Finite Element Structural Analysis on an Excel Spreadsheet

Richard Campbell, P.E., S.E.

Course Outline

The course introduction provides a description of finite element analysis, as well as some of the typical assumptions underlying structural finite element analysis.

The first portion of the course provides definitions and terminology as they apply to this course. Finite element analysis has broad application and in different contexts terms may have different meanings, so this section defines terms as used in this course.

The second portion of the course provides a number of FE analysis example applications for structural engineers. It is important to see applications and results before delving into theory so the purpose of the analysis is clear, much as it it is easier to bake cookies if you are allowed to sample a few before delving into the recipe.

The third portion of the course presents some methods to check results. The complexity of many FE problems makes checking a formidable task. Too often, engineers are enamored by the precision of computer generated results and they forget that accuracy is far more important. Checking is about verifying accuracy, not precision.

FE method is by nature an approximate solution technique. The fourth portion of the course presents the capabilities and limitations of the FE spreadsheet provided with the course. All FE methods will have their strengths and weaknesses, their capabilities and limitations. This section illustrates that point with respect to the provided FE spreadsheet, with the idea that the engineer needs to be aware of similar boundaries for whatever method / software they are using.

The last portion of the course is a summary.

The course includes a multiple-choice quiz at the end, which is designed to enhance the understanding of the course materials.

Learning Objective

After taking this course, the student will:

• know the difference between truss, beam and frame-type members;
• be able to differentiate node data from member data;
• know the difference between local coordinates & global coordinates;
• know some methods to check calculated computer results;
• understand continuous versus discretized systems;
• know the basic assumptions underlying FE theory;
• know some methods to simplify complex FE problems;
• have a basic understanding of the theory used to solve a FE problem;
• understand the transformation of local stiffness values to global stiffness values;
• be able to provide sufficient boundary conditions (supports) for stability;
• understand Microsoft Excel matrix size limitations, and the corresponding FE spreadsheet problem-size limitations; and
• know the benefits, uses and limitations of the provided FE spreadsheet.

Intended Audience and Assumed Knowledge

A typical user would be a structural design engineer working with a beam, truss, frame or elastic foundation problems. The user should:

• have Excel 5.0 or higher software.
• have a working understanding of spreadsheet formulas (Visual Basic [VBA]programming and macro skills are not necessary).
• be able to create a structural 2D frame model with nodes and members.
• be aware of matrix mathematics (addition, multiplication and inversion of matrices), although detailed knowledge of matrices is not needed.

Benefit to Attendees

This course presents Finite Element in an easy to learn format via a FE spreadsheet for Microsoft Excel. All of the intermediate steps and intermediate calculated values in example FE problems are easily viewable on the spreadsheet. Understanding FE theory allows the user to in many cases forego commercial software and use more basic software, such as the FE spreadsheet. In addition to providing FE theory, this course provides a functional FE spreadsheet that is versatile, easy to use and easy to understand. It can be used on any computer that has Microsoft Excel; no license or password or hardware key is required. The spreadsheet can easily be customized by the user. It can expanded or modified for specialized problems. It can be adapted from the structural discipline to other disciplines. It can be shared with others at no cost.

Course Introduction

Finite Element (FE) software is an essential tool for most structural design engineers, and at the cost of most commercial FE software, it had better be essential. The commercial FE software used by many engineering firms will provide you with more computer output than you could read in a month and more than you can understand in a year. Commercial programs are great for impressing clients, and great for performing extensive analysis when really needed. But in design of frame-type structures, rarely is all that power and output really needed.

In 25 years of engineering, I have never seen a design that was flawed because the designer failed to generate enough computer output. I have never seen a structure that was inadequate because the designer didn’t use enough nodes in his analysis model. I have never seen an analysis that was erroneous because there weren’t enough digits to the right of the decimal point. For most frame-type structure problems, use of commercial FE software results in too much output, too many nodes, and too many insignificant digits.

In 10 years of private practice, I have relied almost exclusively on a FE spreadsheet for analyzing frame-type structures. I am presenting that spreadsheet in this course as a practical and effective design tool. Even if you need commercial FE software size and power for some problems, you will probably find the FE spreadsheet to be superior for problems within its range. It is limited to 2-dimensional frames of about 50 nodes, but if your problem is within that range you will find it is easier to use, easier to understand, easier to port, easier to check and much less expensive than commercial programs.

FE method is a numerical solution technique used to analyze continuous systems, in which the system is discretized into a finite number of elements. Continuity of the system is modeled by compatability equations between adjacent elements. This course will focus on frame-type structures in which the elements are the framing members and the compatability is of force and deflection.

Course Content

The course content is in a PDF file:

Finite Element Structural Analysis on an Excel Spreadsheet

Please click on the above underlined hypertext to view, download or print the document for your study. Because of the file size, we recommend that you first save the file to your computer by right-clicking the mouse and choosing "Save Target As ...", and then open the file in Adobe Acrobat Reader from your computer.

Once you purchase the course, you can download the functional FE spreadsheet for 2D Frame and Truss in the quiz section.

DISCLAMER: "This spreadsheet is provided for illustrative teaching purpose only, and is not intended for use in any specific project. Anyone making use of the information contained in this spreadsheet does so at his/her own risk and assumes any and all resulting liability arising therefrom."

Table of Content

• Introduction to FE
• Definitions and terminology
• Finite Element examples / applications
• Finite element theory
• Capabilities and limitations of the FE spreadsheet
• Summary

Course Summary

Finite Element method is a powerful analysis tool used by almost all structural design engineers. Many if not most frame-type structural design problems can be solved with the provided Excel spreadsheet. The software is free, easy to use, easy to port between machines, easy to pre- and post-process. In contrast, commercial FE software can be cumbersome to use, difficult to check, difficult to port between machines, and expensive.

More advanced analyses, such as seismic response spectrum problems or soil-structure p*y problems, can also be solved by enhanced versions of the spreadsheet, subject to the size limitations above. Those problems are beyond the scope of this course, but may become available in subsequent courses.

The Excel Spreadsheets provided with this course are believed to be accurate, but use thereof shall be at the users risk. Results of the software should be independently checked (as when making any calculations or using any software). The user is cautioned that the spreadsheet original shall be saved and only copies used for calculations. The formulas in the spreadsheet have minimal protection, so it would be easy to inadvertently (or intentionally) revise the formulas.

Quiz

Once you finish studying the above course content, you need to take a quiz to obtain the PDH credits.

DISCLAIMER: The materials contained in the online course are not intended as a representation or warranty on the part of PDH Center or any other person/organization named herein. The materials are for general information only. They are not a substitute for competent professional advice. Application of this information to a specific project should be reviewed by a registered architect and/or professional engineer/surveyor. Anyone making use of the information set forth herein does so at their own risk and assumes any and all resulting liability arising therefrom.