The Beam Calculator allows for the analysis of stresses and deflections in straight beams.

Inputs

Input the details for the beam, then click the "Calculate Results" button:

Structure Point Forces Dist Forces Constraints

Structure

(Instructions)

Specify the geometry and material of the beam:

Length:

Material:

NOTE: For more complicated structures, please see the 2D Finite Element Analysis (FEA) calculator.

Point Forces

(Instructions)

---

Distributed Forces

(Instructions)

---

	Start	End
Location:
Dist Force:

Constraints

(Instructions)

---

Fixed Pinned Roller (Horizontal) Roller (Vertical) Custom

TX	TY	Rot

Plot Display Units:

Custom (Edit)

Display Units

Display results in:

Custom (Edit)

Results

The beam analysis results are detailed below. The problem was solved as a finite element model using beam elements. For more information on how these results were derived, refer to the finite element analysis reference and the beam stress & deflection reference.

Results Overview Model Overview Shear-Moment Diagram Stress Plots Deflection Plots Result Tables

Results Overview

The max deflection and slope are given below:

	Value	Location
Max Deflection:
Max Slope:

The Free Body Diagram (FBD) and deformed mesh are shown below.

See full result details on the other tabs (above).

Model Overview

The model with applied forces and constraints is shown below:

Material Properties

Material:

Property	Value
Yield Strength
Ultimate Strength
Elastic Modulus
Poisson's Ratio

Cross Section Properties

Cross Section:

Property	Value
Height (Y)
Width (X)
Web Thickness
Flange Thickness
Area
Centroidal Distance (in primary bending direction)
Moment of Inertia, Centroidal (about primary bending axis)

Shear-Moment Diagram

The shear and moment diagrams are shown below. The standard sign conventions for shear-moment diagrams are followed:

Shear: Positive shear causes clockwise rotation of the beam, negative shear causes counter-clockwise rotation.
Moment: Positive moment will compress the top of the beam and elongate the bottom of the beam (i.e. make the beam 'smile').

Shear Peak Values

Location	Value

Moment Peak Values

Location	Value

Stress Plots

The stress plots are shown below.

The stresses are calculated based on the equations below:

Axial Stress	Shear Stress	Bending Stress	Von Mises Stress

Deflection Plots

The deflection plots are shown below. The sign convention for deflections is:

X: Positive to right, negative to left
Y: Positive up, negative down
Slope: Right hand rule (positive counterclockwise, negative clockwise)

Result Tables

(Details on Result Tables)

This problem was solved as a finite element model. This tab provides the results for the individual nodes and elements in the model.

The plot below shows the mesh with the element numbers labeled:

Nodal Results

Below are the results for each node. There are several things to note:

Certain nodes are associated with points, and for those nodes the number of the associated point is given.
All nodes associated with points are listed first, followed by nodes which were created as part of the meshing process.
External reactions may exist for constrained degrees of freedom. Any nodes which do not have constraints will not have external reactions.

Elemental Results

Below are the results for each element. There are several things to note:

Every element consists of 2 nodes. Within the table, these nodes are referred to as "Node 1" and "Node 2".
The internal reactions are given in terms of the global coordinate system (i.e. X and Y) as well as the local coordinate system (i.e. "axial" along the axis of the element, "shear" perpendicular to the element).

Download Results to Excel

Download an Excel file to your computer containing the nodal results and elemental results.

Download Report

Save a formatted Word document to your computer detailing the inputs and results of the analysis.

Download Inputs File

Save all input data to a file. You can later upload this file to pick back up where you left off.

Need More Functionality?

Sign up for an account to receive full access to all calculators and other content. The subscription types are described below, along with the benefits of each.