A simply supported beam with a length of 10 m carries a point load of 20 kN at 3

A simply supported beam with a length of 10 m carries a point load of 20 kN at 3 m from the left support. What is the reaction at the left support?

A simply supported beam with a length of 10 m carries a point load of 20 kN at 3 m from the left support. What is the reaction at the left support?

Step 1: Identify the beam and its supports. We have a beam that is 10 meters long with a left support (A) and a right support (B).
Step 2: Locate the point load. There is a point load of 20 kN applied at 3 meters from the left support (A).
Step 3: Determine the distances. The distance from the left support (A) to the point load is 3 m, and the distance from the point load to the right support (B) is 10 m - 3 m = 7 m.
Step 4: Use the moment equation. To find the reaction at the left support (R_A), we can take moments about the right support (B).
Step 5: Write the moment equation. The moment caused by the reaction at the left support (R_A) about the right support (B) is R_A * 10 m. The moment caused by the point load is 20 kN * 7 m.
Step 6: Set the moments equal. We have R_A * 10 m = 20 kN * 7 m.
Step 7: Solve for R_A. Rearranging gives R_A = (20 kN * 7 m) / 10 m.
Step 8: Calculate R_A. R_A = 14 kN.

Static Equilibrium – The beam is in static equilibrium, meaning the sum of vertical forces and the sum of moments about any point must equal zero.
Reaction Forces – Understanding how to calculate the reaction forces at supports due to applied loads.
Moment Calculation – Using the moment about a point to find unknown forces in a static system.