In the truss shown in the figure, the force in the member BD, in kN, is __________________ .
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A member connected to a loaded joint will be a zero-force member if the other two members meeting at that joint already carry the load and are not collinear.
Step 1: Observe the symmetry of the truss.
The truss is symmetric about the vertical line passing through joint B. The loads applied are:
- A vertical 5 kN at joint B (symmetric),
- A vertical 2 kN at joint E (not symmetric, but located on the left). Step 2: Identify zero-force members.
At joint B, three members meet: BE, BF, and BD.
A member becomes a zero-force member if two non-collinear members carry load and the third is not aligned with the load.
The 5 kN load at B is purely vertical. The two inclined members BE and BF can resist vertical components. BD is horizontal (or nearly so in the drawing) and therefore cannot resist vertical load at that joint.
By the zero-force member rule:
If two non-collinear members carry the load at a joint, the third member with no external loading is a zero-force member.
Thus, BD is a zero-force member. Step 3: Effect of load at E.
The 2 kN load at E creates forces in members on the left side only. Its influence does not require a force through BD because BD connects joint B to joint D, not joint E. There is no load path that forces BD to carry axial load. Hence, member BD carries zero force. Final Answer: 0
