# How to solve this displacement problem

I have to solve this question, and I've tried multiple things with the angle and displacement but I just cannot figure it out.

I started with a M/EI diagram and i went from there.

Any tips on how to tackle these problems?

I think the aim of this duet of exercises is to make you understand that you can break down problems and superimpose solutions.

# infinite stiffness

In the first case what you do is you have a simply supported beam with moment in one support the beam BC.

$$\theta_1$$ is the angle at the support. (note that Moment is negative and is equal to 40*1.5)

Since you know the angle and AB does not bend then you only need to calculate the $$\theta_1 \cdot 1.5[m]$$.

You should find that $$\delta\approx 1.6875 mm$$

# Finite stiffness

In the finite stiffness case you will have the same deflection due to beam BC, and you need to superimpose the deflection of the beam $$AB$$.

AB is a cantilever beam with an end load.

you'd need to add the deflection $$\delta_{max} \approx 1.125mm$$ to the deflection due to beam BC(=1.6875 mm).