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MAE 157 - Lightweight structures

Winter 2024

Homework 6: Fuselage

Due on Wednesday, March 6 th 2023

Problem 1

Given the following idealized fuselage that has a point force P and a point moment M:

Figure 1: Schematics problem 1.

Where the area of each boom is 220 mm2 , the thickness of the skin is 1 mm and the diameter of the fuselage is 500 mm

To solve this problem you are allowed to use any software (such as Excel). If you use any software you must attach a screenshot of the spreadsheet, write down all the expressions that you used and explain the procedure that you followed. If you only attach the results with no procedure you will receive no credit.

1. Draw the Moment (M), Shear (S) and Axial (N) diagram.

2. Find the coordinate y of each boom and report your results on the table that you can find at the end of this document. Express the result as decimal numbers. NOTE: You will receive no credit if you don’t report the results.

3. Find the second moment of inertia Ixx, Iyy and Ixy.

4. Find the shear flow for each panel indicating the equations you used to find them and report your results on the table that you can find at the end of this document. Express the result as decimal numbers.NOTE: You will receive no credit if you don’t report the results.

5. Find the axial force of each boom at section A-A and report your results on the table that you can find at the end of this document. Express the result as decimal numbers. NOTE: You will receive no credit if you don’t report the results.

Problem 2

Given the following idealized fuselage that has a point force P:

Figure 2: Schematics problem 1.

Where the area of each boom is 250 mm2 , and the thickness of the skin is 1 mm.

To solve this problem in an easier way the following areas (as shown in the right image) have been computed: A1 = 177128 mm2 , A2 = 142955 mm2 , A3 = 165000 mm2 .

To solve this problem you are allowed to use any software (such as Excel). If you use any software you must attach a screenshot of the spreadsheet, write down all the expressions that you used and explain the procedure that you followed. If you only attach the results with no procedure you will receive no credit.

1. Draw the Moment (M), Shear (S) and Axial (N) diagram.

2. Find the coordinate y of each boom and report your results on the table that you can find at the end of this document. Express the result as decimal numbers. NOTE: You will receive no credit if you don’t report the results.

3. Find the second moment of inertia Ixx.

4. Find the shear flow for each panel indicating the equations you used to find them and report your results on the table that you can find at the end of this document. Express the result as decimal numbers. NOTE: You will receive no credit if you don’t have the drawing.

5. Find the axial force of each boom at section A-A and report your results on the table that you can find at the end of this document. Express the result as decimal numbers. NOTE: You will receive no credit if you don’t report the results.

Table to report results

As for the coordinates, use positive when the coordinates are positive. As for the axial force, use positive for tension and negative for compression. As for the shear flow, state your results following the nomenclature in its figure, using positive when the shear flow is in the same direction as shown in the figure and negative when it is in the opposite direction.

Figure 3: Table to report results problem 1.

Figure 4: Table to report results problem 2.