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Beamsolver quickstart

The goal of this tutorial is to get you up and running with Beamsolver as quickly as possible, so you can start solving your own structures.

We start by taking a look at the UI.

Understanding the UI

Beamsolver is divided into an input section, a chart section, and a results section.

The workflow when using Beamsolver to solve structures goes as follows:

Create the beams (or trusses) of your structure using the add beams tab in the input section;
Define the restraints and hinges using the edit nodes tab in the input section;
Add distributed loads using the edit beams tab in the input section;
Add point loads at the nodes using the edit nodes tab in the input section;
If necessary, define section properties using the edit beams tab in the input section;
Once the structure is defined, click solve to calculate the force diagrams and the reactions;
Explore the solution in the results section.

Every time you modify the structure, the chart updates. When you click solve, Beamsolver creates the results section for you, where you can explore the solution.

How Beamsolver models structures

It's important that you understand how structures are defined with Beamsolver. A structure is a collection of members numbered from 0 to n, connected together by nodes also numbered from 0 to n.

Members

A member is a beam or a truss of the structure. Its defining characteristics are the length and the angle, measured in degrees counter clockwise to the horizontal. It is always connected to two nodes, one for each end of the member.

Nodes

Nodes (or "joints") define how the members of the structure are connected together. They also define how the structure is connected to the ground (i.e. how it is restrained).

How to add members to a structure

In order to add members to a structure you need to use the add beams tab of the input section:

When creating a new beam, you always have to specify the two nodes it is connected to. The second node can be either an existing node already present in the structure or a new node. If it is a new node, then you also need to specify the length and angle of the new beam, so that Beamsolver knows where to place it.

Beamsolver is a symbolic beam calculator, meaning that it has an integrated computer algebra system that can be used to get symbolic results. You are not limited to numerical quantities when defining the lengths of beams.

Beamsolver tries to parse the string you input in the length field by looking for a variable portion (e.g. "a") and a numerical protion (e.g. "1.3"). The parser is intelligent enough to understand more complex inputs as well, for example:

2.3*L --> \(2.3 \cdot L\)
L/3 --> \(\cfrac{L}{3}\)
2/3*H --> \(\cfrac{2}{3}\cdot H\)
2^0.5*x --> \(\sqrt{2}\cdot x\)

Beamsolver is unit agnostic, so it is up to you to input your data in a way that is consistent with your units of measurement.

How to add restraints and hinges

Once you have defined the beams of your structure, it's time to add restraints and hinges. You can do this from the edit nodes tab in the input section:

First, you need to select the node you want to edit. You can do this by using the ID dropdown or by clicking on it on the chart.

The restraint section allows you to define how this particular node is restrained to the ground. You have several options to choose from:

icon	name	r_x	r_y	r_r
	Fixed
	Pin
	Skater
	Roller
	Fixed rotation
free	Free

You can also specify the angle of the restraint by using the angle input. As always, angles are measured in degrees counter-clockwise to the horizontal.

The hinge section lets you define how the beams connected to this node interact with one another. In most cases, beams will have either a continuous or pinned internal connection, in which case you don't need to worry about the advanced options section. Simply select the the type using the dropdown and you are done.

However, Beamsolver also allows you to define much more advanced hinges. Due to the more complicated nature of this functionality, the advanced settings are disabled by default. To enable them, select the "advanced options" checkmark, and you will be ready to go.

Advanced hinges with Beamsolver

Our advanced hinges module allows you to create very complicated configurations. The most important thing to understand is the distinction between what Beamsolver calls "ground" beams and "internal" beams:

Ground beams support the beams marked as "internal"
Internal beams are supported by the beams beams marked as "ground".

Take a look at this configuration:

In node 1, beam 0 is acting as "ground" for beam 1, which is being supported by beam 0 using an internal roller. Note that in node 1 there are no external constraints. The roller is internal (hence the gray color) and overall, node 1 is free to move in the plane.

You can move a beam from the "ground" category to the "internal" category by clicking on its id in the ground beams and internal beams lists.

Using the "Ground sub-disc" and "Internal sub-disc" dropdowns you can further customize the node by adding sub-hinges to the two categories:

How to delete beams

Deleting a beam is simple. Simply click on it from the chart, and then click the DEL button in the "Edit beams" tab.

Note that you can delete a beam only if the operation maintains the integrity of the structure. For example, you can't delete the central span of a three span continuous beam, because you would end up with two separate beams not connected to each other.

How to edit section properties

In the Edit beams tab you can customize the section properties of a beam:

The quantities you specify can be either numeric or symbolic. By default all beams have Young's modulus (E), Moment of Inertia (J) and area (A).

Notice how you can enable or disable the inertia and area inputs. Why? Beamsolver uses the Principle of Virtual Work to solve indeterminate structures. If your structure is indeterminate and you leave the area checkbox unchecked, Beamsolver will use the following Virtual Work formula to calculate the additional equations needed to solve the system:

\(\sum_{j=0}^{n}\cfrac{1}{E_i\cdot J_i}\cdot \int\limits_{0}^{L_j}M\cdot \cfrac{\partial M}{\partial X_i}ds_j=0 \)

If you are using symbolic quantities for \(E_i\) and \(J_i\), and all beams are the same, these two terms can be simplified from the equation and will not appear in the diagrams formulas.

If instead you enable the area checkbox, Beamsolver will add the contribution of the axial deformation to the formula:

\(\sum_{j=0}^{n}\cfrac{1}{E_i\cdot A_i}\cdot \int\limits_{0}^{L_j}N\cdot \cfrac{\partial N}{\partial X_i}ds_j+ \sum_{j=0}^{n}\cfrac{1}{E_i\cdot J_i}\cdot \int\limits_{0}^{L_j}M\cdot \cfrac{\partial M}{\partial X_i}ds_j=0 \)

If you are using symbolic quantities, you may get a solution that is a function of both \(A_i\) and \(J_i\). Sometimes, this can dramatically complicate the formulas of the reactions and diagrams (to the point where they won't even fit your computer screen!). In such cases it's better to use numeric quantities, as if you were solving the structure using a standard F.E. method.

How to add loads

With Beamsolver you can add distributed loads to the beams and point loads to the nodes. You do this from the "edit beams" tab and the "edit nodes" tab respectively.

Distributed loads

Like everything with Beamsolver, distributed loads can be either numeric or symbolic. The image above shows an uniform load (the values at the two beam extremes are the same) with an angle of -90, meaning it is a vertical load directed downwards.

Point loads

The loads applied to a node can be either forces or moments. You can use the "type" dropdown to switch between the two categories.

How to solve the structure

Once you have finished configuring your structure, it's time to solve it by clicking the yellow SOLVE button:

Beamsolver will create the results section for you.

There are four tabs in the results section:

Diagrams: The axial force, shear force and bending moment diagrams for the whole structure will be displayed here.
Formulas: From here you can visualize the formulas of the diagrams for every beam. You can also calculate the position along a beam where a particular diagram is equal to zero, as well as calculating the derivative and the maximum values.
Reactions: Here you find the formulas of the external reactions of the structure.
Definitions: Here you find a step-by-step breakdown with all the steps that Beamsolver went through to solve the structure.

Conclusion

You should now have all the information you need to start solving structures using Beamsolver. Remember that some configurations are basically impossible to solve symbolically, so if you see that the calculator gets stuck after you click solve, it's better to reload the page and use numeric quantities instead.

We hope that our software will prove to be a useful addition to your workflow. If you haven't already, check out our resources page for some interesting articles. If you are ready to take the next step and upgrade to beamsolver PRO, check out our pricing page.