Question

A plane truss has \(10\) joints. For it to be a perfect truss, the number of members must be

• A. \(15\)
• B. \(17\)
• C. \(19\)
• D. \(20\)

Hint:

For a perfect plane truss, \[ \boxed{ m=2j-3. } \] If \[ m>2j-3, \] the truss is redundant, whereas if \[ m<2j-3, \] it is deficient.

Answer 1

The Correct Option is B

Step 1: Recall the condition for a perfect plane truss. For a perfect plane truss, \[ \boxed{ m=2j-3, } \] where
• \(m\) = number of members,
• \(j\) = number of joints.

Step 2: Substitute the given value. Given, \[ j=10. \] Hence, \[ m = 2(10)-3 = 20-3 = 17. \] Therefore, \[ \boxed{17} \] is the required number of members. Thus, \[ \boxed{(B)} \] is the correct answer.