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<!DOCTYPE html>
<html>
<head>
<link rel="stylesheet" type="text/css" href="GlassBR_SRS.css">
<title>Software Requirements Specification for GlassBR</title>
<meta charset="utf-8">
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<body>
<div class="title">
<h1>Software Requirements Specification for GlassBR</h1>
</div>
<div class="author">
<h2>Nikitha Krithnan and W. Spencer Smith</h2>
</div>
<div id="Sec:ToC">
<div class="section">
<h1>Table of Contents</h1>
<p class="paragraph">
An outline of all sections included in this SRS is recorded here for easy reference.
</p>
<ul class="list">
<li><a href=#Sec:ToC>Table of Contents</a></li>
<li>
<a href=#Sec:RefMat>Reference Material</a>
<ul class="list">
<li><a href=#Sec:ToU>Table of Units</a></li>
<li><a href=#Sec:ToS>Table of Symbols</a></li>
<li><a href=#Sec:TAbbAcc>Abbreviations and Acronyms</a></li>
</ul>
</li>
<li>
<a href=#Sec:Intro>Introduction</a>
<ul class="list">
<li><a href=#Sec:DocPurpose>Purpose of Document</a></li>
<li><a href=#Sec:ReqsScope>Scope of Requirements</a></li>
<li>
<a href=#Sec:ReaderChars>Characteristics of Intended Reader</a>
</li>
<li><a href=#Sec:DocOrg>Organization of Document</a></li>
</ul>
</li>
<li>
<a href=#Sec:Stakeholder>Stakeholders</a>
<ul class="list">
<li><a href=#Sec:Customer>The Customer</a></li>
<li><a href=#Sec:Client>The Client</a></li>
</ul>
</li>
<li>
<a href=#Sec:GenSysDesc>General System Description</a>
<ul class="list">
<li><a href=#Sec:SysContext>System Context</a></li>
<li><a href=#Sec:UserChars>User Characteristics</a></li>
<li><a href=#Sec:SysConstraints>System Constraints</a></li>
</ul>
</li>
<li>
<a href=#Sec:SpecSystDesc>Specific System Description</a>
<ul class="list">
<li>
<a href=#Sec:ProbDesc>Problem Description</a>
<ul class="list">
<li><a href=#Sec:PhysSyst>Physical System Description</a></li>
<li><a href=#Sec:GoalStmt>Goal Statements</a></li>
</ul>
</li>
<li>
<a href=#Sec:SolCharSpec>Solution Characteristics Specification</a>
<ul class="list">
<li><a href=#Sec:Assumps>Assumptions</a></li>
<li><a href=#Sec:TMs>Theoretical Models</a></li>
<li><a href=#Sec:GDs>General Definitions</a></li>
<li><a href=#Sec:DDs>Data Definitions</a></li>
<li><a href=#Sec:IMs>Instance Models</a></li>
<li><a href=#Sec:DataConstraints>Data Constraints</a></li>
<li>
<a href=#Sec:CorSolProps>Properties of a Correct Solution</a>
</li>
</ul>
</li>
</ul>
</li>
<li>
<a href=#Sec:Requirements>Requirements</a>
<ul class="list">
<li><a href=#Sec:FRs>Functional Requirements</a></li>
<li><a href=#Sec:NFRs>Non-Functional Requirements</a></li>
</ul>
</li>
<li><a href=#Sec:LCs>Likely Changes</a></li>
<li><a href=#Sec:UCs>Unlikely Changes</a></li>
<li>
<a href=#Sec:TraceMatrices>Traceability Matrices and Graphs</a>
</li>
<li>
<a href=#Sec:AuxConstants>Values of Auxiliary Constants</a>
</li>
<li><a href=#Sec:References>References</a></li>
<li><a href=#Sec:Appendix>Appendix</a></li>
</ul>
</div>
</div>
<div id="Sec:RefMat">
<div class="section">
<h1>Reference Material</h1>
<p class="paragraph">
This section records information for easy reference.
</p>
<div id="Sec:ToU">
<div class="subsection">
<h2>Table of Units</h2>
<p class="paragraph">
The unit system used throughout is SI (Système International d'Unités). In addition to the basic units, several derived units are also used. For each unit, the <a href=#Table:ToU>Table of Units</a> lists the symbol, a description and the SI name.
</p>
<div id="Table:ToU">
<table class="table">
<tr>
<th>Symbol</th>
<th>Description</th>
<th>SI Name</th>
</tr>
<tr>
<td><em>kg</em></td>
<td>mass</td>
<td>kilogram</td>
</tr>
<tr>
<td><em>m</em></td>
<td>length</td>
<td>metre</td>
</tr>
<tr>
<td><em>N</em></td>
<td>force</td>
<td>newton</td>
</tr>
<tr>
<td><em>Pa</em></td>
<td>pressure</td>
<td>pascal</td>
</tr>
<tr>
<td><em>s</em></td>
<td>time</td>
<td>second</td>
</tr>
</table>
<p class="caption">Table of Units</p>
</div>
</div>
</div>
<div id="Sec:ToS">
<div class="subsection">
<h2>Table of Symbols</h2>
<p class="paragraph">
The symbols used in this document are summarized in the <a href=#Table:ToS>Table of Symbols</a> along with their units. The symbols are listed in alphabetical order.
</p>
<div id="Table:ToS">
<table class="table">
<tr>
<th>Symbol</th>
<th>Description</th>
<th>Units</th>
</tr>
<tr>
<td><em>a</em></td>
<td>Plate length (long dimension)</td>
<td><em>m</em></td>
</tr>
<tr>
<td><em>AR</em></td>
<td>Aspect ratio</td>
<td>--</td>
</tr>
<tr>
<td><em>AR<sub>max</sub></em></td>
<td>Maximum aspect ratio</td>
<td>--</td>
</tr>
<tr>
<td><em>B</em></td>
<td>Risk of failure</td>
<td>--</td>
</tr>
<tr>
<td><em>b</em></td>
<td>Plate width (short dimension)</td>
<td><em>m</em></td>
</tr>
<tr>
<td><em>capacity</em></td>
<td>Capacity or load resistance</td>
<td><em>Pa</em></td>
</tr>
<tr>
<td><em>d<sub>max</sub></em></td>
<td>Maximum value for one of the dimensions of the glass plate</td>
<td><em>m</em></td>
</tr>
<tr>
<td><em>d<sub>min</sub></em></td>
<td>Minimum value for one of the dimensions of the glass plate</td>
<td><em>m</em></td>
</tr>
<tr>
<td><em>E</em></td>
<td>Modulus of elasticity of glass</td>
<td><em>Pa</em></td>
</tr>
<tr>
<td><em>g</em></td>
<td>Glass type</td>
<td>--</td>
</tr>
<tr>
<td><em>GTF</em></td>
<td>Glass type factor</td>
<td>--</td>
</tr>
<tr>
<td><em>h</em></td>
<td>Minimum thickness</td>
<td><em>m</em></td>
</tr>
<tr>
<td><em>interpY</em></td>
<td>InterpY</td>
<td>--</td>
</tr>
<tr>
<td><em>interpZ</em></td>
<td>InterpZ</td>
<td>--</td>
</tr>
<tr>
<td><em>isSafeLoad</em></td>
<td>Load resistance safety requirement</td>
<td>--</td>
</tr>
<tr>
<td><em>isSafeLR</em></td>
<td>3 second load equivalent resistance safety requirement</td>
<td>--</td>
</tr>
<tr>
<td><em>isSafePb</em></td>
<td>Probability of glass breakage safety requirement</td>
<td>--</td>
</tr>
<tr>
<td><em>isSafeProb</em></td>
<td>Probability of failure safety requirement</td>
<td>--</td>
</tr>
<tr>
<td><em>J</em></td>
<td>Stress distribution factor (Function)</td>
<td>--</td>
</tr>
<tr>
<td><em>J<sub>max</sub></em></td>
<td>Maximum value for the stress distribution factor</td>
<td>--</td>
</tr>
<tr>
<td><em>J<sub>min</sub></em></td>
<td>Minimum value for the stress distribution factor</td>
<td>--</td>
</tr>
<tr>
<td><em>J<sub>tol</sub></em></td>
<td>Stress distribution factor (Function) based on Pbtol</td>
<td>--</td>
</tr>
<tr>
<td><em>k</em></td>
<td>Surface flaw parameter</td>
<td><em>\(\frac{\text{m}^{12}}{\text{N}^{7}}\)</em></td>
</tr>
<tr>
<td><em>LDF</em></td>
<td>Load duration factor</td>
<td>--</td>
</tr>
<tr>
<td><em>Load</em></td>
<td>Applied load (demand) or pressure</td>
<td><em>Pa</em></td>
</tr>
<tr>
<td><em>LR</em></td>
<td>Load resistance</td>
<td><em>Pa</em></td>
</tr>
<tr>
<td><em>LSF</em></td>
<td>Load share factor</td>
<td>--</td>
</tr>
<tr>
<td><em>m</em></td>
<td>Surface flaw parameter</td>
<td><em>\(\frac{\text{m}^{12}}{\text{N}^{7}}\)</em></td>
</tr>
<tr>
<td><em>NFL</em></td>
<td>Non-factored load</td>
<td><em>Pa</em></td>
</tr>
<tr>
<td><em>P<sub>b</sub></em></td>
<td>Probability of breakage</td>
<td>--</td>
</tr>
<tr>
<td><em>P<sub>btol</sub></em></td>
<td>Tolerable probability of breakage</td>
<td>--</td>
</tr>
<tr>
<td><em>P<sub>f</sub></em></td>
<td>Probability of failure</td>
<td>--</td>
</tr>
<tr>
<td><em>P<sub>ftol</sub></em></td>
<td>Tolerable probability of failure</td>
<td>--</td>
</tr>
<tr>
<td><em>q</em></td>
<td>Applied load (demand)</td>
<td><em>Pa</em></td>
</tr>
<tr>
<td><em>q̂</em></td>
<td>Dimensionless load</td>
<td>--</td>
</tr>
<tr>
<td><em>q̂<sub>tol</sub></em></td>
<td>Tolerable load</td>
<td>--</td>
</tr>
<tr>
<td><em>SD</em></td>
<td>Stand off distance</td>
<td><em>m</em></td>
</tr>
<tr>
<td><em>SD<sub>max</sub></em></td>
<td>Maximum stand off distance permissible for input</td>
<td><em>m</em></td>
</tr>
<tr>
<td><em>SD<sub>min</sub></em></td>
<td>Minimum stand off distance permissible for input</td>
<td><em>m</em></td>
</tr>
<tr>
<td><em>SD<sub>x</sub></em></td>
<td>Stand off distance (<em>x</em>-component)</td>
<td><em>m</em></td>
</tr>
<tr>
<td><em>SD<sub>y</sub></em></td>
<td>Stand off distance (<em>y</em>-component)</td>
<td><em>m</em></td>
</tr>
<tr>
<td><em>SD<sub>z</sub></em></td>
<td>Stand off distance (<em>z</em>-component)</td>
<td><em>m</em></td>
</tr>
<tr>
<td><em>t</em></td>
<td>
Nominal thickness <em>t ∈ {2.5,2.7,3.0,4.0,5.0,6.0,8.0,10.0,12.0,16.0,19.0,22.0}</em>
</td>
<td><em>mm</em></td>
</tr>
<tr>
<td><em>t<sub>d</sub></em></td>
<td>Duration of load</td>
<td><em>s</em></td>
</tr>
<tr>
<td><em>TNT</em></td>
<td>TNT equivalent factor</td>
<td>--</td>
</tr>
<tr>
<td><em>w</em></td>
<td>Charge weight</td>
<td><em>kg</em></td>
</tr>
<tr>
<td><em>w<sub>max</sub></em></td>
<td>Maximum permissible input charge weight</td>
<td><em>kg</em></td>
</tr>
<tr>
<td><em>w<sub>min</sub></em></td>
<td>Minimum permissible input charge weight</td>
<td><em>kg</em></td>
</tr>
<tr>
<td><em>w<sub>TNT</sub></em></td>
<td>Equivalent TNT charge mass</td>
<td><em>kg</em></td>
</tr>
</table>
<p class="caption">Table of Symbols</p>
</div>
</div>
</div>
<div id="Sec:TAbbAcc">
<div class="subsection">
<h2>Abbreviations and Acronyms</h2>
<div id="Table:TAbbAcc">
<table class="table">
<tr>
<th>Abbreviation</th>
<th>Full Form</th>
</tr>
<tr>
<td>A</td>
<td>Assumption</td>
</tr>
<tr>
<td>AN</td>
<td>Annealed</td>
</tr>
<tr>
<td>AR</td>
<td>Aspect Ratio</td>
</tr>
<tr>
<td>DD</td>
<td>Data Definition</td>
</tr>
<tr>
<td>FT</td>
<td>Fully Tempered</td>
</tr>
<tr>
<td>GS</td>
<td>Goal Statement</td>
</tr>
<tr>
<td>GTF</td>
<td>Glass Type Factor</td>
</tr>
<tr>
<td>HS</td>
<td>Heat Strengthened</td>
</tr>
<tr>
<td>IG</td>
<td>Insulating Glass</td>
</tr>
<tr>
<td>IM</td>
<td>Instance Model</td>
</tr>
<tr>
<td>LC</td>
<td>Likely Change</td>
</tr>
<tr>
<td>LDF</td>
<td>Load Duration Factor</td>
</tr>
<tr>
<td>LG</td>
<td>Laminated Glass</td>
</tr>
<tr>
<td>LR</td>
<td>Load Resistance</td>
</tr>
<tr>
<td>LSF</td>
<td>Load Share Factor</td>
</tr>
<tr>
<td>N/A</td>
<td>Not Applicable</td>
</tr>
<tr>
<td>NFL</td>
<td>Non-Factored Load</td>
</tr>
<tr>
<td>PS</td>
<td>Physical System Description</td>
</tr>
<tr>
<td>R</td>
<td>Requirement</td>
</tr>
<tr>
<td>SD</td>
<td>Stand Off Distance</td>
</tr>
<tr>
<td>SRS</td>
<td>Software Requirements Specification</td>
</tr>
<tr>
<td>TM</td>
<td>Theoretical Model</td>
</tr>
<tr>
<td>UC</td>
<td>Unlikely Change</td>
</tr>
<tr>
<td>Uncert.</td>
<td>Typical Uncertainty</td>
</tr>
</table>
<p class="caption">Abbreviations and Acronyms</p>
</div>
</div>
</div>
</div>
</div>
<div id="Sec:Intro">
<div class="section">
<h1>Introduction</h1>
<p class="paragraph">
Software is helpful to efficiently and correctly predict the blast risk involved with the glass slab. The blast under consideration is any kind of man-made explosion. The software, herein called GlassBR, aims to predict the blast risk involved with the glass slab using an intuitive interface.
</p>
<p class="paragraph">
The following section provides an overview of the Software Requirements Specification (SRS) for GlassBR. This section explains the purpose of this document, the scope of the requirements, the characteristics of the intended reader, and the organization of the document.
</p>
<div id="Sec:DocPurpose">
<div class="subsection">
<h2>Purpose of Document</h2>
<p class="paragraph">
The primary purpose of this document is to record the requirements of the GlassBR. Goals, assumptions, theoretical models, definitions, and other model derivation information are specified, allowing the reader to fully understand and verify the purpose and scientific basis of GlassBR. With the exception of <a href=#Sec:SysConstraints>system constraints</a>, this SRS will remain abstract, describing what problem is being solved, but not how to solve it.
</p>
<p class="paragraph">
This document will be used as a starting point for subsequent development phases, including writing the design specification and the software verification and validation plan. The design document will show how the requirements are to be realized, including decisions on the numerical algorithms and programming environment. The verification and validation plan will show the steps that will be used to increase confidence in the software documentation and the implementation. Although the SRS fits in a series of documents that follow the so-called waterfall model, the actual development process is not constrained in any way. Even when the waterfall model is not followed, as Parnas and Clements point out <a href=#parnasClements1986>parnasClements1986</a>, the most logical way to present the documentation is still to "fake" a rational design process.
</p>
</div>
</div>
<div id="Sec:ReqsScope">
<div class="subsection">
<h2>Scope of Requirements</h2>
<p class="paragraph">
The scope of the requirements includes determining the safety of a glass slab under a blast loading following the ASTM standard (<a href=#astm2009>astm2009</a>).
</p>
</div>
</div>
<div id="Sec:ReaderChars">
<div class="subsection">
<h2>Characteristics of Intended Reader</h2>
<p class="paragraph">
Reviewers of this documentation should have an understanding of second year calculus, structural mechanics, glass breakage, blast risk, computer applications in civil engineering, and applicable standards for constructions using glass from <a href=#astm2009>astm2009</a>, <a href=#astm2012>astm2012</a>, and <a href=#astm2016>astm2016</a> in <a href=#Sec:References>references</a>. The users of GlassBR can have a lower level of expertise, as explained in <a href=#Sec:UserChars>Sec:User Characteristics</a>.
</p>
</div>
</div>
<div id="Sec:DocOrg">
<div class="subsection">
<h2>Organization of Document</h2>
<p class="paragraph">
The organization of this document follows the template for an SRS for scientific computing software proposed by <a href=#koothoor2013>koothoor2013</a> and <a href=#smithLai2005>smithLai2005</a>, with some aspects taken from Volere template 16 <a href=#rbrtsn2012>rbrtsn2012</a>. The presentation follows the standard pattern of presenting goals, theories, definitions, and assumptions. For readers that would like a more bottom up approach, they can start reading the <a href=#Sec:IMs>data definitions</a> and trace back to find any additional information they require.
</p>
<p class="paragraph">
The <a href=#Sec:GoalStmt>goal statements</a> are refined to the theoretical models and the <a href=#Sec:TMs>theoretical models</a> to the <a href=#Sec:IMs>instance models</a>. The data definitions are used to support the definitions of the different models.
</p>
</div>
</div>
</div>
</div>
<div id="Sec:Stakeholder">
<div class="section">
<h1>Stakeholders</h1>
<p class="paragraph">
This section describes the stakeholders: the people who have an interest in the product.
</p>
<div id="Sec:Client">
<div class="subsection">
<h2>The Client</h2>
<p class="paragraph">
The client for GlassBR is a company named Entuitive. It is developed by Dr. Manuel Campidelli. The client has the final say on acceptance of the product.
</p>
</div>
</div>
<div id="Sec:Customer">
<div class="subsection">
<h2>The Customer</h2>
<p class="paragraph">The customers are the end user of GlassBR.</p>
</div>
</div>
</div>
</div>
<div id="Sec:GenSysDesc">
<div class="section">
<h1>General System Description</h1>
<p class="paragraph">
This section provides general information about the system. It identifies the interfaces between the system and its environment, describes the user characteristics, and lists the system constraints.
</p>
<div id="Sec:SysContext">
<div class="subsection">
<h2>System Context</h2>
<p class="paragraph">
<a href=#Figure:sysCtxDiag>Fig:sysCtxDiag</a> shows the system context. A circle represents an external entity outside the software, the user in this case. A rectangle represents the software system itself (GlassBR). Arrows are used to show the data flow between the system and its environment.
</p>
<div id="Figure:sysCtxDiag">
<figure>
<img src="../../../../datafiles/glassbr/SystemContextFigure.png" alt="System Context" >
<figcaption>System Context</figcaption>
</figure>
</div>
<p class="paragraph">
The interaction between the product and the user is through a user interface. The responsibilities of the user and the system are as follows:
</p>
<ul class="list">
<li>
User Responsibilities
<ul class="list">
<li>
Provide the input data related to the glass slab and blast type, ensuring no errors in the data entry.
</li>
<li>Ensure that consistent units are used for input variables.</li>
<li>
Ensure required <a href=#Sec:Assumps>software assumptions</a> are appropriate for any particular problem input to the software.
</li>
</ul>
</li>
<li>
GlassBR Responsibilities
<ul class="list">
<li>
Detect data type mismatch, such as a string of characters input instead of a floating point number.
</li>
<li>
Determine if the inputs satisfy the required physical and software constraints.
</li>
<li>Predict whether the glass slab is safe or not.</li>
</ul>
</li>
</ul>
</div>
</div>
<div id="Sec:UserChars">
<div class="subsection">
<h2>User Characteristics</h2>
<ul class="list">
<li>
The end user of GlassBR is expected to have completed at least the equivalent of the second year of an undergraduate degree in civil engineering or structural engineering.
</li>
<li>
The end user is expected to have an understanding of theory behind glass breakage and blast risk.
</li>
<li>
The end user is expected to have basic computer literacy to handle the software.
</li>
</ul>
</div>
</div>
<div id="Sec:SysConstraints">
<div class="subsection">
<h2>System Constraints</h2>
<p class="paragraph">There are no system constraints.</p>
</div>
</div>
</div>
</div>
<div id="Sec:SpecSystDesc">
<div class="section">
<h1>Specific System Description</h1>
<p class="paragraph">
This section first presents the problem description, which gives a high-level view of the problem to be solved. This is followed by the solution characteristics specification, which presents the assumptions, theories, and definitions that are used.
</p>
<div id="Sec:ProbDesc">
<div class="subsection">
<h2>Problem Description</h2>
<p class="paragraph">
A system is needed to efficiently and correctly predict whether a glass slab can withstand a blast under given conditions.
</p>
<div id="Sec:TermDefs">
<div class="subsubsection">
<h3>Terminology and Definitions</h3>
<p class="paragraph">
This subsection provides a list of terms that are used in the subsequent sections and their meaning, with the purpose of reducing ambiguity and making it easier to correctly understand the requirements. All of the terms are extracted from <a href=#astm2009>astm2009</a>.
</p>
<ol class="list">
<li>
Glass breakage - The fracture or breakage of any lite or ply in monolithic, laminated, or insulating glass.
</li>
<li>Lateral - Perpendicular to the glass surface.</li>
<li>
Lite - Pieces of glass that are cut, prepared, and used to create the window or door.
</li>
<li>
Specifying authority - The design professional responsible for interpreting applicable regulations of authorities having jurisdiction and considering appropriate site specific factors to determine the appropriate values used to calculate the specified design load, and furnishing other information required to perform this practice.
</li>
<li>
Blast resistant glazing - Glazing that provides protection against air blast pressure generated by explosions.
</li>
<li>
Equivalent TNT charge mass - Mass of TNT placed on the ground in a hemisphere that represents the design explosive threat.
</li>
<li>
Glass Type:
<ul class="list">
<li>
Annealed (AN) - A flat, monolithic, glass lite which has uniform thickness where the residual surface stresses are almost zero, as defined in <a href=#astm2016>astm2016</a>.
</li>
<li>
Fully tempered (FT) - A flat, monolithic, glass lite of uniform thickness that has been subjected to a special heat treatment process where the residual surface compression is not less than 69 MPa (10 000 psi) or the edge compression not less than 67 MPa (9700 psi), as defined in <a href=#astm2012>astm2012</a>.
</li>
<li>
Heat strengthened (HS) - A flat, monolithic, glass lite of uniform thickness that has been subjected to a special heat treatment process where the residual surface compression is not less than 24 MPa (3500psi) or greater than 52 MPa (7500 psi), as defined in <a href=#astm2012>astm2012</a>.
</li>
</ul>
</li>
<li>
Applied load (demand) or pressure - A uniformly distributed lateral pressure.
<ul class="list">
<li>
Load resistance (LR) - The uniform lateral load that a glass construction can sustain based upon a given probability of breakage and load duration as defined in <a href=#astm2009>astm2009</a> (pp. 1 and 53).
</li>
<li>
Non-factored load (NFL) - Three second duration uniform load associated with a probability of breakage less than or equal to 8 lites per 1000 for monolithic AN glass.
</li>
<li>
Glass weight load - The dead load component of the glass weight.
</li>
<li>Short duration load - Any load lasting 3 seconds or less.</li>
<li>
Specified design load - The magnitude in Pa (psf), type (for example, wind or snow) and duration of the load given by the specifying authority.
</li>
<li>
Long duration load - Any load lasting approximately 30 days.
</li>
</ul>
</li>
<li>
Stand off distance (SD) - The distance from the glazing surface to the centroid of a hemispherical high explosive charge. It is represented by the coordinates (<em>SD<sub>x</sub></em>, <em>SD<sub>y</sub></em>, <em>SD<sub>z</sub></em>).
</li>
<li>
Load share factor (LSF) - A multiplying factor derived from the load sharing between the double glazing, of equal or different thicknesses and types (including the layered behaviour of LG under long duration loads), in a sealed IG unit.
</li>
<li>
Glass type factor (GTF) - A multiplying factor for adjusting the LR of different glass type, that is, AN, FT, or HS, in monolithic glass, LG (Laminated Glass), or IG (Insulating Glass) constructions.
</li>
<li>
Aspect ratio (AR) - The ratio of the long dimension of the glass to the short dimension of the glass. For glass supported on four sides, the aspect ratio is always equal to or greater than 1.0. For glass supported on three sides, the ratio of the length of one of the supported edges perpendicular to the free edge, to the length of the free edge, is equal to or greater than 0.5.
</li>
<li>
Probability of breakage (<em>P<sub>b</sub></em>) - The fraction of glass lites or plies that would break at the first occurrence of a specified load and duration, typically expressed in lites per 1000 (<a href=#astm2016>astm2016</a>).
</li>
</ol>
</div>
</div>
<div id="Sec:PhysSyst">
<div class="subsubsection">
<h3>Physical System Description</h3>
<p class="paragraph">
The physical system of GlassBR, as shown in <a href=#Figure:physSystImage>Fig:physSystImage</a>, includes the following elements:
</p>
<div class="list">
<p>PS1: The glass slab.</p>
<p>
PS2: The point of explosion. Where the bomb, or any kind of man-made explosion, is located. The stand off distance is the distance between the point of explosion and the glass.
</p>
</div>
<div id="Figure:physSystImage">
<figure>
<img src="../../../../datafiles/glassbr/physicalsystimage.png" alt="The physical system" width="30.0%" >
<figcaption>The physical system</figcaption>
</figure>
</div>
</div>
</div>
<div id="Sec:GoalStmt">
<div class="subsubsection">
<h3>Goal Statements</h3>
<p class="paragraph">
Given the dimensions of the glass plane, the glass type, the characteristics of the explosion, and the tolerable probability of breakage, the goal statements are:
</p>
<div class="list">
<p>
<div id="willBreakGS">
Predict-Glass-Withstands-Explosion: Analyze and predict whether the glass slab under consideration will be able to withstand the explosion of a certain degree which is calculated based on user input.
</div>
</p>
</div>
</div>
</div>
</div>
</div>
<div id="Sec:SolCharSpec">
<div class="subsection">
<h2>Solution Characteristics Specification</h2>
<p class="paragraph">
The instance models that govern GlassBR are presented in the <a href=#Sec:IMs>Instance Model Section</a>. The information to understand the meaning of the instance models and their derivation is also presented, so that the instance models can be verified.
</p>
<div id="Sec:Assumps">
<div class="subsubsection">
<h3>Assumptions</h3>
<p class="paragraph">
This section simplifies the original problem and helps in developing the theoretical models by filling in the missing information for the physical system. The assumptions refine the scope by providing more detail.
</p>
<div class="list">
<p>
<div id="assumpGT">
glassType: The standard E1300-09a for calculation applies only to monolithic, laminated, or insulating glass constructions of rectangular shape with continuous lateral support along one, two, three, or four edges. This practice assumes that: (1) the supported glass edges for two, three and four-sided support conditions are simply supported and free to slip in plane; (2) glass supported on two sides acts as a simply supported beam; and (3) glass supported on one side acts as a cantilever.
</div>
</p>
<p>
<div id="assumpGC">
glassCondition: Following <a href=#astm2009>astm2009</a> (pg. 1), this practice does not apply to any form of wired, patterned, etched, sandblasted, drilled, notched, or grooved glass with surface and edge treatments that alter the glass strength. (RefBy: <a href=#accAlteredGlass>UC:Accommodate-Altered-Glass</a>.)
</div>
</p>
<p>
<div id="assumpES">
explainScenario: This system only considers the external explosion scenario for its calculations. (RefBy: <a href=#calcInternalBlastRisk>LC:Calculate-Internal-Blask-Risk</a>.)
</div>
</p>
<p>
<div id="assumpSV">
standardValues: The values provided in <a href=#Sec:AuxConstants>Sec:Values of Auxiliary Constants</a> are assumed for the duration of load (<em>t<sub>d</sub></em>), and the material properties of <em>m</em>, <em>k</em>, and <em>E</em>. (RefBy: <a href=#varValsOfmkE>LC:Variable-Values-of-m,k,E</a>, <a href=#DD:sdfTol>DD:sdfTol</a>, <a href=#DD:nFL>DD:nFL</a>, <a href=#DD:loadDurFactor>DD:loadDurFactor</a>, <a href=#DD:dimlessLoad>DD:dimlessLoad</a>, and <a href=#assumpLDFC>A:ldfConstant</a>.)
</div>
</p>
<p>
<div id="assumpGL">
glassLite: Glass under consideration is assumed to be a single lite; hence, the value of LSF is equal to 1 for all calculations in GlassBR. (RefBy: <a href=#accMoreThanSingleLite>LC:Accomodate-More-than-Single-Lite</a>.)
</div>
</p>
<p>
<div id="assumpBC">
boundaryConditions: Boundary conditions for the glass slab are assumed to be 4-sided support for calculations. (RefBy: <a href=#accMoreBoundaryConditions>LC:Accomodate-More-Boundary-Conditions</a>.)
</div>
</p>
<p>
<div id="assumpRT">
responseType: The response type considered in GlassBR is flexural. (RefBy: <a href=#considerMoreThanFlexGlass>LC:Consider-More-than-Flexure-Glass</a>.)
</div>
</p>
<p>
<div id="assumpLDFC">
ldfConstant: With reference to <a href=#assumpSV>A:standardValues</a>, the value of load duration factor (<em>LDF</em>) is a constant in GlassBR. (RefBy: <a href=#varValsOfmkE>LC:Variable-Values-of-m,k,E</a> and <a href=#DD:loadDurFactor>DD:loadDurFactor</a>.)
</div>
</p>
</div>
</div>
</div>
<div id="Sec:TMs">
<div class="subsubsection">
<h3>Theoretical Models</h3>
<p class="paragraph">
This section focuses on the general equations and laws that GlassBR is based on.
</p>
<div id="TM:isSafeProb">
<table class="tdefn">
<tr>
<th>Refname</th>
<td><b>TM:isSafeProb</b></td>
</tr>
<tr>
<th>Label</th>
<td><p class="paragraph">Safety Probability</p></td>
</tr>
<tr>
<th>Equation</th>
<td>
\[\mathit{isSafeProb}={P_{\text{f}}}\lt{}{P_{\text{f}\text{tol}}}\]
</td>
</tr>
<tr>
<th>Description</th>
<td>
<ul class="hide-list-style-no-indent">
<li>
<em>isSafeProb</em> is the probability of failure safety requirement (Unitless)
</li>
<li>
<em>P<sub>f</sub></em> is the probability of failure (Unitless)
</li>
<li>
<em>P<sub>ftol</sub></em> is the tolerable probability of failure (Unitless)
</li>
</ul>
</td>
</tr>
<tr>
<th>Notes</th>
<td>
<p class="paragraph">
If <em>isSafeProb</em>, the structure is considered safe.
</p>
</td>
</tr>
<tr>
<th>Source</th>
<td><p class="paragraph"><a href=#astm2009>astm2009</a></p></td>
</tr>
<tr>
<th>RefBy</th>
<td>
<p class="paragraph">
<a href=#checkGlassSafety>FR:Check-Glass-Safety</a>
</p>
</td>
</tr>
</table>
</div>
<div id="TM:isSafeLoad">
<table class="tdefn">
<tr>
<th>Refname</th>
<td><b>TM:isSafeLoad</b></td>
</tr>
<tr>
<th>Label</th>
<td><p class="paragraph">Safety Load</p></td>
</tr>
<tr>
<th>Equation</th>
<td>
\[\mathit{isSafeLoad}=\mathit{capacity}\gt{}\mathit{Load}\]
</td>
</tr>
<tr>
<th>Description</th>
<td>
<ul class="hide-list-style-no-indent">
<li>
<em>isSafeLoad</em> is the load resistance safety requirement (Unitless)
</li>
<li>
<em>capacity</em> is the capacity or load resistance (<em>Pa</em>)
</li>
<li>
<em>Load</em> is the applied load (demand) or pressure (<em>Pa</em>)
</li>
</ul>
</td>
</tr>
<tr>
<th>Notes</th>
<td>
<p class="paragraph">
If <em>isSafeLoad</em>, the structure is considered safe.
</p>
</td>
</tr>
<tr>
<th>Source</th>
<td><p class="paragraph"><a href=#astm2009>astm2009</a></p></td>
</tr>
<tr>
<th>RefBy</th>
<td>
<p class="paragraph">
<a href=#checkGlassSafety>FR:Check-Glass-Safety</a>
</p>
</td>
</tr>
</table>
</div>
</div>
</div>
<div id="Sec:GDs">
<div class="subsubsection">
<h3>General Definitions</h3>
<p class="paragraph">There are no general definitions.</p>
</div>
</div>
<div id="Sec:DDs">
<div class="subsubsection">
<h3>Data Definitions</h3>
<p class="paragraph">
This section collects and defines all the data needed to build the instance models.
</p>
<div id="DD:riskFun">
<table class="ddefn">
<tr>
<th>Refname</th>
<td><b>DD:riskFun</b></td>