Solving trusses with the Direct Stiffness Method

In summary, the conversation discusses creating a computer implementation to solve planar trusses and how to check if the truss is solvable or not. The speaker's implementation generates unstable or indeterminate trusses and they want to discard these without calculating the determinant of the stiffness matrix or trying to solve them. They propose a condition of 2*j ≤ m + r to filter out bad trusses, but it is noted that this may result in losing some good trusses.
  • #1
Diego Saenz
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I'm creating a computer implementation to solve planar trusses. And I'm not sure how to check if the truss is solvable or not. Can you help me with that?

In my implementation, the trusses are created randomly (needs to be this way), so i get a lot of unstable or indeterminate trusses. I want to discard bad trusses without calculating the determinant of the stiffness matrix or trying to solve them.

Is this condition enough to discard such trusses? If I filter the trusses with this criteria, will i lose some good ones? ----> 2j = m+r

j - number of joints
m - number of members
r - number of reactions

Thanks.
 
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  • #2
Diego Saenz said:
If I filter the trusses with this criterion, will I lose some good ones? ----> 2j = m+r
Diego Saenz: Yes, you would lose some good ones. Instead, discard only the trusses having 2*j > m + r. Keep the trusses having 2*j ≤ m + r.
 
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FAQ: Solving trusses with the Direct Stiffness Method

What is the Direct Stiffness Method?

The Direct Stiffness Method is a structural analysis technique used to solve truss problems. It involves breaking down the truss into smaller elements and using the stiffness matrix method to calculate the forces and displacements at each node.

How does the Direct Stiffness Method work?

The Direct Stiffness Method works by first dividing the truss into smaller elements. Then, the stiffness matrix for each element is determined based on the material properties and geometry. These stiffness matrices are then combined to form the overall stiffness matrix for the entire truss. By solving for the unknown displacements and forces using the equilibrium equations, the solution for the truss can be obtained.

What are the advantages of using the Direct Stiffness Method?

One advantage of using the Direct Stiffness Method is its accuracy in solving truss problems. It takes into account the stiffness of each element, which can vary along the length of the truss. Additionally, it can handle complex truss structures with multiple loading conditions and support types. It also provides a systematic approach to solving truss problems.

Are there any limitations to using the Direct Stiffness Method?

One limitation of the Direct Stiffness Method is that it assumes all elements in the truss are in a linear elastic range. This may not be accurate for trusses with highly non-linear materials or large displacements. Additionally, it can become computationally intensive for large and complex truss structures.

How is the Direct Stiffness Method different from other structural analysis techniques?

The Direct Stiffness Method differs from other structural analysis techniques, such as the Finite Element Method, in that it only considers axial forces in the truss elements. It also assumes that the truss members are only subjected to axial forces and no bending or torsional forces. This simplifies the analysis but may not accurately capture the behavior of the truss in all cases.

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