# Identifying zero force members

My instructor said that if a joint has reaction support attached to it, then it is not a zero force member. However I saw in this figure that joints E and A are attached to a pin and a roller, respectively but it is indicated in the answer key that members DE and AE are zero force members. What is your insight about this?

source: Engineering Mechanics - Statics (R. C. Hibbeler)

## 2 Answers

Use graphics to visualize the force flow and determine zero-force members. (Draw member forces from joint D)

DE and AE are zero are indeed zero.

However you need to start from point C to reason about that.

If you look at this question, when you have a node without external forces with only two members which are not colinear, the forces on the nodes should be zero. So from this $$DC$$ and $$CB$$ are equal to zero.

## Node D:

Now if you take point D and write the equations of equilibrium you obtain:

• for x $$ED - DC =0 \rightarrow$$ $$ED = DC =0$$

• for y: (so all the force is carried from ED $$-DB - 3kN =0 \rightarrow$$ $$DB = - 3kN$$

## Node A:

Again for Node A if you take the equilibrium in the y-axis you get:

$$+AE =0$$

because A has rolling support and it produces only a horizontal reaction.