Mechanics of Materials BEU Model Question Paper Solution 2023

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1. Choose the correct option (any seven) : 2×7=14

(a) If a material has identical properties in all directions, it is said to be
 
(i) homogeneous
(ii) isotropic ✓
(iii) elastic
(iv) orthotropic
 
(b) When a member is subjected to axial tensile load, the greatest normal stress   is equal to
 
 (i) half the maximum shear stress
 (ii) maximum shear stress
 (iii) twice the maximum shear stress ✓
 (iv) none of the above
 
(c) The radius of Mohr’s circle for two equal and unlike principal stresses 
of magnitude “p” is
 
 (i) p ✓
 (ii) p/2
 (iii) zero
 (iv) none of the above
 
(d) The variation of the bending moment in the portion of a beam carrying 
linearly varying load is
 
 (i) linear
 (ii) parabolic
 (iii) cubic ✓
 (iv) constant
 
(e) Degree of static indeterminacy of a rigid-jointed plane frame having 15 
members, 3 reaction components and 14 joints is
 
 (i) 2
 (ii) 3
 (iii) 6 ✓
 (iv) 8

(f) The principle of virtual work can be applied to elastic system by 
considering the virtual work of
 
 (i) internal forces only
 (ii) external forces only  
 (iii) internal as well as external forces ✓
 (iv) none of the above
 
(g) The deflection at any point of a perfect frame can be obtained by applying 
a unit load at the joint in
 
 (i) vertical direction
 (ii) horizontal direction
 (iii) inclined direction
 (iv) the direction in which the deflection is required ✓
 
(h) Buckling load for a given column depends upon
 
 (i) length of column only
 (ii) least lateral dimension only
 (iii) both length and least lateral dimension ✓
 (iv) none of the above
 
(I) If a shaft of diameter d is subjected to a torque ‘T’ the maximum shear 
stress is
 
 (i) 32T/πd3
 (ii) 16T/ πd2
 (iii) 16T/ πd3  ✓
 (iv) 64T/ πd4
 
(j) Proof resilience is the maximum energy stored at
 
 (i) limit of proportionality
 (ii) elastic limit ✓
 (iii) plastic limit
 (iv) none of the above

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2. A steel rod of 30mm diameter is enclosed in a brass tube of 42mm external 
diameter and 32mm internal diameter. Each is 360mm long and assembly 
is rigidly held between two stops 360mm apart. The temperature of the assembly is then raised by 50̊C. determine
 
 (a) stresses in the tube and the rod.
 (b) stresses in the tube and the rod if stops yields by 0.15mm.
 (c) yields of the stops if the forces at the stops is limited to 60kN.
Where Es= 205GPa; Eb= 90GPa; αs=11×10-6
/ ̊C; αb=19×10-6
/ ̊C
.

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3. The stresses on two perpendicular planes through a point in a body are 
30MPa and 15MPa both tensile along with shear stress of 25MPa. Find
 
 (a) the magnitude and direction of principal stresses
 (b) the plane of maximum shear stress  
 (c) the normal and shear stresses on the planes of maximum shearing stress.

 

Solution:-

Answer:

4. A bolt is acted upon by an axial pull of 16kN along with a transverse 
shear force of 10kN. Determine the diameter of the bolt required 
according to the different failure of theories. Elastic limit of the bolt 
material is 250MPa and a factor of safety 2.5 is to be taken. Poisson’s 
ratio is 0.3.

 
Solution:- 

5. A overhang beam ABC of length 9m has left support at left end and 
another support at distance 6m from left end. The beam carries a point 
load at far right end and it also carries a uniformly distributed load of 
4kN/m over a length of 3m as shown in fig. determine the slope and 
deflection at point C. Take E= 2×105 N/mm2  and I= 5×108 mm4
. 

 

Solution:- 

6. A hollow shaft of diameter ratio 3/8(internal dia. to outer dia.) is to 
transmit 375kW power at 100r.p.m. the maximum torque being 20% 
greater than the mean torque. The shear stress is not to exceed 60N/mm2  and twist in a length of 4m is not to exceed 2̊. Calculate its external and  
internal diameters which would satisfy both the above conditions. Assume   modulus of rigidity G= 0.85×105 N/mm2.

 Solution:-

7. A boiler shell is to be made of 15 mm thick plate having a limiting tensile 
stress of 120N/mm2
. If the efficiencies of the longitudinal and circumferential 
joints are 70% and 30% respectively determine:
 
(a) The maximum permissible diameter of the shell for an internal pressure of 
2 N/mm2 , and

(b) permissible intensity of internal pressure when the shell diameter is 1.5m .  

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8.(a) Write the assumptions of Euler’s column theory.

Solution:-

 

 
   (b) Calculate the Euler’s critical load for a strut of T-section, the flange width 
being 10cm, overall depth 8cm and both flange and stem 1cm thick. The strut is 
3m long and is built in both ends. Take E= 2×105 N/mm2
.
 

Solution:-

9. Determine the forces in the truss shown in figure which is subjected to 
horizontal and vertical loads. Mention the nature of forces in each case.

 

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