Question

The following conditions must be satisfied for a perfect truss (m = number of members, j = number of joints):

• A. \( j = \frac{m + 3}{2} \)
• B. \( j = \frac{m - 3}{2} \)
• C. \( j = \frac{2m + 3}{2} \)
• D. \( j = \frac{2m - 3}{2} \)

Hint:

For a perfect truss, the number of joints \( j \) is related to the number of members \( m \) by the formula \( j = \frac{m + 3}{2} \).

Answer 1

The Correct Option is A

Step 1: Understand the condition for a perfect truss.
For a truss to be perfectly stable, the relationship between the number of members \( m \) and the number of joints \( j \) must satisfy the equation: \[ m = 2j - 3 \] Rearranging this equation, we get: \[ j = \frac{m + 3}{2} \] Step 2: Conclusion.
This condition ensures that the truss is statically determinate, meaning that the system has just enough members and joints for stability, with no redundancies. Final Answer: \[ \boxed{j = \frac{m + 3}{2}} \]