Questions and discussion for this lecture live here. Fire away by hitting Reply below 
Calculating the deflection for 1 external load is well and good. Having several external loads applied at different locations would clearly complicate the issue with the cumulative effect of all external loads needing to be taken into acoount. I assume this is where the principle of virtual work comes into its own?
Another thing …
In calculating the deflection at the point of load application you have assumed that the structure has not deformed elsewhere when calculating the internal member forces. Clearly this can’t be the case in reality. I assume the direct stiffness method takes member deformations into account when establishing overall equilibrium?
Hi Alex,
Sorry about the delay in replying to this - a technical problem stopped me receiving email updates on forum questions for the last couple of weeks (things were suspiciously quiet there for a while!!) - but resolved now, so I’m dealing with a bit of a backlog!
So, to your question; Yes, the strain energy approach demonstrated in this lecture is indeed limited to determining the deflection at the point of load application. The virtual work approach that we get to next, addresses this.
Regarding your second question; for the purposes of calculating internal member forces generally, when the deflections are small by comparison to the scale of the structure, it is common to neglect the influence of these deflections (changing the line of action of internal forces for example).
When deflections become large and can no-longer be ignored, we enter the world of geometric nonlinearity - we discuss this in this course BTW. But for our analysis here, it is acceptable to assume the shape of the structure remains unchanged when calculating internal member forces.
Note however that in the next step - the strain energy calculation, we directly capture the change in length of each individual member, since it is required to work out the strain energy for each member.
Hope that helps - and sorry again for the delay in replying!
Seán