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.

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gohar May 14, 2014 at 3:46 pm


ce May 15, 2014 at 12:35 am


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