1. If the length of a column is doubled, the critical load becomes
(a) 1/2 of the original value
(b) 1/4 of the original value
(c) 1/8 of the original value
(d) 1/16 of the original value
(1 Mark, 1988)

Ans: b
2. For the case of a slender column of length l and flexural rigidity EI builtin at its base and free at the top, the Euler’s critical buckling load is
(a) \frac { 4{ \pi }^{ 2 }EI }{ { l }^{ 2 } }
(b) \frac { 2{ \pi }^{ 2 }EI }{ { l }^{ 2 } }
(c) \frac {{ \pi }^{ 2 }EI }{ { l }^{ 2 } }
(d) \frac {{ \pi }^{ 2 }EI }{4{ l }^{ 2 } }
(1 Mark, 1994)

Ans: d
3. The deflection of a spring with 20 active turns under a load of 1000 N is 10 mm. The spring is made into two pieces each of 10 active coils and placed in parallel under the same load. The deflection of the system is:
(a) 20 mm
(b) 10 mm
(c) 5 mm
(d) 2.5 mm
(2 Mark, 1995)

Ans: d
4. A weighing machine consists of a 2 kg pan resting on a spring. In this condition, the pan resting on the spring, the length of the spring is 200 mm. When a mass of 20 kg is placed on the pan, the length of the spring becomes 100 mm. For the spring, the undeformed length l_{o} and the spring constant k (stiffness) are
(a) l_{o} = 220 mm, k = 1862 N/m
(b) l_{o} = 210 mm, k = 1960 N/m
(c) l_{o} = 200 mm, k = 1960 N/m
(d) l_{o} = 200 mm, k = 2156 N/m
(2 Mark, 2005)

Ans: b
5. A pinended column of length L, modulus of elasticity E and second moment of the crosssectional area is I loaded concentrically by a compressive load P. the critical buckling load (P_{cr}) is given by
(a) P_{cr }= \frac { EI }{ { { \pi }^{ 2 }l }^{ 2 } }
(b) P_{cr }= \frac { { \pi }^{ 2 }EI }{ { 3l }^{ 2 } }
(c) P_{cr }= \frac { { \pi }EI }{ { l }^{ 2 } }
(d) P_{cr }= \frac { { \pi }^{ 2 }EI }{ { l }^{ 2 } }
(1 Mark, 2006)

Ans: d
5. The piston rod of diameter 20 mm and length 700 mm in a hydraulic cylinder is subjected to a compressive force of 10 kN due to the internal pressure. The end conditions for the rod may be assumed as guided at the piston end and hinged at the other end. The Young’s modulus is 200 GPa. The factor of safety for the piston rod is
(a) 0.68
(b) 2.75
(c) 5.62
(d) 11.0
(2 Mark, 2007)

Ans: c
6. The rod PQ of length L with flexural rigidity EI is hinged at both ends. For what minimum force F is it expected to buckle?
(a) \frac { { \pi }^{ 2 }EI }{ { l }^{ 2 } }
(b) \frac { { \sqrt { 2 } \pi }^{ 2 }EI }{ { l }^{ 2 } }
(c) \frac { { \pi }^{ 2 }EI }{ { \sqrt { 2 } l }^{ 2 } }
(d) \frac { { \pi }^{ 2 }EI }{ { 2l }^{ 2 } }
(2 Mark, 2008)

Ans: b
7. A compression spring is made of music wire of 2mm diameter having a shear strength and shear modulus of 800 MPa and 80 GPa respectively. The mean coil diameter is 20mm, free length is 40mm and the number of active coils is 10. If the mean coil diameter is reduced to 10mm, the stiffness of the spring is approximately
(a) decreased by 8 times
(b) decreased by 2 times
(c) increased by 2 times
(d) increased by 8 times
(2 Mark, 2008)

Ans: d
8. A column has a rectangular crosssection of 10mm x 20mm and a length of 1 m. The slenderness ratio of the column is close to
(a) 200
(b) 346
(c) 477
(d) 1000
(1 Mark, 2011)

Ans: b
9. For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is
(a) 1
(b) 2
(c) 4
(d) 8
(1 Mark, 2012)

Ans: c
10. Consider a steel (Young’s modulus E = 200 GPa) column hinged on both sides. Its height is 1.0 m and crosssection is 10 mm × 20 mm. The lowest Euler critical buckling load (in N) is ______.
(1 Mark, 2015[1])

Ans: 3289.868
11. The spring constant of a helical compression spring DOES NOT depend on
(a) coil diameter
(b) material strength
(c) number of active turns
(d) wire diameter
(1 Mark, 2016[1])

Ans: b
12.An initially stressfree massless elastic beam of length L and circular crosssection with diameter d (d << L) is held fixed between two walls as shown. The beam material has Young’s modulus E and coefficient of thermal expansion α.
If the beam is slowly and uniformly heated, the temperature rise required to cause the beam to buckle is proportional to
(a) d
(b) d^{2}
(c) d^{3}
(d) d^{4}
(2 Mark, 2017[1])

Ans: b
13. A helical compression spring made of a wire of circular crosssection is subjected to a compressive load. The maximum shear stress induced in the crosssection of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the crosssection of the wire is _______.
(2 Mark, 2017[2])

Ans: 6
14. If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in %) is _____ (correct to two decimal places).
(1 Mark, 2018[1])

Ans: 8.24
15. A steel column of rectangular section (15 mm × 10 mm) and length 1.5 m is simply supported at both ends. Assuming modulus of elasticity, E = 200 GPa for steel, the critical axial load (in kN) is ____ (correct to two decimal places).
(1 Mark, 2018[1])

Ans: 1.1
16. The minimum axial compressive load, P, required to initiate buckling for a pinnedpinned slender column with bending stiffness EI and length L is
(a) P=\frac { { \pi }^{ 2 }EI }{ 4{ L }^{ 2 } }
(b) P=\frac { { \pi }^{ 2 }EI }{ { L }^{ 2 } }
(c) P=\frac { { 3\pi }^{ 2 }EI }{ { 4L }^{ 2 } }
(d) P=\frac { { 4\pi }^{ 2 }EI }{ { L }^{ 2 } }
(1 Mark, 2018[2])

Ans: b