Automated Design of Steel Open Web Joist Floor Framing Systems

199 Pages·2004·1.06 MB·English

Automated Design of Steel Open Web Joist Floor
Framing Systems Using a Genetic Algorithm

by

Christopher Erwin, B.S.C.E.

A Thesis submitted to the Faculty of the Graduate School,
Marquette University, in Partial Fufullment of
the Requirements for the Degree of
Masters of Science

Milwaukee, Wisconsin
August 2004
i
Preface
Engineers consider straightforward calculations of capacity during the design process,
and then subject the design to serviceability checks. For a steel framed floor system,
these checks often include deflection and vibration. Floor systems have become lighter
due to advances in material science and construction methods. While these advances
help to reduce cost, they can result in structures that are susceptible to vibraiton problems
that may cause discomfort for the building’s occupants. The vibration response can be
determined through numerous calculations that are heavily dependent on the entire design
making design for vibration difficult.
This thesis proposes a methodology for designing optimized systems utilizing a
genetic algorithm (GA), which utilizes a search strategy that is modeled on the same
mechanisms found in genetic evolution. The GA operates with a selected population of
solutions. For each of these solutions, the capacity, cost and vibration response can be
determined and used to evaluate each system’s performance. Using a “survival of the
fittest” methodology, the GA combines components of the individual systems to create a
new generation (new population). This new population is evaluated, and the process
cycles again. Through repetition, the optimal solution will present itself.
Steel systems utilize a finite number of steel wide-flange sections, joists, decks
and concrete thicknesses. These discrete design options are perfectly suited to the genetic
algorithm. The GA has been used successfully in the past to obtain optimum or near
optimum solutions to many design problems. The successful record of the GA with steel
framed structures shows that the GA will be well suited to the problem of designing steel
floor framing systems.
ii
Acknowledgements
I would like to express my earnest appreciation to my thesis director, Dr. Christopher
Foley for his guidance and infinite patience. I count myself lucky to have a mentor who
never stops working, is always available, and is able to deal with my idiosyncrasies.
I would like to thank Professor Sriramulu Vinnakota for being on my thesis
committee, and teaching me the steel design procedures. The time spent in his steel
design classes have been put to good use.
I would also like to thank Professor Stephen M. Heinrich, as a member of my
thesis committee, as well as for making my final year at Marquette possible.
I would also like to thank Benjamin T. Shock, who through his work and
discussions presented new ways of looking at the algorithm and the processes, which
make the program work.
I would also like to thank the rest of the Department of Civil Engineering at
Marquette University. They are the reason I came to Marquette, and why I continued at
Marquette to complete my M.S. Degree.
Lastly, I’d like to thank my parents, who provided financial assistance and
unwavering support in my academic endeavors.
iii
Table of Contents
Chapter 1 – Introduction
Section 1.1 – Design Problem Statement 1
Section 1.2 – Introduction to the Genetic Algorithm 2
Section 1.3 – Components of the Genetic Algorithm 3
Section 1.4 – Genetic Algorithm vs. Other Optimization Procedures 5
Section 1.5 – Prior Uses of the Genetic Algorithm 6
Chapter 2 – Design Considerations for a Steel Floor System
Section 2.1 – Basic Components of Floor System 8
Section 2.2 – General Design Procedure 9
Section 2.3 – Evaluation of Serviceability Criteria 13
Chapter 3 – Formulation of the Optimization Problem
Section 3.1 – Development of Objective(s) and Constraints 25
Section 3.2 – Definition of Fitness for the Evolutionary Algorithm 29
Chapter 4 – Programming the Genetic Algorithm in MATLAB
Section 4.1 – Introduction 45
Section 4.2 – Essential Components o the Genetic Algorithm 45
Section 4.3 – Additional Components in the Genetic Algorithm 56
Chapter 5 – Design Examples & Analysis
Section 5.1 – Introduction 64
Section 5.2 – Problem Statement 64
Section 5.3 – Running the Evolutionary Algorithm 65
Section 5.4 – Joist Span Variation 69
Section 5.5 – Superimposed Loading Variation 75
Section 5.6 – Analysis of Results 78
Chapter 6 – Conclusion and Recommendation
Section 6.1 – Introduction 80
Section 6.2 – Improvements to the Algorithm 80
Section 6.3 – Future Research 81
Appendix A – Genetic Algorithm Code 84
Appendix B – Algorithm Design Results 122
Appendix C – Design Solution Checks 183
Reference 190
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List of Figures

Figure 1.1 – Design Problem 1
Figure 2.1 – Typical Floor System 8
Figure 2.2 – Typical Beam Model 12
Figure 2.3 – Shear/Moment Diagrams due to Uniform Load 12
Figure 2.4 – Deflection Cases 14
Figure 2.5 – Composite Joist Cross-Section 18
Figure 2.6 – Girder and Deck Cross-Section 21
Figure 2.7 – Recommended acceleration for human comfort for
vibrations due to human activity. (Allen 1997) 24
Figure 3.1 – Girder Model 33
Figure 3.2 – Composite Joist Cross-Section 38
Figure 3.3 – Girder Composite Cross-Section 41
Figure 4.1 – MATLAB Code for Chromosome Generation 48
Figure 4.2 – Chromosomes for Population of Ten Individuals Systems 48
Figure 4.3 – MATLAB Code for Chromosome Decoding 49
Figure 4.4 – MATLAB Code for Roulette Wheel Selection 52
Figure 4.5 – MATLAB Code for Mutation Implementation 58
Figure 4.6 – Population Plotted in Objective Space (Pre-Domination) 61
Figure 4.7 – Domination Code 62
Figure 4.8 – Population Graphed in Objective Space (Post-Domination). 63
Figure 5.1 – Typical Floor System 64
Figure 5.2 – User Input Section of Master.m File 65
Figure 5.3 – Algorithm Output to Screen 66
Figure 5.4 – Graph Illustrating Generational Variation in Fitness 67
Figure 5.5 – Fitness-Acceleration Plot at End of Evolutionary Algorithm 68
Figure 5.6 – Objective Space Plot at End of Evolutionary Algorithm 69
Figure 5.7 – Input for Algorithm Run 70
v
List of Tables

Table 2.1 – K-Series Joist Selection Table 10
Table 2.2 – Girder Loads to Joists 12
Table 3.1 – Beta and Threshold Values (Allen 1997) 44
Table 5.1 – Configuration 1 (L = 40 ft.) Least Expensive Systems 71
Table 5.2 – System Comparison 71
Table 5.3 – Configuration 2 (L = 30 ft.) Lease Expensive Systems 72
Table 5.4 – Pareto Set of Run 7 for Configuration 3 73
Table 5.5 – Configuration 3 (L = 50 ft.) Least Expensive Systems 74
Table 5.6 – Part of Pareto Set from Run 1 of Configuration 3 75
Table 5.7 – Configuration 4 (L = 30 ft.) Output of Pareto Set 76
Table 5.8 – Configuration 5 (L = 40 ft.) Output of Pareto Set 77
Table 5.9 – Configuration 6 (L = 50 ft.) Output of Pareto Set 78
Table 5.1 – Configuration 2 (L = 40 ft.) Least Expensive Systems 184
Table C.2.1 – Configuration 2 (L = 40 ft.) Least Expensive Systems 185
Table C.2.2 – Joist Checks 185
Table C.2.3 – Girder Information 185
Table C.2.4 – Applied Loads and Deflection 186
Table 5.7 – Configuration 3 (L = 50 ft.) Least Expensive Systems 186
Table C.3.1 – Configuration 3 (L=50) Concrete Decks 187
Table C.3.2 – Joist Checks 187
Table C.3.3 – Girder Information 187
Table C.3.4 – Applied Loads and Deflection 187
Table C.4.1 – Least Expensive Systems 188
Table C.4.2 – Concrete Deck Specifications 188
Table C.4.3 – Joist Checks 188
Table C.4.4 – Girder Information 189
Table C.4.5 – Applied Loads and Deflection 189
1
Chapter 1 – Introduction
1.1 Design Problem Statement
The setup for the design problem considered in this thesis is a standard steel joist floor
system shown in Figure 1.1. The bay is assumed to be an interior part of a larger
continuous system. This simplifies the design of the beams and girders, because both
will be assumed to be loaded symmetrically.

Inputs: Outputs:

W =Bay Width Girder Specification
L=Bay Length Joist Specification
s =Joist Spacing
SDL= Superimposed Dead
t =Concrete Topping
Load c
LL= Live Load t =Steel Deck Rib Height
r
LL =Vibration Live Load g =Steel Deck Gauge
v

Girder

L
Concrete

Deck
t
c
tr
g
s
K-Series Joist
W

Figure 1.1: Design Problem
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The design consists of four components: the girder, the joist, and the composite
steel deck specifications. The engineering design problem consists of objectives and
constraints. The objective is cost, which the designer is trying to minimize. The
constraints apply to each of the components, and provide the limits for the objectives.
The design problem can be stated as
Minimize: Floor Panel Cost
Subject To: Component Flexural Strength
Component Deflection Limits
Four independent components, which are evaluated as a whole, can serve to be an
imposing problem for any solution technique. However, this is definitely not impossible.
At Stanford, a program was created to design entire floor systems for a building. The
floor system for this building was a beam and girder system using wide flange sections
and composite concrete deck (Jain 1991). More recently, optimization algorithms have
provided a means to design an efficient concrete floor system (Lucas 2001). These
problems did not utilize joists in their designs, nor did they consider vibration
performance. This is the first known attempt to develop an algorithm to automatically
design an open web joist steel floor framing system.
1.2 Introduction to the Genetic Algorithm
A Genetic Algorithm (GA) is a general search and optimization methodology inspired by
the process of natural selection (Holland 1975). The algorithm is based on Darwin’s
theory of evolution, with the central concept being that one could start with a primordial
mess and end up with the incredibly diverse set of biological solutions seen today.
Generation by generation the more fit life forms survived while others perished and
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became extinct. This idea is applicable to any system with a defined fitness. Therefore,
the GA is a general method applicable to an extremely wide range of problems.
Continuing with the parallels to the natural world, each system is defined by a
genome. For the ease in implementation on the computer, the genome of the GA is a
series of 1’s and 0’s (Goldberg 1989; Haupt 1998). The assembly of these binary digits
(i.e. a chromosome) represents a solution to the design problem that the GA is attempting
to optimize. The basic operating components of the GA are an initial population
generator, a fitness calculator, selection/crossover methods, and a mutation operator.
These components, working on the genome, create a Darwinian system of the greatest
simplicity. Additional components may be added to assist the algorithm in efficiently
finding a solution (e.g. elitism). To use a genetic algorithm, the design problem must be
established as an unconstrained optimization problem. This is discussed in Chapter 3.
1.3 Components of the Genetic Algorithm
The population generator creates an initial population for evaluation. This process at its
simplest can be as basic as a random number generator creating 1’s and 0’s (Coley 1999).
This would most accurately use the idea of the primordial mess. However, more complex
methods of population creation can be utilized. Some complex design problems require
populations, which are suitable for satisfying fitness. Therefore, when they generate
their initial populations, the process is not random, but calculated.
Fitness can be any method of system evaluation. In other words, it is a
mechanism by which the “quality” of one solution can be weighed against another
solution in satisfying the design objective(s). Suppose a GA was set up to automatically
design a simply supported beam. Fitness could be assigned using deflection, weight, or
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cost. The fitness could also be defined as a weighted function of some or all of these
former items. The method used to carry out fitness calculation is flexible. However,
these aspects that are used in defining fitness when using a GA need to be considered
carefully.
Once fitness is defined and evaluated, the next items to consider become selection
and crossover. This is the equivalent of mating and reproduction. There are many
methods of selection, all based on fitness, ranging from roulette wheel selection to
tournament selection to rank-based selection. These methods provide various ways for
individuals to be selected with the preference for selection going to the fitter individuals
with or without excluding the un-fit. Once two parents are chosen, an offspring will be
created using the genetic data from the parents. This can be accomplished through single
point, multiple point (Coley 1999), or component crossover. Each takes a portion of each
parent’s genome and combines it to create an offspring that is unique from the parents.
This process of selection/mating is repeated until a new population is created for fitness
evaluation.
After an initial population is generated, the cycle of fitness evaluation, selection,
and mating continues for many generations until only the fittest individuals inhabit the
population. Mutation components simulate the random changes found in nature. Others,
like elitism, ensure that each generation is no worse than the previous. Fitness scaling
provides a method of preventing a single individual from dominating a population. With
these additions, the GA can be adjusted and refined to create a set of optimized solutions.