In a wooden beam scenario, what are the values in lbs for R1 and R2 if the beam is 20 feet long and has a concentrated load of 500 pounds at a distance of 15 feet from R2?

To determine the reaction forces R1 and R2 in the given scenario with a wooden beam, we can utilize the principles of static equilibrium. Specifically, we can apply the equations for the sum of vertical forces and the sum of moments.

Given the beam length of 20 feet and a concentrated load of 500 pounds located 15 feet from R2, we first calculate the distance from the load to R1. This distance is 20 feet - 15 feet = 5 feet.

To find R1 and R2, we can set up the following equations:

1. The sum of vertical forces must equal zero:

R1 + R2 - 500 = 0

2. Taking moments about R2 to eliminate R2 from our calculations, we have:

Moment about R2 = (R1 * 20 feet) - (500 pounds * 15 feet) = 0

From the moment equation:

R1 * 20 = 500 * 15

R1 * 20 = 7500

R1 = 7500 / 20

R1 = 375 pounds

Now, substituting R1 back into the first equation:

375 + R2 - 500 = 0