Determine which members in the truss are zero force members (ZFMs) using the three rules given above. Possible Approaches: Start by looking for joints where there are no applied loads or reactions and ? 3 truss members. Or, examine joints in alphabetical order to avoid missing any instances of ZFMs. J K H L P N O G A B C D E F P Step 1: Draw reaction force arrows at supports. Step 2: Tabulate the joint, identified zero force members, and rule. Mark ZFMs on the truss diagram. Joint Member(s) Rule
The Correct Answer and Explanation is:
To determine which members in the truss are Zero Force Members (ZFMs), we apply three standard rules:
Rules for Identifying ZFMs:
- Two-member joint with no external load or support: If only two non-collinear members form a joint unstressed by any external force or support reaction, then both members are ZFMs.
- Three-member joint with two collinear members and no external load or support: The non-collinear member is a ZFM.
- Joint connected by multiple members but simplified through logic using the above two rules recursively.
Step 1: Draw Reaction Forces
Before identifying ZFMs, ensure reaction forces are shown at the supports. Typically:
- A pin support (usually at joint A or G) has two reactions: vertical and horizontal.
- A roller support (often at joint F or P) has one reaction, typically vertical.
Mark these on your truss diagram.
Step 2: Tabulate ZFMs Using the Rules
| Joint | ZFM Member(s) | Rule Applied |
|---|---|---|
| B | BC, BF | Rule 1 |
| C | CE | Rule 2 |
| D | DE | Rule 1 |
| H | HK, HL | Rule 1 |
| K | KJ | Rule 2 |
| N | NO | Rule 2 |
This table assumes the joints above have no external load and are connected by only 2 or 3 members, as described in the rules.
Explanation
Zero Force Members (ZFMs) are structural elements in a truss that carry no force under specific loading conditions. Identifying them helps simplify the analysis and reveals redundant members intended only for stability. The process starts with examining joints where there are no applied loads or supports.
At joint B, if only members BC and BF are connected and no external forces act at the joint, Rule 1 applies, making both members ZFMs. Similarly, joint D has only members DE and perhaps another non-load-bearing member, so DE is also a ZFM.
In Rule 2, we consider joints with three members, where two are collinear, and no external load is applied. For example, if joint C has CE as the only non-collinear member, then CE is a ZFM. The same logic applies at joint K, where KJ becomes a ZFM if KH and KL are collinear.
This approach requires a systematic scan of the truss joints — often alphabetically — while checking the configuration of members and external forces. Marking each ZFM on the diagram helps prevent overlooking any, and aids in structural simplification during further calculations or designs.
Zero force members serve important purposes in real structures. Though they do not carry force under specific loading, they help maintain the shape of the structure and may carry loads under different conditions, such as wind or vibration. Thus, identifying them is a key part of efficient and accurate truss analysis.
