Test: Deflection & Theories of Failure - 3 - Mechanical Engineering MCQ

Who enunciated the following theorem:
If unit loads rest upon a beam at the two points R and S, the deflection at R due to unit load at S equals the deflection at S due to the load at R

When a number of loads rest upon a beam the deflection at any point is equal to the sum of the deflections at this point due to each of the loads taken separately. This is according to

Total strain energy stored in a simply supported beam of span ‘L’ and flexural rigidity 'El' subjected to a concentrated load ‘W‘ at the center is equal to

The strain energy stored in a shaft due to torsion is given by
Where V is the volume, G is modulus of rigidity and τ_s is the maximum shear stress on the surface of the shaft.

 Which one of the following graphs represent Von Mises yield criterion?

Match the List-I with List-ll:
List-I
A. Maximum normal stress theory
B. Maximum principal strain theory
C. Maximum shear stress theory
List-ll
1. Mise's and Henkey’s theory
2. Rankine’s theory
3. St Venant’s theory
4. Guest’s Tresca’s theory
Codes:
     A  B  C
(a) 4  1  2
(b) 2  3  4
(c) 3  2  4
(d) 2  3  1

Which of the following theories of failure is represented by square shape elastic boundary?

Principal stresses at a point in an elastic material are 100 MPa tensile 5 and 50 MPa tensile. What is the factor of safety against failure based on maximum shear strain energy theory? The elastic limit in simple tension is 173.2 MPa and Poisson’s ratio 0.3.

A uniform rod made of ductile material is subjected to tension. The value of octahedral shearing stress developed will be
where σ_y is the yield stress of ductile material.

The value of octahedral shearing stress for a material subjected to hydrostatic pressure will be

Which theory of failure is widely used in machine design dealing with ductile materials?

The ratio of the area under the bending moment diagram to the flexural rigidity between any two points along a beam gives the change in

A cantilever beam rectangular in cross-section is subjected to an isolated load at its free end. If the width of the beam is doubled, the deflection of the free end will be changed in the ratio of

For a simply supported beam of length ‘L' subjected to downward load of uniform intensity w, Match List-I with List-II and select the correct answer using the codes given below the lists:
List-l
A. Slope of shear force diagram
B. Maximum shear force
C. Maximum deflection
D. Magnitude of maximum bending moment
List-II
1. 
2. w
3. 
4. 
Codes:
     A  B  C  D
(a) 1  2  3   4
(b) 3  1  2   4
(c) 3  2  1   4
(d) 2  4  1   3

The Mohr’s circle of plane stress for a point in a body is shown. The design is to be done on the basis of the maximum shear stress theory for yielding. Then, yielding will just begin if the designer chooses a ductile material whose yield strength is

As per the elastic theory of design, the factor of safety is the ratio of

All the failure theories give nearly the same result