In this session, we're going to talk about zero-force members in trusses.
What are they? Why do they come to exist? And how do we identify them?
What is a zero-force member?
When analyzing trusses, we may come across members that carry no force.
These are called zero-force members.
Why are zero-force members in trusses?
Naturally one might question the rationale for having such members in a structure.
If a truss member does not carry any force, why have it in the first place?
There are two main reasons for encountering zero-force members in trusses.
One: A zero-force member could act as a bracing,
for preventing a force carrying compression member from buckling.
That is, a zero-force member adds stability to the structure.
Two: A force having a magnitude of zero could develop in a member at some point in time,
when the structure is subjected to a time-variant load.
Let's examine this scenario in more detail.
Bridge structures are generally designed to withstand the load of moving vehicles,
where the load position changes,
as the vehicle moves across the bridge.
Suppose we have a truss bridge consisting of five joints along its bottom chord.
As a vehicle starts traveling on the bridge, the applied load position changes.
At time t1, the load is distributed between joints 1 and 2.
At time t2, the load is distributed between joints 2 and 3.
At t3, the load is applied to joints 3 and 4, and so on.
This moving load pattern continues until the vehicle leaves the bridge.
The bridge truss must be analyzed under each loading case.
Note that a truss member that actually carries an axial force in one loading case,
may become a zero-force member in another loading case.
For example, when the load is applied at joints 1 and 2,
The vertical member attached to joint 4 carries no internal force.
When the applied load moves to joints 3 and 4,
the vertical member attached to joint 2 becomes a zero-force member.
The ability to identify zero-force members in trusses is important for two reasons.
One: It speeds up the overall analysis of the truss.
Two: It helps developing a better understanding of how internal forces are distributed in a structure.
How do we identify zero-force members in a truss?
There are three basic rules for identifying zero-force members without resorting to any calculations.
If a truss joint is not subjected to any applied loads,
and is not supported by a pin or roller,
then the following rules can be applied repeatedly to identify all the zero-force members.
Rule one: If the joint connects two members only,
where the angle between the members is different than 180 degrees,
both members are zero-force members.
If this structure, joint F connects two members only,
there is no load or support at the joint.
Therefore, both EF and CF are zero-force members.
Rule two: If the joint connects two members only, and the members are collinear,
that is, the angle between them is 180 degrees and one of the members carries no internal force,
the other one is also a zero-force member.
Consider the two members AB and BC.
If the force in member AB is zero since
the members are collinear, BC is also a zero-force member.
Rule three: If a joint connects three members only, and two of the members are collinear,
then the third one is a zero-force member.
Here, joint D connects three members.
Two of the members are collinear, therefore CD is a zero-force member.
Let's look at a few examples.
Here, rule one applies to joint D,
Therefore, CD and DE are zero-force members.
Also, rule three applies to joint H.
Hence, BH is a zero-force member.
If we consider P to be an axial force in a member vertically attached to joint E,
then according to rule three, EF is a zero-force member.
Similarly, if we assume GX is the force in an axial member horizontally attached to joint G,
then according to rule three, AG is a zero-force member.
To determine the force in each of the remaining members,
the simplified truss can be analyzed using The Method of Joints.
In this example, rule three applies to joints C, B, E and D, in that sequence.
Therefore, BC, BE, DE and DG are zero-force members.
See if you can identify the zero-force members in these trusses: