Sathyabama University SCIX5002 ME-P-STRU Theory of Elasticity and Plasticity March 2014

Register Number

                               

SATHYABAMA UNIVERSITY

(Established under section 3 of UGC Act,1956)

Course & Branch :M.E - P-STRU

Title of the Paper :Theory of Elasticity and Plasticity   Max. Marks :80

Sub. Code :SCIX5002(2012/2013)                                Time : 3 Hours

Date :26/03/2014                                                            Session :FN

______________________________________________________________________________________________________________________

                                       PART - A                    (6 x 5 = 30)

                        Answer ALL the Questions

1.     Give Equilibrium equation in 3D form in Cartesian coordinate?

2.     Verify this is airys stress function?

        Φ = B ( y³+ 3 y h²) + Fy²  ;     ∆⁴ Φ = 0

                                    4               8

3.     Two vertical wires of steel and other are aluminium having same length are very close together and hold a weight of 50N. The steel wire has a dia of 1mm and aluminium wire1.5mm dia. Determine the forces in each wire.

4.     Explain Prandtl’s theory on torsion and Warping function?

5.     Define Yield criteria and list out the various theories involved in calculating the stresses.

6.     Define Plastic flow,work ,potential and strain hardening.

PART – B               (5 x 10 = 50)

Answer ALL the Questions

7.     Derive the equations of equilibrium for a 3-D stress state.

(or)

8.     A point P in a body is given by , Z =

It is expressed in MN/mm².Determine the total, normal and shear stress on a plane which is equally inclined to all the three axes.

9.     The state of stress at a point is given by

        σ _x = 200 MPa ;       σ _y = -100 MPa                and σ _z = 50 MPa

        τ _xy =   40 MPa;       τ _yz =    50 MPa               and τ _zx = 60 MPa

        If E= 2x 10⁵ N/mm² and G = 0.8 x 10⁵ N/mm². Find out the corresponding strain components from Hook’s law. Take γ = 0.2.

(or)

10.   Derive the compatibility relation of strain in a 3-D elastic body. What is its significance?

11.   Find out stresses in a cantilever beam by Airy’s stress function approach when it is subjected to a point load at the free end. The width of the beam is h and depth of the beam is d.

(or)

12.   Stress tensor at a point is given by, τ _ij =

        Find out :

(i).Principal stresses and their directions.

(ii).Maximum and minimum shear stresses along with their planes.

13.   A thin wall rectangular shaft of 50x60 mm having a wall thickness of 2.5 mm, length of the shaft is 3 m, it is subjected to a torque of 150Nm at one end while other end is rigidly fixed G = 1.05x10⁵ N/mm². Determine the maximum shear stress developed and angle of twist of shaft.

(or)

14.   Find the shear stress and angle of twist for section shown in fig.

G = 2.7x10⁵ kg/cm² , M = 500 kg/cm.

15.   A circular shaft of inner radius 4 cm and outer radius 10 cm is subjected to a twisting couple so that the outer 2 cm deep shell yields plastically. Determine the twisting couple applied to the shaft. The yield stress in shear for the shaft material is 145 MN/mm². Also determine the couple for full yielding.

(or)

16.   Write in detail about:

        (a) Tresca’s yield criteria.

        (b) Von Mises Hencky’s yield criteria.

Share This