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: Condition for a Stable Truss.
A perfectly stable truss requires a specific relationship between the number of members \( m \) and joints \( j \). This relationship is defined by the equation: \[m = 2j - 3\] Solving for \( j \), we obtain: \[j = \frac{m + 3}{2}\] Step 2: Interpretation.
This equation guarantees that the truss is statically determinate. In other words, the truss possesses the precise number of members and joints necessary for stability, without any redundant elements. Final Answer: \[ \boxed{j = \frac{m + 3}{2}} \]