Solid Mechanics

 👉Plane having principal stress has no tangential stress.

👉Mutually perpendicular planes are 180 degree apart in Mohr circle and have numerically equal value of shear stress.

👉Maximum shear stress = radius of Mohr's circle

👉         Theory of Failure                                               Also Known as  

       Maximum principal stress theory             Rankine theory, Lame's theory, Maximum stress theory

        Maximum principal strain theory                             St. Venant theory

           Maximum shear stress theory                   Tresca theory, Guest theory, Columb theory

          Maximum strain energy theory                              Beltrami Haigh theory

      Maximum shear strain energy theory                 Distortion energy theory, Von-Mises theory

👉 Bending Equation 

                                  M/I = σ/y  = E/R

where, M = Bending Moment

           σ  = Bending stress

           I =  Moment of inertia

          y = Distance of the fibre from Neutral axis

         R = Radius of curvature

         E = young's modulus of elasticity

👉 Torsion Equation:

                      T/Ip = τ/r = τmax/R  = N.θ/l

👉 Strain energy per unit volume = 1/2 x shear stress x shear strain

👉 Strain energy in torsion = 1/2 x T x θ

👉  For Brittle materials, Normal stress theory gives best result

👉 For ductile material maximum shear stress theory is applicable.

                                                                Happy Learning