Structural analysis stiffness method

In summary, the conversation is about solving a problem involving a structure with only one degree of freedom and no loads. The person is trying to set up a matrix equation to solve for the forces, but is having trouble due to the limited information. They try moving the roller to the right to create more variables, but are still unable to solve the problem. Eventually, they figure out the solution by setting the sum of the applied and distributed forces equal to zero and using the equation K11 = 2EA/L to solve for the forces. The final solution includes the values for AR1, AR2, and AR3.
  • #1
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I need to solve this problem but with member 2 as L+e instead of L, and omit the load..

Since I only see one degree of freedom, i don't know how to set up the matrix to solve for the 3 forces.

I have K11 = EA/L + (EA/(L+e))cos2(30) + EA/L cos2(60) but since there is only 1 DOF and no loads, i don't have much to make a matrix equation with..

I tried moving the roller to the right ecos(30) and trying to solve for the forces like that, but couldn't get much.. any ideas?
 
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  • #2
I figured it out..

AD = Adm + kD

AD = 0

K11 = EA/L + (EA/(L+e))cos2(30) + EA/L cos2(60) = 2EA/L

Adm = PL/EA = ecos(30) --> P = EAe√3/2L

--> D = √3e/4

AR1 = Arm + FrD

AR1 = EA√3e/4L
AR2 = -5EAe/8L
AR3 = EA√3e/8L
 
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Related to Structural analysis stiffness method

1. What is the stiffness method in structural analysis?

The stiffness method is a mathematical approach used in structural analysis to determine the forces and displacements of a structure. It involves breaking down a complex structure into smaller elements and using the stiffness of each element to calculate the overall stiffness of the structure. This method is often used in conjunction with the equilibrium equations to solve for unknown forces and displacements.

2. How is stiffness calculated in the stiffness method?

Stiffness is calculated by determining the stiffness coefficient or stiffness matrix for each element of the structure. This coefficient takes into account the material properties, geometry, and boundary conditions of the element. The overall stiffness of the structure is then calculated by assembling the stiffness coefficients of all the elements together.

3. What are the advantages of using the stiffness method?

One of the main advantages of the stiffness method is its ability to handle complex structures with multiple elements and supports. It also allows for the analysis of indeterminate structures, where the number of unknowns is greater than the number of equations. The stiffness method also provides a more accurate and detailed analysis compared to other methods, such as the flexibility method.

4. What are the limitations of the stiffness method?

The stiffness method requires a significant amount of computational effort, especially for larger and more complex structures. It also assumes that the structure is linearly elastic, which may not always be the case in real-world scenarios. Additionally, the stiffness method may not be suitable for structures with large displacements or those with non-linear behavior.

5. How does the stiffness method account for support conditions and boundary conditions?

The stiffness method takes into account support conditions and boundary conditions through the use of boundary conditions equations. These equations are used to relate the known and unknown displacements and forces at each support. By solving these equations, the unknown forces and displacements can be determined for the entire structure.

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