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Mathematical Model of Influence Lines for Indeterminate Beams

Dr. Moujalli Hourani Associate Professor

Department of Civil Engineering Manhattan College Riverdale, NY 10471

Abstract

The purpose of this paper is to present an improved and easy way for dealing with the influence lines for indeterminate beams. This paper describes the approach used to teach the topic of influence lines for indeterminate beams in the structural analysis and design courses, in the Civil Engineering Department at Manhattan College. This paper will present a simple method for teaching influence lines for indeterminate beams based on a mathematical model derived from the fundamental use of the flexibility method. The mathematical model is based on describing the forces and the deformations of the beam as mathematical functions related by consecutive integration processes.

Introduction

Many civil engineering students have difficulties dealing with the effects of live loads on structures because of the lack of knowledge of influence lines in general, and in particular, of the influence lines for indeterminate beams. These difficulties are perhaps due to the minimal amount of time spent on covering this very important topic in a structural analysis course, or due to unclear and confusing methods used to present the topic of influence lines. Several textbooks, 1,2,3,4 cover the topic of influence lines, theories, examples dealing with determinate structures. Since these textbooks put little emphasis on indeterminate beams, this paper will focus on this topic. Two years ago, while the faculty of the Civil Engineering Department at Manhattan College, were conducting the assessment of the topics covered in the structural analysis courses, we found out that there was a great concern from our students about their capabilities to deal with influences lines for indeterminate beams. Based on the input from the students, we went back, and took another look at the way the topics of influence lines are being covered. Last year, the new approach was introduced in a structural analysis course, Advanced Structural Analysis II. At the end of the semester the student’s assessments of the topic, showed a major improvement in their capabilities to solve problems of influence lines for indeterminate beams. After learning the new approach, the students were capable of developing their own computer programs using Excel/ Quattro, and Maple/MathCAD, to solve the problems of influence lines for multi-span beams with various boundary conditions. Proceeding of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright © 2002, American Society for Engineering Education

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Hourani, M. (2002, June), Mathematical Model Of Influence Lines For Indeterminate Beams Paper presented at 2002 Annual Conference, Montreal, Canada. 10.18260/1-2--11191