1. A ductile material having an endurance limit of 196 N/mm^{2} and the yield point at 294 N/mm^{2} is stressed under variable load. The maximum and minimum stresses are 147 N/mm^{2} and 49 N/mm^{2}. The fatigue stress concentration factor is 1.32. The available factor of safety for this loading is _______.
(a) 3.0
(b) 1.5
(c) 1.33
(d) 4.0
(2 Mark, 1987)

Ans: b
Explanation:
2. In the design of shafts made of ductile materials subjected to twisting moment and bending moment, the recommended theory of failure is
(a) maximum principal stress theory
(b) maximum principal strain theory
(c) maximum shear stress theory
(d) maximum strain energy theory
(1 Mark, 1988)

Ans: c
Explanation:
3. Stress concentration in a machine component of a ductile material is not so harmful as it is in a brittle material because
(a) In ductile material local yielding may distribute stress concentration.
(b) Ductile material has larger young’s material.
(c) Poisson’s ratio is larger in ductile materials.
(d) Modulus of rigidity is larger in ductile materials.
(1 Mark, 1989)

Ans: a
Explanation:
4. The processes of shot peening increases the fatigue life of steel springs mainly because it results in
(a) Surface hardening
(b) Increased stiffness of the material
(c) Structural changes in the material
(d) Residual compression at the surface
(1 Mark, 1990)

Ans: d
Explanation:
5. Torque to weight ratio for a circular shaft transmitting power is directly proportional to the
(a) square root of the diameter
(b) diameter
(c) square of the diameter
(d) cube of the diameter
(1 Mark, 1991)

Ans: b
We know, T=\frac { \pi }{ 16 } { d }^{ 3 }\tau
=> T=\frac { \pi }{ 16 } { d }^{ 3 }\times \frac { W }{ \frac { \pi }{ 4 } { d }^{ 2 } }
=> \frac { T }{ W } \propto d
6. In a shaft with a transverse hole, as the hole to the shaft diameter ratio _____(increase/ decrease), the torsional stress concentration factor ______.(increases/ decreases)
(1 Mark, 1991)

Ans: Increase, decrease
7. Fatigue strength of a rod subjected to cyclic axial force is less than that of a rotating beam of the same dimensions subjected to steady lateral force because
(a) Axial stiffness is less than bending stiffness
(b) Of absence of centrifugal effects in the rod
(c) The number of discontinuities vulnerable to fatigue are more in the rod
(d) At a particular time the rod has only one type of stress whereas the beam has both the tensile and compressive stresses
(1 Mark, 1992)

Ans: c
Explanation:
8. The yield strength of a steel shaft is twice its endurance limit. Which of the following torque fluctuations represent the most critical situation according to soderberg criterion?
(a) –T to +T
(b) –T/2 to +T
(c) 0 to +T
(d) +T/2 to +T
(1 Mark, 1993)

Ans: a
Explanation:
9. A small element at the critical section of a component is in a biaxial state of stress with the two principal stresses being 360 MPa and 140 MPa. The maximum working stress according to Distortion Energy Theory is:
(a) 220 MPa
(b) 110 MPa
(c) 314 MPa
(d) 330 MPa
(2 Mark, 1997)

Ans: c
According to Distortion energy theory,
\sqrt { { \sigma }_{ 1 }^{ 2 }+{ \sigma }_{ 2 }^{ 2 }{ \sigma }_{ 1 }{ \sigma }_{ 2 } } = \frac { { S }_{ yt } }{ FOS }
For maximum working stress, FOS = 1
Now, \sqrt { 360^{ 2 }+140^{ 2 }360\times 140 } ={ S }_{ yt }
=> { S }_{ yt }\simeq 314MPa
10. Which theory of failure will you use for aluminium components under steady loading:
(a) Principal stress theory
(b) Principal strain theory
(c) Strain energy theory
(d) Maximum shear stress theory
(1 Mark, 1999)

Ans: d
11. A static load is mounted at the centre of a shaft rotating at uniform angular velocity. This shaft will be designed for
(a) The maximum compressive stress (static)
(b) The maximum tensile (static)
(c) The maximum bending moment (static)
(d) Fatigue loading
(1 Mark, 2002)

Ans: d
12. In terms of theoretical stress concentration factor (K_{t}) and fatigue stress concentration factor (K_{f}), the notch sensitivity ‘q’ is expressed as
(a) \frac { \left( { k }_{ f }1 \right) }{ \left( { k }_{ t }1 \right) }
(b) \frac { \left( { k }_{ f }1 \right) }{ \left( { k }_{ t }+1 \right) }
(c) \frac { \left( { k }_{ t }1 \right) }{ \left( { k }_{ f }1 \right) }
(d) \frac { \left( { k }_{ f }+1 \right) }{ \left( { k }_{ t }1 \right) }
(1 Mark, 2004)

Ans: a
13. The SN curve for steel becomes asymptotic nearly at
(a) 10^{3} cycles
(b) 10^{4} cycles
(c) 10^{6} cycles
(d) 10^{9} cycles
(1 Mark, 2004)

Ans: c
14. A cylindrical shaft is subjected to an alternating stress of 100 MPa. Fatigue strength to sustain 1000 cycle is 490 MPa. If the corrected endurance strength is 70 MPa, estimated shaft life will be
(a) 1071 cycles
(b) 15000 cycles
(c) 281914 cycles
(d) 928643 cycles
(1 Mark, 2004)

Ans: c
15. A thin spherical pressure vessel of 200 mm diameter and 1 mm thickness is subjected to an internal pressure varying from 4 to 8MPa. Assume that the yield, ultimate and endurance strength of material are 600, 800 and 400MPa respectively. The factor of safety as per Goodman’s relation is
(a) 2.0
(b) 1.6
(c) 1.4
(d) 1.2
(2 Mark, 2007)

Ans: b
16. A forged steel link with uniform diameter of 30mm at the centre is subjected to an axial force that varies from 40kN in compression to 160kN in tension. The tensile (S_{u}), yield (S_{y}) and corrected endurance (S_{e}) strengths of the steel material are 600MPa, 420MPa and 240MPa respectively. The factor of safety against fatigue endurance as per Soderberg’s criterion is
(a) 1.26
(b) 1.37
(c) 1.45
(d) 2.00
(2 Mark, 2009)

Ans: a
17. A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The material has yield strength of 240 MPa and endurance limit in reversed bending is 160 MPa. According to the Soderberg principle, the area of crosssection in mm^{2} of the bar for a factor of safety of 2 is
(a) 400
(b) 600
(c) 750
(d) 1000
(2 Mark, 2013)

Ans: d
18. In a structure subjected to fatigue loading, the minimum and maximum stresses developed in a cycle are 200 MPa and 400 MPa respectively. The value of stress amplitude (in MPa) is
(1 Mark, 2014[2])

Ans: 100
19. A rotating steel shaft is supported at the ends. It is subjected to a point load at the centre. The maximum bending stress developed is 100 MPa. If the yield, ultimate and corrected endurance strength of the shaft material are 300 MPa, 500 MPa and 200 MPa, respectively, then the factor of safety for the shaft is ____.
(1 Mark, 2014[3])

Ans: 2
The rotating steel shaft is subjected to both tensile and compressive stress.
{ \sigma }_{ max }=100MPa, { \sigma }_{ min }=100MPa
Here, { \sigma }_{ m }=\frac { { \sigma }_{ max }+{ \sigma }_{ min } }{ 2 } = 0
{ \sigma }_{ a }=\frac { { \sigma }_{ max }{ \sigma }_{ min } }{ 2 } = 100 MPa
Since steel is ductile, By applying Soderberg’s criteria,
\frac { { \sigma }_{ m } }{ { \sigma }_{ y } } +\frac { { \sigma }_{ a } }{ { \sigma }_{ e } } = \frac { 1 }{ FOS }
=> 0+\frac { 100 }{ 200 } =\frac { 1 }{ FOS }
=> FOS = 2
20. Which one of following is NOT correct?
(a) Intermediate principal stress is ignored when applying the maximum principal stress theory.
(b) The maximum shear stress theory gives the most accurate results amongst all the failure theories.
(c) As per the maximum strain energy theory, failure occurs when the strain energy per unit volume exceeds a critical value.
(d) As per the maximum distortion energy theory, failure occurs when the distortion energy per unit volume exceeds a critical value.
(1 Mark, 2014[3])

Ans: b
21. A shaft is subjected to pure torsional moment. The maximum shear stress developed in the shaft is100 MPa. The yield and ultimate strengths of the shaft material in tension are 300 MPa and 450 MPa, respectively. The factor of safety using maximum distortion energy (vonMises) theory is _______.
(2 Mark, 2014[4])

Ans: 1.73
22. A machine element is subjected to the following biaxial state of stress: σ_{x} = 80 MPa; σ_{y} = 20 MPa; τ_{xy} = 40 MPa. If the shear strength of the material is 100 MPa, the factor of safety as per Tresca’s maximum shear stress theory is
(a) 1.0
(b) 2.0
(c) 2.5
(d) 3.3
(2 Mark, 2015[1])

Ans: b
23. Which one of the following is the most conservative fatigue failure criterion?
(a) Soderberg
(b) Modified Goodman
(c) ASME Elliptic
(d) Gerber
(1 Mark, 2015[1])

Ans: a
24. The uniaxial yield stress of a material is 300 MPa. According to von Mises criterion, the shear yield stress (in MPa) of the material is _______.
(1 Mark, 2015[2])

Ans: 173.2
According to Vonmises theory,
Shear yield stress \left( { \sigma }_{ ys } \right) =\frac { { { \sigma }_{ y } } }{ \sqrt { 3 } }
=> { \sigma }_{ ys }=\frac { { 300 } }{ \sqrt { 3 } } = 173.28 MPa
26. A machine component made of a ductile material is subjected to a variable loading with σ_{min} = 50 Mpa and σ_{max} = 50 Mpa. If the corrected endurance limit and the yield strength for the material are σ_{e}’ = 100 MPa and σ_{y} = 300 MPa, respectively, the factor of safety is ______.
(1 Mark, 2017[2])

Ans: 2
27. A machine element has an ultimate strength of 600 N/mm^{2}, and endurance limit of 250 N/mm^{2}. The fatigue curve for the element on a loglog plot is shown below. If the element is to be designed for a finite life of 10000 cycles, the maximum amplitude of a completely reversed operating stress is ______ N/mm^{2}.
(2 Mark, 2017[1])

Ans: 386.34
28. Fatigue life of a material for a fully reversed loading condition is estimated from σ_{a} = 1100N^{0.15}, where σ_{a} is the stress amplitude in MPa and N is the failure life in cycles. The maximum allowable stress amplitude (in MPa) for a life of 1\times { 10 }^{ 5 } cycles under the same loading condition is ________ (correct to two decimal places).
(1 Mark, 2018[2])

Ans: 195.61
We know, { \sigma }_{ a }=\frac { { \sigma }_{ max }{ \sigma }_{ min } }{ 2 }
Fora fully reverse loading, { \sigma }_{ min }={ \sigma }_{ max }
So, { \sigma }_{ a }=\frac { { \sigma }_{ max }\left( { \sigma }_{ max } \right) }{ 2 } ={ \sigma }_{ max }
Given, σ_{a} = 1100N^{0.15}
=> { \sigma }_{ max }=1100\times { \left( { 10 }^{ 5 } \right) }^{ 0.15 }
=> { \sigma }_{ max } = 195.61 MPa
29. Endurance limit of a beam subjected to pure bending decreases with
(a) Decrease in the surface roughness and increase in the size of the beam
(b) Increase in the surface roughness and decrease in the size of the beam
(c) Increase in the surface roughness and increase in the size of the beam
(d) Decrease in the surface roughness and decrease in the size of the beam
(1 Mark, 2019[2])

Ans: c