GATE (CE) 2022 : Strength Of Materials Quiz #5

Two identical wooden beams of same cross section are joined together rigidly to form a composite beam. The ratio of moment of inertia of the soldered beam to the moment of inertia when beams are simply placed on each other without soldering is

Statement 1: For a rigidly connected composite material, moment of resistance of composite section will be equal to sum of individual moment of resistance of component material.

Statement 2: All component material will have same radius of curvature.

Kern of a section is

(i) The region in which compressive load can be applied without producing any tension.

(ii) Of square shape for a rectangular cross section.

(iii) Depends upon eccentricity of loading

Which of the above statements are correct?

The ratio of moment of inertia of the composite beam when the whole section is transformed into wood to when the whole section is transformed into steel is

(Here m is the modular ratio of steel and wood)

A circular cantilever beam 2m long and 150 mm dia is subjected to a twisting moment of 30 kNm. The angle of twist of the beam if the modulus of elasticity of material is 1.9 ×10⁵ N/mm². Assume Poisson ratio to be 0.25.

A solid circular shaft is used to transmit a torque equal to 50 kN-m. If the circular shaft is replaced by a hollow shaft of same material having same torsional rigidity inside diameter of which is half the outside diameter, the ratio of diameter of solid shaft to outer diameter of hollow shaft will be

A circular shaft of diameter 300 mm and length 2.5 m is subjected to a torque, such that the angle of twist due to torsion is 0.025 radian. If the diameter and length of the shaft is doubled, the percentage decrease in the angle of twist will be