Truss modelling, axial force and the effect of Diaphragms

If you model a truss within Tekla Structural Designer, you would perhaps expect it to take axial compression or tension in the top or bottom chords. The magnitude being dependant upon the load and direction.

This axial force expectation is clearly shown in the screenshot below where no diaphragm is defined at the level of the truss chords, when the truss is subject to gravity loads.

 

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What effect do we think applying a diaphragm to the chord level will make to our modelling?

Before answering the above question it is important to understand what a diaphragm is.

Tekla Structural Designer allows two different diaphragms to be defined:

• Rigid diaphragm - Rigid diaphragms have infinite in-plane stiffness and zero out of plane stiffness properties and therefore they neither exhibit membrane deformation nor report the associated forces. When a rigid diaphragm is specified, nodal constraints are automatically applied to all nodes within the diaphragm plane and thus they move together as a single unit. Since they do not move relative to one another no axial force can develop within any member within the plane of the diaphragm.
• Semi-rigid diaphragm - When a semi-rigid diaphragm is specified it simulates the in-plane stiffness properties and zero out of plane stiffness behaviour of the slab by providing a mesh of semi-rigid 2D elements. A semi-rigid diaphragm distributes loads based on both the stiffness of elements which connect to it and on the stiffness of the diaphragm itself.
• None - Whilst not a diaphragm, the option None, ensures that no diaphragm exists and the area is totally flexible.

The Include in diaphragm option is a property of the slab or roof panel when it is initially placed into the model.

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Note that the default values are as follows:
 

With the Include in diaphragm option checked and the diaphragm option set to Rigid, we can see the effect of the diaphragm to the bottom chord. The axial force is carried by the diaphragm and hence we see no axial force within the bottom chord of the truss.

Rigid diaphragm modelling creates a rigid 2-dimensional body in the plane of the floor and all nodes within the body are constrained by what are called constraint equations to maintain their relative positions in their respective levels. i.e. they cannot distort in shape in that plane, but can translate and rotate in 3D space.  The effect is that it is infinitely stiff in plane. The resulting (forced) displacements of the entire diaphragmed area as a rigid body – and everything they connect to - produces the distribution of lateral force.

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With the Include in diaphragm option checked and the diaphragm option set to Semi-rigid, we can see the effect of the diaphragm to the bottom chord. Linear elastic 2D elements are created which can be seen by viewing the Solver view regime.The axial force is carried in part by the diaphragm and in part by the truss chord.

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The parameters of the mesh are controlled by selecting Structure at the top of the Project Workspace, Structure tree.

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No diaphragm. Axial force (flexible) = 173.4 kN
Rigid diaphragm. Axial force = 0 kN
Flexible diaphragm. Stiffness factor 1.0, Axial force = 133.5 kN

You will notice from the summary table above that there is a Divide stiffness by factor that can be set.
The default is 1.0 but can be used to modify the calculated stiffness.

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With the Divide stiffness by value set to 2 the following results are obtained.

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With the Divide stiffness by value set to 10 the following results are obtained.

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Ultimately, the stiffness of the diaphragm would be the judgement of the engineer and should be set up to give results that are realistic for the system being used.

Including/Excluding Panels and Nodes from a diaphragm

It is possible to control which nodes or panels are included within a diaphragm. This easiest way to visualize and amend the model is by switching the view to the Review view regime and use the Diaphragm On\Off command.
 

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Some elements, for examples beams and columns have p-delta nodes at their mid-point which are automatically generated. Since these are automatically generated they cannot be selected for exclusion. If an end node is selected then the automatically generated mid-point node is automatically excluded.

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Left truss shows nodes excluded. Right truss shows nodes included.

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Care is required in using this command. The command can be used to allow axial force to travel along a required path. When it reaches a node connected to the diaphragm. At this point all the force goes directly into the diaphragm.

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