What is zero force members?
Zero-force members are the members in the truss with no force acting on it. There are generally three types of force acting on the member of the truss. They are compressive, tensile, and axial force.
If there is no force in the member, it does not mean that it should be avoided during construction. Zero Force members also have many functions, which I will discuss with you at the end of the article.
In this article, I will show you how to find the zero-force member in a truss. Here we will see which members have zero force on loading. It is very important to design structures like bridges, steel-framed buildings, and also vehicles.
How to find zero force members in Truss?
Generally, we can calculate the different forces in the member of truss by method of joints and method of joints. But here we see directly how can find out the zero force member in a truss.
Here I will tell you two rules by which you can find out the zero force member easily. They are,
- Two member points
- Three member points
Two-member points are the joints where two members are connected with each other at a point. And three member points are the joints where three members are connected with each other at a point as shown in the figure.
There are three conditions of rule number 1 i.e. two-point member.
- The two forces acting on the point should not be collinear, i.e. they should not be in the same line at 180 degree.
- There is no support reaction point
- No external force at the point
So, this condition should be kept in mind while analyzing the member for zero force member within a second.
Now, let us talk about three point member. There are two conditions for this rule also. They are.
- The two forces acting on points should be collinear, i.e. they should be in the same line (180 degrees).
- There is no support reaction point
- There is no external force at the point
Now, let us take an example,
- Two member points Example
In the above figure, There are two members connected at point A. They are noncollinear. There is not any support at this point, and finally, there is no external force acting at this point.
So, in the above figure, members AB and AC are zero-force members. i.e., there is no force acting on it. We can say it directly and can be found in numerical data.
- Three member points Example
In the above figure, There are three members connected at point A. Two of them are collinear and one of them is noncollinear. There is not any support at this point and finally, there is no external force acting at this point.
So, in the above figure, Member AB and AD are nonzero force members while Member AC is a zero force member which is noncollinear among them. i.e. there is no force acting in it. We can say directly and can be found from numerical.
So, in this way, we can understand the zero force member in the truss.
Let us take another example with some differences in it.
In the above figure, member AD is zero force member, but how? In this truss, we can see that the force F is acting at point D. So, there are three members at that point. Two of them (CD and Force F) are collinear, and member AD is non-collinear. Here the force F will be balanced by the force in member CD.
So, the remaining member AD is non-collinear in which case the force is zero. Hence, in this way, we can say which force has zero force and acts as a zero force member easily.
Take an other Example,
How to find zero force members in Truss – Numerical
Q) Which of the members in a truss below has zero force?
In the figure below, we have to remember the two rules that I have discussed above.
- Member BC is zero force member because of rule number 2 i.e members AC and CE act as collinear members and there is no extra force and support, so the noncollinear members will be zero-force members here.
- Now, remove the member BC and look after the three-point joint at B by the combination of member BA, BE, and BD. Here you will see again rule no. 2 is applying. So, in this case, member BA and BD act as collinear, and BE act as an non-collinear which makes it zero force member.
- Again, remove the member BE and look after the three-point joint at E by the combination of member EA, EG, and ED. Here you will see again rule no. 2 is applying. So, in this case, member EA and EG act as collinear and ED act as an noncollinear which makes it zero force member.
- Again, remove the member ED and look after the three point joint at D by the combination of members DA, DG, and DF. Here you will see again rule no. 2 is applying. So, in this case member DA and DF act as collinear and DG act as an non-collinear, which make it a zero force member.
Finally, at point A, F and G an external force and support exist, so no any rule will be applied for the zero force member. Hence, here you will get total of 4 numbers of zero force members, which are BC, BE, DE, and DG.
Functions of Zero force member in Truss
- It makes the truss lighter by removing excess material.
- It enables to construct longer cantilever trusses in case of single-side support.
- Adding more bracing, i.e., members, increases the stiffness of the truss.
- It prevents from buckling of long member of truss, and increase the stability of truss.
- Simplify the balance equations to facilitate the analysis of the truss.