Tapered Frames and Monopoles

Marvin Liebler, PE

Course Outline

1. Introduction
2. First Order Stiffness Matrices
3. First Order Assemblies
4. First Order Examples
5. Second Order Stiffness Matrices
6. Second Order Assemblies
7. Second Order Examples
8. Concluding Remarks

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

Learning Objective

At the conclusion of this course, the student will learn:

• P-Δ and P-δ effects;
• First order stiffness matrix definition;
• The virtual force method;
• Derivation of first order stiffness matrix;
• First order tapered beam assembly method;
• Flagpole analysis procedure;
• First order frame and monopole examples;
• Power series representation of a function;
• Chebyshev polynomials;
• Conversion of Chebyshev polynomials to power series;
• Series solution for second order stiffness matrix;
• Second order tapered beam assembly method; and
• Second order frame and monopole examples.

Intended Audience

Structural engineers
Structural designers
Architects
Code review officers

Benefit to Attendees

The student will have a working knowledge of the analysis  of tapered frames and monopoles.

Course Introduction

First and Second order tapered beam stiffness matrices, assembly programs, and examples are presented in detail.

Course Content

In this lesson, you are required to download and study the following course content in PDF format:

Tapered Frames and Monopoles

Please click on the above underlined hypertext to view, download or print the document for your study. Because of the large 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. If you still experience any difficulty in downloading or opening this file, you may need to close some applications or reboot your computer to free up some memory.

Course Summary

Through the use of derivations and practical examples, the analysis of tapered frames and monopoles, differing significantly from constant cross-section members, is presented.

Quiz

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

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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.

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