MAE 157 - Lightweight structures
Winter 2024
Homework 7: Tapered wing box
Due on Wednesday, March 13th 2024
Problem 1
Given the following idealized wing spar, compute the shear flow distribution in the walls at the largest cross section (z = 0) by following the given steps. Also compute the resultant axial forces on each boom.
Figure 1: Schematics problem 1.
1. Draw the Moment (M), Shear (S) and Axial diagram (N)
2. Compute the moment of inertia Ixx at z = 0.
3. Compute σz of each boom.
4. Find the force Px , Py and Pz of each boom, and the resultant force by filling out the following table.
Figure 2: Table to fill out.
5. Find the shear force Sy,w and Sx,w that is going to be carried by the skin.
6. Split the problem in two: the open section and closed section and find the shear flow of the open section.
7. Write down the moment equilibrium equation and find the constant shear flow of the closed section.
8. Use the superposition principle to find the final shear flow of the wing spar and draw a picture of the final results indicating the value and the direction of the shear flow. Note: use the sign convention that we used to report the results using s as shown in Figure 1.