1. Normal and shear stresses in unsymmetrical cross sections
Lecture #12
Normal and shear stresses in unsymmetrical cross sections

2. UNSYMMETRY OF CROSS SECTION
Most of real cross sections of the wing are unsymmetrical.
The calculation of normal stresses and shear flows could be done in two ways:
1. Transfer to principal coordinate system and usage of simple formulas.
2. Usage of central axes and more complicated formulas. 2

3. FORMULAS FOR THE NORMAL STRESS
Formula for principal axes:
Formula for central axes: 3

4. FORMULAS FOR THE SHEAR FLOW
Formula for principal axes:
Formula for central axes: 4

5. CALCULATION USING PRINCIPAL AXES
Find the centroid and calculate moments of inertia Ix, Iy and product of inertia Ixy for central axes.
Find the angle of rotation for principal axes and calculate moments of inertia Iu, Iv in principal axes.
Compose static moment diagrams (Su, Sv). Use these formulas to convert coordinates:
Use the simple formula for shear flow
(positive a is
counterclockwise) 5

6. CALCULATION USING CENTRAL AXES
Find the centroid and calculate moments of inertia Ix, Iy and product of inertia Ixy for central axes.
Compose static moment diagrams (Sx, Sy).
Use the following formula for shear flow 6

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WHERE TO FIND MORE INFORMATION?
Megson. An Introduction to Aircraft Structural Analysis. 2010
Chapters 15 & 16
For normal stresses, see example 15.14
For shear flows, see example 16.1
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