self-weight of the beam is negligible with respect to the applied load. Assuming small deflections, the tension developed in the string at C is ________ kN (round off to 2 decimal places).

Diagram for Mechanical Engineering question 51

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GATE ME concept:stress PYQs

Question 26

Question 27

Question 40

Question 46

Question 16

Question 18

Question 26

Question 38

Question 50

Question 51