Example Question

Example Question

Castigliano’s Theorem example question

Find the horizontal displacement of point B (Δ_B →) using the Castigliano's theorem.

Find the horizontal displacement of point B (Δ_B →) using the Castigliano's theorem.

Click below to show answer. X

Step 1:
Apply load P (→) at B and solve for reactions

Step 1:
Apply load P (→) at B and solve for reactions

Castigliano’s Theorem solution step 1

Step 2:
Calculate internal forces in truss members in terms of P

Step 2:
Calculate internal forces in truss members in terms of P

Castigliano’s Theorem solution step 2

Step 3:
Construct table for N, ∂N/∂P, N(P = 0), L and N(∂N/∂P)L

Step 3:
Construct table for N, ∂N/∂P, N(P = 0), L and N(∂N/∂P)L

Castigliano’s Theorem solution step 3

Step 4:
Use Castigliano's formula to get Δ_B (→)

Step 4:
Use Castigliano's formula to get Δ_B (→)

Castigliano’s Theorem solution step 4

Useful formula:

Useful formula:

Castigliano’s Theorem formula

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