B.TECH - Semester 5 mechanics of materials Question Paper 2021 (mar)
Practice authentic previous year university questions for better exam preparation.
Sample Questions
- Write down the differential equation of equilibrium of static solid body.
- Differentiate between true stress-strain and engineering stress-strain diagrams.
- Explain the state of pure shear with a stress elements.
- Write the stress tensor for a system where the dimensions of the body in ' $z$ ' direction is approximated as zero. Justify your statement.
- What is Airy's proposal of stress function?
- Give the schematic sketch of variation of hoop stress and radial stress in thick cylinder.
- Define strain energy.
- State the Castigliano's theorem for angular movements.
- What do you understand by the term 'warps'?
- What is Prandtl stress function? ( $\mathbf{1 0} \boldsymbol{\times} \mathbf{2} \boldsymbol{=} \mathbf{2 0}$ Marks) P.T.O.
- (a) Derive the Cauchy's stress formula.
- (b) At a point P , the rectangular stress components are $\sigma_{x}=1, \sigma_{v}=-2, \sigma_{z}=4, \tau_{x y}=2, \tau_{y z=-3}$ and $\tau_{x z}=1$ all in units of kPa . Find the principal stresses and check for invariance. OR
- The state of plane stress at a failure point on the shaft is shown on the element in Fig. Represent this stress state in terms of the principal stresses. Module - II
- (a) A thick-wall cylinder is made of steel ( $E=200 \mathrm{GPa}$ and $v=0.29$ ), has an inside diameter of 20 mm , and has an outside diameter of 100 mm . The cylinder is subjected to an internal pressure of 300 MPa . Determine the stress components...
- (b) Show the different stress components in a cylindrical volume element of thickness ' $d z$ ' and state the strain compatibility condition for the thick wall cylinder.
- A thick cylinder of 100 mm internal radius and 150 mm external radius is subjected to an internal pressure of $60 \mathrm{MN} / \mathrm{m}^{2}$ and an external pressure of 30 $\mathrm{MN} / \mathrm{m}^{2}$. Determine the hoop and radial stresses at t...
- Two shafts are of the same material, length and weight. One is solid and 100 mm diameter, the other is hollow. If the hollow shaft is to store $25 \%$ more energy than the solid shaft when trasmitting torque, what must be its internal and external di...
- Derive the deflection of cantilever beam carrying point load at the end using Castigliano's theorem. 20
- (a) Derive the equations for angle of twist, shear stress and maximum shear stress of a rectangular bar with very small thickness in terms of the torque transmitted breadth, thickness, Young's modulus and Poisson's ratio. 14
- (b) Write down the governing equation of torsion of a bar with stress function as dependent variable. Simplify this equation for a rectangular bar with very small thickness. State the assumptions made.
- (a) Define Saint Venant theory and drive the expression for torison of circular bar cross section.
- (b) Describe membrane analogy and describe torison of thin walled section.10 ( $\mathbf{4} \boldsymbol{\times} \mathbf{2 0} \boldsymbol{=} \mathbf{8 0}$ Marks) 3