Solving Forces in Structures: Eliminating Members & Calculating Forces

In summary, the conversation is about using the stiffness matrix method to find displacements and force in a structure. The problem at hand is pre-eliminating members and determining forces in a given structure. The conversation includes diagrams and equations of static equilibrium, with the goal of finding the reaction forces that can be applied to the remaining structure. The conversation also mentions difficulties with a distributed load and the need to consider both force and moment equations for a complete understanding.
  • #1
MMCS
151
0
See attachment for question and diagrams.
This problem is concerned with using the stiffness matrix method to find displacements and force in a structure. My problem is pre-eliminating the members. i have attached 2 diagrams. i would like help in trying to get from the first diagram, to the second diagram ( with eliminated members and forces calculated)

I know that

∑Fx=0
∑Fy=0
∑M=0

However, the UDL and other factors are causing me problems.
I don't know where to start with this

Thanks
 

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  • #2
From the diagram attached, it's not clear what the magnitude of the distributed load q is.

If you are trying to eliminate the beam 1-6-7 and the support strut 5-6 from the rest of the structure,
isolate it and draw a FBD for these members. You should be able to write equations of static equilibrium using the FBD and solve those to find the reaction forces, which can be applied to the remaining structure.
 
  • #3
ok so my attempt,
I have isolated 1-6-7 and 5-6.
Taking moments about point 1 i have

6metres * 5kn/m * 3metres = Force at 5 * sqrt(2^2 + 2^2)
Force at 5 = 31.8

This value seems correct. I have tried the get the forces at 1 but have had no luck. Where is the best place to take moments from ? intuitively it seems odd that the force in the x direction is greater than P, as P seems like the only force acting this way

Thanks
 
  • #4
SteamKing said:
From the diagram attached, it's not clear what the magnitude of the distributed load q is.

If you are trying to eliminate the beam 1-6-7 and the support strut 5-6 from the rest of the structure,
isolate it and draw a FBD for these members. You should be able to write equations of static equilibrium using the FBD and solve those to find the reaction forces, which can be applied to the remaining structure.

ok so my attempt,
I have isolated 1-6-7 and 5-6.
Taking moments about point 1 i have

6metres * 5kn/m * 3metres = Force at 5 * sqrt(2^2 + 2^2)
Force at 5 = 31.8

This value seems correct. I have tried the get the forces at 1 but have had no luck. Where is the best place to take moments from ? intuitively it seems odd that the force in the x direction is greater than P, as P seems like the only force acting this way

Thanks
 
  • #5
SteamKing said:
From the diagram attached, it's not clear what the magnitude of the distributed load q is.

If you are trying to eliminate the beam 1-6-7 and the support strut 5-6 from the rest of the structure,
isolate it and draw a FBD for these members. You should be able to write equations of static equilibrium using the FBD and solve those to find the reaction forces, which can be applied to the remaining structure.

q=5kn/m
 
  • #6
MMCS said:
ok so my attempt,
I have isolated 1-6-7 and 5-6.
Taking moments about point 1 i have

6metres * 5kn/m * 3metres = Force at 5 * sqrt(2^2 + 2^2)
Force at 5 = 31.8

This value seems correct. I have tried the get the forces at 1 but have had no luck. Where is the best place to take moments from ? intuitively it seems odd that the force in the x direction is greater than P, as P seems like the only force acting this way

Thanks

Static equilibrium is more than just taking moments about an arbitrary point. You've got to write both the force and the moment equations to get the complete picture.
 

1. What is the purpose of solving forces in structures?

Solving forces in structures is important for understanding how different members of a structure contribute to its overall stability and strength. By calculating forces, we can determine which members are essential for supporting the structure and which ones can be eliminated without compromising its integrity.

2. How do you eliminate members in a structure?

To eliminate members in a structure, we first need to calculate the forces acting on each member using principles of physics and structural analysis. Then, we can remove any members that are not contributing significant force to the overall structure. However, it is important to keep in mind that eliminating too many members can weaken the structure and compromise its stability.

3. What types of forces are typically involved in solving forces in structures?

There are typically three types of forces involved in solving forces in structures: compression, tension, and shear. Compression forces push on a structure, while tension forces pull on it. Shear forces act parallel to the surface of the structure. These forces can be calculated using principles of physics, such as Newton's laws of motion and Hooke's law.

4. What are some common methods for calculating forces in structures?

There are several methods for calculating forces in structures, including the method of joints, the method of sections, and the method of virtual work. The method of joints involves analyzing the forces at each joint in a structure, while the method of sections involves cutting the structure into smaller sections and analyzing the forces in each section. The method of virtual work uses the principle of virtual work to calculate forces.

5. Can solving forces in structures be applied to real-world structures?

Yes, solving forces in structures is a fundamental concept in structural engineering and is used in the design and analysis of real-world structures. By understanding how forces act on a structure, engineers can ensure that it is strong and stable enough to withstand the expected loads and conditions. This is essential for ensuring the safety and longevity of structures such as buildings, bridges, and other infrastructure.

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