1. Principal Stresses and Strain and Theories of Failure Strength of Materials Prof. A. S. PATIL Department of Mechanical Engineering Sinhgad Academy of Engineering, Pune

2. 6.2 NUMERICALS 2Strength of Materials06-12-2014

3. 3Strength of Materials06-12-2014

4. 2. The state of stress at a point in a strained material is shown in Fig. (i) Locate the principal planes and find the principal stresses, (ii) Locate the Max. shear stress planes and find the max. shear stress. Solution- A D C B 32 30 80 32 Stresses are in MPa Inclination of Principal planes θ P wrt Vertical : 4Strength of Materials06-12-2014

5. Inclination of Max. shear stress planes θ S = θ P + 45 0. θ S = 14.09 0 + 45 0 = 59.09 0 &149.09 0. (wrt Vertical) Max. shear stress τ max : Principal stresses, σ P : 5Strength of Materials06-12-2014

6. 6 80 30 32 45 0 Strength of Materials06-12-2014

7. 3. Fig. shows the normal and tangential stresses on the two plane. Determine the principal stresses. Solution – Let the plane ED be at Ɵ with major principal plane. ……..i 7 45° E D F Strength of Materials06-12-2014

8. 8 ……….ii On plane EF, ……..iii Strength of Materials06-12-2014

9. Strength of Materials9