For the cross section and loading shown, determine

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

Use the Java screen shown below to modify this example and see the results.

EQUATION USED: Eq. A13.13

SOLUTION

(a) As seen in the figure above, the cross section is symmetric about the
horizontal axis, therefore, the product of inertia is zero in this case.
Furthermore, with the bending moment applied about the x axis, the y component
of moment is zero. As a result of the previous two conditions, the NA
orientation according to eqn. A13.15
will be horizontal - passing through the centroid as expected. This problem
is an example of **symmetric bending**.

**NOTE:** There is no need to find the horizontal position of centroid
because there is no need to calculate the moment of inertia about the y axis
as y component of bending moment is zero.

(b) Because of the conditions stated in part (a) of solution, eq. A13.13 reduces to

The bending stress distribution will be linear with a zero value at the NA.

(c) In this case, the maximum stress is at the farthest point from the NA. Because of horizontal symmetry about the NA, the stress at the top and bottom of the section will have equal magnitude with the one on top being compressive. To get the maximum value of stress, the reduced equation given previously will be used.

The moment of inertia about the x axis is

This makes the maximum bending stress

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