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I am learning about the basics of truss analysis in mechanics. As part of this, I learnt that a truss/frame is composed of at least 3 members, its joints are pinned and that any loading is applied at a joint.

I thought that it needs to have at least 3 members as this is the minimum to create a shape (triangle). This got me thinking could this diagram qualify as a truss/frame in reality despite only consisting of 2 members?

image of truss. Black background with two blue semi-circles connected at two points by pinned connections denoted as light blue circles

Faithfully, Guest3301

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    $\begingroup$ Assuming the blue pieces are truss members, then the overall concoction here produces a single equivalent truss member. Whether a truss that contains one member qualifies as a truss is where the debate is. If we say 3 is required because of 2 dimensional effects, we can say that 3 is insufficient due to 3 dimensional effects. $\endgroup$
    – Abel
    Nov 15, 2023 at 13:57

3 Answers 3

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My perspective on this is no. You may have two members that are connecting the two joints, but in a mathematical sense, those two members would be combined together to simplify the problem. With only two members connecting two joints, you effectively have two "joints" connected by one member.

Also, remember that a "joint" is a point where two different objects are combined. If both objects are attached to the same joints, they will act as one unit.

For a calculation to be performed on a truss, it must be fastened in two places, otherwise, it will just rotate on whatever single joint it is fastened to. With both(all) joints fixed, there wouldn't be any calculations to perform.

E.g. this truss could be simplified by combining the properties of the two middle truss members. Members in a truss

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From my perspective this qualify as a frame, but not as a truss (provided the green circles are intended as pins).

Trusses and Frames differ from a structural point of view in two aspects:

  • connections: Trusses are pin connected which theoretically cannot transfer moments, on the other hand frames have connections that can carry moments.
  • Loading of the members: Because of the pins used in connections Truss members can carry only axial loads , while frames member have members that can carry moments and transverse loads.

Additionally, trusses can be composed only by linear members (called rods), while frames can accommodate more complex shapes - like the one in the image above (linear members in frames are called beams)

In the above example, it would be impossible for the member (blue bits) to carry only an axial load. So in that respect, it can only be a frame (and not a truss).

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It is not a truss. It might not even be a frame.

Trusses are composed of axial members and nodes, and loads are assumed to act through the nodes, and at minimum two nodes are reaction points at the support. It is assumed that truss members do not transfer bending moments across the nodes. Otherwise the result is an indeterminate truss for which statics alone will not solve for member forces. The curved elements you show as truss members are not axially loaded members for truss analysis as they will have bending stresses. The 'truss' you drew is either irrelevant structurally (the two points are the fixed reaction points of support), or unstable (one or both truss reaction points have too many degrees of freedom).

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