Important Point

## What Is Zero Force Member?

In a truss system, some **members are not carrying any force**. This **called a zero-force member**.

This member may be **added to increase truss stability**. Identifying these members will** simplify the process of analyzing truss**.

## What Is Zero Force Member for Truss?

Truss analysis using the method of joints is **greatly simplified if one is able to first determine those members that support no loading**.

These zero force members may be necessary for the stability of the **truss during construction and to provide support if the applied loading is changed**.

The zero-force members of a truss can generally be determined by **inspection of the joints, and they occur in two cases.**

**Case – 1. **

Consider the truss in above Fig -1 (Truss). The **two members at joint “****C” are connected** together at a right angle and there is **no external load on the joint**.

The free-body **diagram of joint “C”**, Fig – 2 (Truss Joint), indicates that the** force in each member must be zero in order to maintain equilibrium**.

Furthermore, as **in the case of joint “A”**, Fig – 3 (Truss Joint) this must be true regardless of the **angle say θ. between the members**.

**Case – 2. **

Zero-force members also occur at joints having a **geometry as joint “D”** in above fig -4 (Truss).

Here no external load acts on the joint, so that a **force summation in the y-direction**, Fig – 5 (Truss Joint), which is **perpendicular to the two collinear members, requires that FDF = 0**.

Using this result. “**FC” is also a zero-force member**, as indicated by the **force analysis of joint “F”**, Fig – 6 (Truss Joint).

Also, read: One Way Slab and Two Way Slab Design Step by Step

**Summary of Zero Force Member for Truss,**

Then, if only two non-collinear members form a **truss joint and no external load or support reaction** is applied to the joint, the members must be zero-force members, **Case 1**.

Also, if three members form a **truss joint for which two of the members are collinear**, the third member is a zero-force member,** provided no external force or support** reaction is applied to the joint, **Case 2**.

Particular attention should be directed to these **conditions of joint geometry and loading**. since the analysis of a truss can be considerably simplified by first spotting the zero-force members.

## How to Identification of Zero Force Members in Truss

Because trusses are usually **designed to support several different loading conditions**, it is not uncommon to find members with zero forces in them when a truss is being analyzed for a particular loading condition.

Zero-force members are also added to trusses to brace compression members against buckling and slender tension members against vibrating.

The analysis of trusses can be expedited if we can identify the zero-force members by inspection.

Two common types of member arrangements that result in zero-force members are the following:

### Step – 1. Noncollinear Members

If only two **noncollinear members are connected to a joint that has no external loads or reactions applied** to it, then the** force in both members is zero**.

### Step – 2. Collinear Member

If three members,** two of which are collinear**, are connected to a** joint that has no external loads or reactions applied** to it, then the force in the **member that is not collinear is zero**.

### Zero Force Members

If a joint has only two non-collinear **members** and there is no external load or support reaction at that joint, then those two **members** are **zero**– **force members**. In this example **members** DE, DC, AF, and AB are **zero force members**. Again, this can easily be proven.

### Zero Force Members in a Loaded Truss

If three **members** form a **truss** joint for which two of the **members** are collinear and there is no external **load** or reaction at that joint, then the third non-collinear **member** is a **zero force member**, e.g., DA. Find: The **forces** in each **member** of the **truss.**

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