Q1:

If two springs of stiffness $k_1{\text{ and k}}_{\text{2}}$are connected in series, the stiffness of the equivalent spring is

Q2:

Two closed springs of stiffness "k" and "2k" are arranged in series in one case and in parallel in the other case. The ratio of stiffness of springs connected in series to parallel is -

Q3:

If three close -coiled and two open - coiled helical springs, each having the stiffness K are connected in series then the overall stiffness is - 

Q4:

Two co-axial springs are subjected to a force of 1 KN. Springs constant of larger diameter springs is 80 N/mm and that of smaller diameter spring is 120 N/mm. The deformation in the spring combination will be equal to -

Q5:

What is the equivalent spring stiffness for the system of springs shown in the figure given below?

Q6:

A close helical spring of 100 mm mean diameter is made of 10 mm diameter rod, and has 20 turns, The spring carries an axial load of 200 KN with $G=8.4\times {10}^{4}N/m{m}^2.$The stiffness of the spring is nearly

Q7:

A closely coiled helical spring of round steel wire 5 mm in diameter having 12 complete coils of 50 mm mean diameter is subjected to an axial load of 100 N. Modulus of rigidity of the spring is 80 KN/mm². What is the deflection of the spring?

Q8:

Two closely coiled helical springs, A and B are equal in all respects but for the number of turns, with A having just half the number of turns of that of B. What is the ratio of deflections in terms of spring A to spring B?

Q9:

A closed coiled spring is cut into two identical halves. The stiffness of each of the resulting springs will -

Q10:

Which one of the following pairs is not correctly matched?

Boundary conditions of column	Euler’s buckling load
a) pin – pin	$\frac{{\pi }^{2}EI}{l^2}$
b) fixed – fixed	$\frac{4{\pi }^{2}EI}{l^2}$
c) fixed – free	$\frac{0.25{\pi }^{2}EI}{l^2}$
d)fixed – pin	$\frac{\sqrt{2}{\pi }^{2}EI}{l^2}$

 

Q11:

For a circular column having its ends hinged, the slenderness ratio is 160. The (l/d) ratio of the column is

Q12:

Assertion (A) :  The buckling load for a column of specified material, cross – section and end conditions calculated as per euler’s formula varies inversely with the column length.

Reason (R) : Euler’s formula takes into account the end conditions in determining the effective length of column.

Of these statements -

Q13:

The ratio of the theoretical critical buckling load for a column with fixed ends to that of another column with the same dimensions and material, but with pinned ends is equal to

Q14:

A circular column of length 2 m has euler’s crippling load of 1.5 KN. If the diameter of the column is reduced by 10% the reduction in the crippling load will be

Q15:

The dimensions ration of a compressive member in the context of rankine’s formula is defined as -

Q16:

If the euler load for a steel column is 1000 KN and crushing load is 1500 KN, the rankine load is equal to

Q17:

The strain energy per unit volume of a round bar under uniaxial tension with stress $\sigma$and modulus of elasticity E is

Q18:

A cantilever beam, 2m in length, is subjected to a uniformly distributed load of 5 kN/m. If E = 200 GPa and I = 1000 cm⁴, the strain energy stored in the beam will be

Q19:

A power transmission solid shaft of diameter d, length l and rigidity modulus G is subjected to a pure torque. The maximum allowable shear stress is${\tau }_{\max }$. The maximum strain energy unit volume in the shaft is given by:

Q20:

Match List-I 3with List-II and select the correct answer using the code given below the lists:

List-I	List-II
A. Point of inflection	1. Strain energy
B. Shearing strain	2. Equation of bending
C. Section modulus	3. Equation of torsion
D. Modulus of resilience	4. Bending moment diagram

Code:

$\begin{array}{cccc}A& B& C& D\end{array}$

Q21:

A steel specimen 150 mm² in cross-section stretches by 0.05 mm over a 50 mm gauge length under an axial load of 30 kN. What is the strain energy stored in the specimen?

(Take E = 200 GPa)

Q22:

The maximum distortion energy theory of failure is suitable to predict the failure of which one of the following types of materials?

Q23:

A rod of cross- sectional area $100\times {10}^{-6}{m}^2$is subjected to a tensile load. Based on the Tresca failure criterion. If the uniaxial yield stress of the material is 200 MPa, the failure load is

Q24:

A circular solid shaft is subjected to bending moment of 400 kN-m and a twisting moment of 300 kN-m. On the basis of the maximum principal stress theory, the direct stress is $\sigma$and according to the maximum shear stress theory, the shear is $\tau$. The ratio $\sigma /\tau$is

Q25:

Permissible bending moment in a circular shaft under pure bending is M according to maximum principal stress theory of failure. The permissible bending moment in the same shaft  as per maximum shear stress of failure is