# Beam with two supports + spring

1. Jan 8, 2019

### Jakob

1. The problem statement, all variables and given/known data

I have beam supported in three points (one of the support is spring) .
What i know:
PR = 100kN/m
spring constant Z = 10kN/m
I have to calculate bending moments and shear forces in points A, B and Z.

2. Relevant equations

ΣM = 0
ΣF = 0
Spring force : Fz=-zx
This is not enoug to solve the problem. I have two equations and three unknowns (VA, VB, and x)

3. The attempt at a solution

I was thinking about finding deflection of the beam in point Z however the shape of the beam between points Z and A is quite complicated. Maybe there is some simpler method and I can't see?

I will be very gratefull for help/hint with that!

Last edited: Jan 8, 2019
2. Jan 17, 2019 at 5:55 PM

### haruspex

That is the right approach, but of course it is a bit more complicated here because the deflection and the force at Z depend on each other.
You will need to step through the usual procedure for figuring out the shape of the beam, but treating the force at Z as an unknown.