Zero-force Members in Trusses: Examples

by ce on December 16, 2011

In the followings, we will give you a couple of example problems on how to determine zero-force members in trusses.

Problem 1: Identify the zero-force members in the truss subjected to loading configuration as shown in the Figure below:

Zero force members in a truss structure: Problem #1

Solution 1: The first step you need to do is examining each joint in the truss and check that joint against three guidelines mentioned here. Obviously you can disregard loaded joints with three or more members. Consider the Figure below in which the free-body diagrams for each joint in the truss are shown.

Zero force members in a truss strcuture: Problem #1

      • Joint A has two members and a force from roller support reaction. The action line of the force is not colinear with any member at the joint, thus based on the guideline #2, the two members are not zero-force members.
      • Joint D has two members and no load or force. Based on the guideline #1, both of the members are zero-force members.
      • Joint C has three members and no load or force. Since two of the members are colinear, based on the guideline #3, the other member (member CB) is a zero-force member.
      • After removing zero-force member (member ED), joint E has two members and theoretically two forces from the pin support reaction. Based on the load configuration, the horizontal reaction force is zero. Thus the action line from the resultant external of forces is vertical. Neither member EC nor EB is colinear with the action line of external force, thus based on guideline #2,  both members EC and EB are not zero-force members.
      • Finally, after removing the zero-force members (members BC and BD), joint B has two members and the appllied force (2 kN). The action line of the force is not colinear with either member BA and BE, and thus applying guideline #2 again, we can conclude that both members BA and BE are not zero-force members.


Problem 2: Find the zero-force members in the truss structure with loading configuration shown in Figure below by method of inspection:

Zero force members in a truss structure: Problem #2

Solution 2: Let examine the joints in the truss one by one and check them against three guidelines presented here.

  • Joint A has two members and a force from roller support reaction (in vertical direction). The action line of the reaction force is colinear with the member AB, therefore the member AF is a zero-force member. Guideline #2 applies here.
  • Joint B has more than three members so forget about it.
  • Joint C has two members and two forces. The actiion line of resultant of those two forces is not colinear with either of the two members, thus both of these members are not zero-force members (check guideline #2).
  • Joint D has three members and a force, thus based on guideline # 3, there will be no zero-force member from this joint. If a joint has three members, there must be no force for it to have a possibility of zero-force member coming from the joint.
  •  Joint E has three members and no force, thus it has a chance to have a zero-force member.  Two of the members are colinear, thereforce the other member (member EB) must be a zero-force member. Guideline #3 is in work here!
  • Finally joint F has two members left after removing the zero-force member AF and has two reaction forces from pin support. Since the resultant of these two forces might not be colinear with either of two members (FB and FE), then we cannot say that one of or two of them are not zero-force members.
  • As summary, there are two zero-force members, AF and EB, in the truss structure.

{ 50 comments… read them below or add one }

Usman January 13, 2012 at 2:47 pm

Its a very good material to know a good knowledge of zero force member.. Good work

Sonu February 21, 2012 at 2:26 pm

Good material.

origbemide May 12, 2012 at 10:10 pm

this is a very good tool for zero-force member identification just by inspection

a.basit July 16, 2012 at 2:18 pm

i’ve been looking 4 it
its amazing

Qrex123 September 15, 2012 at 3:14 pm

rily helpful,gret work

Qrex123 September 15, 2012 at 3:15 pm

rily helpful…gret work..

sabari September 20, 2012 at 10:21 am


Sarvesh October 3, 2012 at 7:55 pm

can anyone tell me why FB is not a zero force member. Isn’t the reaction force at F is colinear with FE, just like the reaction force at A is colinear with AB?

ce October 11, 2012 at 2:44 am

The support F is a pin, not a roller, thus in general has vertical and horizontal reaction forces.

taiga November 1, 2012 at 4:36 pm

If the pin at B has both vertical and horizontal reaction forces, how do we know that the resultant is not colinear with FB without solving for them?

sam November 3, 2012 at 8:23 pm

cool man…..u teach beta that harvard lecturers 😛

Khaatab November 23, 2012 at 2:13 pm

Nice material, helpful and simple .. good work
thank you

ce December 1, 2012 at 1:42 am

I think you mean the pin at F right?. A very good question! But our job here is to find zero force member visually. It might happen that the resultant at F is colinear with FB, but not always. The key is we cannot always say the resultant at F is colinear with FB.

Josh December 4, 2012 at 8:28 pm

It’s spelled collinear. ;o)

mauricio December 19, 2012 at 9:57 am

wow great help, exam tomorrow thanks for the clear up

Rami January 3, 2013 at 2:44 pm

Thx allot
It’s allot helpful, I had exam the day after 2morrow
if you add 2 more examples it will be great 😉

ce January 10, 2013 at 8:43 am

Sorry I missed your comment. Glad it’s useful for you.

Mohamed January 14, 2013 at 9:10 am

That was very helpful, the examples were clear and good, thanks for the help.

Vb February 6, 2013 at 7:09 pm

Thanks for your help ce. God bless.

Vb February 6, 2013 at 11:08 pm

Ce, on problem 2 joint D, what would be the members status if there was no load F1?

kevin bezanson February 13, 2013 at 8:15 am

what if you have four members that run perpendicular to one another?? It seems like four members can never be zero force members at all….please email me with a response 🙂


ce March 6, 2013 at 3:21 am

Since the joint has three members and none of them is colinear, then we cannot determine whether there is zero force member or not.

ce March 6, 2013 at 3:32 am

Yup, we cannot determine zero force member on the joint that has four members run perpendicular to one another. It means that we have 2 colinear members that are perpendicular each other.
We know the forces in two members that are colinear are in equilibrium, but don’t know what their magnitudes. Thus cannot draw any conclusion.

Michael March 12, 2013 at 10:05 pm

Been struggling on this topic….. untill i read this!

ce March 16, 2013 at 2:12 pm

Glad it helps you!

aRTS April 17, 2013 at 2:52 pm

good very clear

ce April 25, 2013 at 9:32 pm


David April 27, 2013 at 10:01 pm

Would CD be a zero force member if F2 wasn’t applied? Because it appears F1 is collinear with member CB… does that F2 force make it so CD isn’t zero in that case?

ce May 5, 2013 at 2:31 am

If there is no F2, then yes member CD will be zero-force member.

Ahmed May 9, 2013 at 5:50 am

Thanks a lot. Very helpful and nicely explained. 🙂

ce May 17, 2013 at 2:31 pm

Thank you for the compliment…

ali May 20, 2013 at 6:08 am

thx alot

Aseel June 12, 2013 at 1:09 am

You really saved me. Thxxxx in advance 🙂

ce June 16, 2013 at 5:45 am

glad you like it

Shivanshu mohan singh August 31, 2013 at 9:34 am

Great work…….thanks a lot…:)

jaggu September 27, 2013 at 4:45 pm

great work and thank you very much as i am much interested to know this but i didn’t find it anywhere.

AB October 11, 2013 at 12:13 am

thanks a lot

lesotho October 19, 2013 at 10:00 am

thank you..

Hudson October 25, 2013 at 8:36 am

I wish I had seen this before our test I was not going to fail.

ce November 13, 2013 at 9:32 am

I’m glad to help you understand this topic. Hope you perform better next time.

ce November 13, 2013 at 9:34 am

Glad that this piece of article useful for you.

ce November 13, 2013 at 9:34 am

You’re welcome

ce November 13, 2013 at 9:35 am

You’re welcome

ce November 13, 2013 at 9:35 am

You’re welcome

Greene Emmet November 21, 2013 at 1:28 pm

fine for us as student

ce November 24, 2013 at 2:35 pm

Glad it’s useful for you

shubham chourasia January 10, 2014 at 3:07 am

Thanks a lot , it is really very helpfull.

ce January 10, 2014 at 3:57 am

Glad it helps you

Mapola April 9, 2014 at 8:35 pm

wow, very helpful

ce April 10, 2014 at 1:22 am

Thanks for the compliment!!!

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