For the cross section and loading shown, determine

- (a) Neutral axis location and orientation,
- (b) Location and magnitude of the maximum bending stress.

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EQUATIONS USED: Eq. A13.13 and Eq. A13.15

SOLUTION

This problem requires more analysis as both the loading and cross-sectional shape are unsymmetric. The procedure is similar to the previous example. First need to find the centroid, moments of inertia about the x and y axes, and the product of inertia.

The centroid is at

and the moments of inertia and product of inertia are

The components of the applied bending moment are determined as

The x component is negative because it causes tension in the first quadrant.

(a) Since this is a homogeneous section, and it is assumed to be within its elastic limits, the neutral axis will pass through the centroid. Its angle with respect to the x axis is

(b) The maximum bending stress occurs at the farthest point from the NA, either at point A or B.

Therefore, point B is the location of maximum bending stress.

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