Question

In the truss shown in the figure, all the members are pin jointed to each other. The members AB, BD, DE and DC have the same length. For the given loading, which of the following is the correct statement?

• A. BD is a zero-force member, and AB and ED are in compression
• B. AB is in tension, ED is in compression, and BD is a zero-force member
• C. AB and DC are in tension, and BC is in compression
• D. ED is in tension, and DC and BC are in compression

Hint:

To identify zero-force members, examine joints with two non-collinear members and no external load or reaction. These members carry no internal force and greatly simplify truss analysis.

Answer 1

The Correct Option is B

Step 1: Identify load path and basic geometry.
The truss consists of points A, B, C, D, and E. Supports are at A and E. A vertical downward load $F$ is applied at point C. The members AB, BD, DE, and DC all have equal length, giving a symmetric geometry about the line BD. Thus, BD lies exactly along the internal vertical axis of the truss.
Step 2: Determine if BD can carry force.
Consider joint B. Three members meet at this joint – AB, BD, and BC. The only external force near this joint is the force transmitted from member BC (since C carries the downward load). At joint B, if a member is to carry force, the force must have a component along the direction of that member.
BD is vertical. BC is slanted. The load from C comes into B through BC and has both horizontal and vertical components. The horizontal component is balanced by AB. The vertical component is carried downward toward D and E through other members.
Since there is no external horizontal load at B and AB already balances the horizontal component from BC, there is no need for BD to carry force. Thus, BD does not carry any force and becomes a zero-force member.
Step 3: Determine the force in member AB.
At joint B, the slanted member BC pulls downward and slightly left due to the load at C. To maintain equilibrium at joint B, AB must pull B back horizontally toward A (the support). Therefore, AB carries a force directed toward A, meaning AB is being pulled at both ends. This implies that AB is in tension.
Step 4: Determine the force in ED.
Move to joint D. The load transmitted from C through DC pushes joint D toward the left. Since DE connects D to the support at E, this member resists that leftward push. If a member resists being pushed inward toward a joint, it develops compressive force. Hence, DE experiences force directed from E toward D. This indicates ED is in compression.
Step 5: Conclusion from force analysis.
- BD carries no force → zero-force member.
- AB pulls to balance forces at B → tension.
- ED pushes against the load from C → compression.
This corresponds exactly to option (B).