Triangulated Truss

This example shows how to make a complete triangulated truss in IGS. We will show how to interpret the results and update the equilibrium for modifications in the geometry of the form diagram and its

This example analyses the truss structure below:

The hypothesis of our analysis will be:

• Forces applied at each node have a magnitude of 10 kN.

• Reaction forces should be considered in the extreme left (vertical and horizontal) and extreme right (horizontal only).

1. Making Form Diagram.

As in the first example at IGS toolbar go to Create Form Diagram and select the option FromLines . The created diagram should look like this:

2. Setting loaded edges.

The truss is an isostatic example. It is composed of m=33 edges and ni=14 internal nodes. Therefore we are able to specify the force in 5 edges (DOF = m - 2*ni = 5) as explained in Section 1, which matches the number of externally applied loads. In IGS you can click the button Check DoF to check the required number of forces that should be selected.We go to the command Assign Forces and we are asked to choose the independent edges, therefore we select the applied forces and input the corresponding force of +10 kN in each with the help of the table. This table shows the index of each edge in the column "Name" and the force should be assigned to the column "Value". The edge indices are shown in the diagram while the table is open to help the identification. Note the positive sign because the forces applied in the bottom chord tend to pull the structure down. Once we press OK, and the forces are assigned, and this can be checked by the colour-coding having the independent edges with cyan colour.

After we hit OK, the forces applied are shown in the edges with an arrow. Verify that the arrow direction corresponds to the desired direction of the applied loads. The supports don't show any value since the equilibrium has not been calculated yet.

3. Set the support points.

Supports should be assigned to the nodes where reaction forces are applied. Go to the function Identify Anchors and select the two extreme nodes in the base of the truss. These nodes will be highlighted in red as in the figure below:

4. Compute the Force Diagram.

After setting the loads we can compute the equilibrium by calculating the force diagram in the button Create Force Diagram, the force diagram is automatically generated right to the form diagram. The result should be as below:

Note that the reaction forces now show the value and direction of its non-null resultants (25 kN up vertically). The default visualisation for form and force is the red-blue colouring. Blue represents compression and red for the edges in tension. At this point, the scale and location of the force diagram is automatically set by IGS. In the next section we will learn how to scale and position the diagram as required in this tutorial.

5. Scale and Location of the Force Diagram.

The scale and location of the diagram can be set in the IGS Menu on Display > ForceDiagram location / ForceDiagram scale as shown in the image below. By using these you can position the force diagram in the box indicated.

Once the diagram is placed in the required location and scale, the maximum force in one edge can be easily calculated using the inspector, which is 45 kN and given the scale used 0.2 the edge in the force diagram has real lengthL=45x0.2 = 9.0

6. Exploring sturctural geometry

Geometric modifications, such as dragging nodes in the form diagram can be executed with the button Move FormDiagram Nodes. Once one modification is performed, the form diagram can be updated by pressing the button Update ForceDiagram from FormDiagram.One example of modification is done below: we move up one of the nodes of the structure, and as a result, a large force is attracted to the edge connected to it. This higher magnitude can be seen due to the increased size shown by it in the force diagram. The force magnitude rises from initially 7.1 kN to 37.9 kN.

(In the figure above, forcepipes are activated so the new magnitude of the forces can be seen directly in the form diagram. To better visualise the pipes, the view is selected as ghosted with opacity 80%).Additionally, feedback on the cost of the structure can be assessed by activating the optionCompute loadpath that shows an increase in the cost/loadpath of the structure:

The total load-path of the structure is 1962.3 kNm.

Further dragging of nodes can be executed, such as, increasing the structural height of the structure, what results in a global decrease on the forces in the members and also a reduction in the cost of the structure.

The total load-path of the structure is 1326.6 kNm.

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The total load-path of the structure is 1425.3 kNm.

An option to auto-update the diagrams is available in the display settings tabs and it is turned OFF by default. If ON, this function update the force diagram at each node movement of the form diagram.

7. Analysis of different Load Cases.

To finish we show how the load case could be changed. Since this corresponds to a triangulated (isostatic) structure different loads can be carried without changing its shape (unlike the funicular arch). Here the force applied in the highlighted position is increased from 10 kN to 30 kN to simulate the hanging of a very heavy object on the truss. We can see the increase in the loads in the internal edges. (In the following figure, force pipes are also activated so the new magnitude of the forces can be seen directly in the form diagram).