Starting with two-dimensional stress transformation relation (3.3.5), set dx/d = 0, and thus show that the relation

Starting with two-dimensional stress transformation relation (3.3.5), set dσ′x/dθ = 0, and thus show that the relation to determine the angle to the principal stress direction θ_p is given by tan 2θ_p = 2τ _xy/σ_x–σ_y. Next explicitly develop relation (3.6.2).

Equation 3.3.5

Equation 3.6.2

Transcribed Image Text:

o'x o'y = Ox+dy 2 + -cos 20+ Ty sin 20 Ox-dy 2 x + ay 2 dy - Ox 2 Oxycos 20-Txy sin 20 2 sin 20 + Try cos 20