A truss is in static equilibrium with a horizontal member AB subjected to a load. If the member AB is oriented horizontally and supports a vertical load of $1000N$ at its midpoint, what is the force in member AB according to Newton's First and Second Laws?

• A. The force in member AB is $1000N$ in tension.
• B. The force in member AB is $500N$ in compression.
• C. The force in member AB is $0N$ because it only supports vertical loads.
• D. The force in member AB is $2000N$ in compression.

Answer: (A)

Verified step by step guidance

1. Identify the type of structure and loading: The member AB is a horizontal truss member subjected to a vertical load of 1000 N at its midpoint. Since the truss is in static equilibrium, the sum of forces and moments must be zero.
2. Draw a free-body diagram of the member AB, showing the 1000 N vertical load acting downward at the midpoint, and the reaction forces at the supports (points A and B). Assume the supports provide vertical reactions and axial forces in the member.
3. Apply the equilibrium equations. First, use the sum of vertical forces: \(\sum F_y = 0\). Since the load is centered, the vertical reactions at A and B will each be half of the load, i.e., 500 N upward at A and 500 N upward at B.
4. Next, consider the axial force in member AB. Because the member is horizontal and the load is vertical, the member experiences tension or compression due to the reactions at the supports. Use the sum of moments or analyze the internal forces to find the axial force in AB.
5. Conclude that the force in member AB is related to the vertical load and the reactions. The member will experience a compressive force equal to half the applied load (500 N) due to the support reactions balancing the vertical load, according to Newton's First and Second Laws.