Statics - Support Reaction in Truss

In summary, the homework statement is having a hard time finding the support reactions in this truss. The attempt at a solution involved using equilibrium conditions to find the forces and moments on the ends of the truss, but it doesn't seem to have a solution. One possible solution is to replace one of the end supports with a roller.
  • #1
Philippe
9
1

Homework Statement


I'm having a hard time finding the support reactions [tex] R_{fx} ; R_{fy} ; R_{kx} ; R_{ky} [/tex] in this truss.

2. The attempt at a solution

I got four equations using the equilibrium conditions (sum of forces along x and y ; sum of moments on F and on C) but the system doesn't seem to have a solution. Am i missing something?

[tex]
(\Sigma x = 0) R_{fx} + R_{ky} = 0 \\
(\Sigma y = 0) R_{fy} + R_{ky} = 530 \\
(\Sigma M_{f} = 0) -8R_{kx} + 40R_{ky} = 11100 \\
(\Sigma M_{c} = 0) -20R_{fx} + 20R_{fy} -12 R_{kx} - 20R_{ky} = -500
[/tex]

Thanks!
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  • #2
You have treated the whole girder system as a single rigid structure. That means there are only three independent equations available. Any further you write down, whether linear forces or moments, can be deduced from those three.

Is it a single rigid structure?
 
  • #3
Yes exactly, I noticed that I can obtain the fourth equation from the first three so I need a fourth independent one.
But I'm under the impression that it is a single structure, I guess I'm wrong!
 
  • #4
Philippe said:
Yes exactly, I noticed that I can obtain the fourth equation from the first three so I need a fourth independent one.
But I'm under the impression that it is a single structure, I guess I'm wrong!
Imagine replacing one of the end supports with a roller. Can you visualise what would happen in reality?
 
  • #5
The horizontal component of the reaction force would be zero as it free to move in this direction on the end support, right?
 
  • #6
Philippe said:
The horizontal component of the reaction force would be zero as it free to move in this direction on the end support, right?
Yes, but what would happen to the structure? Would it stay up?
 
  • #7
No, it would collapse.
 
  • #8
Philippe said:
No, it would collapse.
How, exactly?
 
  • #9
The whole structure would "flatten" and be pushed to the right?
 
  • #10
Philippe said:
The whole structure would "flatten" and be pushed to the right?
To change shape, some joint must flex. Which one?
 
  • #11
Joint e ?
 
  • #12
Philippe said:
Joint e ?
Right. So the truss system is not in itself a rigid body. Rather, it is two rigid bodies hinged at e. This allows you to write a torque balance equation which is independent of the equations you already have.
Can you see how to do that?
 
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  • #13
Yes it worked!
Thanks a million!
 

1. What is a support reaction in a truss?

A support reaction in a truss refers to the forces exerted on the truss at its points of support, such as the joints or connections to the ground. These reactions are necessary to keep the truss in equilibrium and prevent it from collapsing under the weight of the load.

2. How do you calculate support reactions in a truss?

The support reactions in a truss can be calculated using the principles of statics, specifically the equations of equilibrium. By taking into account the external forces acting on the truss and the geometry of the truss, the support reactions can be determined using methods such as the method of joints or the method of sections.

3. What factors affect the magnitude of support reactions in a truss?

The magnitude of support reactions in a truss is affected by various factors, including the weight and distribution of the load on the truss, the type and strength of the truss members, and the type and location of the supports. Changes in any of these factors can alter the support reactions and must be considered in the calculation process.

4. Can support reactions in a truss be negative?

Yes, support reactions in a truss can be negative. A negative support reaction indicates that the support is pulling away from the truss rather than pushing against it. This can occur in situations where the support is not strong enough to withstand the forces acting on the truss or when the truss design places too much weight on the support.

5. What happens if there is a support failure in a truss?

If a support fails in a truss, the truss may collapse or experience excessive deflection. This can result in damage to the structure and potential harm to people or objects in the surrounding area. It is important to ensure that the supports in a truss are strong enough to withstand the expected forces and that they are properly designed and installed to prevent failure.

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