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Calculating Modulus of Rupture

Please help with the following problem. See the attached wood block diagrams.

If a break load of 250 lbs. is applied to the first wood specimen, how do I determine the Moment of Inertia and calculate the Modulus of Rupture?

The only difference between the specimens per the attached diagram is that a 1/4" x 1/4" key-way is cut into the center of the 2nd specimen.

This is a simply supported beam analysis....but how do I calculate what I need and determine the difference in break load between the two??


Solution Preview

We take MOR = 3250 psi for the wood

Let F be the force acting in the middle of the wood block.
Let L = 6" be half the length of the block.
As the point of application of the force is in the middle, each support applies F/2 to its end of the block.
As the arm of each support relative to the middle is L/2, we find the bending momentum to be

M = (F/2)*(L/2) = FL/4 (1)

Now, refer to the useful explanations for "Pure Bending" at link ...

Solution Summary

The solution computes modulus of rupture. Step by step calculations are given.