# Formation of an internally statically determinate truss

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In summary, a internally statically determinate truss is formed by starting with one basic triangular truss and then adding two members and a joint repeatedly. The truss in the third figure can be formed this way, but it is unclear how the last figure can be formed using this method. The speaker suggests building clusters of triangles on each side and then joining them with a pin and a member. However, it is unclear if this would result in a statically determinate truss. The speaker also questions why all trusses made of solely triangles are considered internally statically determinate.
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I am unable to understand how a given truss is internally statically determinate.
My professor taught me that a internally statically determinate truss is formed by having one basic truss - the triangular truss consisting of three joints and three members:

and then repeatedly adding two members and a joint:

So, it makes sense why this is a statically determinate truss:

However, I don't understand how this can be a statically determinate truss under the same reasoning:

Can someone can help?

Do you not see triangles in the last figure?

Dr.D said:
Do you not see triangles in the last figure?

The truss in the third figure can be easily formed by starting with one triangle and then successively adding two members and a joint between them (first and second figures). However, I don't see how this can be done with the last figure, even if it is made of triangles.

Why not build the cluster of triangles on the left side, then build the cluster of triangles on the right, and finally add one pin and one member to joint the two clusters?

anorlunda
So if what you
Dr.D said:
Do you not see triangles in the last figure?

So if I understand you correctly, what you're saying is that all trusses made of solely triangles are internally statically determinate. Then can you explain why this is (internally) statically determinate?

I never said anything about being statically determinate or not, and certainly not about your last figure. You are moving the goal posts here.

Being statically determinant or not is, to some degree, dependent upon how the frame is loaded. You last figure may not be statically determinant if the extreme left and right nodes are not externally loaded.

## 1. What is an internally statically determinate truss?

An internally statically determinate truss is a type of structural system that is composed of interconnected members, typically made of steel or timber, that are arranged in a triangular pattern. This arrangement allows for the truss to remain stable and support loads without any additional external supports.

## 2. How is a truss determined to be internally statically determinate?

A truss is considered to be internally statically determinate if its internal forces can be determined using only the equations of static equilibrium. This means that the sum of all forces and moments acting on the truss must equal zero, and there must be no redundant or indeterminate members within the truss.

## 3. What are the advantages of using an internally statically determinate truss?

One of the main advantages of using an internally statically determinate truss is its stability and ability to support heavy loads without the need for additional external supports. Additionally, trusses are lightweight and can be easily prefabricated, making them cost-effective and efficient for construction projects.

## 4. What factors should be considered when designing an internally statically determinate truss?

When designing an internally statically determinate truss, factors such as the type of load it will be supporting, the span and height of the truss, and the materials used for the truss members should all be taken into consideration. Other factors such as wind and seismic forces should also be considered to ensure the truss can withstand external forces.

## 5. Can an internally statically determinate truss fail?

While an internally statically determinate truss is designed to be stable and support loads, it can still fail if it is not properly designed or constructed. Factors such as incorrect calculations, material defects, or external forces beyond the truss's design capacity can all lead to failure. It is important to carefully consider all factors and properly design and construct an internally statically determinate truss to prevent failure.

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