Question Bank

Program: M. Tech (Structural Engineering)

Course Name: Advanced Solid Mechanics Course Code: 24CVL511

Academic year: 2024-25 Sem/Year: I/I

S. No. Questions CO*
Q1 What is meant by the state of stress at a point, explain it? 1

Q2 What do you mean by one degree freedom? 3

Q3 State Castigliano’s First and Second theorem. 5

Q4 Explain the terms, ‘Anisotropic’, ‘Orthotropic’ and ‘Isotropic’ as applied to

1
material properties.

Q5 Explain about components of strain at a point. 3

Q6 Write down the Prandtl-Rauss equations. 4

Q7 What is meant by octahedral plane? 3

Q8 Explain the term “complementary strain energy”. 2

Q9 What is plane strain? Explain it 1

Q10 Define stress vector. 1

Q11 Write the generalized Hooke’s law for an isotropic material 1

Q12 Briefly explain elasto-plastic behavior of material. 5

Q13 What is torsional rigidity? 4

Q14 What are the assumptions involved in axisymmetric problems? 3

Q15 State and explain principle of virtual work. 2

Q16 Describe about the significance of stress invariants. 1

Q17 Write down boundary condition equations for stress analysis problem? 3

Q18 What is isotropic hardening for materials? 5

Q19 What is meant by shear centre? 2

Q20 State Hooke’s law and explain about pure shear. 1
Q21 What is the flow or normality rule for plastic deformation? 5

Q22 Explain the Elasto-plastic problems in torsion (residual stress in torsion). 5

Q23 Deduce the constitutive relation for a linear elastic isotropic material. 2

Q24 What are the assumptions involved in axisymmetric problems? Write the
governing equilibrium equations for the axisymmetric problem with sketch 3
indicating stress components.

Q25 Show that 𝛷 = x4y + 4 x2y3 – y5 is a valid stress function and compute the
stress tensor for this case assuming a state of plane strain with Poisson ratio 3
= 0.25.

Q26 Write short notes on Von Mises Yield Criterion, Tresca Yield Criterion. 5

Q27 Describe the Airy’s stress function with the help of second-degree
3
polynomial?

Q28 State and explain generalized Hooke’s law. 3

Q29 Write all six-compatibility equation, given the following plane strain 3
distribution.

Q30 The state of stress at a point is characterised by the components, σx = 12.31, 3

σy = 8.96, σz = 4.34, 𝜏xy = 4.20, 𝜏yz =5.27, 𝜏zx =0.84MPa. Determine the
values of principal stresses and maximum shear stress.

Q31 Derive the compatibility equation in terms of Airy’s stress function for a
3
two-dimensional elastic problem. Assume body forces are not acting.

Q32 Obtain the strain energy in terms of material properties for a shaft subjected
4
to a torque T.

Q33 If the stress tensor at a point is given by σx= 0, σy= 0, σz= 0, τxy= 10, τxz= -
3
10, τyz=20, find stress invariants, characteristic equation, principal stresses.

Q34 Explain the plane stress and strain with one example each? 3
Q35 A bar of 25mm diameter is subjected to a pull of 65 kN. The majored
extension on gauge length of 200 mm is 0.1 mm and change in diameter is 1
0.0004 mm. Calculate Young’s modulus, Poisson Ratio and Bulk modulus.

Q36 Write down the differential equation of equilibrium in polar co-ordinate 1

system in 2-dimensions.

Q37 Derive the Torsion equation for a thin-walled hollow circular rod subjected 4
to a torque T. Also state the assumptions used in the derivation.

Q38 Derive expressions for (i) Angle of twist per unit length, (ii) Torsional 4
rigidity and (iii) Stresses, for elliptical cross section under torsion, by
Prandtl’s method?

Q39 Figure shows the cross sections of two tubular rods. The thickness and 3
circumference of the two sections are equal. Find the ratio of shear stress
induced if:

i) Equal twisting moment are applied

ii) Equal angle of twist are applied.

Q40 A cantilever of rectangular cross section of breadth 4cm and depth 6 cm is 3

subjected to an inclined load W at free end as shown in figure. The length of
cantilever is 2.5m and the angle of inclination of the load with vertical is 25◦.
What is the maximum value of W if the maximum stress due to bending is
not to exceed 200 N/mm2

Q41 Show that the equilibrium conditions for stresses in a membrane loaded due 2
to pressure (P) is analogous to the condition that Prandtl’s torsion stress
function should obey. Describe the experimental procedure of finding (i)
stresses and (ii) torsional rigidity, using the membrane analogy.
Q42 The state of stress at a point is characterized by σx= 18, σy= -50, σz= 32, 3
τxy=0, τxz=24, τyz=0 (All stress values are in kPa). Calculate the principal
stresses and the direction of largest tensile principal stress?

Q43 A thick walled tube with an internal radius of 12cm is subjected to an 4

internal pressure of 200MPa. (E = 2.1x105MPa) and µ = 0.3). Determine
the optimum value of the external radius if the maximum shear stress
developed is limited to 350MPa.

Q44 Obtain the bending stress on the cross section of a cantilever beam carrying 5
point load at the free end using polynomial stress function method?

Q45 A rod with rectangular cross section is used to transmit torque to a machine 4
frame (see figure). It has a width of 40mm. The first 3.0m length of rod has
a depth of 60mm and the remaining 1.5 m length has a depth of 30mm. The
rod is made of steel having G=77.5 GPa. Given T1=750Nm and
T2=400Nm, determine the maximum shear stress in the rod. Also
determine the angle of twist of the free end.

Q46 A shaft of square section of outer side 55mm and inner side 50mm is 4
subjected to a twisting moment such that the maximum shear stress
developed is 250N/mm2. What is the torque acting on the shaft and what is
the angular twist if the shaft is 1.6 m long and G = 70000 N/mm2?

Q47 Drive the equation of elasticity for stress. 4

Q48 Derive the equations of equilibrium in case of a three dimensional stress 4

system.