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GATE ME 2019 National Champion Quiz: Strength of Materials (App update required to attempt this test)

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Question 1

Wall thickness of a cylindrical shell of 800 mm internal diameter and 2m long is 10 mm. If the shell is subjected to an internal pressure of 1.5 MPa. Find the maximum intensity of shear stress induced in Mpa. Consider the cylindrical shell to be thin cylinder and circumferential stress remains constant along the wall thickness.

Question 2

A thin pressure vessel cylindrical in shape is subjected to a guage pressure of 50Mpa and it is of diameter 700mm and thickness 10 mm. Under such pressure diameter of the shell increases, find the final diameter (in mm) of the cylindrical vessel. If E=210Gpa and poisson ratio =0.15

Question 3

A boiler shell having a capacity of 2m3 is subjected to an internal pressure of 1600kPa. The strain guage readings in the longitudinal and perpendicular directions are 25×10-6 and
112.5×10-6. Due to this, the change in volume suffered by the boiler shell is (in cm3)

Question 4

For a hollow shaft under pure torsion, the maximum permissible value of torque is 3000Nm and its outer diameter is 50mm. Then, the value of ‘k’  (ration of inner diameter to outer diameter) will be? The allowable shear stress is 80 GPa

Question 5

A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of . Its elastic modulus varies along its length as given by , Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.

Question 6

For a shaft transmitting torque, the equivalent twisting moment is 20 kN-m and equivalent bending moment is 14 kN-m. If the allowable stresses in shear and bending are 50 MPa and 100 MPa respectively, then the minimum diameter of the shaft is ___ mm.

Question 7

For the simply supported beam shown in the figure, the location of maximum bending moment from left hand side will be
20.jpg

Question 8

A strain gage is a resistor where resistance changes with strain. It is a thin piece of conducting material which looks as wire. It gets glued on device where you want to measure strain. The small elongation in the strain gage produces a small change in the resistance of the strain gage.
An aluminium tube of length 500 mm having inside and outside diameters as 40 mm and 50 mm is compressed by forces F. A strain gage is placed outside the bar which measure normal strains in longitudinal direction. Calculate the shortening of bar if strain measures 350 x 10-5?

Question 9

A simply supported beam of length 2L is subjected to a moment M at the mid-point x = 0 as shown in the figure. The deflection in the domain 0 ≤ x ≤ L is given by

where E is the Young’s modulus, I is the area moment of inertia and c is a constant (to be determined) .

The slope at the center x = 0 is

Question 10

A slender bar of 100 mm2 cross-section is subjected to loading as shown in the figure. If the modulus of elasticity is taken as 200 × 109 Pa, then the elongation produced in the bar will be ____ mm.
16.jpg

Question 11

A spherical shell of internal diameter 0.9m and of thickness 10mm is subjected to internal pressure of 1.4N/. Determine the increase in volume (mm3). Take E=2×N/ and Poisson’s ratio of 1/3

Question 12

Consider a cantilever beam, having neglible mass and uniform flexural rigidity, with length 0.01m. The natural frequency of vibration of the beam, with 0.5kg mass attached at the free tip is 100Hz. The flexural rigidity (in Nm2)of the beam is
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