Finite Element Analysis of a Beam

Introduction

In this article, we will perform a finite analysis of a simple beam using FEA Online. As illustrated in the diagram below, the left end of the beam is fixed; the right end is supported by a spring. The beam is also supported in midspan.

The properties of the beam are as follows:

• L = 3 m
• E = 210 GPa
• I = 0.0002 m⁴
• P = 50 kN
• k = 200 kN/m

The manual solution to this problem is presented in Solved problem on Finite element analysis on beam elements.

In this article, we will solve the same beam problem using an online finite element analysis program: FEA Online. You may register for a free account (Basic tier) and if you would like to follow along, just click on the Sign-Up button to register.

The process of analyzing a structure is as follows:

1. Create a new Model
2. Define the nodes
3. Define the constraints (supports)
4. Define the material properties
5. Define the beam section properties
6. Define the elements (beam and spring will be used in this example)
7. Define the applied loads
8. Perform the static analysis
9. Print analysis results or review the axial, shear, and moment diagrams

Create A New Model

To start a new finite element model, click on the Model > New…

In the New Model dialog, select “Metric” as the system unit, “Meter (m)” for the Length Unit, and “Kilonewton (kN)" for the Force Unit. Then click on the Create button to create the model.

Define Nodes

Once the model is created, you can start defining the model geometry by navigating to the “Nodes” tab. Clicking on the Add button will add a new node to the model. The screen below shows 4 nodes have been added to match the diagram in the beginning of this article. Nodes 1, 2, 3 are on the same line with 3m between them. Node 4 is 0.20m below node 3. Since we will be using a spring element to connect Nodes 3 and 4, the distance between them is not important (0.2m is arbitrary selected).

Define Constraints

Constraints are used to model supports in structures. They are the boundaries conditions in a finite element model. The “Constraints / Supports” tab is used define Constraints. Use the “Add” button to add new constraints.

The above screen shows all displacements and rotations of Node 1 are restricted in all directions. The Y direction displacement of Node 2 is constrained. The X, Y, Z displacements of Node 4 is restricted.

Note: All models in FEA Online are 3-dimensional. When modelling 2D structure, it is important the supports in your structure are modelled appropriately so the structure is stable.

Define Material

FEA Online supports beam, truss, and spring elements at time. For beams and trusses, we must specify the material. The “Materials” tab is used to define materials in a model. For Material 1 in the screen below, E is set to 210 GPa.

Define Sections

Beam and truss elements also require a section be specified in a finite element model. The “Sections” tab is used to define sections in a model. Clicking on the Add button will create a new section.

Define Elements

The “Elements” tab is used to define beams, trusses, and spring elements in a finite element model. You can click on the Add button to add a new element. The Type attribute allows you to specify if a beam, truss, or spring element. The Node ID attribute is used to define the nodes the element is connected. This is a comma separated list of node IDs. You can use the Material ID and Section ID to reference the material and section, respectively, of the element.

Since the model in FEA Online is always a 3D model, it is necessary to specify the orientation of elements in the model. This is done using the Reference ID attribute. If no Reference ID is specified, it is assumed the 2-axis is parallel to the global Y-axis. The reference node you specified is located in the 1–2 plane of the beam with the 1-axis defined as the line connecting the i (start) and j (end) nodes.

For spring elements, the Spring Stiffness is required.

Define Loads

The “Loads” tab is used to specify the external loads applied to the structure.

FEA Online organizes loads into Basic Load Cases (BLCs). Every load must be assigned a “BLC ID”. BLCs are used to define Load Combinations that will be used to design the structure. So before defining the load, we must first define the BLCs using the “Manage BLCs” button.

FEA Online initializes each model with a list of BLCs (based on ASCE 7 standard). the D (Dead Load) and L (Live Load) are active by default.

After BLCs have been defined, you can add the loads to the model using the “Add” button. The “Type” attribute allows you to specify the type of load:

1. nodal: Load applied at a node
2. distributed: Distributed load applied in the span of a beam
3. concentrated: Concentrated load applied in the span of a beam
4. temperature: Thermal load applied to the beam

In the screen below, a nodal load is specified to be applied at Node 3.

Perform Static Analysis

After the model geometry, constraints, and load have been complete, you can perform a static analysis of the model using the Tools > Analyze command to submit the model for analysis. For small models, the result should return quickly. For very large models, it may take some time, and you may need to click on the Tools > Get Analysis Result to get the result.

Analysis Result

The Displacements tab shows the nodal displacement for each basic load case.

For our model, Nodes 1, and 4 are constrained. So all displacement components are 0. The translation displacements of Node 2 are all 0s since the Y direction is constrained; rotation at Node 2 is -0.002492 radians.

The Y displacement is -0.017442m and Z rotation is -0.007475 radians.

These values closely match the values in the YouTube video (see 10:41 minute of the video).

Reactions

The “Reactions” tab shows the reactions at each constraint.

Again, the values are very close to the value in the YouTube video (see time 13:15)

Element Forces

FEA Online shows the forces at each element in the “Element Forces” tab. You can click on each element to see the Axial, Shear, Moment, and Torsion diagrams.

Element 1

Element 2

Element 3

Output

You can also generate a PDF output document from FEA Online that echos the model data you have entered

The PDF also contains the computed displacements, reactions, element forces, and load combination forces (if load combination is defined in the model).

Summary

With FEA Online, you can model structures using the finite element method online without the need to install any software or purchase expansive hardware. You can perform finite element analysis using a web browser. Only an Internet connection and a device that has a web browser is needed. You can run FEA Online in your desktop, laptop, notepad, and yes, even your mobile phone!