GOKARAJU RANGARAJU INSTITUTE OF ENGINEERING AND TECHNOLOGYDepartment of Civil Engineering

THEORY OF ELASTICITY AND PLASTICITY

M.Tech (Structural Engineering) 1ST Semester 1ST Mid Exam ( 20-01-2015)

Time: 2 hrs Answer any Five. All questions carry equal marks Marks: 30

1. At a point in a stressed body, the Cartesian components of stresses are x =80 MPa, y = 50 MPa, z = 30 MPa, xy =30 MPa, yz =20 MPa, zx =40 MPa. Determine a) the normal and shear stresses on a plane whose normal has the direction cosines of cos(n,x)= 1/3 , cos(n,y)=2/3, cos(n,z)=2/3 ; b) angle between resultant stress and outward normal n.2. a) Derive the differential equations of equilibrium for the case of 3-D problem in elasticity.b) Derive the compatibility equations for a 3-D system.3. Derive the compatibility equations in terms of stress components for a) A plane stress case and b) A Plane strain case4. Express the solutions for 2-Dimentional problems by the use of polynomials.5. a) Derive Biharmonic equation in terms of Airys stress function.b) Derive Airys stress function for beam subjected to pure bending.6. Write short notes ona) Components of Stresses and Strainsb) Hookes Law relationships7. The state of stress at a point with respect to x,y,z system is 105-15 51020 kN/sq.m-152025 Determine the stress relative to x1, y1, z1 coordinate systems obtained by a rotation through 450 about Z axis.