# Tutorial 2: Frame Structure - Resultant Forces

This Tutorial is a follow up of the previous Tutorial1. In this exercise we are gonna analyze the resultant forces on the beams.

## The Beam Element

A beam as we explained in the previous tutorial is a 2D line with the cross section defining the third dimension. The 2D line is divided into sub-segments. The nodes found on the axis of each sub segment represent the points which we can get results for. Karamba3D also allows us to display the beam as a rendered mesh.

## Step 1: Isolate the Beams

Let's begin by isolating the elements that we want to study:

• Connect a panel with the name of the elements that you want to isolate to the Ids|Brep Input in the Model View.

## Step 2: Display Displacements

Now let's display the resultant displacements on the rendered beams:

• In the Beam View click on the Render Settings and check the Displacement bullet.

## Step 3: Add Segments to the Beam

As you can see the beam-mesh consists of four sub-segments. This is because by default karamba assigns one meter as the length of each sub-segment. By increasing the number of sub-segments we get more accurate results, but also we increase the computation time of the analysis.

• In the Model View decrease the length of the subsegments by lowering the value of Length//Segment under the Render Settings.

## Step 4: Display of Resultant Forces

Now let's check the resultant forces. The picture on the right shows the orientation of the forces in a beam section.

• Mx,My: Resultant bending Moments in kNm
• Vy,Vz: Resultant shear forces in kN
• Nx: Resultant axial for in kN

In Beam View we can see the sum of resultant forces due to the load cases:

• In Beam View under the Render Settings uncheck the Cross section to disable the render of the beam's mesh.
• In Beam View under Section Forces check the Filled, Numbers option.
• Check the Force you want to display (For example My) and adjust the scale to the desired size.

Try to display the Shear Forces and the Normal Forces as well

## Step 5: Retrieve data for the resultant forces

The Beam Viewer is useful as we can get a quick sense of the force distribution. But as our structures become more complicated, we need to be able to get the numbers instead of previewed results. Lets see how we can do that:

• Connect the Model from Analyze (Karamba 3D) to the Beam Forces (Karamba3D) found at Karamba3D » 6.Results » Beam Forces (Karamba3D)
• Connect a panel with the name of the elements that you want to study to the Ids|Brep input, in this case it is "beams".

Let's see now how Karamba3D provides results without specifying the loadcase. Each branch represents the analysis results for one beam and for one only load case. Each branch also contains a list of results as many as the nodes of the beam.

So how can we get the sum of the resultant forces at the nodes? An easy way is the following:

• Create two Beam Forces (Karamba3D), one for every load case. Remember we have two, one for gravity (load case:0) and one for a uniformly distributed load (load case: 1). Assign the load case to the batteries by connecting a panel with the number of each load case.
• You can either increase the number of the beam's nodes by either adjusting the maxL (maximum distance between results) or the NRes(number of results per beam element). In this case we put 8 at NRes.
• Adding the data from Beam Forces (Karamba3D) for the LCase 0 and LCase 1 will give as the sum of the resultant forces.

Try to repeat the same step for Shear Forces and Normal Forces

## Step 6: Retrieve the Maximum of Resultant Forces

Karamba provides a component for retrieving the maximum resultant forces, the "Beam Resultant Forces(Karamba3D)".

• Repeat the Step 4 only this time instead of Beam Forces (Karamba3D) use the Beam Resultant Forces(Karamba3D) found at Karamba3D » 6.Results » Beam Resultant Forces(Karamba3D)

In the resulting panel you can see 4 results representing the maximum bending moments for each one of the four beams.

## Step 7: Retrieve the Displacement Results

• Use in a similar way as in step 5 the Beam Displacements(Karamba3D) component found at Karamba3D » 6.Results » Beam Displacements(Karamba3D)
• The results translate in the global x, y, z directions. For example the first list item at the first branch is the {-4.0649e-6,-4.0649e-6,-0.00011}. That represents the displacement of the first node of the first beam. In the global x axis it is -4.0649e-6m, in the global y axis is 4.0649e-6m and in the global z axis is -0.00011m.
• If we want to get the total displacement with respect to all axes we simply need to connect the number component found at Params » Primitive » Number to the results.

Let's get the maximum displacement for each beam:

• Use the Sort List component found at Set » List » Sort List. Connect the translations to the K(keys input).
• Reverse the list using the reverse component to get the maximum value at the index 0 of the lists.
• Choose the list item 0

The final data includes 4 branches each for each beam, with a single item representing the maximum displacement.