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)
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.
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 $$ -DB - 3kN =0 \rightarrow $$ $$ DB = - 3kN $$
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.
