## Structural Analysis

## Application of MS-Excel "Solver" to Non-linear Beam Analysis

Written by Toshimi Taki

Prepared on March 4, 2007

**Introduction**

There are some types of beam structures as shown in figure 1.

Figure 1. Types of Beam Structtures

If beam elements of "simple beam" structures are subject to lateral load only, this type of beam structure shows linear behaviour. "Simple beam" structures can be analyzed easily.

When beam elements in a beam structure are subject to lateral load and axial load, the structure shows non-linear behaviour. The examples of the non-linear beam problems are beam columns, Elastica and arch strucures. Analytical method is applicable only to idealized structures such as uniform cross section beam column. You need to use non-linear finite element analysis to solve non-linear beam structures in real world.

I have developed a new method to solve non-linear beam structures. This is a direct application of energy principle using MS-Excel "Solver".

**Application of MS-Excel "Solver" to Non-linear Beam Analysis**

"Elastica" is used as an example to show the method. Following figures show the results.

For detail of the method, see my paper.

Click here to download "Application of MS-Excel 'Solver' to Non-linear Beam Analysis (Rev. A)" (150KB) in pdf file.

Click here to download MS-Excel template "elastica.xls" (112KB).

You need to install add-in tool "Solver" to MS-Excel. This template can be used for the other non-linear beam problems than "Elastica".

Figure 2. Model for Elastica

Figure 3. Result -- Deflection

Figure 4. Result -- Load-Deflection Curve