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QUESTION: 1

Two shaft of same material and same length are connected in series and subjected to a torque T as shown in the figure given below?

If d_{2}/d_{1} = 2, what is the value of τ_{1}/τ_{2}?

(where τ_{1} and τ_{2} are extreme shear stresses in either of the two segments)

Solution:

QUESTION: 2

A shaft PQRS is subjected to torques at P,Q, R, S as shown in the given figure. The maximum torque for the shaft section occurs between

Solution:

QUESTION: 3

A spring of stiffness 1 kN/m is stretched initially by 100 mm from the underformed position. The work required to stretch it by another 100 mm is

Solution:

k = 10^{3}/10^{3} = 1N/mm

s_{i} = 100 mm

F_{i} = 1 x 100 = 100 N

Additional work required,

QUESTION: 4

A close-coifed helical spring of stiffness 4 N/mm is in series with another spring of stiffness 6 N/mm. What is the stiffness of composite spring?

Solution:

Let the stiffness of composite spring = k

∴ 1/k = 1/k_{1} + 1/k_{2}

∴

QUESTION: 5

Stiffness of a close-coiled helical spring of wire diameter d, modulus of rigidity G number of coils n, mean coil radius R, is

Solution:

QUESTION: 6

Wahl’s factor takes into account

Solution:

QUESTION: 7

A spring with 25, active Coils cannot be accommodated within a given space. Hence 5 coils of the spring are cut. What is the stiffness of the new spring.

Solution:

As we know, k ∝ 1/n

∴ k_{2}/k_{1} = n_{1}/n_{2} = 25/20 = 1.25

⇒ k_{2} = 1.25 k_{1}

QUESTION: 8

A close-coiled helical spring has 100 mm mean diameter and is made of 20 turns of 10 mm diameter steel wire. The spring carries an axial load of 100 N. Modulus of rigidity is 84 GPa. The shearing stress developed in the spring in N/mm^{2} is

Solution:

Closed coiled helical spring subjected to axial load (W) means that every section is subjected to torsion of WR where R is the radius of spring. From torsion formula,

d= diameter of wire

d = 10mm

W = 100 N

Shear stress due to load,

QUESTION: 9

A carriage spring of span 'l’ consists of n plates each of thickness ‘t' and width b. If the spring carries a load w and modulus of elasticity of the spring is E, then the central deflection of the spring is

Solution:

QUESTION: 10

A solid shaft of diameter d is subjected to twisting moment T, such that the maximum shear stress developed is τ. Now a hole of 0.5 d diameter is drilled throdghout the length of the shaft along the axis. How much torque Tmust be reduced so that shear stress remain the same?

Solution:

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