Zero-Force Members: Definition & Examples

[mike41]

Homework Statement

Homework Equations

* If the only members of an unloaded joint are two noncollinear members, both members are zero-force members.
* If an unloaded joint has two collinear members and one noncollinear member only, the noncollinear member is a zero-force member.

The Attempt at a Solution

i can't seem to grasp this idea. would BE be the only zero force member? Even then i don't understand because BE would have the Force P heading towards it in the x direction wouldn't it?

 

[nvn]

mike41: Member BE is not the only zero-force member. Use the rules you posted under relevant equations to identify all zero-force members.

 

[mike41]

well from the rules what i got was AB, BE, BC, CE, DE, AE

do you guys see any problems with that. what seems to be really getting me on these is this; do you account for action reaction forces? like at EB you would have P going towards B right. Well at BE then wouldn't you need an x component of P to cancle out point P because its on the same axis?

 

[nvn]

At EB, you would have P going towards B, right?

No. Look at joint B, and check the rules you wrote in post 1. A so-called unloaded joint has no external load applied and has no support reaction force applied. You don't need an x component of P in member BE, because the x component can be provided by other members connected at joint E. Try again.

 

[mike41]

ok well AB , BC are collinear and BE is the non collinear line so it would be a zero force.

BC and CD are two unloaded joints and non collinear. So they would be zero force.
This would be the same case with AB and Ae wouldn't it? OR do u have to account for any components ?

 

[nvn]

One member you listed as a zero-force member in post 5 is not a zero-force member. Joint C is not an unloaded joint. Reread my definition of unloaded joint in post 4. Look at each joint and check the rules in post 1 for each joint. Try again.

 

[mike41]

what is the reasoning for joint c not being unloaded? it has no force maybe this is why I am getting stuck on this. Joint C has no force being pushed on it

 

[mike41]

this is my reasoning. BC then would NOT be a zero force because if you take the forces at C becue it has 3 forces coming off of it. CE and CB do not equal 0, in any direction but CD = 0 in Y and the x direction

 

[nvn]

Joint C is a support. Therefore, it is externally loaded, because there is a support reaction force at joint C. Look at each joint and check the rules in post 1, using my definition of unloaded in post 4. Whenever you see joint members that meet the rules, put a zero on them. Keep trying.

 

[mike41]

Is joint c a support because of the little image under it showing its connected to ground?

 

[nvn]

Yes.

 

[Xand888]

This question might help you better identify zero-force members: If you were to remove some trusses from this structure, which ones could you remove in order for the structure to still support the P load acting at joint E? Hint: You only need three trusses to do this.

 

[mike41]

Well point A is unloaded then right? and A has two unloaded joints so according to rule 1 they would be zero force members. So AE, AB are zero force members. Then BE is a zero force because its perpendicular to two collinear joints. BC is also a zero force member because it is carrying no load if AB, AE, and BE are not carrying a load either. Pin D would be a support just like C.

 

[nvn]

Yes, joint A is unloaded. Nice work, mike41. Your answer is correct. And the way you analyzed and described the problem is correct. The zero-force members are AB, AE, BC, BE.

 

[mike41]

thank you it makes sense now, i did other practice problems and got them right too.

 

[mchei]

sorry for replying an old thread.
i know that BC is zero force member but by my calculation,
the reaction at support C is 86.6N upward. the problem is that:
if i hvn't remove the zero force member before calculation,
i will assume that BC will cancel 86.6N. and go on, EC will be "no load" thus i can remove it.
also BE can be remove. as a result CE and BE are zero member by my calculation.

why there are different between ous answer?

 

[PhanthomJay]

sorry for replying an old thread.
i know that BC is zero force member but by my calculation,
the reaction at support C is 86.6N upward.

I'm not sure where your numbers are coming from, since i don't see any dimensions or loads numerically given, but yes, the reaction at C is up

the problem is that:
if i hvn't remove the zero force member before calculation,
i will assume that BC will cancel 86.6N.

This is not correct, the vert force up at C will transfer as the vert component down of the force in EC, and the horiz component in EC to the right will be balanced by the leftward tension force in DC...look up thr method of Joints.

why there are different between ous answer?

You are not doing it correctly. maybe my response to your other post will help.