Questions
7 questions per paper
Difficulty
Medium
Importance
High yield for HPCL/NTPC/ONGC
Overview
Strength of Materials is the bedrock of Mechanical engineering, focusing on how structural components respond to external forces. It is a high-yield topic for PSU exams like NTPC and BHEL, where candidates are tested on their ability to predict material failure and deformation. Mastering the relationship between stress, strain, and geometric properties is essential for solving numerical problems efficiently.
Stress, Strain & Elastic Constants
This section covers the fundamental behavior of materials under axial loads and the relationship between various elastic moduli. It forms the basis for all higher-level structural calculations.
- Hooke's Law: stress = E * strain
- E = 2G(1 + mu) = 3K(1 - 2mu) = 9KG / (3K + G)
- Volumetric strain: ev = e1 + e2 + e3
- Thermal stress in restrained bar: sigma = E * alpha * deltaT
- Elongation of tapered bar: deltaL = 4PL / (pi * E * d1 * d2)
Bending Moment & Shear Force Diagrams
Analyzing beams under different loading conditions requires understanding the graphical representation of internal forces. Direct questions involve finding maximum bending moments and points of contra-flexure.
- Relationship: dV/dx = -w; dM/dx = V
- Bending formula: M/I = sigma/y = E/R
- Section modulus Z = I / y_max
- Point of contra-flexure: Where bending moment changes sign
- Standard cases for cantilever and simply supported beams are high-frequency questions
Torsion of Shafts
This subtopic deals with circular members subjected to twisting moments. PSU exams frequently ask for the calculation of polar moment of inertia and maximum shear stress in shafts.
- Torsion equation: T/J = tau/R = G * theta / L
- Polar moment of inertia (J) for solid shaft: pi * D^4 / 32
- Polar moment of inertia (J) for hollow shaft: pi * (D^4 - d^4) / 32
- Power transmitted: P = (2 * pi * N * T) / 60
- Strength of shaft is directly proportional to Zp
Columns & Buckling
Columns are analyzed based on their buckling load rather than yield strength. Euler's theory is the cornerstone here, with specific focus on effective length conditions.
- Euler's critical load: P_cr = pi^2 * E * I / (L_e^2)
- Effective length (L_e) for both ends hinged: L
- Effective length (L_e) for both ends fixed: L/2
- Effective length (L_e) for one fixed/one free: 2L
- Rankine's formula is used for intermediate length columns
Pressure Vessels
Thin-walled pressure vessels are analyzed by assuming uniform stress distribution across the thickness. You must distinguish between hoop stress and longitudinal stress.
- Hoop stress (sigma_h) = pd / 2t
- Longitudinal stress (sigma_l) = pd / 4t
- Volumetric strain: ev = (pd / 4tE) * (5 - 4mu)
- Hoop stress is always twice the longitudinal stress
- Maximum shear stress = (sigma_h - sigma_l) / 2
Formula Sheet
sigma = P/A
epsilon = deltaL / L
E = 2G(1+mu)
M/I = sigma/y = E/R
T/J = tau/R = G*theta/L
P_cr = pi^2*E*I / L_e^2
sigma_h = pd / 2t
sigma_l = pd / 4t
Exam Tip
Memorize the table of effective lengths for columns and the elastic constant relations; they are the fastest marks you can pick up in a PSU paper.
Common Mistakes
- Confusing the effective length factor for different end conditions of columns.
- Mixing up diametral and radial values in the pressure vessel and shaft torsion formulas.
- Neglecting the sign convention in shear force diagrams, leading to incorrect bending moment values.
More Revision Notes
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