Beam with two supports + spring

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SUMMARY

The discussion focuses on calculating bending moments and shear forces for a beam supported at three points, with one support being a spring. The beam experiences a uniform load of 100 kN/m and has a spring constant of 10 kN/m. The user faces a challenge due to having two equations and three unknowns (VA, VB, and x), indicating the need for a more complex analysis involving deflection at point Z, which is interdependent with the force at that point.

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Homework Statement



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.

20190107_184740.jpg

Homework Equations


[/B]
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)

The Attempt at a Solution


[/B]
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!
 

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Jakob said:
I was thinking about finding deflection of the beam in point Z
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.
 

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