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SYLLABUS

UNIT-I

SIMPLE STRESSES AND STRAINS Concept of stress and strain - St. Venant’s principle – Stress and strain Diagram – Pure shear and complementary shear – Elasticity and plasticity – Types of stresses and strains – Hooke’s Law – Stress – Strain diagram for mild steel – Working stress – Factor of safety – Lateral strain, Poisson’s ratio and Volumetric strain – Elastic modulii – Elastic constants and the relationship between them – Bars of varying section – Composite bars – Temperature stresses. STRAIN ENERGY Resilience – Gradual, Sudden, Impact and shock loadings – Simple applications.

UNIT-II

SHEAR FORCE AND BENDING MOMENT Types of beams – Concept of shear force and bending moment – S.F and B.M diagrams for cantilever, Simply supported including overhanging beams subjected to point loads, Uniformly distributed load, Uniformly varying load, couple and Combination of these loads – Point of contra-flexure – Relation between S.F., B.M and rate of loading at a section of a beam.

UNIT-III

FLEXURAL STRESSES Theory of simple bending – Assumptions – Derivation of bending equation. Section Modulus – Determination of flexural – Bending stresses of rectangular and circular sections (Solid and Hollow), I,T, Angle and Channel sections – Design of simple beam sections. SHEAR STRESSES Derivation of formula for shear stress distribution – Shear stress distribution across various beam sections like rectangular, Circular, Triangular, I, T, angle and channel sections.

UNIT-IV

DEFLECTION OF BEAMS Slope, deflection and radius of curvature – Differential equation for the elastic line of a beam – Double integration and Macaulay’s methods – Determination of slope and deflection for cantilever and simply supported beams subjected to point loads, U.D.L, Uniformly varying load and couple – Mohr’s theorems – Moment area method – Application to simple cases. CONJUGATE BEAM METHOD Introduction – Concept of conjugate beam method. Difference between a real beam and a conjugate beam. Deflections of determinate beams with constant and different moments of inertia.

UNIT-V

PRINCIPAL STRESSES Introduction – Stresses on an oblique plane of a bar under axial loading – Compound stresses – Normal and tangential stresses on an inclined plane for biaxial stresses – Two perpendicular normal stresses accompanied by a state of simple shear – Principal stresses – Mohr’s circle of stresses – Ellipse of stress – Analytical and graphical solutions. THEORIES OF FAILURE Introduction – Various theories of failure – Maximum Principal Stress Theory, Maximum Principal Strain Theory, Maximum Shear Stress Theory – Strain Energy and Shear Strain Energy Theory (Von Mises Theory)