Test: Solid Mechanics- 2 - SSC JE MCQ

Effective length of columns under different end conditions are:

1. For both ends hinged: L_e = L

2. One end fixed and another end free: L_e = 2L

3. Both ends fixed = 

4. One end fixed and other is hinges: 

Radius of Mohr’s circle is given by:

At principal plane, σ_x = σ₁, σ_y = σ₂

τ_xy = 0

σ₁ = p , σ₂ = -p

r = p

Relation between Modulus of elasticity (E), Shear Modulus (G) and Bulk modulus (K) is given by:

Now, rewriting the equation as follows:

3KE + GE = 9KG

3KE – 9KG = - GE

K(3E – 9G) = - GE

SF_y = 0

R_A + R_B = 

Taking moment of all the forces about B = 0.

The general relationship between the shear force diagram, bending moment diagram and loading diagram will be:

1. Shear force diagram is 1^o higher than loading diagram.

2. Bending moment diagram is 1^o higher than shear force diagram.

3. For the uniformly varying load on the beam, the shear force diagram is parabolic in nature.

4. For the uniformly varying load on the beam, the bending moment diagram is also parabolic but is 1^o higher than shear force diagram.

Using the relation: 

Where,

T = Torque applied to the shaft

I_P = Polar section modulus

τ = shear stress in the material

R = radius of the shaft

= 0.982 kN-m

1. Maximum Principal stress theory was postulated by Rankine. It is suitable for brittle materials.

2. Maximum Principal strain theory was postulated by St Venant. This theory is not accurate for brittle and ductile materials both.

3. Maximum Shear stress theory was postulated by Tresca. This theory is suitable for ductile materials. Its results are the safest.

4. Maximum shear strain energy theory was postulated by Von-mises. Its results in case of pure shear are the accurate for ductile materials.

When a material undergoes a change in temperature, it either elongates or contracts depending upon whether temperature is increased or decreased of the material. If the elongation or contraction is not restricted, i. e. free then the material does not experience any stress despite the fact that it undergoes a strain. 

Correct Answer :- c

Explanation : Non isotropic or anisotropic materials have different properties in different directions. They show non- homogeneous behaviour. The number of elastic constants is 21.

Deflection of beam is inversely proportional to area moment of inertia of the beam.

Moment of inertia for rectangular section,  

Let the final deflection is y_final when the depth is doubled.

As we know,

M ∝ Z

For short or long columns Rankine’s Formula is used.

Where P is crippling load by Rankine formula;  P_C is crushing load; P_E is crippling load by Euler’s formula.

For Short column: P_E is very large so

 will be very small and negligible as compared to   so 

For Long column: P_E is small so   will be large as compared to   

Hence the value of   can be neglected. So

Hence the crippling load by Rankine’s formula for long column is approximately equal to the crippling load by Euler’s formula.