GATE XE Mechanics of deformable bodies PYQs & Answers — Page 4

Questions 31–40 of 133. Imported answers require independent review unless marked reviewed.

A 0-45-90 strain gauge rosette is mounted on an aircraft wing. The co-ordinate system is placed such that the strain gauges p, q and r are oriented at angles 0°, 45° and 90°, respectively, from the x axis (see figure). The strain readings associated to p, q and r are denoted by

, and

, respectively. While conducting a test the strain gauges show the following readings.

The developed engineering shear strain

associated to the strain gauge data is

Diagram for Engineering Sciences question 75

Your answerChoose one option.

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A rigid bar PQ is hinged at its end P. As shown in the figure, the bar is pin-connected through two identical links QS and RT at points Q and R, respectively. The other ends of the links, S and T, are fixed. Both links are made of the same material. If the temperature of the links is uniformly increased by

, then which one of the following statements is correct? (Neglect the weight of the rigid bar)

Diagram for Engineering Sciences question 76

Your answerChoose one option.

Both QS and RT will be stress free.

Both QS and RT will be under tension.

Both QS and RT will be under compression.

QS will be under compression and RT will be under tension.

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A critical point on a component is subjected to the state of stress

as given in the following. The yield strength of the material is 400 MPa. By considering maximum shear stress (Tresca) theory, the possible value(s) of

at the onset of yielding is/are,

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

340

680

−120

−460

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A plane passing through a point Q inside a body is shown. The unit normal of the plane is

, as shown in the figure. The traction (stress) vector on the plane at point Q is given by

MPa. Given that at point Q,

, the shear stress component

(in MPa, rounded off to two decimal places) is __________ .

Diagram for Engineering Sciences question 80

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A rigid massless bar PQ is hinged at its end P and supported through a spring of stiffness

at point Q. A vertically downward force

is applied at the free end R of the bar. If the vertical component of the displacement at R is 30 mm, then the stiffness of the spring (in kN/m, rounded off to one decimal place) is ___.

Diagram for Engineering Sciences question 81

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A beam of rectangular cross-section, as shown in the figure, is made of two perfectly bonded layers of different materials and equal thickness. The Young’s moduli of the two materials are

and

, where

. The beam is subjected to pure bending. If

mm, the distance of the neutral plane from the top surface of the beam is ______ (in mm, rounded off to two decimal places).

Diagram for Engineering Sciences question 82

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A stepped beam is made of a material whose Young’s modulus is E. The dimensions of the two stepped sections are such that the sectional moments of inertia,

and

, are related as

. The beam is fixed at one end and a load of F is applied at the free end as shown in the figure. Under this loading condition, if the strain energy of the stepped beam is written as

, then the value of

is ______ (rounded off to two decimal places).

Diagram for Engineering Sciences question 83

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A cylindrical pressure vessel is constructed by bolting two symmetric halves of flanged semi-cylindrical shells. A cross-sectional view of the vessel is shown in the figure. The inner diameter of the vessel is 2 m and the length is 10 m. Each row comprises 100 bolts along the length of the vessel. If the vessel is pressurized to a net pressure of

N/m

, and assuming that the end caps of the vessel do not take any load in the radial direction, then the load borne by each bolt is __________ (in kN, rounded off to one decimal place).

Diagram for Engineering Sciences question 84

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Two equivalent descriptions of the state of stress at a point are shown in the figure. The normal stresses

and

as shown on the right must be, respectively,

Diagram for Engineering Sciences question 68

Your answerChoose one option.

and

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The state of strain at a point in a machine component is given as

. The volumetric strain at this point is

Your answerChoose one option.

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GATE XE Mechanics of deformable bodies PYQs

Question 75

Question 76

Question 79

Question 80

Question 81

Question 82

Question 83

Question 84

Question 68

Question 69