
A tapering bar (diameters of end sections being \[{{d}_{1}}\] and\[{{d}_{2}}\]) and a bar of uniform crosssection 'd' have the same length and are subjected to the same axial pull. Both the bars will have the same extension if 'd' is equal to
A)
\[\frac{{{d}_{2}}+{{d}_{2}}}{2}\] done
clear
B)
\[\sqrt{{{d}_{1}}{{d}_{2}}}\] done
clear
C)
\[\sqrt{\frac{{{d}_{1}}{{d}_{2}}}{2}}\] done
clear
D)
\[\sqrt{\frac{{{d}_{2}}+{{d}_{2}}}{2}}\] done
clear
View Solution play_arrow

Which of the following is true (\[\mu =\] Poisson's ratio):
A)
\[0<\mu <\text{1/2}\] done
clear
B)
\[1<\mu <0\] done
clear
C)
\[1<\mu <1\] done
clear
D)
\[\infty <\mu <\infty \] done
clear
View Solution play_arrow

For most brittle materials, the ultimate strength in compression is much larger than the ultimate strength is tension. That is mainly due to:
A)
Presence of flaws and microscopic cracks or cavities done
clear
B)
Necking in tension done
clear
C)
Severity of tensile stress as compared to compressive stress done
clear
D)
nonlinearity of stressstrain diagram. done
clear
View Solution play_arrow

Bending moment M and torque T is applied on a solid circular shaft. If the maximum bending stress equals to maximum shear stress developed, then M is equal to:
A)
\[\frac{T}{2}\] done
clear
B)
T done
clear
C)
2T done
clear
D)
4T done
clear
View Solution play_arrow

When bending moment M and torque T is applied on a shaft then equivalent torque is:
A)
M+T done
clear
B)
\[\sqrt{{{M}^{2}}+{{T}^{2}}}\] done
clear
C)
\[\frac{1}{2}\sqrt{{{M}^{2}}+{{T}^{2}}}\] done
clear
D)
\[\frac{1}{2}\left( m+\sqrt{{{M}^{2}}+{{T}^{2}}} \right)\] done
clear
View Solution play_arrow

A helical spring has N turns of coil of diameter D, and a second spring, made of same wire diameter and of same material, has N/2 turns of coil of diameter 2D. If the stiffness of the first spring is k, then the stiffness of the second spring will be:
A)
k/4 done
clear
B)
k/2 done
clear
C)
2k done
clear
D)
4k done
clear
View Solution play_arrow

If a prismatic bar be subjected to an axial tensile stress \[\sigma \] then shear stress induced on a plane inclined at \[\theta \] with the axis will be:
A)
\[\frac{\sigma }{2}\,\sin 2\theta \] done
clear
B)
\[\frac{\sigma }{2}\,\cos 2\theta \] done
clear
C)
\[\frac{\sigma }{2}\,{{\cos }^{2}}\theta \] done
clear
D)
\[\frac{\sigma }{2}\,{{\sin }^{2}}\theta \] done
clear
View Solution play_arrow

Select the proper sequence
1. Proportional Limit 
2. Elastic limit 
3. Yielding 
4. Failure 
A)
2, 3, 1, 4 done
clear
B)
2, 1, 3, 4 done
clear
C)
1, 3, 2, 4 done
clear
D)
1, 2, 3, 4 done
clear
View Solution play_arrow

The relationship between constants E. G and K given by:
A)
\[E=\frac{G+3K}{9KG}\] done
clear
B)
\[E=\frac{3G+K}{9KG}\] done
clear
C)
\[E=\frac{9KG}{G+3K}\] done
clear
D)
\[E=\frac{9KG}{3G+K}\] done
clear
View Solution play_arrow

For the two shafts in parallel, find which statements is true?
A)
Torque in each shaft is the same done
clear
B)
Shear stress in each shaft is the same done
clear
C)
Angle of twist of each shaft is the same done
clear
D)
Torsional stiffness of each shaft is the same done
clear
View Solution play_arrow

A vertical hanging bar of length L and weighing w N/unit length carries a load W at the bottom. The tensile force in the bar at a distance y from the support will be given by:
A)
\[W+wL\] done
clear
B)
\[W+w\,(Ly)\] done
clear
C)
\[(W+w)\,\text{y/L}\] done
clear
D)
\[W+\frac{W}{w}(Ly)\] done
clear
View Solution play_arrow

In the case of biaxial state of normal stress, the normal stress on \[45{}^\circ \] plane is equal to:
A)
The sum of the normal stresses done
clear
B)
Difference of the normal stresses done
clear
C)
Half the sum of the normal stresses done
clear
D)
Half the difference of the normal stresses done
clear
View Solution play_arrow

The temperature stress is a function of
1. Coefficient of linear expansion 
2. Temperature rise 
3. Modulus of elasticity 
The correct answer is:
A)
1 and 2 only done
clear
B)
1 and 3 only done
clear
C)
2 and 3 only done
clear
D)
1, 2 and 3 done
clear
View Solution play_arrow

When two springs of equal length are arranged to form a cluster spring then which of the following statements are true:
1. Angle of twist in both the springs will be equal 
2. Deflection of both the springs will be equal 
3. Load taken by each spring will be half the total load 
4. Shear stress in each spring will be equal 
A)
1 and 2 only done
clear
B)
2 and 3 only done
clear
C)
2 and 4 only done
clear
D)
1, 2 and 4 only done
clear
View Solution play_arrow

When \[\sigma \] and Young's Modulus of Elasticity constant, the energyabsorbing capacity subject to dynamic forces, is a function of its.
A)
Length done
clear
B)
crosssection done
clear
C)
Volume done
clear
D)
none of the above done
clear
View Solution play_arrow

Principal stresses at a point in plane stressed element are \[{{\sigma }_{x}}={{\sigma }_{y}}=500k\text{g/c}{{\text{m}}^{\text{2}}}.\] Normal stress on the plane inclined at \[45{}^\circ \] to xaxis will be:
A)
0 done
clear
B)
\[500\,k\text{g/c}{{\text{m}}^{\text{2}}}\] done
clear
C)
\[707\,k\text{g/c}{{\text{m}}^{\text{2}}}\] done
clear
D)
\[1000\,k\text{g/c}{{\text{m}}^{\text{2}}}\] done
clear
View Solution play_arrow

Two coiled springs, each having stiffness K, are placed in parallel. The stiffness of the combination will be:
A)
\[4K\] done
clear
B)
\[2K\] done
clear
C)
\[\frac{K}{2}\] done
clear
D)
\[\frac{K}{4}\] done
clear
View Solution play_arrow

A steel rod of 1 sq. cm. cross sectional area is 100 cm long and has a Young's modulus of elasticity \[2\times {{10}^{6}}\,\text{kg/c}{{\text{m}}^{\text{2}}}.\]it is subjected to an axial pull of 2000 kgf. The elongation of the rod will be:
A)
0.05 cm done
clear
B)
0.1 cm done
clear
C)
0.15 cm done
clear
D)
0.20 cm done
clear
View Solution play_arrow

If the area of crosssection of a wire is circular and if the radius of this circle decreases to half its original value due to the stretch of the wire by a load, then the modulus of elasticity of the wire will be:
A)
Onefourth of its original value done
clear
B)
Halved done
clear
C)
Doubled done
clear
D)
Unaffected done
clear
View Solution play_arrow

Match ListI with ListII and select the correct answer using the codes' giver below the lists:
ListI  ListII 
A.  Ductility  1.  Impac test 
B.  Toughness  2.  Fatigue test 
C.  Endurance limit  3.  Tension test 
D.  Resistance to penetration  4.  Hardness test 
Codes:
A)
A\[\to \]3, B\[\to \]2, C\[\to \]1, D\[\to \]4 done
clear
B)
A\[\to \]4, B\[\to \]2, C\[\to \]1, D\[\to \]3 done
clear
C)
A\[\to \]3, B\[\to \]1, C\[\to \]2, D\[\to \]4 done
clear
D)
A\[\to \]4, B\[\to \]1, C\[\to \]2, D\[\to \]3 done
clear
View Solution play_arrow

If a material had a modulus of elasticity of \[2.1\times {{10}^{6}}\text{kgf/c}{{\text{m}}^{\text{2}}}\] and a modulus of rigidity of \[0.8\times {{10}^{6}}\text{kgf/c}{{\text{m}}^{\text{2}}}\] then the approximate value of the Poisson's ratio of the material would be:
A)
0.26 done
clear
B)
0.31 done
clear
C)
0.47 done
clear
D)
05 done
clear
View Solution play_arrow

A Long slender bar having uniform rectangular cross action \['B\times H'\] is acted upon by an axial compressive force. The sides B and H are paralled to xand yaxes respectively. The ends of the bar are fixed such that they behave as pinpointed when the bar buckles in a plane normal to xaxis, and they behave as builtin when the bar buckles in a plane normal to yaxis. If load capacity in either mode of buckling is same, then the value of \[\frac{H}{B}\] will be B:
A)
2 done
clear
B)
4 done
clear
C)
8 done
clear
D)
16 done
clear
View Solution play_arrow

Match ListI with ListII and select correct answer using the codes given below the lists:
ListII (Condition of beam)  ListII (Bending moment diagram) 
A.  Subjected to bending moment at the end of a cantilever.  1.  Triangle 
B.  Cantilever carrying uniformly distributed load over the whole length  2.  Cubic parabola 
C.  Cantilever carrying linearly varying load from zero at the fixed end to maximum at the support.  3.  Parabola 
D.  A beam having load at the centre and supported at the ends  4.  Rectangle 
Codes:
A)
A\[\to \]4, B\[\to \]1, C\[\to \]2, D\[\to \]3 done
clear
B)
A\[\to \]4, B\[\to \]3, C\[\to \]2, D\[\to \]1 done
clear
C)
A\[\to \]3, B\[\to \]4, C\[\to \]2, D\[\to \]1 done
clear
D)
A\[\to \]3, B\[\to \]4, C\[\to \]1, D\[\to \]2 done
clear
View Solution play_arrow

The number of independent elastic constants required to express the stress strain relationship for a linearly elastic isotropic materials is
A)
One done
clear
B)
Two done
clear
C)
Three done
clear
D)
Four done
clear
View Solution play_arrow

A simply supported beam of rectangular section 4 cm by 6 cm carries a midspan concentrated load such that the 6 cm side lies parallel to line of action of loading; deflection under the load is\[\delta \]. If the beam is now supported with the 4cm side parallel to line of action of loading, the deflection under the load will be:
A)
0.44 \[\delta \] done
clear
B)
0.67 \[\delta \] done
clear
C)
1.5 \[\delta \] done
clear
D)
2.25 \[\delta \] done
clear
View Solution play_arrow

A shaft was initially subjected to bending moment and then was subjected to torsion. If the magnitude of bending moment is found to be the same as that of the torque, then the ratio of maximum bending stress to shear stress would be:
A)
0.25 done
clear
B)
0.50 done
clear
C)
2.0 done
clear
D)
4.0 done
clear
View Solution play_arrow

A horizontal beam with square crosssection is simply supported with sides of the square horizontal and vertical and carries a distributed loading that produces maximum bending stress \[\sigma \] in the beam. When the beam is placed with one of the diagonals horizontal the maximum bending stress will be:
A)
\[\frac{1}{\sqrt{2}}\sigma \] done
clear
B)
\[\sigma \] done
clear
C)
\[\sqrt{2\sigma }\] done
clear
D)
\[2\sigma \] done
clear
View Solution play_arrow

The property by which an amount of energy is absorbed by a material without plastic deformation, is called:
A)
Toughness done
clear
B)
impact strength done
clear
C)
Ductility done
clear
D)
resilience done
clear
View Solution play_arrow

In the assembly of pulley, key and shaft:
A)
Pulley is made the weakest done
clear
B)
Key is made the weakest done
clear
C)
Key is made the strongest done
clear
D)
All the three are designed for equal strength done
clear
View Solution play_arrow

Circumferential and longitudinal strains in cylindrical boiler under internal steam pressure, are \[{{\varepsilon }_{1}}\] and \[{{\varepsilon }_{2}}\] respectively. Change in volume of the boiler cylinder per unit volume will be:
A)
\[{{\varepsilon }_{1}}+2{{\varepsilon }_{2}}\] done
clear
B)
\[{{\varepsilon }_{1}}+{{\varepsilon }_{2}}^{2}\] done
clear
C)
\[2{{\varepsilon }_{1}}+{{\varepsilon }_{2}}\] done
clear
D)
\[{{\varepsilon }_{1}}^{2}+{{\varepsilon }_{2}}\] done
clear
View Solution play_arrow

A metal pipe of 1 m diameter contains a fluid having a pressure of \[10\,\,\text{kgf/c}{{\text{m}}^{\text{2}}}\text{.}\] If the permissible tensile stress in the metal is \[200\,\,\text{kgf/c}{{\text{m}}^{\text{2}}}\] then the thickness of the metal required for making the pipe would be:
A)
5 mm done
clear
B)
10 mm done
clear
C)
20 mm done
clear
D)
25 mm done
clear
View Solution play_arrow

A length of 10 mm diameter steel wire is coiled to a close coiled helical spring having 8 coils of 75 mm mean diameter, and the spring has a stiffness k. If the same length of wire is coiled to 10 coils of 60 mm mean diameter, then the spring stiffness will be:
A)
k done
clear
B)
1.25 k done
clear
C)
1.56 k done
clear
D)
1.95 k done
clear
View Solution play_arrow

The buckling load will he maximum for a column, if:
A)
One end of the column is clamped and the other end is free done
clear
B)
Both ends of the column are clamped done
clear
C)
Both ends of the column are hinged done
clear
D)
One end of the column is hinged and the other end is free done
clear
View Solution play_arrow

If the principal stresses corresponding to a twodimensional state of stress are \[{{\sigma }_{1}}\] and \[{{\sigma }_{2}}.\] If \[{{\sigma }_{1}}\] is greater than \[{{\sigma }_{2}}\] and both are tensile, then which one of the following would be the correct criterion for failure by yielding, according to the maximum shear stress criterion?
A)
\[({{\sigma }_{1}}+{{\sigma }_{2}})/2=\pm \,{{\sigma }_{yp}}/2\] done
clear
B)
\[{{\sigma }_{1}}/2=\pm \,{{\sigma }_{yp}}/2\] done
clear
C)
\[{{\sigma }_{2}}/2=\pm \,{{\sigma }_{yp}}/2\] done
clear
D)
\[{{\sigma }_{1}}=\pm \,{{\sigma }_{yp}}\] done
clear
View Solution play_arrow

A state of pure shear m a biaxial stress is gives by:
A)
\[\left[ \begin{matrix} {{\sigma }_{1}} & {{\sigma }_{1}} \\ 0 & {{\sigma }_{2}} \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} {{\sigma }_{1}} & 0 \\ 0 & {{\sigma }_{2}} \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} {{\sigma }_{x}} & {{\tau }_{xy}} \\ 0 & {{\sigma }_{Y}} \\ \end{matrix} \right]\] done
clear
D)
none of the above done
clear
View Solution play_arrow

The number of strain readings (using strain gauges) needed on a plane surface to determine the principal strains and their direction is:
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow

When two mutually perpendicular principal stresses are unequal but alike, the maximum shear stress represented by:
A)
The diameter of the Mohr's circle done
clear
B)
Half the diameter of the Mohr's circle done
clear
C)
Onethird the diameter of the Mohr's circle done
clear
D)
Onefourth the diameter of the Mohr's circle done
clear
View Solution play_arrow

If the value of Poisson's ratio is zero, then it means that:
A)
The material is rigid done
clear
B)
There is no longitudinal strain in the material done
clear
C)
The material is perfectly plastic done
clear
D)
The longitudinal strain in the material is infinite done
clear
View Solution play_arrow

The deformation of a bar under its own weight as compared to that when subjected to a direct axial lo equal to its own weight will be
A)
The same done
clear
B)
Onefourth done
clear
C)
Half done
clear
D)
Double done
clear
View Solution play_arrow

When a weight of 100 N falls on a spring of stiffness 1 kN/m from a height of 2m, the deflection caused in the first fall is:
A)
Equal to 0.1 m done
clear
B)
Between 0.1 and 0.2 done
clear
C)
Equal to 0.2 m done
clear
D)
More than 0.2 m done
clear
View Solution play_arrow

Two hollow shafts of the same material have the same length and outside diameter. Shaft 1 has internal diameter equal to onethird of the outer diameter and shaft 2 has internal diameter equal to half of the outer diameter. If both the shafts are subject to the same torque, the ratio of their twists \[{{\theta }_{1}}/{{\theta }_{2}}\] will be equal
A)
16/81 done
clear
B)
8/27 done
clear
C)
19/27 done
clear
D)
243/256 done
clear
View Solution play_arrow

A solid shaft of diameter 'D' caries a twisting moment that develops maximum shear stress \[\tau .\] If the shaft is replaced by a hollow one of outside diameter 'D' and inside diameter D/2, then the maximum shear stress
A)
\[1.067\,\tau \] done
clear
B)
\[1.143\,\tau \] done
clear
C)
\[1.333\,\tau \] done
clear
D)
\[2\,\tau \] done
clear
View Solution play_arrow

A circular shaft can transmit a torque of 5 kNm. the torque is reduced to 4 kNm then the maximum value of bending moment that can be applied to the shaft is
A)
1 kNm done
clear
B)
2 kNm done
clear
C)
3 kNm done
clear
D)
4 kNm done
clear
View Solution play_arrow

A thin cylinder contains fluid at a pressure of \[500\,N/{{m}^{2}},\] the internal diameter of the shell is 0.6 m and the tensile stress in the material is to be limited to \[9000\,N/{{m}^{2}}.\] The shell must have a minimum wall thickness of nearly
A)
9 mm done
clear
B)
11 mm done
clear
C)
17 mm done
clear
D)
21 mm done
clear
View Solution play_arrow

A steel hub of 100 mm internal diameter and uniform thickness of 10 mm was heated to a temperature \[300{}^\circ C\] to shrinkfit on a shaft. On cooling, a crack developed parallel to the direction of the length of the hub. Consider the following factors in this
1. Tensile hoop stress 
2. Tensile radial stress 
3. Compressive hoop stress 
4. Compressive radial stress 
The cause of failure is attributable to:
A)
1 alone done
clear
B)
1 and 3 done
clear
C)
1, 2 and 4 done
clear
D)
2, 3 and 4 done
clear
View Solution play_arrow

A compound cylinder with inner radius 5 cm and outer radius 7 cm is made by shrinking one cylinder on to the other cylinder. The junction radius is 6 cm and the junction pressure is \[11\,kg/c{{m}^{2}}.\] The maximum hoop stress developed in the inner cylinder is:
A)
\[36\,\text{kgf/c}{{\text{m}}^{\text{2}}}\] Compression done
clear
B)
\[36\,\text{kgf/c}{{\text{m}}^{\text{2}}}\] Tension done
clear
C)
\[72\,\text{kgf/c}{{\text{m}}^{\text{2}}}\] Compression done
clear
D)
\[72\,\text{kgf/c}{{\text{m}}^{\text{2}}}\]Tension done
clear
View Solution play_arrow

Cracks in helical springs used in railway carriages usually start on the inner side of the coil because of the fact that:
A)
It is subjected to a higher stress flan the outer side done
clear
B)
it is subjected to a higher cyclic loading than the outer side done
clear
C)
It is more stretched than the outer side during the manufacturing process done
clear
D)
It has a lower curvature than the outer side done
clear
View Solution play_arrow

Two helical springs of the same material and of equal circular crosssection and length and number of turns, but having radii 90 mm and 40 nun, kept concentrically (smaller radius spring within the larger radius spring), arc compressed between two parallel planes with a load P. The inner spring will carry a load equal to:
A)
\[\frac{P}{2}\] done
clear
B)
\[\frac{P}{3}\] done
clear
C)
\[\frac{P}{1.088}\] done
clear
D)
\[\frac{P}{2.088}\] done
clear
View Solution play_arrow

RankineGordon formula for buckling is valid for:
A)
Long column done
clear
B)
Short column done
clear
C)
Short and long column done
clear
D)
Very long column done
clear
View Solution play_arrow

If failure in shear along \[45{}^\circ \] planes is to be avoided then a material subjected to uniaxial tension should have its shear strength equal to at least:
A)
Tensile strength done
clear
B)
Compressive strength done
clear
C)
Half the difference between the tensile and compressive strengths done
clear
D)
Half the tensile strength done
clear
View Solution play_arrow

A shaft is subjected to a maximum bending stress of \[80\,N/m{{m}^{2}}\] and maximum shearing stress equal to \[30\,N/m{{m}^{2}}\] at a particular section. If the yield point in tension of the material is \[280\,N/m{{m}^{2}},\] and maximum shear stress theory of failure is used, then the factor of safety obtained will be:
A)
2.5 done
clear
B)
2.8 done
clear
C)
3.0 done
clear
D)
3.5 done
clear
View Solution play_arrow

If \[{{\sigma }_{y}}\] is the yield strength of a particular material, then the distortion energy theory is expressed as:
A)
\[{{({{\sigma }_{1}}{{\sigma }_{2}})}^{2}}+{{({{\sigma }_{2}}{{\sigma }_{3}})}^{2}}+{{({{\sigma }_{3}}\sigma )}^{2}}=2s_{y}^{2}\] done
clear
B)
\[({{\sigma }_{1}}^{2}+{{\sigma }_{2}}+{{\sigma }_{3}})2v({{\sigma }_{1}}{{\sigma }_{2}}+{{\sigma }_{2}}{{\sigma }_{3}}+{{\sigma }_{3}}{{\sigma }_{1}})=\sigma _{y}^{2}\] done
clear
C)
\[({{\sigma }_{1}}+{{\sigma }_{2}}^{2})+{{({{\sigma }_{2}}{{\sigma }_{3}})}^{2}}+{{({{\sigma }_{3}}{{\sigma }_{1}})}^{2}}=3{{\sigma }_{y}}^{2}\] done
clear
D)
\[(12v){{({{\sigma }_{1}}+{{\sigma }_{2}}+{{\sigma }_{3}})}^{2}}=2(1+v){{\sigma }_{y}}\] done
clear
View Solution play_arrow

Hoop stress and longitudinal stress in a boiler shell under internal pressure are \[100\,\text{MN/}{{\text{m}}^{\text{2}}}\] and \[50\,MN/{{m}^{2}}\] respectively. Young's modulus of elasticity and Poisson's ratio of the shell material are \[200\,\text{GN/}{{\text{m}}^{\text{2}}}\] and 0.3 respectively. The hoop strain in boiler shell is:
A)
\[0.425\times {{10}^{\,3}}\] done
clear
B)
\[0.5\times {{10}^{\,3}}\] done
clear
C)
\[0.585\times {{10}^{\,3}}\] done
clear
D)
\[0.75\times {{10}^{\,3}}\] done
clear
View Solution play_arrow

The stretch in a steel rod of circular section, having a length ?l' subjected to a tensile load 'P' and tapering uniformly from a diameter \[{{d}_{1}}\] at one end to a diameter \[{{d}_{2}}\] at the other end, is given:
A)
\[\text{Pl/4}\,E{{d}_{1}}{{d}_{2}}\] done
clear
B)
\[\text{Pl}\,\pi \,E{{d}_{1}}{{d}_{2}}\] done
clear
C)
\[\text{Pl/4}E({{d}_{1}}.{{d}_{2}})\] done
clear
D)
\[\text{4P}\text{.l/}\pi \text{.}E.{{d}_{1}}.{{d}_{2}}\] done
clear
View Solution play_arrow

A simply supported beam of constant flexural rigidity and length 2 L carries a concentrated load 'P' at its midspan and the deflection under that load is \[\delta .\] If a cantilever beam of the same flexural rigidity and length is subjected to load 'P' at its free end, them the deflection at the free end will be
A)
\[1/2\delta \] done
clear
B)
\[\delta \] done
clear
C)
\[2\delta \] done
clear
D)
\[4\delta \] done
clear
View Solution play_arrow

If Poisson's ratio for a material is 0.5, then the elastic modulus for the material is:
A)
Three times its shear modulus done
clear
B)
Four times its shear modulus done
clear
C)
Equal to its shear modulus done
clear
D)
Indeterminate. done
clear
View Solution play_arrow

From a tension test, the yield strength of steel is found to be \[200\,\text{N/m}{{\text{m}}^{\text{2}}}\text{.}\] Using a factor of safety of 2 and applying maximum principal stress theory of failure, the permissible stress in the steel shaft subjected to torque will be:
A)
\[50\,\text{N/m}{{\text{m}}^{\text{2}}}\] done
clear
B)
\[57.7\,\text{N/m}{{\text{m}}^{\text{2}}}\] done
clear
C)
\[86.6\,\text{N/m}{{\text{m}}^{\text{2}}}\] done
clear
D)
\[100\,\text{N/m}{{\text{m}}^{\text{2}}}\] done
clear
View Solution play_arrow

A solid shaft of diameter 100 mm, length 1000 mm is subjected to a twisting moment 'T'. The maximum shear stress developed in the shaft is 60 N/mm. A hole of 50 mm diameter is now drilled throughout the length of shaft. To develop a maximum shear stress of 60 N/ mm in the hollow shaft, the torque 'T' must he reduced by
A)
T/4 done
clear
B)
T/8 done
clear
C)
T/12 done
clear
D)
T/16 done
clear
View Solution play_arrow

A rectangular section beam subjected to a bending moment M varying along its length is required to develop same maximum bending stress at any cross section. If the depth of the section is constant, then its width will vary as:
A)
\[M\] done
clear
B)
\[\sqrt{M}\] done
clear
C)
\[{{M}_{2}}\] done
clear
D)
\[\text{1/M}\] done
clear
View Solution play_arrow

Consider the following statements:
If at section distant from one of the ends of the beam, M represents the bending moment, V the shear force and w the intensity of loading, then 
1. dM/dx = V 
2. dV/dx = w 
3. dw/dx = y (the deflection of the beam at the section) 
Of these statements: 
A)
1 and 3 are correct done
clear
B)
1 and 2 are correct done
clear
C)
2 and 3 are correct done
clear
D)
1, 2 and 3 are correct done
clear
View Solution play_arrow

A cantilever beam having 5 m length is so loaded that it develops a shearing force of 20 T and a bending moment of 20 Tm at a section 2m from the free end. Maximum shearing force and maximum, bending moment developed in the beam under this load, are respectively 50 T and 125 Tm. The load on the beam is:
A)
25 T concentrated load at free end. done
clear
B)
20 T concentrated load at free end. done
clear
C)
5 T concentrated load at free end and 2 T/m load over entire length. done
clear
D)
10 T/mudl over entire length done
clear
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Consider the following statements:
State of stress in two dimensions at a point in a loaded component can be completely specified by indicating the normal and shear stresses on 
1. A plane containing the point 
2. Any two planes passing through the point 
3. Two mutually perpendicular planes passing through the point 
Of these statements
A)
1 and 3 are correct done
clear
B)
2 alone is correct done
clear
C)
1 alone is correct done
clear
D)
3 alone is correct done
clear
View Solution play_arrow

Which one of the following properties is more sensitive to increase in strain rate?
A)
Yield strength done
clear
B)
Proportional limit done
clear
C)
Elastic limit done
clear
D)
Tensile strength done
clear
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A simply supported beam carrying a concentrated load W at midspan deflects by \[{{\delta }_{1}}\] under the lode. If the same beam carries the load W such that it is distributed uniformly over entire length and undergoes a deflection \[{{\delta }_{2}}\] at the mid span. The ratio, \[{{\delta }_{1}}:{{\delta }_{2}}\] is:
A)
2 : 1 done
clear
B)
\[\sqrt{2}:1\] done
clear
C)
1.6 : 1 done
clear
D)
1 : 2 done
clear
View Solution play_arrow

Match ListI with ListII and select the correct answer using the codes given below the lists:
ListI (End conditions of columns)  ListII (Lowest critical load) 
A.  Column with both ends hinged  1.  \[({{\pi }^{2}}El)/{{L}^{2}}\] 
B.  Column with both ends fixed  2.  \[(2{{\pi }^{2}}El)/{{L}^{2}}\] 
C.  Column with one end fixed and the other end hinged  3.  \[({{\pi }^{2}}El)/{{L}^{2}}\] 
D.  Column with one end fixed and the other end free  4.  \[({{\pi }^{2}}El)/4{{L}^{2}}\] 
(E is the young's modulus of elasticity of column material, L is the length and I is the second moment of area of crosssection of the column). Codes:
A)
A\[\to \]1, B\[\to \]2, C\[\to \]3, D\[\to \]4 done
clear
B)
A\[\to \]3, B\[\to \]2, C\[\to \]1, D\[\to \]4 done
clear
C)
A\[\to \]1, B\[\to \]3, C\[\to \]2, D\[\to \]4 done
clear
D)
A\[\to \]2, B\[\to \]4, C\[\to \]3, D\[\to \]1 done
clear
View Solution play_arrow

Euler's formula can be used for obtaining crippling load for a M.S. column with hinged ends. Which one of the following conditions for the slenderness ratio l/k is to be satisfied?
A)
\[5<\frac{1}{k}<8\] done
clear
B)
\[9<\frac{1}{k}<8\] done
clear
C)
\[19<\frac{1}{k}<40\] done
clear
D)
\[\frac{1}{k}\ge 80\] done
clear
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A 3meter long steel cylindrical shaft is rigidly held at its two ends. A pulley is mounted on the shaft at 1 meter from one end; the shaft is twisted by applying torque on the pulley. The maximum shearing stresses developed in 1m and 2m lengths are respectively \[{{\tau }_{1}}\] and \[{{\tau }_{2}}.\]the ratio \[{{\tau }_{2}},{{\tau }_{1}}\] is:
A)
1/2 done
clear
B)
1 done
clear
C)
2 done
clear
D)
4 done
clear
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A closelycoiled helical spring is acted upon by an axial force. The maximum shear stress developed in the spring is t. Half of the length of spring is cut off and the remaining spring is acted upon by the same axial force. The maximum shear stress in the spring in the new condition will be:
A)
\[\text{1/2}\,\tau \] done
clear
B)
\[\tau \] done
clear
C)
\[\text{2}\,\tau \] done
clear
D)
\[\text{4}\,\tau \] done
clear
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A circular shaft is subjected to the combined action of bending, twisting and direct axial loading. The maximum bending stress \[\sigma \]maximum shearing stress \[\sqrt{3\sigma }\] and a uniform axial stress \[\sigma \](compressive) are produced. The \[\sigma \]maximum compressive normal stress produced in the shaft will be
A)
\[3\,\sigma \] done
clear
B)
\[2\,\sigma \] done
clear
C)
\[\sigma \] done
clear
D)
Zero done
clear
View Solution play_arrow

Permissible bending moment in a circular shaft under pure bending is M according to maximum principal stress theory of failure. According to maximum shear stress theory of failure, the permissible bending moment in the same shaft is:
A)
1/2M done
clear
B)
M done
clear
C)
\[\sqrt{M}\] done
clear
D)
2M done
clear
View Solution play_arrow

A long helical spring having a springstiffness of 12 kN/m and number of turns 20, breaks into two equal parts. The resultant spring stiffness will be:
A)
6 kN/m done
clear
B)
12 kN/m done
clear
C)
24 kN/m done
clear
D)
30 kN/m done
clear
View Solution play_arrow

Consider the following statements.
State of stress at a point when completely specified, enables one to determine the 
1. Principal stresses at the point. 
2. Maximum shearing stress at the point 
3. Stress components on any arbitrary plane containing the point 
Of these statements:
A)
1, 2 and 3 are correct done
clear
B)
1 and 3 are correct done
clear
C)
2 and 3 are correct done
clear
D)
1 and 2 are correct done
clear
View Solution play_arrow

Match ListI (End conditions of columns) with ListII (Equivalent length in terms of length of hingedhinged column) and select the correct answer using the codes given below the lists:
ListI  ListII 
A.  Both ends hinged  1.  L 
B.  One end fixed and other end free  2.  \[L\,/\sqrt{2}\] 
C.  One end fixed and the other pinjointed  3.  \[\frac{L}{2}\] 
D.  Both ends fixed  4.  2L 
Codes:
A)
A\[\to \]1, B\[\to \]4, C\[\to \]3, D\[\to \]2 done
clear
B)
A\[\to \]1, B\[\to \]4, C\[\to \]2, D\[\to \]3 done
clear
C)
A\[\to \]3, B\[\to \]1, C\[\to \]2, D\[\to \]4 done
clear
D)
A\[\to \]3, B\[\to \]1, C\[\to \]4, D\[\to \]2 done
clear
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Two closedcoil springs are made from the same small diameter wire, one wound on 2.5 cm diameter core and the other on 1.25 cm diameter core. If each spring has V coils, then the ratio of their spring constants would be
A)
1/16 done
clear
B)
1/8 done
clear
C)
1/4 done
clear
D)
1/2 done
clear
View Solution play_arrow

The maximum bending moment in a simply supported beam of length L loaded by a concentrated load W at the midpoint is given by:
A)
\[WL\] done
clear
B)
\[\frac{WL}{2}\] done
clear
C)
\[\frac{WL}{4}\] done
clear
D)
\[\frac{WL}{8}\] done
clear
View Solution play_arrow

'Match ListI with ListII and select the correct answer using the codes given below the list:
ListI  ListII 
A.  Bending moment is constant  1.  Point of contraflexure 
B.  Bending moment is maximum or minimum  2.  Shear force changes sign 
C.  Bending moment is zero  3.  Slope of shear force diagram is zero over the portion of the beam 
D.  Loading is constant  4.  Shear force is zero over the portion of the beam. 
Codes:
A)
A\[\to \]4, B\[\to \]1, C\[\to \]2, D\[\to \]3 done
clear
B)
A\[\to \]1, B\[\to \]4, C\[\to \]2, D\[\to \]3 done
clear
C)
A\[\to \]3, B\[\to \]1, C\[\to \]2, D\[\to \]4 done
clear
D)
A\[\to \]3, B\[\to \]1, C\[\to \]4, D\[\to \]2 done
clear
View Solution play_arrow

If the shear force acting at every section of a beam is of the same magnitude and of the same direction then it represents a:
A)
Simply supported beam with a concentrated load at the centre done
clear
B)
Overhung beam having equal overhang at both supports and carrying equal concentrated loads acting in the same direction at the free ends done
clear
C)
Cantilever subjected to concentrated load at the free end done
clear
D)
Simply supported beam having concentrated loads of equal magnitude and in the same direction acting at equal distances from the supports done
clear
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A cantilever beam carries a load W uniformly distributed over its entire length. If the same load is placed at the free and of the same cantilever, then the ratio of maximum deflection in the first case to that in the second case will be:
A)
3/8 done
clear
B)
8/3 done
clear
C)
5/8 done
clear
D)
8/5 done
clear
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Circumferential stress in a cylindrical steel boiler shell under internal pressure is 80 MPa, Young's modulus of elasticity and Poisson's ratio are respectively \[2\times {{10}^{5}}\] MPa and 0.28. The magnitude of circumferential strain in the boiler shell will be
A)
\[3.44\times {{10}^{\,4}}\] done
clear
B)
\[3.84\times {{10}^{\,4}}\] done
clear
C)
\[4\times {{10}^{\,4}}\] done
clear
D)
\[4.56\times {{10}^{\,4}}\] done
clear
View Solution play_arrow

For a cantilever beam of length 'L' flexural rigidity El and loaded at its free end by a concentrated load 'M' match listI with listII and select the correct answer:
ListI  ListII 
A.  maximum bending moment  1.  WL 
B.  Strain energy  2.  \[\text{W}{{\text{L}}^{\text{2}}}\text{/2EI}\] 
C.  Maximum slope  3.  \[\text{W}{{\text{L}}^{3}}\text{/2EI}\] 
D.  Maximum deflection  4.  \[{{\text{W}}^{2}}{{\text{L}}^{2}}\text{/6EI}\] 
Codes:
A)
A\[\to \]1, B\[\to \]4, C\[\to \]3, D\[\to \]2 done
clear
B)
A\[\to \]1, B\[\to \]4, C\[\to \]2, D\[\to \]3 done
clear
C)
A\[\to \]4, B\[\to \]2, C\[\to \]1, D\[\to \]3 done
clear
D)
A\[\to \]4, B\[\to \]2, C\[\to \]1, D\[\to \]2 done
clear
View Solution play_arrow

At a certain section at a distance 'x' from one of the supports of a simply supported beam, the intensity of loading, bending moment and shear force are \[{{\text{W}}_{x}},{{M}_{x}},\] and \[{{V}_{x}},\] respectively, if the intensity of loading is varying continuously along the length of the beam, them the invalid relation is:
A)
\[Slop,\,\,{{Q}_{x}}=\frac{Mx}{Vx}\] done
clear
B)
\[{{V}_{x}}=\frac{dMx}{dx}\] done
clear
C)
\[{{W}_{x}}=\frac{{{d}^{2}}Mx}{d{{x}^{2}}}\] done
clear
D)
\[{{W}_{x}}=\frac{d{{V}_{x}}}{dx}\] done
clear
View Solution play_arrow

The equivalent bending moment under combined action of bending moment M and torque T is:
A)
\[\sqrt{{{M}^{2}}+{{T}^{2}}}\] done
clear
B)
\[\frac{1}{2}\,\sqrt{{{M}^{2}}+{{T}^{2}}}\] done
clear
C)
\[\frac{1}{2}\,\sqrt{{{M}^{3}}+{{T}^{2}}}\] done
clear
D)
\[\frac{1}{2}\,\left( M+\sqrt{{{M}^{3}}+{{T}^{2}}} \right)\] done
clear
View Solution play_arrow

The bending moment (M) is constant over a length segment / of a beam. The shearing force will also be constant over this length and is given by:
A)
M/l done
clear
B)
M/2l done
clear
C)
M/4l done
clear
D)
none of the above done
clear
View Solution play_arrow

In a thick cylinder, subjected to internal and external pressures, let \[{{r}_{1}}\] and \[{{r}_{2}}\] be the internal and external radii respectively. Let u be the radial displacement of a material element at radius \[r,{{r}_{2}}\ge {{r}_{1}}.\] Identifying the cylinder axis as z axis, the radial strain component \[{{\varepsilon }_{r}}\] is:
A)
\[u/r\] done
clear
B)
\[u/\theta \] done
clear
C)
\[du/dr\] done
clear
D)
\[du/d\theta \] done
clear
View Solution play_arrow

Autofrettage is the method of:
A)
Joining thick cylinders done
clear
B)
Calculating stresses in thick cylinders done
clear
C)
Prestressing thick cylinders done
clear
D)
Increasing the life of thick cylinders done
clear
View Solution play_arrow

Given that
d = diameter of spring. 
R = mean radius of coils. 
n = number of coils, and 
G = modulus of rigidity. 
The stiffness of the closecoiled helical spring subject to an axial load W is equal to:
A)
\[\frac{G{{d}^{4}}}{64{{R}^{3}}n}\] done
clear
B)
\[\frac{G{{d}^{3}}}{64{{R}^{3}}n}\] done
clear
C)
\[\frac{G{{d}^{4}}}{32{{R}^{3}}n}\] done
clear
D)
\[\frac{G{{d}^{4}}}{64{{R}^{3}}n}\] done
clear
View Solution play_arrow

When a closecoiled helical spring is subjected to a couple about its axis, the stress induced in the material of the spring is:
A)
Bending stress only done
clear
B)
Direct shear stress only done
clear
C)
A combination of torsional shear stress and bending stress done
clear
D)
A combination of bending stress and direct shear stress done
clear
View Solution play_arrow

If a shaft made from ductile material is subjected to combined bending and twisting moments, calculation based on which one of the following failure theories would give the most conservative value?
A)
Maximum principal stress theory done
clear
B)
Maximum shear stress theory done
clear
C)
Maximum strain energy theory done
clear
D)
Maximum distortion energy theory done
clear
View Solution play_arrow

During tensiletesting of a specimen using Universal Testing Machine, the parameters actually measures include:
A)
True stress and true strain done
clear
B)
Poisson's ratio and Young's modulus done
clear
C)
Engineering stress and engineering strain done
clear
D)
Load and elongation done
clear
View Solution play_arrow

The state of plane stress in a plate of 100 mm thickness is given as
\[{{\sigma }_{xx}}=100\,\text{N/m}{{\text{m}}^{\text{2}}}\text{,}\] \[{{\sigma }_{xy}}=200\,\text{N/m}{{\text{m}}^{\text{2}}}\] 
Young's modulus \[=300\,\text{N/m}{{\text{m}}^{\text{2}}}\] 
Poission?s ratio = 0.3 
The stress developed in the direction of thickness
A)
zero done
clear
B)
\[90\text{ }N/m{{m}^{2}}\] done
clear
C)
\[100\text{ }N/m{{m}^{2}}\] done
clear
D)
\[200\text{ }N/m{{m}^{2}}\] done
clear
View Solution play_arrow

A plane stressed clement is subjected to the state of stress given by \[{{\sigma }_{x}}={{\tau }_{xy}}=10\,\text{kgf/c}{{\text{m}}^{\text{2}}}\] and \[{{\sigma }_{x}}=0.\] Maximum shear stress in the element is equal to:
A)
\[50\sqrt{3}\,\text{kgf}\,\,\text{c}{{\text{m}}^{\text{2}}}\] done
clear
B)
\[100\,\text{kgf/c}{{\text{m}}^{\text{2}}}\] done
clear
C)
\[50\sqrt{5}\,\text{kgf/c}{{\text{m}}^{\text{2}}}\] done
clear
D)
\[150\,\text{kgf/c}{{\text{m}}^{\text{2}}}\] done
clear
View Solution play_arrow

Match ListI (Elastic properties of an isotropic elastic material) with0 ListII (Nature of strain produced) and select the correct answer using the codes given below the list:
ListI  ListII 
A.  Young's modulus  1.  Shear strain 
B.  Modulus of rigidity  2.  Normal strain 
C.  Bulk modulus  3.  Transverse strain 
D.  Poisson's ratio  4.  Volumetric strain 
Codes:
A)
A\[\to \]2, B\[\to \]1, C\[\to \]3, D\[\to \]4 done
clear
B)
A\[\to \]2, B\[\to \]1, C\[\to \]4, D\[\to \]3 done
clear
C)
A\[\to \]3, B\[\to \]4, C\[\to \]1, D\[\to \]2 done
clear
D)
A\[\to \]4, B\[\to \]3, C\[\to \]1, D\[\to \]2 done
clear
View Solution play_arrow

The relationship between the Lame's constant \['\lambda '.\] Young's modulus 'E' and the Poisson's ratio 'v' is:
A)
\[\lambda =\frac{Ev}{(1+v)(12y)}\] done
clear
B)
\[\lambda =\frac{Ev}{(1+2v)(1v)}\] done
clear
C)
\[\lambda =\frac{Ev}{(1+v)}\] done
clear
D)
\[\lambda =\frac{Ev}{(1v)}\] done
clear
View Solution play_arrow

A 10 cm long and 5 cm diameter steel rod fits snugly between two rigid walls 10 cm apart at room temperature. Young's modulus of elasticity and coefficient of linear expansion of steel are \[2\times {{10}^{6}}\,\text{kg/c}{{\text{m}}^{\text{2}}}\] and \[12\times {{10}^{\,6}}\] per \[{}^\circ C\] respectively. The stress developed in rod due to a \[100{}^\circ C\] rise in temperature will be:
A)
\[6\times {{10}^{\,10}}\,\text{kg/c}{{\text{m}}^{\text{2}}}\] done
clear
B)
\[6\times {{10}^{\,10}}\,\text{kg/c}{{\text{m}}^{\text{2}}}\] done
clear
C)
\[2.4\times {{10}^{3}}\,\text{kg/c}{{\text{m}}^{\text{2}}}\] done
clear
D)
\[2.4\times {{10}^{4}}\,\text{kg/c}{{\text{m}}^{\text{2}}}\] done
clear
View Solution play_arrow

The number of elastic constants for a completely anisotropic elastic material which follows Hooks laws is
A)
3 done
clear
B)
4 done
clear
C)
21 done
clear
D)
25 done
clear
View Solution play_arrow

The bending moment equation, as a function of distance x measured from the left end, for a simply supported beam of span. L m carrying a uniformly distributed load of intensity w N/m will be given by
A)
\[M=wL/2(Lx)W/2(Lx)N.m\] done
clear
B)
\[M=wL/2xw{{x}^{2}}/2N.m\] done
clear
C)
\[M=wL/2{{(Lx)}^{2}}w/2(Lx)N.m\] done
clear
D)
\[M=w{{x}^{2}}/2wLx/2N.m\] done
clear
View Solution play_arrow

If a beam is subjected to a constant bending moment along its length, then the shear force will:
A)
Also have a constant value everywhere along its length done
clear
B)
Be zero at all sections along the beam done
clear
C)
Be maximum at the centre and zero at the ends done
clear
D)
Zero at the centre and maximum at the ends done
clear
View Solution play_arrow

A simply supported beam with width 'b' and depth ?d? carries a central load Wand undergoes deflection 8 at the centre. If the width and depth are interchanged the deflection at the centre of the beam would attain the value:
A)
\[\frac{d}{b}\delta \] done
clear
B)
\[{{\left( \frac{d}{b} \right)}^{2}}\delta \] done
clear
C)
\[{{\left( \frac{d}{b} \right)}^{3}}\delta \] done
clear
D)
\[{{\left( \frac{d}{b} \right)}^{3/2}}\delta \] done
clear
View Solution play_arrow

For a composite consisting of a bar enclosed inside a tube of another material when compressed under a load 'W? as a whole through rigid collars at the end of the bar. The equation of compatibility is given by (suffixes 1 and 2) refer to bar and tube respectively:
A)
\[{{W}_{1}}+{{W}_{2}}=W\] done
clear
B)
\[{{W}_{1}}+{{W}_{2}}=\text{constant}\] done
clear
C)
\[\frac{{{W}_{1}}}{{{A}_{1}}{{E}_{1}}}=\frac{{{W}_{2}}}{{{A}_{2}}{{E}_{2}}}\] done
clear
D)
\[\frac{{{W}_{2}}}{{{A}_{2}}{{E}_{1}}}=\frac{{{W}_{2}}}{{{A}_{1}}{{E}_{2}}}\] done
clear
View Solution play_arrow

A rod of material with \[E=200\times {{10}^{3}}\] MPa and \[\propto ={{10}^{\,3}}\text{mm/mm }\!\!{}^\circ\!\!\text{ C}\] is fixed at both the ends. It is uniformly heated such that the increase in temperature is\[\text{30 }\!\!{}^\circ\!\!\text{ C}\]. The stress, developed in the rod is
A)
\[6000\,\,\text{N/m}{{\text{m}}^{\text{2}}}\](Tensile) done
clear
B)
\[6000\,\,\text{N/m}{{\text{m}}^{\text{2}}}\](Compressive) done
clear
C)
\[2000\,\,\text{N/m}{{\text{m}}^{\text{2}}}\](Tensile) done
clear
D)
\[2000\,\,\text{N/m}{{\text{m}}^{\text{2}}}\](Compressive) done
clear
View Solution play_arrow

A wooden beam of rectangular crosssection 10 cm deep by 5 cm wide carries maximum shear force of 2000 kg. Shear stress at neutral axis of the beam section is:
A)
Zero done
clear
B)
\[40\,\,kgf\text{/c}{{\text{m}}^{\text{2}}}\] done
clear
C)
\[60\,\,kgf\text{/c}{{\text{m}}^{\text{2}}}\] done
clear
D)
\[80\,\,kgf\text{/c}{{\text{m}}^{\text{2}}}\] done
clear
View Solution play_arrow

Two beams of equal crosssectional area arc subjected to equal bending moment. If one beam has square crosssection and the other has circular section, then
A)
Both beams will be equally strong done
clear
B)
Circular section beam will be stronger done
clear
C)
Square section beam will be stronger done
clear
D)
The strength of the beam will depend on the nature of loading done
clear
View Solution play_arrow

A cantilever beam of rectangular crosssection is subjected to a load W at its free end. If the depth of the beam is doubled and the load is halved, the deflection of the free end as compared to original deflection will be
A)
Half done
clear
B)
Oneeighth done
clear
C)
Onesixteenth done
clear
D)
Double done
clear
View Solution play_arrow

The ratio of the compressive critical load for a long column fixed at both the ends and a column with one end fixed and the other end free is:
A)
2 : 1 done
clear
B)
4 : 1 done
clear
C)
8 : 1 done
clear
D)
16 : 1 done
clear
View Solution play_arrow

Maximum shear stress in a solid shaft of diameter D and length L twisted through an angle \[\theta \] is \[\tau \] A hollow shaft of same material and length having outside and inside diameters of D and D/2 respectively is also twisted through the same angle of twist \[\theta .\] The value of maximum shear stress in the hollow shaft will be.
A)
\[\frac{16}{15}\tau \] done
clear
B)
\[\frac{8}{7}\tau \] done
clear
C)
\[\frac{4}{3}\tau \] done
clear
D)
\[\tau \] done
clear
View Solution play_arrow

From design point of view, spherical pressure vessel are preferred over cylindrical pressure vessels because they:
A)
Are cost effective in fabrication done
clear
B)
Have uniform higher circumferential stress done
clear
C)
Uniform lower circumferential stress done
clear
D)
Have a larger volume for the same quantity of material used done
clear
View Solution play_arrow

A solid circular shaft is subjected to pure torsion. The ratio of maximum shear stress to maximum norms stress at any point would be
A)
1 : 1 done
clear
B)
1 : 2 done
clear
C)
2 : 1 done
clear
D)
2 : 3 done
clear
View Solution play_arrow

Which one of the following gives the correct expression for strain energy stored in a beam of length L and of uniform crosssection having moment of inertia I and subjected to constant bending moment M?
A)
\[\frac{ML}{EI}\] done
clear
B)
\[\frac{ML}{2EI}\] done
clear
C)
\[\frac{{{M}^{2}}L}{EI}\] done
clear
D)
\[\frac{{{M}^{2}}L}{2EI}\] done
clear
View Solution play_arrow

Plane stress at a point in a body is defined by principal stresses \[3\sigma \] and \[\sigma .\] The ratio of the maximum normal stress to the maximum shear stress on the plane of maximum shear stress is:
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow

A cylindrical vessel with flat bottom can be deep drawn by:
A)
Shallow drawing done
clear
B)
Single action deep drawing done
clear
C)
Double action deep drawing done
clear
D)
Triple action deep drawing. done
clear
View Solution play_arrow

A short column of external diameter D and internal diameter d carries an eccentric load d. The greatest eccentricity which the load can have without producing tension on the cross section of the column would be
A)
\[\frac{d+D}{8}\] done
clear
B)
\[\frac{{{d}^{2}}+{{D}^{2}}}{8d}\] done
clear
C)
\[\frac{{{d}^{2}}+{{D}^{2}}}{8d}\] done
clear
D)
\[\sqrt{\frac{{{d}^{2}}+{{D}^{2}}}{8}}\] done
clear
View Solution play_arrow

A bar of length L and of uniform crosssection are A and second moment of area l is subjected to a pull P. If Young's modulus of elasticity of the bar material is E, the expression for strain energy stored in the bar will be
A)
\[\frac{{{P}^{2}}L}{2AE}\] done
clear
B)
\[\frac{P{{L}^{2}}}{2EI}\] done
clear
C)
\[\frac{P{{L}^{2}}}{AE}\] done
clear
D)
\[\frac{{{P}^{2}}L}{AE}\] done
clear
View Solution play_arrow

If a thick cylindrical shell is subjected to internal pressure, then hoop stress, radial stress and longitudinal stress at a point in the thickness will be
A)
Tensile, compressive and tensile respectively done
clear
B)
All compressive done
clear
C)
All tensile done
clear
D)
Tensile, compressive and compressive respectively. done
clear
View Solution play_arrow

A thin cylinder with both ends closed is subjected internal pressure p. The longitudinal stress at surface has been calculated as \[{{\sigma }_{0}}.\] Maximum shear stress at the surface will be equal to
A)
\[2{{\sigma }_{0}}\] done
clear
B)
\[1,5{{\sigma }_{0}}\] done
clear
C)
\[{{\sigma }_{0}}\] done
clear
D)
\[0.5{{\sigma }_{0}}\] done
clear
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The maximum shear occurs on the outermost of a circular shaft under torsion. In a close helical spring, the maximum shear stress occurs the
A)
Outermost fibres done
clear
B)
Fibres at mean diameter done
clear
C)
Innermost fibres done
clear
D)
End coils done
clear
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A circular solid shaft is subjected to a bending 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 o and according to the maximum shear stress theory, the shear stress is t The ratio \[\sigma /t\] is
A)
\[\frac{1}{5}\] done
clear
B)
\[\frac{3}{4}\] done
clear
C)
\[\frac{9}{5}\] done
clear
D)
\[\frac{11}{6}\] done
clear
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According to the maximum shear stress theory failure, permissible twisting moment in a circular shaft is T. The permissible twisting moment in the same shaft as per the maximum principal stress 6 theory of failure will be
A)
T/2 done
clear
B)
T done
clear
C)
\[\sqrt{2T}\] done
clear
D)
2T done
clear
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The state of plane stress at a point is described by \[{{\sigma }_{x}}={{\sigma }_{y}}\] and \[{{\tau }_{xy}}=0.\] The normal stress on the plane inclined at \[45{}^\circ \] to the xplane will be
A)
\[\sigma \] done
clear
B)
\[\sqrt{2\sigma }\] done
clear
C)
\[\sqrt{3\sigma }\] done
clear
D)
\[2\sigma \] done
clear
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Consider the following statements:
State of stress in two dimensions at a point in a component can be completely specified by indicating the normal and shear stresses on 
1. A plane containing the point 
2. Any two planes passing through the point 
3. Two mutually perpendicular planes passing through the point 
Of these statements
A)
1 and 3 are correct done
clear
B)
2 alone is correct done
clear
C)
1 alone is correct done
clear
D)
3 alone is correct done
clear
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For a composite consisting of a bar enclosed inside: a tube of another material when compressed under a load 'W' as a whole through rigid collars at the end of the bar. The equation of compatibility is given by (suffixes 1 and 2) refer to bar and tube respectively
A)
\[{{W}_{1}}+{{W}_{2}}=W\] done
clear
B)
\[{{W}_{1}}+{{W}_{2}}=\text{constant}\] done
clear
C)
\[\frac{{{W}_{1}}}{{{A}_{1}}{{E}_{1}}}=\frac{{{W}_{2}}}{{{A}_{2}}{{E}_{2}}}\] done
clear
D)
\[\frac{{{W}_{2}}}{{{A}_{2}}{{E}_{1}}}=\frac{{{W}_{2}}}{{{A}_{1}}{{E}_{2}}}\] done
clear
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