# Combined Loads (forces and moments) on composite lamina

1. Oct 4, 2014

### spggodd

1. The problem statement, all variables and given/known data

I have a laminate subject to 3 forces and 3 moments:
• Nx = normal force resultant in the x direction (N/m)
• Ny = normal force resultant in the y direction (N/m)
• Nxy = shear force resultant (N/m)
• Mx = Bending moment resultant in the x direction (Nm/m)
• My = Bending moment resultant in the y direction (Nm/m)
• Mxy = Turning moment resultant (Nm/m)
The questions are below and ask me to find the FOS using various methods.
1. Factor of safety of each ply and the whole laminate based on maximum stress criterion
2. Factor of safety of each ply and the whole laminate based on Energy Based Interaction Theory – Tsai-Hill Criterion
3. Factor of safety of each ply and the whole laminate based on Interactive Tensor Polynomial Theory - Tsai-Wu Criterion
I feel I am stuck at the first hurdle as I can't figure out how to treat all the loads at once, all loads/materials properties etc are variables and I have been asked to design an interactive spreadsheet for 8 plies.

2. Relevant equations

Compliance/Stiffness matrix methods.

3. The attempt at a solution

I think I am supposed to use the stiffness/compliance matrix method to work out the stresses in the global co-ordinates. However I have done this for 3 forces but I'm not sure how to combine this with moments?

Do I have to extend the matrices from 3x3 to include the moments somehow?

2. Oct 9, 2014