1. The state of stress at a point is given by the following array of terms
[200 -100 50
-100 200 100 kg/cm^2
50 100 50

Determine the normal and shear stresses on a plane whose direction cosines are, Also determine the direction of the shear stress.

2. A straight torsion-tension member with a solid circular cross-section has a length L 6 m and radius R 10 mm. The member is subject to tension and torsion loads that produce an elongation M. =10 mm and a rotation of one end of the member with respect to the other end of n/3 rad. Let the origin of the cylindrical coordinate axes lie at the centroid of one end of the member, with z-axis extending along the centroidal axis of the member. The deformation of the member is assumed to occur under conditions of constant volume. The end z is constrained so that only radial displacements are possible there.

Determine the displacements for any point in the member and the state of strain for a point on the output surface.

Determine the principal strains for the point where the state of strain was determined.

3. Explain the construction and working of the following gauges

Acoustical strain gauge

Pneumatic strain gauge

Scratch gauge

Diffraction strain gauge

4. Determine the stresses in a brittle coating applied to a component made of steel for which E8= 2 x 10^6 Vs= 0·30 when the specimen stresses are 2100 kg/cm^2 and -1400 kg/cm^2

for a resin based coating with E 1·40 x 10 kg/cm^2 and Vo=0·42
and

for a ceramic based coating with 70 x 10^4 kg/cm^2 and V 0·25. If the threshold strain is 500 Mcm/cm, what is the corresponding state of stress in the coating during calibration

5. A strain gauge has gauge length of 10 mm and is looped around to a radius of 0·2 mm. Calculate its cross-sensitivity factor. If this gauge is to be used on steel in a strain field for which Eyy/ Exx =0·3, calculate corrected gauge factor if prescribed gauge factor is 2·1. What will be the gauge factor, if Eyy/Exx 0·8?

6. A delta rosette yields the following strain indication:

Ea Mcm/cm;

Eab 1220 Mcm/cm

Ec =710 Mcm/cm

Determine the maximum principal strain direction, the principal stresses and the maximum shear stress.
E 2 x 10^6 kg/cm^2 0·285

Describe the basic elements of a plane polariscope.

Derive an expression for the intensity of the emergent light from a plane polariscope with a stressed model and show how it enables us to determine the isoclinic and the isochromatic.

8. A photo-elastic coating CR-39 having material fringe value 17·2 kg/cm^2/cm per fringe, thickness ho 2 mm, Vo 3·5 and modulus of elasticity Eo 2 x 10^4 kg/cm^2 is used to measure stresses on aluminum for which 0·7 x 10^6 kg/cm^2,Vs 0.32. At a point of ·interest the normal incidence gave the fringe order to be 4·25 and an isoclinic of 30° passed through that point. Oblique incidence measurement by a rotation about the maximum principal stress axis by 15° gave the fringe order to be 4·05. Determine the principal stresses at this point.

9. Given a fringe order of a model thickness of 6·25 mm, a fringe value of 16 kg/cm^2/cm per fringe and an isoclinic parameter of 25° defining the angle between (Jl and x-axis, determine the shear stress txy.

10. Explain the Tardy's compensation method in detail. Why is this method preferred over other methods?