Zero-force member problem (Statics)

In summary, to determine zero force members in a truss, there are several rules to follow. If only two members meet at an unloaded joint, both are zero-force members. If three members meet at an unloaded joint and two are in a direct line with each other, the third member is also a zero-force member. Additionally, if two members meet at a loaded joint and the line of action of the load coincides with one of the members, the other member is a zero-force member. Using these rules, we can determine that the zero-force members in the given truss are HF, HI, OQ, QR, BC, DE, BE, and IJ.
  • #1
aero_zeppelin
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Homework Statement


Determine the zero force members in the following truss


Homework Equations



- If only two members meet in an unloaded joint, both are zero-force members.
- If three members meet in an unloaded joint of which two are in a direct line with one another, then the third member is a zero-force member.

- If two members meet in a loaded joint and the line of action of the load coincides with one of the members, the other member is a zero-force member.




The Attempt at a Solution



Ok, I got 6 (there are 8 according to the solution) using the above rules:
HF, HI, OQ, QR, BC, and DE

The solution says that BE and LJ are also zero force members, but I have no clue why...

Any help please?

Thanks in advance!
 

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  • #2
Not LJ, its IJ, why? If BC is a zero force member, that should tell you something about BE (and DE).
 
  • #3
Ok, I had thought about IJ before but since the solution didn't mention it I didn't count it...

Now, for BE: since BC is a zero-force member, can we "ignore" it and then consider the other 3 with Rule #2?
 
  • #4
aero_zeppelin said:
Ok, I had thought about IJ before but since the solution didn't mention it I didn't count it...

Now, for BE: since BC is a zero-force member, can we "ignore" it and then consider the other 3 with Rule #2?
yes.
 
  • #5
Thank you sir ;)
 

1. What is a zero-force member?

A zero-force member is a structural element in a system that does not experience any external forces or moments. It remains in a state of static equilibrium, with no internal stresses or deformations.

2. How can I identify a zero-force member in a system?

To identify a zero-force member, you can use the method of joints or method of sections. In the method of joints, a zero-force member can be identified if it connects two joints that are already in equilibrium and no external forces are acting on it. In the method of sections, a zero-force member can be identified if it is not cut by the section plane or if it forms a redundant member in the free body diagram.

3. What is the significance of zero-force members in structural analysis?

Zero-force members have no influence on the overall stability and strength of a structure. They can be removed from the system without affecting the equilibrium or internal forces of other members. Identifying and eliminating zero-force members can simplify the analysis and calculation process.

4. Can a zero-force member exist in a real-world structure?

Yes, a zero-force member can exist in a real-world structure. It is common in truss structures where certain members do not experience any external loads or moments due to the arrangement of loads and supports. However, in some cases, a member may appear to be a zero-force member but may actually have a small, negligible force acting on it due to imperfections in the structure or external factors.

5. What are some common mistakes to avoid when dealing with zero-force members?

One common mistake is assuming that all members connected to a pin joint are zero-force members. This is not always the case as some members may be carrying loads or experiencing internal forces due to deformations. Another mistake is neglecting zero-force members altogether, as they can be important in determining the stability and redundancy of a structure.

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