# How to Calculate Maximum Bending Stress

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When a piece of metal is bent, one surface is stretched while the other surface is compressed. There is then an area between the two surfaces that experiences zero stress, called the neutral axis. The maximum stress occurs at the surface of the beam farthest from the neutral axis. This is called "maximum surface stress" and is typically represented by the sigma sign. In order to calculate maximum surface stress, you must know the bending moment, the distance from the neutral axis to the outer surface where the maximum stress occurs and the moment of inertia.

## Step 1

Calculate the bending moment, represented by "M." The bending moment, or the force required to bend the object, can be found using formulas specific to the type of object being bent.

## Step 2

Calculate the moment of inertia, represented by "I." The moment of inertia, which is the object's resistance to change in its rotation, depends on the cross-sectional shape and thickness, not its length or makeup. For a rectangular solid object, I = (b*h^3)/12, where "b" is the width of the cross-section, and "h" is the measure of the cross-section in the direction force is being applied.

For a round solid object, I = (pi*r^4)/4, where "r" is the radius of the cross-section.

## Step 3

Determine the distance between the neutral axis and the outer surface where maximum stress occurs. This is represented by "c."

## Step 4

Calculate maximum surface stress, or MSS, using the following equation: MSS = (M*c)/I

references & resources

### Mike Goldstein

Mike Goldstein has been writing since 2005 and has been published in "Science" and Boston College's "Intellectual Property and Technology Forum Law Review." He studied Shakespeare at Rutgers University, pursuing a Bachelor of Arts in English literature. Music and photography are two of his specialties.

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