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??
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 ...
The solution computes modulus of rupture.