UNIT I ENERGY PRINCIPLES Strain energy and strain energy density – strain energy due to axial load, shear, flexure and torsion – Castigliano's theorems – Maxwell's reciprocal theorems – Principle of virtual work – application of energy theorems for computing deflections in beams and trusses – Williot Mohr’s Diagram. UNIT II INDETERMINATE BEAMS Concept of Analysis – Propped cantilever and fixed beams-fixed end moments and reactions – Theorem of three moments – analysis of continuous beams – shear force and bending moment diagrams. UNIT III COLUMNS AND CYLINDER Euler's theory of long columns – critical loads for prismatic columns with different end conditions; Rankine-Gordon formula for eccentrically loaded columns – Eccentrically loaded short columns – middle third rule – core section – Thick cylinders – Compound cylinders. UNIT IV STATE OF STRESS IN THREE DIMENSIONS Determination of principal stresses and principal planes – Volumetric strain –Theories of failure – Principal stress – Principal strain – shear stress – Strain energy and distortion energy theories – application in analysis of stress, load carrying capacity. UNIT V ADVANCED TOPICS IN BENDING OF BEAMS Unsymmetrical bending of beams of symmetrical and unsymmetrical sections – Shear Centre – curved beams – Winkler Bach formula.
