What is the Modulus of Rupture for a simply supported beam with two point loads symmetrically placed at 5 inches from each end?
Understanding Modulus of Rupture
The Modulus of Rupture of a beam is a crucial parameter that indicates the material's strength when subjected to bending stress. In the given scenario, we have a 20-inch long simply supported beam with two point loads symmetrically placed at 5 inches from each end. The beam started cracking at 500 lbs and ultimately failed at 800 lbs. It is mentioned that the Modulus of Rupture of the beam is 250 psi, meaning that the material used in the beam can withstand a bending stress of up to 250 psi before it fails.
Calculation of Modulus of Rupture
To calculate the Modulus of Rupture of the beam, we can use the formula: MR = FL/ (bd²), where MR is the Modulus of Rupture, F is the load at failure, L is the span length, b is the width of the beam, and d is the depth of the beam.
In this case, the span length is 20 inches, and the loads are symmetrically placed at 5 inches from each end, making the distance between the loads 10 inches. Assuming the beam is rectangular with a width of 2 inches and a depth of 4 inches, we can substitute the values into the formula:
MR = 800 lbs x 20 inches / (2 inches x 4 inches²)
MR = 8000 in-lbs / 32 in³
MR = 250 psi
Therefore, the Modulus of Rupture of the beam is 250 psi, indicating that the material used in the beam can withstand a bending stress of up to 250 psi before it fails.