Software Requirements Specification for GlassBR

Nikitha Krithnan and W. Spencer Smith

Table of Contents

An outline of all sections included in this SRS is recorded here for easy reference.

Reference Material

This section records information for easy reference.

Table of Units

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 Table of Units lists the symbol, a description, and the SI name.

Symbol Description SI Name
kg mass kilogram
m length metre
N force newton
Pa pressure pascal
s time second

Table of Units

Table of Symbols

The symbols used in this document are summarized in the Table of Symbols along with their units. The symbols are listed in alphabetical order.

Symbol Description Units
a Plate length (long dimension) m
AR Aspect ratio --
ARmax Maximum aspect ratio --
B Risk of failure --
b Plate width (short dimension) m
capacity Capacity or load resistance Pa
dmax Maximum value for one of the dimensions of the glass plate m
dmin Minimum value for one of the dimensions of the glass plate m
E Modulus of elasticity of glass Pa
g Glass type --
GTF Glass type factor --
h Minimum thickness m
interpY InterpY --
interpZ InterpZ --
isSafeLoad Load resistance safety requirement --
isSafeLR 3 second load equivalent resistance safety requirement --
isSafePb Probability of glass breakage safety requirement --
isSafeProb Probability of failure safety requirement --
J Stress distribution factor (Function) --
Jmax Maximum value for the stress distribution factor --
Jmin Minimum value for the stress distribution factor --
Jtol Tolerable stress distribution factor --
k Surface flaw parameter \(\frac{\text{m}^{12}}{\text{N}^{7}}\)
LDF Load duration factor --
Load Applied load (demand) or pressure Pa
LR Load resistance Pa
LSF Load share factor --
m Surface flaw parameter \(\frac{\text{m}^{12}}{\text{N}^{7}}\)
NFL Non-factored load Pa
Pb Probability of breakage --
Pbtol Tolerable probability of breakage --
Pf Probability of failure --
Pftol Tolerable probability of failure --
q Applied load (demand) Pa
q̂ Dimensionless load --
q̂tol Tolerable load --
SD Stand off distance m
SDmax Maximum stand off distance permissible for input m
SDmin Minimum stand off distance permissible for input m
SDx Stand off distance (x-component) m
SDy Stand off distance (y-component) m
SDz Stand off distance (z-component) m
t Nominal thickness t is in {2.5,2.7,3.0,4.0,5.0,6.0,8.0,10.0,12.0,16.0,19.0,22.0} mm
td Duration of load s
TNT TNT equivalent factor --
w Charge weight kg
wmax Maximum permissible input charge weight kg
wmin Minimum permissible input charge weight kg
wTNT Equivalent TNT charge mass kg

Table of Symbols

Abbreviations and Acronyms

Abbreviation Full Form
A Assumption
AN Annealed
AR Aspect Ratio
DD Data Definition
FT Fully Tempered
GS Goal Statement
GTF Glass Type Factor
HS Heat Strengthened
IG Insulating Glass
IM Instance Model
LC Likely Change
LDF Load Duration Factor
LG Laminated Glass
LR Load Resistance
LSF Load Share Factor
N/A Not Applicable
NFL Non-Factored Load
PS Physical System Description
R Requirement
RefBy Referenced by
Refname Reference Name
SD Stand Off Distance
SRS Software Requirements Specification
TM Theoretical Model
UC Unlikely Change
Uncert. Typical Uncertainty

Abbreviations and Acronyms

Introduction

Explosions in downtown areas are dangerous from the blast itself and also potentially from the secondary effect of falling glass. Therefore, software is needed to predict whether a glass slab can withstand a blast under given conditions. For example, we might wish to know whether a pane of glass fails from a gas main explosion or from a small fertilizer truck bomb. The document describes the program called GlassBR , which is based on the original, manually created version of GlassBR.

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.

Purpose of Document

The primary purpose of this document is to record the requirements of 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 system constraints, this SRS will remain abstract, describing what problem is being solved, but not how to solve it.

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 parnasClements1986, the most logical way to present the documentation is still to "fake" a rational design process.

Scope of Requirements

The scope of the requirements includes determining the safety of a glass slab under a blast loading following the ASTM standard (astm2009).

Characteristics of Intended Reader

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 astm2009, astm2012, and astm2016 in references. The users of GlassBR can have a lower level of expertise, as explained in Sec:User Characteristics.

Organization of Document

The organization of this document follows the template for an SRS for scientific computing software proposed by koothoor2013, smithLai2005, smithEtAl2007, and smithKoothoor2016. 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 data definitions and trace back to find any additional information they require.

The goal statements are refined to the theoretical models and the theoretical models to the instance models. The data definitions are used to support the definitions of the different models.

Stakeholders

This section describes the stakeholders: the people who have an interest in the product.

The Client

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.

The Customer

The customers are the end user of GlassBR.

General System Description

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.

System Context

Fig:sysCtxDiag 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.

System Context
Figure: System Context

The interaction between the product and the user is through a user interface. The responsibilities of the user and the system are as follows:

  • User Responsibilities
    • Provide the input data related to the glass slab and blast type, ensuring no errors in the data entry.
    • Ensure that consistent units are used for input variables.
    • Ensure required software assumptions are appropriate for any particular problem input to the software.
  • GlassBR Responsibilities
    • Detect data type mismatch, such as a string of characters input instead of a floating point number.
    • Determine if the inputs satisfy the required physical and software constraints.
    • Predict whether the glass slab is safe or not.

User Characteristics

  • 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.
  • The end user is expected to have an understanding of theory behind glass breakage and blast risk.
  • The end user is expected to have basic computer literacy to handle the software.

System Constraints

There are no system constraints.

Specific System Description

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.

Problem Description

A system is needed to predict whether a glass slab can withstand a blast under given conditions.

Terminology and Definitions

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 astm2009.

  1. Glass breakage - The fracture or breakage of any lite or ply in monolithic, laminated, or insulating glass.
  2. Lateral - Perpendicular to the glass surface.
  3. Lite - Pieces of glass that are cut, prepared, and used to create the window or door.
  4. 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.
  5. Blast resistant glazing - Glazing that provides protection against air blast pressure generated by explosions.
  6. Equivalent TNT charge mass - Mass of TNT placed on the ground in a hemisphere that represents the design explosive threat.
  7. Glass Type:
    • Annealed (AN) - A flat, monolithic, glass lite which has uniform thickness where the residual surface stresses are almost zero, as defined in astm2016.
    • 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 astm2012.
    • 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 astm2012.
  8. Applied load (demand) or pressure - A uniformly distributed lateral pressure.
    • 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 astm2009 (pp. 1 and 53).
    • 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.
    • Glass weight load - The dead load component of the glass weight.
    • Short duration load - Any load lasting 3 seconds or less.
    • Specified design load - The magnitude in Pa (psf), type (for example, wind or snow) and duration of the load given by the specifying authority.
    • Long duration load - Any load lasting approximately 30 days.
  9. 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 (SDx, SDy, SDz).
  10. 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.
  11. 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.
  12. 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.
  13. Probability of breakage (Pb) - 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 (astm2016).

Physical System Description

The physical system of GlassBR, as shown in Fig:physSystImage, includes the following elements:

PS1: The glass slab.

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.

The physical system
Figure: The physical system

Goal Statements

Given the dimensions of the glass plane, the glass type, the characteristics of the explosion, and the tolerable probability of breakage, the goal statement is:

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.

Solution Characteristics Specification

The instance models that govern GlassBR are presented in the Instance Model Section. The information to understand the meaning of the instance models and their derivation is also presented, so that the instance models can be verified.

Assumptions

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.

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.

glassCondition: Following astm2009 (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: UC:Accommodate-Altered-Glass.)

explainScenario: This system only considers the external explosion scenario for its calculations. (RefBy: LC:Calculate-Internal-Blast-Risk.)

standardValues: The values provided in Sec:Values of Auxiliary Constants are assumed for the duration of load (td), and the material properties of m, k, and E. (RefBy: IM:sdfTol, IM:nFL, IM:dimlessLoad, LC:Variable-Values-of-m,k,E, DD:loadDurFactor, and A:ldfConstant.)

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: LC:Accomodate-More-than-Single-Lite.)

boundaryConditions: Boundary conditions for the glass slab are assumed to be 4-sided support for calculations. (RefBy: LC:Accomodate-More-Boundary-Conditions.)

responseType: The response type considered in GlassBR is flexural. (RefBy: LC:Consider-More-than-Flexure-Glass.)

ldfConstant: With reference to A:standardValues, the value of load duration factor (LDF) is a constant in GlassBR. (RefBy: LC:Variable-Values-of-m,k,E and DD:loadDurFactor.)

Theoretical Models

This section focuses on the general equations and laws that GlassBR is based on.

Refname TM:isSafeProb
Label

Safety Probability
Equation \[\mathit{isSafeProb}={P_{\text{f}}}\lt{}{P_{\text{f}\text{tol}}}\]
Description
  • isSafeProb is the probability of failure safety requirement (Unitless)
  • Pf is the probability of failure (Unitless)
  • Pftol is the tolerable probability of failure (Unitless)
Notes

If isSafeProb, the structure is considered safe.

Source

astm2009
RefBy

Refname TM:isSafeLoad
Label

Safety Load
Equation \[\mathit{isSafeLoad}=\mathit{capacity}\gt{}\mathit{Load}\]
Description
  • isSafeLoad is the load resistance safety requirement (Unitless)
  • capacity is the capacity or load resistance (Pa)
  • Load is the applied load (demand) or pressure (Pa)
Notes

If isSafeLoad, the structure is considered safe.

Source

astm2009
RefBy

General Definitions

There are no general definitions.

Data Definitions

This section collects and defines all the data needed to build the instance models.

Refname DD:minThick
Label

Minimum thickness
Symbol

h
Units

m
Equation \[h=\frac{1}{1000}\,\begin{cases} 2.16, & t=2.5\\ 2.59, & t=2.7\\ 2.92, & t=3.0\\ 3.78, & t=4.0\\ 4.57, & t=5.0\\ 5.56, & t=6.0\\ 7.42, & t=8.0\\ 9.02, & t=10.0\\ 11.91, & t=12.0\\ 15.09, & t=16.0\\ 18.26, & t=19.0\\ 21.44, & t=22.0 \end{cases}\]
Description
  • h is the minimum thickness (m)
  • t is the nominal thickness t is in {2.5,2.7,3.0,4.0,5.0,6.0,8.0,10.0,12.0,16.0,19.0,22.0} (mm)
Notes

t is a function that maps from the nominal thickness (h) to the minimum thickness.

Source

astm2009
RefBy

IM:sdfTol, IM:riskFun, IM:nFL, and IM:dimlessLoad

Refname DD:loadDurFactor
Label

Load duration factor
Symbol

LDF
Units

Unitless
Equation \[\mathit{LDF}=\left(\frac{{t_{\text{d}}}}{60}\right)^{\frac{m}{16}}\]
Description
  • LDF is the load duration factor (Unitless)
  • td is the duration of load (s)
  • m is the surface flaw parameter (\(\frac{\text{m}^{12}}{\text{N}^{7}}\))
Notes

td and m come from A:standardValues.

LDF is assumed to be constant (from A:ldfConstant).

Source

astm2009
RefBy

IM:sdfTol and IM:riskFun

Refname DD:gTF
Label

Glass type factor
Symbol

GTF
Units

Unitless
Equation \[\mathit{GTF}=\begin{cases} 1, & g=\text{``AN''}\\ 4, & g=\text{``FT''}\\ 2, & g=\text{``HS''} \end{cases}\]
Description
  • GTF is the glass type factor (Unitless)
  • g is the glass type (Unitless)
Notes

AN is annealed glass.

FT is fully tempered glass.

HS is heat strengthened glass.
Source

astm2009
RefBy

IM:calofCapacity and IM:dimlessLoad

Refname DD:standOffDist
Label

Stand off distance
Symbol

SD
Units

m
Equation \[\mathit{SD}=\sqrt{{\mathit{SD}_{\text{x}}}^{2}+{\mathit{SD}_{\text{y}}}^{2}+{\mathit{SD}_{\text{z}}}^{2}}\]
Description
  • SD is the stand off distance (m)
  • SDx is the stand off distance (x-component) (m)
  • SDy is the stand off distance (y-component) (m)
  • SDz is the stand off distance (z-component) (m)
Source

astm2009
RefBy

DD:calofDemand
Refname DD:aspectRatio
Label

Aspect ratio
Symbol

AR
Units

Unitless
Equation \[\mathit{AR}=\frac{a}{b}\]
Description
  • AR is the aspect ratio (Unitless)
  • a is the plate length (long dimension) (m)
  • b is the plate width (short dimension) (m)
Notes

a and b are the dimensions of the plate, where (a ≥ b).

Source

astm2009
RefBy

IM:tolLoad and IM:stressDistFac

Refname DD:eqTNTW
Label

Equivalent TNT charge mass
Symbol

wTNT
Units

kg
Equation \[{w_{\mathit{TNT}}}=w\,\mathit{TNT}\]
Description
  • wTNT is the equivalent TNT charge mass (kg)
  • w is the charge weight (kg)
  • TNT is the TNT equivalent factor (Unitless)
Source

astm2009
RefBy

DD:calofDemand
Refname DD:calofDemand
Label

Applied load (demand)
Symbol

q
Units

Pa
Equation \[q=\mathit{interpY}\left(\text{``TSD.txt''},\mathit{SD},{w_{\mathit{TNT}}}\right)\]
Description
  • q is the applied load (demand) (Pa)
  • interpY is the interpY (Unitless)
  • SD is the stand off distance (m)
  • wTNT is the equivalent TNT charge mass (kg)
Notes

q, or applied load (demand), is the 3 second duration equivalent pressure obtained from Fig:demandVSsod by interpolation using stand off distance (SD) and wTNT as parameters. wTNT is defined in DD:eqTNTW. SD is the stand off distance as defined in DD:standOffDist.

Source

astm2009
RefBy

IM:isSafeLR and IM:dimlessLoad

Instance Models

This section transforms the problem defined in the problem description into one which is expressed in mathematical terms. It uses concrete symbols defined in the data definitions to replace the abstract symbols in the models identified in theoretical models and general definitions.

The goal GS:Predict-Glass-Withstands-Explosion is met by IM:isSafePb, IM:isSafeLR.

Refname IM:riskFun
Label

Risk of failure
Input

E, LDF, J, k, m, h, a, b

Output

B
Input Constraints \[a\gt{}0\] \[0\lt{}b\leq{}a\]
Output Constraints
Equation \[B=\frac{k}{\left(a\,b\right)^{m-1}}\,\left(E\,h^{2}\right)^{m}\,\mathit{LDF}\,e^{J}\]
Description
  • B is the risk of failure (Unitless)
  • k is the surface flaw parameter (\(\frac{\text{m}^{12}}{\text{N}^{7}}\))
  • a is the plate length (long dimension) (m)
  • b is the plate width (short dimension) (m)
  • m is the surface flaw parameter (\(\frac{\text{m}^{12}}{\text{N}^{7}}\))
  • E is the modulus of elasticity of glass (Pa)
  • h is the minimum thickness (m)
  • LDF is the load duration factor (Unitless)
  • J is the stress distribution factor (Function) (Unitless)
Notes

a and b are the dimensions of the plate, where (a ≥ b).

h is defined in DD:minThick and is based on the nominal thicknesses.

LDF is defined in DD:loadDurFactor.

J is defined in IM:stressDistFac.

Source

astm2009, beasonEtAl1998 (Eqs. 4-5), and campidelli (Eq. 14)

RefBy

IM:probOfBreak
Refname IM:stressDistFac
Label

Stress distribution factor (Function)
Input

AR, q̂
Output

J
Input Constraints \[\mathit{AR}\geq{}1\]
Output Constraints \[{J_{\text{min}}}\leq{}J\leq{}{J_{\text{max}}}\]
Equation \[J=\mathit{interpZ}\left(\text{``SDF.txt''},\mathit{AR},\hat{q}\right)\]
Description
  • J is the stress distribution factor (Function) (Unitless)
  • interpZ is the interpZ (Unitless)
  • AR is the aspect ratio (Unitless)
  • q̂ is the dimensionless load (Unitless)
Notes

J is obtained by interpolating from data shown in Fig:dimlessloadVSaspect.

AR is defined in DD:aspectRatio.

q̂ is defined in IM:dimlessLoad.

Source

astm2009
RefBy

IM:riskFun
Refname IM:nFL
Label

Non-factored load
Input

q̂tol, E, h, a, b

Output

NFL
Input Constraints \[a\gt{}0\] \[0\lt{}b\leq{}a\]
Output Constraints
Equation \[\mathit{NFL}=\frac{{\hat{q}_{\text{tol}}}\,E\,h^{4}}{\left(a\,b\right)^{2}}\]
Description
  • NFL is the non-factored load (Pa)
  • q̂tol is the tolerable load (Unitless)
  • E is the modulus of elasticity of glass (Pa)
  • h is the minimum thickness (m)
  • a is the plate length (long dimension) (m)
  • b is the plate width (short dimension) (m)
Notes

q̂tol is defined in IM:tolLoad.

E comes from A:standardValues.

h is defined in DD:minThick and is based on the nominal thicknesses.

a and b are the dimensions of the plate, where (a ≥ b).

Source

astm2009
RefBy

IM:calofCapacity

Refname IM:dimlessLoad
Label

Dimensionless load
Input

q, E, h, GTF, a, b

Output

q̂
Input Constraints \[a\gt{}0\] \[0\lt{}b\leq{}a\]
Output Constraints
Equation \[\hat{q}=\frac{q\,\left(a\,b\right)^{2}}{E\,h^{4}\,\mathit{GTF}}\]
Description
  • q̂ is the dimensionless load (Unitless)
  • q is the applied load (demand) (Pa)
  • a is the plate length (long dimension) (m)
  • b is the plate width (short dimension) (m)
  • E is the modulus of elasticity of glass (Pa)
  • h is the minimum thickness (m)
  • GTF is the glass type factor (Unitless)
Notes

q is the 3 second duration equivalent pressure, as given in DD:calofDemand.

a and b are the dimensions of the plate, where (a ≥ b).

E comes from A:standardValues.

h is defined in DD:minThick and is based on the nominal thicknesses.

GTF is defined in DD:gTF.

Source

astm2009 and campidelli (Eq. 7)

RefBy

IM:stressDistFac

Refname IM:tolLoad
Label

Tolerable load
Input

AR, Jtol
Output

q̂tol
Input Constraints \[\mathit{AR}\geq{}1\]
Output Constraints
Equation \[{\hat{q}_{\text{tol}}}=\mathit{interpY}\left(\text{``SDF.txt''},\mathit{AR},{J_{\text{tol}}}\right)\]
Description
  • q̂tol is the tolerable load (Unitless)
  • interpY is the interpY (Unitless)
  • AR is the aspect ratio (Unitless)
  • Jtol is the tolerable stress distribution factor (Unitless)
Notes

q̂tol is obtained by interpolating from data shown in Fig:dimlessloadVSaspect.

AR is defined in DD:aspectRatio.

Jtol is defined in IM:sdfTol.

Source

astm2009
RefBy

IM:nFL
Refname IM:sdfTol
Label

Tolerable stress distribution factor
Input

LDF, Pbtol, E, a, b, m, k, h

Output

Jtol
Input Constraints \[0\leq{}{P_{\text{b}\text{tol}}}\leq{}1\] \[a\gt{}0\] \[0\lt{}b\leq{}a\]
Output Constraints
Equation \[{J_{\text{tol}}}=\ln\left(\ln\left(\frac{1}{1-{P_{\text{b}\text{tol}}}}\right)\,\frac{\left(a\,b\right)^{m-1}}{k\,\left(E\,h^{2}\right)^{m}\,\mathit{LDF}}\right)\]
Description
  • Jtol is the tolerable stress distribution factor (Unitless)
  • Pbtol is the tolerable probability of breakage (Unitless)
  • a is the plate length (long dimension) (m)
  • b is the plate width (short dimension) (m)
  • m is the surface flaw parameter (\(\frac{\text{m}^{12}}{\text{N}^{7}}\))
  • k is the surface flaw parameter (\(\frac{\text{m}^{12}}{\text{N}^{7}}\))
  • E is the modulus of elasticity of glass (Pa)
  • h is the minimum thickness (m)
  • LDF is the load duration factor (Unitless)
Notes

Pbtol is entered by the user.

a and b are the dimensions of the plate, where (a ≥ b).

m, k, and E come from A:standardValues.

h is defined in DD:minThick and is based on the nominal thicknesses.

LDF is defined in DD:loadDurFactor.

Source

astm2009
RefBy

IM:tolLoad
Refname IM:probOfBreak
Label

Probability of breakage
Input

B
Output

Pb
Input Constraints
Output Constraints \[0\leq{}{P_{\text{b}}}\leq{}1\]
Equation \[{P_{\text{b}}}=1-e^{-B}\]
Description
  • Pb is the probability of breakage (Unitless)
  • B is the risk of failure (Unitless)
Notes

B is defined in IM:riskFun.

Source

astm2009 and beasonEtAl1998

RefBy

IM:isSafePb
Refname IM:calofCapacity
Label

Load resistance
Input

NFL, GTF, LSF
Output

LR
Input Constraints
Output Constraints
Equation \[\mathit{LR}=\mathit{NFL}\,\mathit{GTF}\,\mathit{LSF}\]
Description
  • LR is the load resistance (Pa)
  • NFL is the non-factored load (Pa)
  • GTF is the glass type factor (Unitless)
  • LSF is the load share factor (Unitless)
Notes

LR is also called capacity.

NFL is defined in IM:nFL.

GTF is defined in DD:gTF.

Source

astm2009
RefBy

IM:isSafeLR
Refname IM:isSafePb
Label

Safety Req-Pb
Input

Pb, Pbtol

Output

isSafePb
Input Constraints \[0\leq{}{P_{\text{b}}}\leq{}1\] \[0\leq{}{P_{\text{b}\text{tol}}}\leq{}1\]
Output Constraints
Equation \[\mathit{isSafePb}={P_{\text{b}}}\lt{}{P_{\text{b}\text{tol}}}\]
Description
  • isSafePb is the probability of glass breakage safety requirement (Unitless)
  • Pb is the probability of breakage (Unitless)
  • Pbtol is the tolerable probability of breakage (Unitless)
Notes

If isSafePb, the glass is considered safe. isSafePb and isSafeLR (from IM:isSafeLR) are either both True or both False.

Pb is defined in IM:probOfBreak.

Pbtol is entered by the user.

Source

astm2009
RefBy

IM:isSafeLR and FR:Check-Glass-Safety

Refname IM:isSafeLR
Label

Safety Req-LR
Input

LR, q
Output

isSafeLR
Input Constraints \[\mathit{LR}\gt{}0\] \[q\gt{}0\]
Output Constraints
Equation \[\mathit{isSafeLR}=\mathit{LR}\gt{}q\]
Description
  • isSafeLR is the 3 second load equivalent resistance safety requirement (Unitless)
  • LR is the load resistance (Pa)
  • q is the applied load (demand) (Pa)
Notes

If isSafeLR, the glass is considered safe. isSafePb (from IM:isSafePb) and isSafeLR are either both True or both False.

LR is defined in IM:calofCapacity and is also called capacity.

q is the 3 second duration equivalent pressure, as given in DD:calofDemand.

Source

astm2009
RefBy

IM:isSafePb and FR:Check-Glass-Safety

Data Constraints

The Data Constraints Table shows the data constraints on the input variables. The column for physical constraints gives the physical limitations on the range of values that can be taken by the variable. The uncertainty column provides an estimate of the confidence with which the physical quantities can be measured. This information would be part of the input if one were performing an uncertainty quantification exercise. The constraints are conservative to give the user of the model the flexibility to experiment with unusual situations. The column of typical values is intended to provide a feel for a common scenario. The auxiliary constants give the values of the specification parameters used in the Data Constraints Table.

Var Physical Constraints Software Constraints Typical Value Uncert.
a a > 0 ∧ a ≥ b dmin ≤ a ≤ dmax 1.5 m 10%
AR AR ≥ 1 AR ≤ ARmax 1.5 10%
b 0 < b ≤ a dmin ≤ b ≤ dmax 1.2 m 10%
Pbtol 0 ≤ Pbtol ≤ 1 -- 0.008 0.1%
SD SD > 0 SDmin ≤ SD ≤ SDmax 45 m 10%
TNT TNT > 0 -- 1 10%
w w > 0 wmin ≤ w ≤ wmax 42 kg 10%

Input Data Constraints

Properties of a Correct Solution

The Data Constraints Table shows the data constraints on the output variables. The column for physical constraints gives the physical limitations on the range of values that can be taken by the variable.

Var Physical Constraints
Pb 0 ≤ Pb ≤ 1
J Jmin ≤ J ≤ Jmax

Output Data Constraints

Requirements

This section provides the functional requirements, the tasks and behaviours that the software is expected to complete, and the non-functional requirements, the qualities that the software is expected to exhibit.

Functional Requirements

This section provides the functional requirements, the tasks and behaviours that the software is expected to complete.

Input-Values: Input the values from Tab:ReqInputs, which define the glass dimensions, type of glass, tolerable probability of failure, and the characteristics of the blast.

System-Set-Values-Following-Assumptions: The system shall set the known values as described in the table for Required Assignments.

Check-Input-with-Data_Constraints: The system shall check the entered input values to ensure that they do not exceed the data constraints. If any of the input values are out of bounds, an error message is displayed and the calculations stop.

Output-Values-and-Known-Values: Output the input values from FR:Input-Values and the known values from FR:System-Set-Values-Following-Assumptions.

Check-Glass-Safety: If isSafePb ∧ isSafeLR (from IM:isSafePb and IM:isSafeLR), output the message "For the given input parameters, the glass is considered safe." If the condition is false, then output the message "For the given input parameters, the glass is NOT considered safe."

Output-Values: Output the values from the table for Required Outputs.

Symbol Description Units
a Plate length (long dimension) m
b Plate width (short dimension) m
g Glass type --
Pbtol Tolerable probability of breakage --
SDx Stand off distance (x-component) m
SDy Stand off distance (y-component) m
SDz Stand off distance (z-component) m
t Nominal thickness t is in {2.5,2.7,3.0,4.0,5.0,6.0,8.0,10.0,12.0,16.0,19.0,22.0} mm
TNT TNT equivalent factor --
w Charge weight kg

Required Inputs following FR:Input-Values

Symbol Description Source Units
AR Aspect ratio DD:aspectRatio --
E Modulus of elasticity of glass A:standardValues Pa
GTF Glass type factor DD:gTF --
h Minimum thickness DD:minThick m
k Surface flaw parameter A:standardValues \(\frac{\text{m}^{12}}{\text{N}^{7}}\)
LDF Load duration factor DD:loadDurFactor --
LSF Load share factor A:glassLite --
m Surface flaw parameter A:standardValues \(\frac{\text{m}^{12}}{\text{N}^{7}}\)
SD Stand off distance DD:standOffDist m
td Duration of load A:standardValues s

Required Assignments following FR:System-Set-Values-Following-Assumptions

Symbol Description Source Units
AR Aspect ratio DD:aspectRatio --
B Risk of failure IM:riskFun --
GTF Glass type factor DD:gTF --
h Minimum thickness DD:minThick m
isSafeLR 3 second load equivalent resistance safety requirement IM:isSafeLR --
isSafePb Probability of glass breakage safety requirement IM:isSafePb --
J Stress distribution factor (Function) IM:stressDistFac --
Jtol Tolerable stress distribution factor IM:sdfTol --
LR Load resistance IM:calofCapacity Pa
NFL Non-factored load IM:nFL Pa
Pb Probability of breakage IM:probOfBreak --
q̂ Dimensionless load IM:dimlessLoad --
q̂tol Tolerable load IM:tolLoad --

Required Outputs following FR:Output-Values

Non-Functional Requirements

This section provides the non-functional requirements, the qualities that the software is expected to exhibit.

Correctness: The outputs of the code have the properties of a correct solution.

Verifiability: The code is tested with complete verification and validation plan.

Understandability: The code is modularized with complete module guide and module interface specification.

Reusability: The code is modularized.

Maintainability: If a likely change is made to the finished software, it will take at most 10% of the original development time, assuming the same development resources are available.

Portablity: The code shall be portable to multiple environments, particularly Windows, Mac OSX, and Linux.

Likely Changes

This section lists the likely changes to be made to the software.

Calculate-Internal-Blast-Risk: A:explainScenario - The system currently only calculates for external blast risk. In the future, calculations can be added for the internal blast risk.

Variable-Values-of-m,k,E: A:standardValues, A:ldfConstant - Currently, the values for m, k, and E are assumed to be the same for all glass. In the future, these values can be changed to variable inputs.

Accomodate-More-than-Single-Lite: A:glassLite - The software may be changed to accommodate more than a single lite.

Accomodate-More-Boundary-Conditions: A:boundaryConditions - The software may be changed to accommodate more boundary conditions than 4-sided support.

Consider-More-than-Flexure-Glass: A:responseType - The software may be changed to consider more than just flexure of the glass.

Unlikely Changes

This section lists the unlikely changes to be made to the software.

Predict-Withstanding-of-Certain-Degree: The goal of the system is to predict whether the glass slab under consideration can withstand an explosion of a certain degree.

Accommodate-Altered-Glass: A:glassCondition requires that the glass is not altered in any way. Therefore, this cannot be used on altered glass.

Traceability Matrices and Graphs

The purpose of the traceability matrices is to provide easy references on what has to be additionally modified if a certain component is changed. Every time a component is changed, the items in the column of that component that are marked with an "X" should be modified as well. Tab:TraceMatAvsA shows the dependencies of the assumptions on each other. Tab:TraceMatAvsAll shows the dependencies of the data definitions, theoretical models, general definitions, instance models, requirements, likely changes, and unlikely changes on the assumptions. Tab:TraceMatRefvsRef shows the dependencies of the data definitions, theoretical models, general definitions, and instance models on each other. Tab:TraceMatAllvsR shows the dependencies of the requirements and goal statements on the data definitions, theoretical models, general definitions, and instance models.

The purpose of the traceability graphs is also to provide easy references on what has to be additionally modified if a certain component is changed. The arrows in the graphs represent dependencies. The component at the tail of an arrow is depended on by the component at the head of that arrow. Therefore, if a component is changed, the components that it points to should also be changed. Fig:TraceGraphAvsA shows the dependencies of assumptions on each other. Fig:TraceGraphAvsAll shows the dependencies of data definitions, theoretical models, general definitions, instance models, requirements, likely changes, and unlikely changes on the assumptions. Fig:TraceGraphRefvsRef shows the dependencies of data definitions, theoretical models, general definitions, and instance models on each other. Fig:TraceGraphAllvsR shows the dependencies of requirements and goal statements on the data definitions, theoretical models, general definitions, and instance models. Fig:TraceGraphAllvsAll shows the dependencies of dependencies of assumptions, models, definitions, requirements, goals, and changes with each other.

TraceGraphAvsA
Figure: TraceGraphAvsA
TraceGraphAvsAll
Figure: TraceGraphAvsAll
TraceGraphRefvsRef
Figure: TraceGraphRefvsRef
TraceGraphAllvsR
Figure: TraceGraphAllvsR
TraceGraphAllvsAll
Figure: TraceGraphAllvsAll

For convenience, the following graphs can be found at the links below:

Values of Auxiliary Constants

This section contains the standard values that are used for calculations in GlassBR.

Symbol Description Value Unit
ARmax maximum aspect ratio 5 --
dmax maximum value for one of the dimensions of the glass plate 5 m
dmin minimum value for one of the dimensions of the glass plate 0.1 m
E modulus of elasticity of glass 71.7⋅109 Pa
Jmax maximum value for the stress distribution factor 32 --
Jmin minimum value for the stress distribution factor 1 --
k surface flaw parameter 28.6⋅10-54 \(\frac{\text{m}^{12}}{\text{N}^{7}}\)
LSF load share factor 1 --
m surface flaw parameter 7 \(\frac{\text{m}^{12}}{\text{N}^{7}}\)
SDmax maximum stand off distance permissible for input 130 m
SDmin minimum stand off distance permissible for input 6 m
td duration of load 3 s
wmax maximum permissible input charge weight 910 kg
wmin minimum permissible input charge weight 4.5 kg

Auxiliary Constants

References

Appendix

This appendix holds the graphs (Fig:demandVSsod and Fig:dimlessloadVSaspect) used for interpolating values needed in the models.

3 second duration equivalent pressure (<em>q</em>) versus Stand off distance (SD) versus Charge weight (<em>w</em>)
Figure: 3 second duration equivalent pressure (q) versus Stand off distance (SD) versus Charge weight (w)
Non dimensional lateral applied load (demand) or pressure (<em>q̂</em>) versus Aspect Ratio (AR) versus Stress distribution factor (Function) (<em>J</em>)
Figure: Non dimensional lateral applied load (demand) or pressure (q̂) versus Aspect Ratio (AR) versus Stress distribution factor (Function) (J)