ENERGY PRINCIPLES , INDETERMINATE BEAMS , COLUMNS , STATE OF STRESS IN THREE DIMENSIONS , ADVANCED TOPICS IN BENDING OF BEAMS ,
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STRENGTH OF MATERIALS
This subject is useful for a detailed study of forces and their effects along with some suitable
protective measures for the safe working condition. This knowledge is very essential for an
engineer to enable him in designing all types of structures and machines.
1. ENERGY PRINCIPLES
Strain energy and strain energy density – strain energy in traction, shear in flexure and torsion –
castigliano‟s theorems – principle of virtual work – application of energy theorems for
computing deflections in beams and trusses – Maxwell‟s reciprocal theorems
2. INDETERMINATE BEAMS
Propped cantilever and fixed beams-fixed end moments and reactions for concentrated load
(central, non central), uniformly distributed load, triangular load (maximum at centre and
maximum at end) – theorem of three moments – analysis of continuous beams – shear force and
bending moment diagrams for continuous beams – slope & deflections in continuous beams
(qualitative study only)
Eccentrically loaded short columns – middle third rule – core section – columns of
unsymmetrical sections – (angle channel sections) – Euler‟s theory of long columns – critical
loads for prismatic columns with different end conditions; Rankine-Gordon formula for
eccentrically loaded columns – thick cylinders – compound cylinders.
4. STATE OF STRESS IN THREE DIMENSIONS
Spherical and deviatory components of stress tensor - determination of principal stresses and
principal planes – volumetric strain – dilatation and distortion – theories of failure – principal
stress dilatation – principal strain – shear stress – strain energy and distortion energy theories –
application in analysis of stress, load carrying capacity and design of members – residual stresses
5. ADVANCED TOPICS IN BENDING OF BEAMS
Unsymmetrical bending of beams of symmetrical and unsymmetrical sections – curved beams –
Winkler Bach formula – stress concentration – fatigue and fracture.
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