GATE CE 2021: STRENGTH OF MATERIAL#12 (App update required to attempt this test)
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Question 1
The Euler’s crippling load for a 2 m long slender steel rod of uniform cross section hinged at both the ends is 1 KN. The Euler’s crippling load for 1m long steel rod of the same cross section and hinged at both ends will be __________.
Question 2
A cantilever beam of length 2 m with a square section of side length 0.1m is loaded vertically at the free end. The vertical displacement at the free end is 5mm. The beam is made of steel with Young’s modulus of 2×1011N/m2. The maximum bending stress (in MPa) at the fixed end of the cantilever is
Question 3
A member of a beam is subjected to axial compressive load & moment as shown in figure
Stress at point ‘A’ will be (in MPa)
Question 4
Statement – I: In a beam of I-Cross section most of shear force is carried out by the web.
Statement – II: In I-sections with thin flanges the vertical stress values are quite small and usually are Ignored.
Question 5
Determine the final volume (in mm3) of steel bar which has 4 m length, 30 mm wide and 20 mm thick and which has an axial pull of 30 kN in the direction of its length. Take, E= 2×105 N/mm2 and Poisson’s ratio is 0.3
Question 6
The ratio of power transmission capacities of a solid and hollow circular shaft when they are rotating at the same rpm. Given that material, weight and length are same for both the shafts and k is the ratio of inner to outer diameter of the hollow shaft.
Question 7
What is the ratio of volumetric strain of a thin cylinder to that of a thin spherical shell having the same internal pressure, same material and same internal diameter and thickness of spherical is twice that of cylindrical? [Take poisson’s ratio = 0.4]
Question 8
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 , respectively, the magnitude of the longitudinal stress (in MPa) developed in the rod
is _______
Question 9
A steel rod of 200mm length held between two rigid supports is heated by 35 K. If the coefficient of thermal expansion is 15 × 10-6 per K and modulus of elasticity is 200 GPa. The stress induced in the rod is _____
Question 10
A 45° strain rosette used for testing of an airplane wing gave the following readings :
The figure shows a steel bar subjected to various loads. The bar has area and modulus of elasticity. The strain energy stored in the bar is :
Question 12
A simply supported beam has the square cross-section having moment of inertia 1728 mm4. It carries a uniformly distributed load of intensity 10 N/m. Considering only the top fibre of beam, the correct representation of the longitudinal variation of the bending stress is (consider sagging B.M positive & compressive bending stress positive)
Question 13
A simply supported beam AB is subjected to two point loads of 5N each as shown in the figure below. The bending moment at the mid-point of the beam is_____Nm (correct to one decimal place)
Question 14
A steel beam of breadth 120 mm and height 750 mm is loaded as shown in the figure. Assume Esteel = 200GPa.
The beam is subjected to a maximum bending moment of
Question 15
In the cantilever beam ABC as shown in figure, the segment AB has flexural rigidity EI and the segment BC has infinite flexural rigidity. The deflection and slope of the beam at C are respectively.
, respectively, the magnitude of the longitudinal stress (in MPa) developed in the rod 
and modulus of elasticity 
. The strain energy stored in the bar is :
