In the pin-jointed truss shown in the figure, the members that carry zero force are identified. Which of the following options is/are zero-force members?
Show Hint
In truss analysis, zero-force members are those which carry no load under the given loading conditions. They can be identified using specific rules such as the absence of external load or reaction at the joint or having two non-collinear members at a joint with no external load or support.
In truss analysis, zero-force members are identified using the following rules:
1. If two non-collinear members meet at a joint without an external load or reaction, both members are zero-force members.
2. If three members form a joint, and two of them are collinear (i.e., in a straight line) with no external load or reaction at that joint, the third member is a zero-force member.
Step 1: Analyzing Joint B
At joint B, there are two non-collinear members, BC and AB, with no external load or reaction at B.
- According to Rule 1, both BC and AB are zero-force members.
- Hence, \( F_{BC} = 0 \).
Step 2: Analyzing Joint J
At joint J, the members are JK and JL. There is no external load or reaction at joint J, and these two members are non-collinear.
- By Rule 1, JK is a zero-force member.
- Hence, \( F_{JK} = 0 \).
Step 3: Analyzing Joint F
Joint F has three members: DF, EF, and FG.
- Since joint F is subject to an external load at point D, it cannot be classified as a zero-force joint.
Final Answer:
The zero-force members are BC and JK. Correct options: (A) BC and (D) JK.
