Strength Of Materials In Me - Study Mode

Show All Answers

[#116] A composite bar made up of steel and copper bars of equal lengths are heated through 100°C. The stresses developed shall be

(A) Tensile in both the material

(B) Tensile in steel and compressive in copper

(C) Compressive in steel and tensile in copper

(D) Compressive in both the materials

Correct Answer

(B) Tensile in steel and compressive in copper

Explanation

Solution: When a composite bar made up of different materials, such as steel and copper, is heated, it experiences thermal expansion. Since steel has a higher coefficient of thermal expansion compared to copper, the following stress distribution occurs: Steel (outer material) expands more and tends to elongate, resulting in tensile stress.
Copper (inner material) expands less and tends to contract, resulting in compressive stress. So, in a composite bar made up of steel and copper bars of equal lengths heated through 100°C, the stresses developed shall be tensile in steel and compressive in copper . This is represented by Option B .

[#117] The extension of a circular bar tapering uniformly from diameter d 1 at one end to diameter d 2 at the other end and subjected to an axial pull of ‘P’ is given by

(A) $$delta l = frac{{4{ ext{PE}}}}{{pi {l^2}}}$$

(B) $$delta l = frac{{4pi l{{ ext{d}}^2}}}{{{ ext{PE}}}}$$

(C) $$delta l = frac{{4{ ext{P}}l}}{{pi { ext{E}}{{ ext{d}}_1}{{ ext{d}}_2}}}$$

(D) $$delta l = frac{{4{ ext{P}}l{ ext{E}}}}{{pi {{ ext{d}}_1}{{ ext{d}}_2}}}$$

Correct Answer

[#118] The polar moment of inertia of a solid circular shaft of diameter (D) is

(A) $$frac{{pi {{ ext{D}}^3}}}{{16}}$$

(B) $$frac{{pi {{ ext{D}}^3}}}{{32}}$$

(C) $$frac{{pi {{ ext{D}}^4}}}{{32}}$$

(D) $$frac{{pi {{ ext{D}}^4}}}{{64}}$$

Correct Answer

[#119] The polar modulus for a solid shaft of diameter (D) is

(A) $$frac{{pi {{ ext{D}}^2}}}{4}$$

(B) $$frac{{pi {{ ext{D}}^3}}}{{16}}$$

(C) $$frac{{pi {{ ext{D}}^3}}}{{32}}$$

(D) $$frac{{pi {{ ext{D}}^4}}}{{64}}$$

Correct Answer

(B) $$frac{{pi {{ ext{D}}^3}}}{{16}}$$

[#120] Which of the following statement is wrong?

(A) The deformation of the bar per unit length in the direction of the force is called linear strain.

(B) The Poisson's ratio is the ratio of lateral strain to the linear strain.

(C) The ratio of change in volume to the original volume is called volumetric strain.

(D) The bulk modulus is the ratio of linear stress to the linear strain.

(E) In the theory of simple bending, the assumption is that the plane sections before bending remains plane after bending.

(F) In a beam subjected to bending moment, the strain is directly proportional to the distance from the neutral axis.

(G) At the neutral axis of a beam, the bending stress is maximum.

(H) The bending stress in a beam is inversely proportional to the section modulus.

Correct Answer

(D) The bulk modulus is the ratio of linear stress to the linear strain.
(G) At the neutral axis of a beam, the bending stress is maximum.