Solid Machenics /SOM

Question 1

Principal Stress in form of strain and Elastic modulus

Answer 1

Stress= E *(ε1+u.ε2) /(1-u^2)

Question 2

Different Theories of failure

Answer 2

1. Max principal Stress (Rankine theory)
   σ_max<=σy
2. Maximum principal strain (St. Venant’s theory)
   [σ1 -u.(σ2+σ2)]/E <= σy
3. Maximum shear stress (Guest and Tresca’s theory)
   tau_max <= σy/2
4. Maximum strain energy (haigh’s theory)
   σ1^2 +σ2^2 +σ3^2 - 2u.(σ1.σ2+σ2.σ3+σ1.σ3) < σy^2
5. Maximum strain/distortion energy (Mises -Henky theory)
   (1/2)*[(σ1-σ2)^2 +(σ2-σ3)^2 +(σ3-σ1)^2] < σy^2

Question 3

Stress at a point in terms of angle and coordinate stresses

Answer 3

σ= σx. Cosθ^2  +σy. Sinθ^2 + tau. Sin2θ
tan(2θ) = 2*tau/(σx - σy)

Question 4

principal stress in terms of Torque and Moment

Answer 4

σ = (16/π.D^3) * [M +- sqrt(M^2 +T^2)]

Question 5

Angle of neutral axis for lateral and virtical loaded beam

Answer 5

Tan(c) = Mh. Iv / Mv. Ih