This learning solution comprises the topics of Simple stresses and strains, strain energy, thin cylindrical shell, Shear force and bending moment diagrams, Theory of simple bending deflection of beams, Deflection of beams and Torsion in shafts.
Introduction of materials- Materials - Strength of materials. Mechanical properties of materials- Strength - Mechanical properties of materials- Elasticity - Brittleness - Hardness - Stress - Strain. Types of loads - Load - According to the manner of application - According to nature of application - According to the effect produced. Different types of stress and strain- Types of stresses - Types of strains. Statement of Hooke's Law and elastic constant- Hooke's law - Elastic constants - Modulus of elasticity - Modulus of rigidity - Bulk modulus. Stress-Strain diagram for ductile materials- Stress - strain diagram for ductile material - Features of stress - strain curve. Problems on stress and strain in uniform cross section bars - Example. Lateral strain, Poisson's ratio and factor of safety - Lateral strain - Poisson's ratio - Factor of safety. Elastic constants and their relations - Elastic constants - Relation between young's modulus 'E' and rigidity modulus 'C - Relation between young's modulus 'E' and Bulk modulus 'K - Relation between young's modulus 'E' , rigidity modulus 'C' and Bulk modulus 'K. Problems on elastic constants and their relationship - Example. Analysis on varying cross sections- Bars of varying cross - sections - Example. Simple problems on varying cross section bars - Example. Analysis on bars of varying cross sections with varying loads- Bars subjected to varying loads - Example. Volumetric strain of different cross – sections- Volumetric strain. Problems based on volumetric strain - Example. Temperature stresses and strains - Temperature stresses and strains - Example - Thermal stresses in composite bars. Temperature stresses in composite sections- Example.
Definition of strain energy, proof resilience - Strain energy - Resilience. Strain energy – gradual load - Strain energy – gradual load - Example. Strain energy - Maximum instantaneous stress due to suddenly applied loading - Example. Impact loading - Impact loading - Example. Shock loading - Shock loading - Example.
Thin cylindrical shells - Thin cylindrical shells. Hoop stresses - Hoop stresses - Longitudinal stresses. Maximum shear stress - Maximum shear stress - Design of thin cylindrical shells. Spherical shells - Spherical shells- Cylindrical Shell with hemispherical ends. Built – up spherical shells - Built – up spherical shells - Example. Examples of thin cylinder - Example.
Types of beams - Introduction - Types of supports - Types of beams - Types of loads. Determine shear force and bending moment - Shear force and bending moment - Shear force - Bending moment- Sign convention for S.F - Sign convention for B.M. Cantilever with a concentrated load at the free end- Shear force and bending moment - Example - SFD and BM for a cantilever with point load at a distance 'a' from the fixed end - Example. Cantilever with UDL on the entire span - SF and BM for a Cantilever beam subjected to UDL on the whole span - Example. Cantilever subjected to UDL over a part span from fixed end - SFD and BMD for a cantilever subjected to UDL over a part span from the fixed end - Example. Cantilever subjected to UDL and point loads - Bending moment - Example. Simply supported beam with eccentric point load - SFD and BMD in case of S. S. beam with a non-central point load - Example. Simply supported beam carrying several point loads - Example. Simply supported beam with a point load at the centre and with two or more point loads - SFD and BMD in case of simply supported beam with a central point load - Example. Simply supported beam with uniformly distributed load - Simply supported beam carrying UDL over the entire span - Example. SS beam subjected to point and UDL - Example. Over –hanging beam with point loads, at the centre and at free ends - Overhanging beams - Example. Over – hanging beam with uniformly distributed load throughout - Example.
Beam deflection - Beam - Shear force - Bending moment - Sign convention for SF - Sign convention for BM - Relation between loading, shear force and bending moment - Pure bending / simple bending - Beam subjected to sagging / positive bending moment - Beams subjected to hogging / Negative bending moment. Assumptions in theory of simple bending - Theory of simple bending - Assumptions in theory of pure bending / simple bending- Bending stresses and neutral axis - Neutral axis for symmetrical sections - Neutral axis for unsymmetrical sections - Example - Section modulus of rectangular section - Section modulus of circular section - Section modulus for other sections - Example. Derivation of simple bending equation - Derivation of simple bending formula - Example. Problems on moment of resistance- Example. Problems on bending stresses - Example.
Beam deflection- Beam deflection - Elastic curve of neutral axis of the beam under normal load - Relationship between loading S.F, B.M, Slope and Deflection.Slope and Deflection - Finding slope and deflection - Double integration method. Cantilever with concentrated load at the end - Cantilever with concentrated load at the end. Cantilever with uniformly distributed load at the end- Cantilever with uniformly distributed load at the end. Simply supported Beam - Simply Supported beam with uniformly distributed load at the end - Simply supported beam with concentrated load at mid-span. Solved Problem in deflection of beam - Example. Solved Problem in deflection of beam- Example.
Function of shafts, shaft materials, and standard sizes of shafts- Shaft - Transmission of Power - Properties of Shafts. Polar moment of inertia for solid and hollow shafts - Polar moment of inertia - Example - Polar Section Modulus - Example. Torsion equation - Torsion - Torsion equation for shaft - Example. Design of the solid and hollow shafts- Design of solid shaft - Example - Strength of a hollow shaft - Example. Torsional rigidity equation - Torsional rigidity - Example. Power transmitted by shaft - Power transmitted by shaft - Example - Comparison between solid and hollow shaft - Example.
Springs- Introduction- Functions of spring - spring materials - Types of springs - Terms used in helical springs. Design of coil spring based on the load and deflection- Design of coil spring based on the load and deflection. Problems on coil Springs - Example. Leaf springs- Leaf springs - Types of leaf spring - Stresses and deflection of leaf springs. Problems on leaf springs - Example.
