ME-304 Strength of Materials - Dec 2025 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aTwo rods, one of steel and the other of aluminium, are connected in parallel and carry a total load of 100 kN, Areas are 1000 mm$^2$ (steel) and 1500 mm$^2$ (aluminium). Find the stress in each rod. Take $E_s = 200$ GPa, $E_a = 70$ GPa.
   How to answer

   • Compatibility: equal elongation/deformation in parallel rods
   • Equilibrium: P_s + P_a = 100 kN with P = sigma*A
   • Compatibility using sigma*L/E to relate stresses: sigma_s/E_s = sigma_a/E_a
   • Solve for sigma_s and sigma_a
2. 7 Marks
   bDraw and explain stress-strain diagram for mild steel.
   How to answer

   • Draw stress-strain curve with proportional limit, elastic limit, yield points, ultimate stress, fracture
   • Explain elastic, yielding, strain hardening, necking regions
   • Mark salient points for mild steel
   • Distinguish upper/lower yield and ductile behaviour
3. 7 Marks
   aA Steel bar of 1.5 m length and 25 mm dimeter is subjected to an axial tensile load of 40 kN. Determine the strain energy stored in the bar. Take E = 200 GPa.
   How to answer

   • Volume and cross-section: A = pi*d^2/4
   • Axial stress sigma = P/A and elongation delta = P*L/(A*E)
   • Strain energy formula U = P^2*L/(2*A*E)
   • Substitute values to get U in joules
4. 7 Marks
   bDescribe the bending of composite sections and derive the expression for bending stress.
   How to answer

   • Concept of composite/flitched section and neutral axis
   • Strain compatibility and modular ratio m = E1/E2
   • Transformed section method
   • Derivation of bending stress sigma = -M*y*E/(EI)_equivalent
5. 7 Marks
   aDraw shear force and bending moment diagrams for the cantilever shown in fig.1.

   How to answer

   • Calculate support reactions at fixed end A
   • Write SF equations for segments AB, BC, CD, DE including UDL
   • Write BM equations and evaluate at A,B,C,D,E
   • Draw SFD and BMD with values and shapes (linear/parabolic)
6. 7 Marks
   bExplain the concept of deflection of beams. List the factors affecting deflection.
   How to answer

   • Definition of beam deflection and elastic curve
   • Governing differential equation EI d2y/dx2 = M
   • Factors: load, span, EI, support, cross-section
7. 7 Marks
   aExplain the advantages of hollow shafts over solid shafts for power transmission applications.
   How to answer

   • Higher strength-to-weight and stiffness-to-weight ratio
   • Larger polar moment for same area, efficient shear stress distribution
   • Material saving and ease for internal services
8. 7 Marks
   bDerive the torsion equation for a circular shaft and explain the terms involved.
   How to answer

   • Assumptions: circular, homogeneous, elastic, plane sections remain plane
   • Shear strain variation gamma = r*theta/L
   • Equilibrium leading to T/J = tau/r = G*theta/L
   • Meaning of T, J, tau, r, G, theta, L
9. 7 Marks
   aIn a tensile test, a test piece 25 mm in diameter, 200 mm gauge length stretched 0.0975 mm under a pull of 50,000 N. In a torsion test, the same rod twisted 0.025 radian over a length of 200 mm, when a torque of 400 Nm was applied. Evaluate the Poisson's ratio and the three elastic moduli for the material.
   How to answer

   • Tensile test: E = P*L/(A*deltaL) from stress/strain
   • Torsion test: G = T*L/(J*theta) with J = pi*d^4/32
   • Relate E,G,nu: E = 2G(1+nu) to get Poisson's ratio
   • Compute K = E/(3(1-2nu)) for bulk modulus
10. 7 Marks
    bExplain the Maximum Distortion Energy Theory (Von Mises theory) and derive the failure condition.
    How to answer

    • Distortion energy concept and von Mises stress
    • Strain energy decomposition into volumetric and distortional parts
    • Failure condition in terms of principal stresses
    • Expression for plane stress and uniaxial equivalence
11. 7 Marks
    aA bolt is subjected to an axial pull of 8 kN and a transverse shear force of 3 kN. Determine the diameter of the bolt required based on

    1. (i))The maximum principal stress theory
    2. (ii))The maximum shear stress theory
    How to answer

    • Compute axial stress sigma = P/A and shear stress tau = V/A
    • Principal stresses sigma1,2 = sigma/2 +/- sqrt((sigma/2)^2+tau^2)
    • Apply max principal stress <= sigma_allow = 270/3
    • Apply max shear stress (Tresca) with FOS to solve diameter
12. 7 Marks
    bDiscuss the selection of appropriate failure theories for different materials and loading conditions.
    How to answer

    • Brittle vs ductile criteria (Rankine, Tresca, von Mises)
    • Effect of hydrostatic vs biaxial/triaxial loading
    • Temperature, strain rate and stress concentration considerations
    • Examples of selection for shafts, pressure vessels, cast iron
13. 7 Marks
    aExplain slenderness ratio. Discuss its significance in determining the behaviour of columns.
    How to answer

    • Definition lambda = effective length / radius of gyration
    • Euler buckling dependence on slenderness
    • Short vs intermediate vs long column classification
    • Critical slenderness and end-condition effects
14. 7 Marks
    bDerive Rankine's formula for columns and explain the significance of constants used.
    How to answer

    • Combine crushing and Euler buckling loads: 1/PR = 1/Pc + 1/PE
    • Derive PR = sigma_c*A/(1+a*(Le/k)^2)
    • Meaning of Rankine constant a and crushing stress
    • Applicability to short/long columns and end conditions
15. 14 Marks
    Write short notes on the any **two** of the following:

    1. (a))Column and strut.
    2. (b))Maximum Shear Strain Theory
    3. (c))Elastic curve of a beam
    4. (d))Hooke's law
    How to answer

    • Select any two topics with definition and key points
    • Give relevant formula/theory and assumptions
    • Add illustrative example or diagram where applicable
    • Conclude with application/significance