Theory Of Elasticity

Find the expressions of stress for a bending of simply supported beam subjected to uniformat distributed loading.

b. Write short notes on

ii) Airy's stress function  

b. Write short notes on

    i) St. Venant's principle 

a. Show that the stress function satisfy for torsion problems.

Discuss the effect of circular hole on the stress distribution of retangular plate.

b. Derive Lame's equation for thick cylinders.

A. Define axlsymmetric problem with example.

b. Check if represents a stross function. 

a. drive the parital differential equations of equilibriumin polar coordinates for 2-  dimensional system. 

a. Derive the expression for normal stress and write the comparison equations in y and z directions.

b. Write a note on:

iii) Mohrs circle.

b. Write a note on:

ii) Plano strain problem

b. Write a note on:

i) Plane stress problem

a. Write a note on strain Rosette. By means of strain rosette, the following strains were recorded during the test on a structural member.determine: i) Magnitude of pincipal strains

                   ii) Orientation principal planes. 

b. The displacement field in micro units for a body is given by u = (x² + y)i + (3+2)j + (x²+2y)K. determing the principal strains at (3, 1, -2) and the direction of the minimum principal strain. 

a. At a point P in a 3-D system the rectangular stress corushents are  =1;   = -2;  =4;  =2;  = -3 and = 1 all units are in KP Find the principal stresses and check for invariance. 

b. Derive the differential equations of equilibrium for a 3 - dimensions system in Cartesian coordinate.