Example Question

The toroidal shell with the dimensions shown is loaded with a pressure of 6 MPa. Calculate the principal stresses σ_θ, σ_Φ, σ_r at point A, which sits at the mid-thickness of the shell.

Click below to show answer. X

Step 1:
Get values for r_o, r_Φ, r_θ, Φ, p, t

Step 1:
Get values for r_o, r_Φ, r_θ, Φ, p, t

Step 2:
[+↑ΣF_y = 0], find σ_Φ

Step 2:
[+↑ΣF_y = 0], find σ_Φ

Step 3:
Membrane stress equation, find σ_θ

Step 3:
Membrane stress equation, find σ_θ

Step 4:
Final answer for σ_θ, σ_Φ, σ_r

Step 4:
Final answer for σ_θ, σ_Φ, σ_r

Useful formula:

Useful formula:

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

Example Question

Example Question

Step 1: Get values for ro, rΦ, rθ, Φ, p, t Step 1: Get values for ro, rΦ, rθ, Φ, p, t

Step 2: [+↑ΣFy = 0], find σΦ Step 2: [+↑ΣFy = 0], find σΦ

Step 3: Membrane stress equation, find σθ Step 3: Membrane stress equation, find σθ

Step 4: Final answer for σθ, σΦ, σr Step 4: Final answer for σθ, σΦ, σr

Useful formula: Useful formula:

Step 1:
Get values for r_o, r_Φ, r_θ, Φ, p, t

Step 1:
Get values for r_o, r_Φ, r_θ, Φ, p, t

Step 2:
[+↑ΣF_y = 0], find σ_Φ

Step 2:
[+↑ΣF_y = 0], find σ_Φ

Step 3:
Membrane stress equation, find σ_θ

Step 3:
Membrane stress equation, find σ_θ

Step 4:
Final answer for σ_θ, σ_Φ, σ_r

Step 4:
Final answer for σ_θ, σ_Φ, σ_r

Useful formula:

Useful formula: