Mechanics
Exam Duration: 45 Mins Total Questions : 30
The shear stress at any section at a distance y from neutral axis is given by
- (a)
\(\tau =\frac { VA\bar { y } }{ lb } \)
- (b)
\(\tau =\frac { VAb }{ \sqrt { y } } \)
- (c)
\(\tau =\frac { ib\bar { y } }{ VA } \)
- (d)
\(\tau =\frac { IA\bar { y } }{ Vb } \)
The shear stress distribution diagram of a beam is shown in the given figure.
The cross-section of the beam is
- (a)
1
- (b)
\(\Box \)
- (c)
T
- (d)
\(\triangle \)
As soon as the external forces causing deformation in a perfectly elastic body are withdrawn, the elastic deformation, disappears causing deformation in a perfectly elastic body are withdrawn, the elastic deformation, disappears
- (a)
only partially
- (b)
completely and instantaneously
- (c)
completely over a prolonged period of time
- (d)
completely after an initial period of rest
A fixed beam AB carrier two concentrated loads 2 kN and 1kN at distance of 0.5m on either side of centre of span in a direction normal to the axis of the beam as shown below
- (a)
0.5kN-m
- (b)
1.0 kN-m
- (c)
1.5 kN-m
- (d)
zero
A propeller shaft is subjected to maximum compressive stress of 20 N/mm2 and maximum shear of 80 N/mm2 due to torque. The maximum tensile stress induced is closed to
- (a)
70 N/mm2
- (b)
60 N/mm2
- (c)
50 N/mm2
- (d)
140 N/mm2
A composite section shown in the figure below was formed at \({ 20 }^{ \circ }C\)and was made of two materials A and B. If the coefficient of thermal expansion of A is greater than that of B and composite section is heated to \({ 40 }^{ \circ }C\), then A and B will
- (a)
be in tension and compression respectively
- (b)
both be in compression
- (c)
both be in tension
- (d)
be in compression and tension respectively
At a point in a strained material, if two mutually perpendicular tensile stresses of 200\({ kg }/{ cm^{ 2 } } \)are acting, then the intensity of tangential stress on a plane inclined at \({ 15 }^{ \circ }\)to the axis of the minor stress will be
- (a)
1000\({ kg }/{ cm^{ 2 } }\)
- (b)
500\({ kg }/{ cm^{ 2 } }\)
- (c)
250\({ kg }/{ cm^{ 2 } }\)
- (d)
125\({ kg }/{ cm^{ 2 } }\)
In a biaxial stress problem, the stresses in x and y-direction are \(\sigma _{ X }\)=200 MPa and \(\sigma _{ Y}\)=100 MPa. The maximum principal stress in MPa is
- (a)
50
- (b)
100
- (c)
150
- (d)
200
The free end of a cantilever beam is supported by the free end of another cantilever using a roller as shown in the figure. What is the deflection at the roller support B?
- (a)
\(\frac { 8Pa^{ 3 } }{ 3EI } \)
- (b)
\(\frac { 9Pa^{ 3 } }{ 3EI } \)
- (c)
\(\frac { 64Pa^{ 3 } }{ 35EI } \)
- (d)
\(\frac { 216Pa^{ 3 } }{ 35EI } \)
The effective length of a column AB shown in the figure is
- (a)
0.7L
- (b)
<0.7L
- (c)
>0.7L but<L
- (d)
L
For a hollow circular having its end hinged, the slenderness ratio is 160. The l/d ratio of the column is
- (a)
80
- (b)
57
- (c)
40
- (d)
20
A hollow circular column of internal diameter d and external diameter 1.5d is subjected to compressive load. The maximum distance of the point of application of load from the centre for no tension is
- (a)
d/8
- (b)
13d/48
- (c)
d/4
- (d)
13d/96
The following statements are related to bending of beams
I. The slope of bending moment diagram is equal to the shear force
II. The slope of the shear force diagram is equal to the load intensity
III. The slope of the curvature is equal to the flexural rotation
IV. The second derivative of the deflection is equal to the curvature.
The only false statements is
- (a)
I
- (b)
II
- (c)
III
- (d)
IV
If the maximum flexural stress in timber joint of the flitched beam as shown in figure is 7 N/mm2, the maximum stress in the steel is
(Given m = \(\frac{E_s}{E_t}\) = 20 )
- (a)
7 N/mm2
- (b)
140 N/mm2
- (c)
240 N/mm2
- (d)
280 N/mm2
A wooden beam of width B and depth D is strengthened by two steel plates of thickness t and depth D on the both sides of the beam. The allowable stress in wood is \(\sigma\) and modulus ratio of steel to wood is m.The allowable bending moment is
- (a)
\(\frac { { \sigma D }^{ 2 } }{ 6 } (B+mt)\)
- (b)
\( \frac { { \sigma D }^{ 2 } }{ 6 } (B+2mt)\)
- (c)
\(\frac { { \sigma D }^{ 2 } }{ 6 } (2B+mt)\)
- (d)
\(\frac { { \sigma D }^{ 2 } }{ 6 } (2B+2mt)\)
A simply supported beam is subjected to a uniformly distributed load of intensity w per unit length on half of the span from one end. The length of the span and the flexural stiffness are denoted as L and EI respectively. The deflection at the mid span of the beam is
- (a)
\(\frac { 5 }{ 6144 } \frac { wL^{ 4 } }{ EI } \)
- (b)
\(\frac { 5 }{ 384 } \frac { wL^{ 4 } }{ EI } \)
- (c)
\(\frac { 5 }{ 768 } \frac { wL^{ 4 } }{ EI } \)
- (d)
\(\frac { 5 }{ 192 } \frac { wL^{ 4 } }{ EI } \)
In the bending moment diagram for shimply supported beanm is of the form given below, then the load acting on the beam is
- (a)
a concentrated load at C
- (b)
equal and opposite moments at A and B
- (c)
a udl distributed load over the beam
- (d)
a moment applied at C
A homogeneous, simply supported prismatic beam of width B, depth D and span L is subjected to a concentrated load of magnitude P. The load can be placed anywhere along the span of the beam. The maximum flexural stress developed in the beam is.
- (a)
\(\frac { 2PL }{ 3BD^{ 2 } } \)
- (b)
\(\frac { 3 }{ 4 } \frac { PL }{ BD^{ 2 } } \)
- (c)
\(\frac { 4 }{ 3 } \frac { PL }{ BD^{ 2 } } \)
- (d)
\(\frac { 3 }{ 2 } \frac { PL }{ BD^{ 2 } } \)
A simply supported beam of uniform rectangular cross-section of width b and depth h is subjected to linear temperature gradient\( { 0 }^{ o }\) at the top and\( { T }^{ o }\) at the bottom as shown in figure. The coefficient of linear expansion of the beam material is\( \alpha .\) The resulting vertical deflection at the mid span of the beam is
- (a)
\(\frac { \alpha Th^{ 2 } }{ 8L } (upward)\)
- (b)
\(\frac { \alpha TL^{ 2 } }{ 8h } (upward)\)
- (c)
\(\frac { \alpha Th^{ 2 } }{ 8h } (downward)\)
- (d)
\(\frac { \alpha TL^{ 2 } }{ 8h } (downward)\)
The shear force diagram of a loaded beam is shown in the figure. The maximum bending moment in the beam is
- (a)
16 kN-m
- (b)
11 kN-m
- (c)
28 kN-m
- (d)
8 kN-m
The plane of maximum shear stress has normal stress that is
- (a)
maximum
- (b)
minimum
- (c)
zero
- (d)
None of the above
A simply supported beam as shown in the figure. The resultant reaction at B is equal to
- (a)
2kN (up)
- (b)
2 kN (down)
- (c)
2\(\sqrt{2}\) kN (up)
- (d)
2\(\sqrt{2}\) kN (inclined)
A cantilever beam shown n the given figure has load p acting at point A and B. The deflection at B is When the load at B is removed when the load at A is removed, the deflection at A will be
- (a)
\(\frac { \triangle }{ 4 } \)
- (b)
\(\frac { \triangle }{ 2 } \)
- (c)
\(\triangle \)
- (d)
\(\frac { 2\triangle }{ 3 } \)
The buckling load P=Pcr for the column AB in the figure, as approches infinity becomes \(\frac { \alpha \pi ^{ 2 }EI }{ L^{ 2 } } \) where \(\alpha \) is equal to
- (a)
0.25
- (b)
1.00
- (c)
2.05
- (d)
4.00
A mild steel plate is stressed as shown in figure . Before stressing a circle of 300 mm diameter is drawn on the plate. Poisson's ratio=0.3, modulus of elasticity =200 GN/m2
The length of major axis in mm is
- (a)
310.11
- (b)
301.12
- (c)
300.112
- (d)
299.88
The plane of maximum shear stress has normal stress, that is
- (a)
maximum
- (b)
minimum
- (c)
zero
- (d)
None of the above
In a plane stress problems, there are normal tensile stresses \({ \sigma }_{ x }and{ \quad \sigma }_{ y }\)accompanied by shear stress \({ \tau }_{ xy }\)at a point along orthogonal cartesian coordinates x and y respectively. If it is observed that the minimum principal stress on a certain plane is zero, then
- (a)
\({ \tau }_{ xy }=\sqrt { \left( { \sigma }_{ x }+{ \sigma }_{ y } \right) } \)
- (b)
\({ \tau }_{ xy }=\sqrt { \left( { \sigma }_{ x }-{ \sigma }_{ y } \right) } \)
- (c)
\({ \tau }_{ xy }=\sqrt { \left( { \sigma }_{ x }.{ \sigma }_{ y } \right) } \)
- (d)
\({ \tau }_{ xy }=\sqrt { \frac { { \sigma }_{ x } }{ { \sigma }_{ y } } } \)
A simply supported beam is made of two wooden planks of same width resting upon the one another without friction and connection.The upper plank is of half the thickness as compared to lower plank .The assembly is loaded by a uniformly distributed load on th entire span. The ratio of maximum stress developed between top and bottom planks will be
- (a)
1 : 16
- (b)
1 : 8
- (c)
1 : 4
- (d)
1 : 2
The state of stress at a point P in a two dimensional loading is such that the Mohr's circle is a point located at 175 MPa on the positive normal stress axis. The maximum and minimum principal stress will be respectively
- (a)
+175 MPa, -175 MPa
- (b)
+175 MPa , +175 MPa
- (c)
0 , -175 MPa
- (d)
0,0
A circular shaft of length L is held at two ends without rotation. A twisting moment T is applied at a distance L/3 from left as shown in the given figure. The twisting moment in the AB will be
- (a)
T
- (b)
T/3
- (c)
T/2
- (d)
2T/3