Example Question

Example Question

Generalised Hooke’s Law example question

Given the stresses acting on the element, calculate the principal strains ε₁, ε₂ and the angle θ_p1 at which it occurs.

Given the stresses acting on the element, calculate the principal strains ε₁, ε₂ and the angle θ_p1 at which it occurs.

Click below to show answer. X

Step 1:
Use Hooke's law to convert σ_x, σ_y, τ_xy to ε_x, ε_y, γ_xy

Step 1:
Use Hooke's law to convert σ_x, σ_y, τ_xy to ε_x, ε_y, γ_xy

Generalised Hooke’s Law solution step 1

Step 2:
Construct 2D Mohr's circle using ε_x, ε_y, γ_xy

Step 2:
Construct 2D Mohr's circle using ε_x, ε_y, γ_xy

Generalised Hooke’s Law solution step 2

Step 3:
Calculate ε₁, ε₂ and θ_p1 using Mohr's circle

Step 3:
Calculate ε₁, ε₂ and θ_p1 using Mohr's circle

Generalised Hooke’s Law solution step 3

Useful formula:

Useful formula:

Generalised Hooke’s Law formula

Now that you've mastered this question, you can try Question 1.