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ENCE151

Strength of Materials

Syllabus

  1. Simple Stress and Strain (10 hours)
    1. Introduction to Strength of Materials
    2. Deformable bodies, external forces, internal stresses and strains
    3. Types of stresses: Normal stress, shear stress, bearing stress
    4. Material behavior under axial loading: Stress-strain diagram for mild steel, yield stress, proportional limit, elastic limit, Hooke's law, Young's modulus of elasticity, strain hardening, ultimate stress/strength, ductility, toughness, elastic and inelastic strains, concept of factor of safety and allowable/permissible stress
    5. Stress-strain behavior for ductile and brittle materials, proof stress
    6. Fatigue and creep strength
    7. Thermal stress and strain in simple, compound, composite and indeterminate bars
    8. Lateral strains and Poisson's ratio
    9. Shear deformation and shear angle; Hooke's law for shearing deformations, modulus of rigidity
    10. Multi-axial loading and generalized Hooke's law
    11. Definitions of isotropic, anisotropic and orthotropic materials
    12. Volumetric stress-strain, bulk modulus
    13. Relationships between elastic constants
    14. Saint-Venant's principle and stress concentrations
    15. Elongation of bars under axial loadings: Uniform and varying cross sections, tapered sections, compound and composite bars
    16. Use of compatibility equations for axially loaded indeterminate bars
  2. Geometric Properties of Sections (5 hours)
    1. Axes of symmetry
    2. Centre of gravity of plane and built-up sections
    3. Moment of inertia of standard and built-up sections
    4. Parallel and perpendicular axis theorems
    5. Polar moment of inertia
    6. Radius of gyration
    7. Product moment of inertia
    8. Principal axes and principal moment of inertia
    9. Mohr's circle for principal moment of inertia
  3. Principal Stress Analysis in 2D Planes (5 hours)
    1. Stresses in inclined plane: Normal stress under uniaxial loading, Normal and shear stress subjected to two mutually perpendicular planes
    2. Principal planes and principal stresses
    3. Relationships between normal and shear stresses
    4. Maximum shear stresses
    5. Mohr's circle diagram for principal stresses
  4. Principal Strain Analysis (4 hours)
    1. Plane strain: Normal and shear strains in inclined planes
    2. Principal strains, maximum in-plane shear strains and their positions
    3. Mohr's circle diagram for plane strain
    4. Absolute maximum shear strain
    5. Strain rosettes
    6. Modes of failure for different materials
    7. Introduction of failure theories
  5. Thin Walled Vessels (3 hours)
    1. Introduction and characteristics
    2. Types of stresses and strains in cylindrical and spherical pressure vessels
    3. Calculation of stresses and strains in pressure vessels
  6. Torsion (5 hours)
    1. Introduction to torsion
    2. Stress-strain behavior in torsion
    3. Derivation of torsion formula for a circular shaft
    4. Torsional moments: Series and parallel combination of shafts and composite shaft
    5. Torsional stress in shafts, torsional resilience
    6. Comparison between solid and hollow shafts
    7. Power transmitted by shafts
    8. Statically indeterminate shafts
    9. Introduction to non-circular shafts
    10. Combined bending and torsion
  7. Theory of Flexure (8 hours)
    1. Introduction to flexure
    2. Coplanar and pure bending
    3. Derivation of bending equation
    4. Distribution of bending stress across the different beam cross-sections
    5. Analysis of beams for symmetric and composite sections
    6. Shear equation, shear stress variation in rectangular, circular, I and T sections
    7. Concept of slope and deflection in beams using double integration method: Simply supported and cantilever beams
  8. Column Theory (5 hours)
    1. Introduction: Buckling and stability of columns
    2. Classification based on slenderness ratio
    3. Effect of support conditions and effective length
    4. Derivation of Euler's formula for different end conditions, limitations and applicability
    5. Intermediate columns: Rankine's hypothesis
    6. Introduction to uniaxial and biaxial eccentric loading, condition for no tension

Practicals

  1. Tensile test and stress-strain curve for mild steel bar, HYSD bar, timber
  2. CG of simple plane figure
  3. Simple bending test on timber, steel, aluminum beams: Deflection, flexural relations and MoI comparisons
  4. Torsion test on simple shaft to determine modulus of rigidity
  5. Test on column behavior and buckling