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GATE ME Strength of Materials : National Champion Test

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Question 1

For a circular shaft of diameter d subjected to torque T, the maximum value of the shear stress is:

Question 2

Which option is correct if torsion load is applied on cylindrical bar as shown?

Question 3

A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of T. The Young’s modulus is E and the coefficient of linear expansion is α. The thermal stress in the rod is Δ

Question 4

One-half length of 50 mm diameter steel rod is solid while the remaining half is hollow having a bore of 25 mm. The rod is subjected to equal and opposite torque at its ends. If the maximum shear stress in solid portion is Description: Description:ISROME2009_files\image021.png, the maximum shear stress in the hollow portion is

Question 5

In a body, thermal stress is induced because of the existence of:

Question 6

The ratio of Euler’s buckling loads of columns with the same parameters having (i) both ends fixed, and (ii) both ends hinged is

Question 7

Four vertical columns of same material, height and weight have the same end conditions .Which cross-section will carry the maximum load?

Question 8

A metal rod of initial length Lo is subjected to a drawing process. The length of the rod at any instant is given by the expression, L(t)= Lo (1+t2) , where t is the time in minutes. The true strain rate (in min-1) at the end of one minute is ________.

Question 9

A 1.5 mm thick sheet is subject to unequal biaxial stretching and the true strains in the directions of stretching are 0.05 and 0.09. The final thickness of the sheet in mm is

Question 10

A simply supported beam carries a load ‘P’ through a bracket, as shown in figure. The maximum bending moment in the beam is

Question 11

A simply supported beam of span length 6 m and 75 mm diameter carries a uniformly distributed load of 1.5 kN/m.
What is the maximum value of bending moment?

Question 12

A 4 m long solid round bar is used as a column having one end fixed and the other end free. If Euler’s critical load on this column is found as 10 kN and E =210 GPa for the material of the bar, the diameter of the bar is ___________.

Question 13

A simply-supported beam of length 3L is subjected to the loading shown in the figure.
 
It is given that P = 1 N, L = 1 m and Young’s modulus E = 200 GPa. The cross-section is a square with dimension 10 mm × 10 mm. The bending stress (in Pa) at the point A located at the top surface of the beam at a distance of 1.5L from the left end is_____________ (Indicate compressive stress by a negative sign and tensile stress by a positive sign.)

Question 14

A hollow shaft (do = 2di where do and di are the outer and inner diameters respectively) needs to transmit 20 kW power at 3000 RPM. If the maximum permissible shear stress is 30 MPa, do is

Question 15

The diameter of a solid shaft made of mild steel, rotating at 250 rpm is 45 mm. the shaft is designed to transmit 50 kW. What will be the factor of safety if the ultimate sear stress at yield is 427 N/mm2?

Question 16

What is the safe working pressure for a spherical pressure vessel 1.5m internal diameter and 1.5 cm wall thickness? If the maximum allowable tensile stress is 45 MPa?

Question 17

A beam ABCD ,6 m along, is supported at B and C, 3 m apart with overhangs AB=2 m and CD=1m . It carries a uniformly distributed load of 100 kN/m over its entire length:
Description: F:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE-22-April\GATE-IES-ME-Strength-of-Materials_files\image277.jpg
The maximum magnitude of bending moment and shear force are

Question 18

The maximum and minimum shear stresses in a hollow circular shaft of outer diameter 20mm and thickness 2mm. Subjected to a torque of 92.7 N.m will be

Question 19

A symmetric I–section (with width of each flange = 50 mm, thickness of each flange = 10 mm, depth of web = 100 mm, and thickness of web = 10 mm) of steel is subjected to a shear force of 100 kN. Find the magnitude of the shear stress (in N/mm2) in the web at its junction with the top flange.____________

Question 20

An axially loaded bar is subjected to a normal stress of 173 MPa. The maximum shear stress in the bar is

Question 21

A beam has the same section throughout its length I= 1108 mm4. It is subjected to a uniform Bm=40 kN-m, E=2 105 N/mm2. What is the radius of curvature of the circle into which the beam will bend in the form of an arc of a circle?

Question 22

Which one of the following diagrams indicates the shear stress distribution for the beam as shown in the figure below?

Question 23

Two plates each of 50 mm 50 mm section are glued together along the length to form a section 50 mm 100 mm, used as a beam. If the shear force at a section is 1000 N. What is the maximum shear stress on the glue?

Question 24

Cross–section of a column consisting of two steel strips, each of thickness t and width b is shown in the figure below. The critical loads of the column with perfect bond and without bond between the strips are P and P0 respectively. The ratio P/P0 is

Question 25

A metal bar of length 100mm is inserted between two rigid supports and its temperature is increased by 10 °C. If the coefficient of thermal expansion is 12 x 10–6 per °C and the Young's modulus is 2 x 105 MPa the stress in the bar is

Question 26

The rod PQ of length L and with flexural rigidity EI is hinged at both ends. For what minimum force F is it expected to buckle?

Question 27

A simply supported beam of length l is loaded by a uniformly distributed load w over the entire span. It is propped at the mid span so that the deflection at the centre is zero. The reaction at the prop is:

Question 28

It is observed that Fracture voids are usually form at

Question 29

A 200 mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by 250 °C. If the Young's modulus and coefficient of thermal expansion are 200 GPa and Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE-ME-2014-Set-1_files\image133.png, respectively, the magnitude of the longitudinal stress (in MPa) developed in the rod

is _______

Question 30

The bending moment (M) and twisting moment (T) at four particular section P, Q, R and S along the length of a shaft are as follows:
Description: F:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE-22-April\GATE-IES-ME-Strength-of-Materials_files\image410.jpg
Which section is to be considered for designing the shaft?
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