Question

A beam is supported and loaded as shown in figure 1. Suppose that a = 0.10 m, b = 0.15 m, l = 0.20 m, w = 150 N/m, and f = 80 N. Follow the sign convention for the internal forces and moments. Calculate the reaction forces at the supports (A and B) using the given dimensions and applied loads. Consider both vertical and horizontal components.

Answer 1

To calculate the reaction forces at the supports A and B, we need to consider the equilibrium of forces in both the vertical and horizontal directions.

Step-by-step explanation:

To calculate the reaction forces at the supports A and B, we need to consider the equilibrium of forces in both the vertical and horizontal directions.

1. Vertical equilibrium:
   • Summing the forces in the vertical direction, we have: A_y + B_y - w = 0
   • Since the beam is in equilibrium, the vertical reaction forces at A and B can be determined by taking the weight of the beam into account. So, A_y + B_y = w
2. Horizontal equilibrium:
   • Summing the forces in the horizontal direction, we have: A_x + B_x - f = 0

Since there are no external horizontal forces acting on the beam, the horizontal reaction forces at A and B can be determined by taking the applied force f into account. So, A_x + B_x = f.

Combining both the vertical and horizontal equilibrium equations, we can solve for the reaction forces at A and B.