# Identification of zero-force members

• ChloeYip
In summary: It might help you if you understood the logic behind these rules. If there were a force in strut 5 then at its joint, it would be zero force.
ChloeYip

1. Homework Statement

I am not sure about the concept of zero-forced members.
There are forces applied on the members, why are they zero-forced members? Or it seems no force in implied on them why are they non-zero-forced members

## Homework Equations

the method of joints

## The Attempt at a Solution

If two non-collinear members are connected to a joint that has no external loads or reactions applied to it or three members, two of which are collinear, are connected to a joint that has no external loads or reactions applied to it, it is zero-forced members.

Thank you.

ChloeYip said:
If two non-collinear members are connected to a joint that has no external loads or reactions applied to it or three members, two of which are collinear, are connected to a joint that has no external loads or reactions applied to it, it is zero-forced members.
Is that a rule you have been given, or one you have thought up?
If you look at the second diagram, the first part of that rule appears to say that the two diagonal members are unforced, which is not true.
Anyway, such a rule will not help with the third diagram since it depends critically on the two F forces being equal.

In the first two diagrams, imagine removing the vertical strut. What to you think would happen in each case?
(Note: it appears that the midpoint at the bottom of the triangle is a joint, so there are 5 struts altogether.)

haruspex said:
Is that a rule you have been given, or one you have thought up?
It is given by the powerpoint given by my instructor, who have given no explanation for the part...
After watching ,
Do you agree with this definition rather than the one given by my instructor?
Is that all the zero forced members in first 3 diagram & member 6+7 are because there are truss joint not support by pin or roller and not carry loads?

haruspex said:
it appears that the midpoint at the bottom of the triangle is a joint, so there are 5 struts altogether
Thanks for reminding me on this. For 2nd diagram, after removing the vertical strut, the 2 bottom struts shouldn't have component to support y-axis force, thus the structure will fail, am I right?

However, I still don't understand the third diagram... (member 3,4,5,8,9)
Thank you for helping me.

Ok, that video helps.
In the first part of the rule in your initial post, you need to clarify that it refers to exactly two members meeting at a joint.
In the second part, the two collinear members may be under tension. It is only the third member that is sure to be zero force.

In the third diagram, you can use the rules (from the video) to eliminate three struts. Which three? The other two can only be solved by analysing the forces. That is because if the applied forces were a bit different then those two would be carrying forces.

haruspex said:
In the first part of the rule in your initial post, you need to clarify that it refers to exactly two members meeting at a joint.
In the second part, the two collinear members may be under tension. It is only the third member that is sure to be zero force.
I understand this part now. Thanks.

haruspex said:
In the third diagram, you can use the rules (from the video) to eliminate three struts. Which three? The other two can only be solved by analysing the forces.
However, I am sorry but I don't really understand what you mean by here. Which three and which two?

haruspex said:
If you look at the second diagram, the first part of that rule appears to say that the two diagonal members are unforced, which is not true.
That is exactly what I feel like for member 3 and 4... Which I think it is not correct. Why is there a pin support exert on member 3&4 and force applied on 4&5 but still they are zero force member?

Thanks.

ChloeYip said:
Why is there a pin support exert on member 3&4
Quite so, which is why the rules you have do not eliminate 3 and 4. As I posted, there are two members which will turn out to have zero force, but you cannot eliminate them by the rules. Those are the two. If you were to change one of the Fs to 2F, say, they would not be zero force.
ChloeYip said:
force applied on 4&5
Watch the video again. There is a similar situation in one of the diagrams analysed there. You can invent an extra strut above the joint where 4 and 5 meet that carries the force F. That leaves strut 5, meeting the two horizontal struts at the bottom, satisfying the the three strut rule.
It might help you if you understood the logic behind these rules. If there were a force in strut 5 then at its joint with the two horizontal struts there would be no force capable of balancing it, so the joint would move. The rules assume the system is in equilibrium.

Do you mean the strut within the rectangle 5,6,7,8,9 are already balanced, so strut 3+4 are zero-forced?
Strut 5 is because the bottom is connect to horizontal joint which have no support or load, therefore it is zero forced too?
But why is strut 8 is still non-zero forced? Isn't strut 9 already can balanced the y-component of "the strut of diagonal of force and roller support"?
Thanks.

ChloeYip said:
the strut within the rectangle 5,6,7,8,9 are already balanced, so strut 3+4 are zero-forced?
Yes.
ChloeYip said:
Strut 5 is because the bottom is connect to horizontal joint which have no support or load, therefore it is zero forced too
Yes.
ChloeYip said:
why is strut 8 is still non-zero forced?
You are right, 8 also carries no force.

Last edited:
Thank you very much~

## 1. What are zero-force members?

Zero-force members are structural elements in a truss or frame that do not experience any internal force or stress when the structure is subjected to external loads. This means that they do not contribute to the overall stiffness or strength of the structure.

## 2. How can I identify zero-force members in a truss or frame?

Zero-force members can be identified by analyzing the forces acting on each member in the structure. If a member is not connected to any external load or support, or if the forces acting on the member are balanced and cancel each other out, then it is considered a zero-force member.

## 3. Why is it important to identify zero-force members in a structure?

Identifying zero-force members in a structure is important for structural analysis and design. These members can be removed from the structure without affecting its stability or strength, which can lead to a more efficient and cost-effective design.

## 4. Can zero-force members exist in real-world structures?

Yes, zero-force members can exist in real-world structures. They are more commonly found in statically determinate structures, where the forces can be calculated using equations of equilibrium. In real-world structures, zero-force members are often used to provide stability or to connect other members together.

## 5. Are there any limitations or assumptions when identifying zero-force members?

When identifying zero-force members, it is important to make certain assumptions and simplifications. These include assuming the structure is rigid and perfectly connected, neglecting the weight of the members, and considering only external loads and reactions. These assumptions may not hold true in all cases, so it is important to carefully analyze the structure and make any necessary adjustments.

• Engineering and Comp Sci Homework Help
Replies
5
Views
883
• Engineering and Comp Sci Homework Help
Replies
3
Views
1K
• Engineering and Comp Sci Homework Help
Replies
1
Views
1K
• Engineering and Comp Sci Homework Help
Replies
1
Views
3K
• Engineering and Comp Sci Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
960
• Engineering and Comp Sci Homework Help
Replies
4
Views
3K
• Introductory Physics Homework Help
Replies
10
Views
3K
• Introductory Physics Homework Help
Replies
8
Views
896
• Engineering and Comp Sci Homework Help
Replies
2
Views
2K