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

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

6.2 NUMERICALS 2Strength of Materials

3Strength of Materials

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 Stresses are in MPa Inclination of Principal planes θ P wrt Vertical : 4Strength of Materials

Inclination of Max. shear stress planes θ S = θ P θ S = = & (wrt Vertical) Max. shear stress τ max : Principal stresses, σ P : 5Strength of Materials

Strength of Materials

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 Materials

8 ……….ii On plane EF, ……..iii Strength of Materials

Strength of Materials9