Beam with two supports + spring

In summary, the conversation is about calculating bending moments and shear forces at three points on a beam with three supports, one of which is a spring. The known values are PR = 100kN/m and spring constant Z = 10kN/m. However, there are three unknowns (VA, VB, and x) and only two equations (ΣM = 0 and ΣF = 0). The suggested approach is to find the deflection of the beam at point Z, but this is complicated due to the interdependence of the force and deflection at that point. The solution will require the usual procedure for determining beam shape, but with the added complexity of treating the force at Z as an unknown.
  • #1
Jakob
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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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  • #2
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.
 

1. What is a beam with two supports and a spring?

A beam with two supports and a spring is a structural element used in engineering and physics. It consists of a beam that is supported by two fixed points or supports on either end, and a spring attached to the beam at one or both ends.

2. What is the purpose of a beam with two supports and a spring?

The purpose of a beam with two supports and a spring is to provide stability and support to a structure, while also allowing for some flexibility or movement. The spring helps to absorb and distribute any external forces or loads applied to the beam.

3. How does a beam with two supports and a spring work?

When a load is applied to the beam, the spring will compress or stretch, depending on the direction of the load. This allows the beam to bend or deform slightly, while still maintaining its overall structural integrity. The supports on either end also help to distribute the load and prevent the beam from collapsing.

4. What are the applications of a beam with two supports and a spring?

A beam with two supports and a spring can be used in various applications, such as bridges, buildings, and other structures. It is also commonly used in mechanical systems, such as in suspension systems for vehicles, to provide stability and absorb shock.

5. What factors should be considered when designing a beam with two supports and a spring?

When designing a beam with two supports and a spring, factors such as the type and strength of the materials used, the expected load or weight to be supported, and the desired amount of flexibility or movement should be taken into consideration. The dimensions and placement of the supports and spring should also be carefully determined to ensure the stability and functionality of the beam.

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