In the figure given below, a plane bamboo truss is shown which is made up of five equilateral triangles with all angles within the triangles as 60° and length of each segment of the equilateral triangle is “L”. All the connections are rigid enough to transfer the load completely. Which one of the following is a correct option for the reactions generated in the system? (Pin at A, roller at B; load P acts vertically downward at D, directly above B)
- AVA = P; HA = 0; VB = 0
- BVA = P/2; HA = P sin 60°; VB = P/2
- CVA = P/2; HA = P cos 60°; VB = P/2
- DVA = 0; HA = 0; VB = PCorrect
Solution
Concept
Reactions of a truss
Step-by-step solution
1. D lies on the vertical through B. 2. Moments about A: VB × 2L = P × 2L ⇒ VB = P. 3. ΣV = 0 ⇒ VA = 0; ΣH = 0 ⇒ HA = 0.
Explanation
The load acts directly over the roller support.
Why the other options are wrong
Other options split the load incorrectly.
Shortcut
Take moments about A.
Correct answer: D) VA = 0; HA = 0; VB = P