NBS BUILDING SCIENCE SERIES 154

Wind Loading

and Strength of Cladding Glass

U.S. DEPARTMENT OF COMMERCE • NATIONAL BUREAU OF STANDARDS
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress on March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and

the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

systems of other nations and furnishes essentia! services leading to accurate and uniform

physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

institutions, and Government; provides advisory and research services to other Government

agencies; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Absolute Physical Quantities^ — Radiation Research — Chemical Physics —

Analytical Chemistry — Materials Science

THE NATIONAL ENGINEERING LABORATORY provides technology and technical ser- vices to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement capabilities;

provides engineering measurement traceability services; develops test methods and proposes

engineering standards and code changes; develops and proposes new engineering practices;

and develops and improves mechanisms to transfer results of its research to the ultimate user. The Laboratory consists of the following centers:

Applied Mathematics — Electronics and Electrical Engineering^ — Manufacturing

Engineering — Building Technology — Fire Research — Chemical Engineering^

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing the Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and

provides the technical foundation for computer-related policies of the Federal Government.

The Institute consists of the following centers:

Programming Science and Technology — Computer Systems Engineering.

'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Washington, DC 20234. 'Some divisions within the center are located at Boulder, CO 80303.
NBS BUILDING SCIENCE SERIES 154

Wind Loading

and Strength of Cladding Glass

D. A. Reed

E. Simiu

Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued May 1983
Library of Congress Catalog Card Number: 83-600515

National Bureau of Standards Building Science Series 154

Natl. Bur. Stand. (U.S.), Bldg. Sci. Ser. 154, 49 pages (May 1983)

CODEN: BSSNBV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1983

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402

Price $4.00

(Add 25 percent for other than U.S. mailing)
ABSTRACT

A procedure for investigating glass cladding behavior under arbitrary loads,

including fluctuating wind loads, is presented. The procedure accounts for

the fact that internal stresses are nonlinear functions of the external loads

that initial glass strengths are random functions of position and direction,

and that glass strength undergoes degradation under the action of external

loads in accordance with basic fracture mechanics laws. Numerical examples

are presented, and corresponding probability distribution curves are calculat

indicating the probability of failure of a specified panel subjected to fluctuating wind loads and to 1-minute constant loads. These curves are used to

illustrate a method for assessing current glass cladding design procedures.

For the case considered in the paper, it was found that transformation of

the peak wind load averaged over 1-2 seconds into an equivalent 1-minute load

appears to underestimate the probability of failure of glass cladding. The

work reported in the paper is part of an ongoing window cladding research

program being conducted at the National Bureau of Standards.

Key words: aerodynamics; buildings; deformation; engineering mechanics;

failure; glass; loads (forces); probability theory.

iii
ACKNOWLEDGMENTS

Cover photo: Guaranty Bank Building, Corpus Christi, Texas, following

Hurricane Celia, August 3, 1980. View is of the east face of the building.

The photograph was graciously supplied by Dr. Joseph E. Minor, Director of

the Institute for Disaster Research, Texas Tech University, Lubbock, Texas,

79409.

The writers are indebted to S. M. Wiederhorn, E. R. Fuller, and S. W. Freiman

of the Center for Materials Science, NBS , J. E. Minor of Texas Tech

University, and W. A. Dalgliesh of the National Research Council of Canada

for useful exchange and advice.

iv
TABLE OF CONTENTS

Page

ABSTRACT ill

ACKNOWLEDGMENTS iv

LIST OF FIGURES vi

LIST OF TABLES vii

1. INTRODUCTION 1

2. FRACTURE MECHANICS OF GLASS 3

3. STRESS ANALYSIS 6

4. WIND LOADING 7

5. PROPOSED PROCEDURE FOR INVESTIGATING GLASS BEHAVIOR 8

6. INPUT DATA FOR NUMERICAL CALCULATIONS 9

7. PROBABILITIES OF GLASS FAILURE 10

8. ASSESSMENT OF CURRENT PROCEDURES FOR DESIGNING GLASS CLADDING 12

9. CONCLUSIONS 14

REFERENCES 15

APPENDIX I. NOTATION 17

APPENDIX II. COMPUTER LISTING 19

V
^ -

LIST OF FIGURES

Page

Figure 1. Crack velocity vs. iin (Kj) for soda-lime silica glass [23] .... 36

Figure 2, Center and corner maximum principal stresses for a square plate ^7

Figure 3. Schematic representation of angles = kAa 38

Figure 4. Cumulative distribution function for p(t) 39

Figure 5. Evolution of strength and stresses with time for breaking panel 40

Figure 6. Cumulative distribution function for pgg ^1

vi
LIST OF TABLES

Page

Table 1. Estimated Probabilities of Failure Based on Stress Time

History, and on 1-Minute Loads Estimated in Accordance with

References 12 and 3. Units of pressure = psf 35

vii

1. INTRODUCTION

The improvement of design procedures for cladding glass subjected to wind

loads has been the focus of a considerable amount of research in recent years.

In 1979, Pittsburgh Plate Glass (PPG) published revised design charts [2] based

upon nonlinear stress analyses used in conjunction with elementary statistical

methods. In a number of instances, these charts differ from those issued by

other manufacturers, notably LOF [8], and exhibit internal inconsistencies as well. For example, according to the PPG charts, a 3.67 ft x 18.33 ft (1.12 m

X 5.60 m) glass panel with a thickness of 12.7 mm supported on four sides

deflects 11.9 mm under a load of 100 psf (4790 Pa)); for a panel with a span

of 1.12 m, with the same thickness and under the same load but supported on two sides, the deflection as obtained from the PPG charts is only 9.1 mm,

rather than being equal to or in excess of 11.9 mm. Inconsistencies with

respect to design loads exist as well. As an example, for a 1/8 in (3 mm)

thick annealed float glass panel supported on four sides the PPG charts specify

a 15 psf (719 Pa) one-minute load if the dimensions of the panel are 2.83 ft x 7.07 ft (0.865 m X 2.15 m) , and the same - rather than a larger - one-minute

load if the dimensions are 2.24 ft x 6.70 ft (0.68 m x 2.04 m) . Inconsistencies such as these, and discrepancies with respect to other manufacturers'

charts [8], suggest that the development of an improved theoretical framework

for the design of glass cladding is a necessary task.

An important step toward such an improvement was proposed in 1980 by Beason

[2]. Reference 2 combined nonlinear stress analysis with the classic Weibull

theory to estimate the probability of failure of a glass panel subjected to a specified load, given the parameters of the Weibull distribution of the glass

strength. Conversely, the procedure of reference 2 can be applied to estimate

these parameters from information obtained by loading glass panels up to the

failure point.

The procedure of reference 2 requires the transformation of the stresses

induced by actual, time-dependent loads into nominal stresses corresponding to

a 1-minute constant load. It is suggested in reference 2 that the

transformation be carried out by using the following relationship:

J^f (M,t)dt l/n

^60(M) =

] (1)

where a5o(M) = equivalent one-minute stress at point M, a(M,t) = stress induced

by actual load at point M and time t, tf = duration of loading or time to

failure in seconds, whichever is smaller, and n = material constant. However,

the time to failure t^ in equation 1 is unknown for panels that would fail

under wind loads. To the extent that an arbitrary value for tf is used in

equation 1 , and that this value could differ by as much as one or even two more orders of magnitude from actual values, significant errors would be

introduced in estimating a^Q(M). Note also that if equation 1 were used, it

would be necessary to evaluate the integral at each point M, since the system

is nonlinear (i.e., in general a(M,t) is not proportional to the wind loading

at time t, p(t)).

1
On account of the difficulty—or impossibility—of specifying tf, and of

estimating the integrals in equation 1, to the writers' knowledge, no previous

attempts have been made to study the behavior of glass cladding subjected to

fluctuating wind loads. Instead, previous research has focused on the study of

the behavior of glass cladding subjected to nominal 1-minute loads purported to

be representative of fluctuating loads.

The purpose of this paper is to present a procedure for studying the behavior

of glass under arbitrary time-dependent loads, including fluctuating wind

loads. Like reference 2, the present procedure is based on a nonlinear analysis

of stresses that develop under the action of the external loads, and on a Weibull probabilistic model for the strength of glass. However, unlike

reference 2, the procedure presented here incorporates phenomenological models

describing the fracture mechanisms of glass developed in the last decade by

Wiederhorn and other workers (e.g., see references 5, 25, 26), as well as information on the fluctuating character of the wind loads. No a priori

assumptions are needed with regard to the time to failure, tf, which is one of

the outputs of the procedure. As in reference 2, it is assumed that temperature

and humidity effects can be neglected. Additional outputs include the location

and direction of the failure initiation crack, and the amount of strength

degradation due to the action of the fluctuating wind load.

To provide a background for the development of the proposed procedure, basic

elements of the fracture mechanics of glass will be briefly summarized. A

method for obtaining time-dependent stresses from time-dependent loads, which

utilizes a computer program developed at Texas Tech University, will be

described. A brief section will be devoted to the subject of time-dependent

wind loading on cladding glass. The proposed procedure for investigating glass

behavior under arbitrary loads will- then be presented. The procedure will be

applied to obtain estimates of probabilities of failure of a glass panel under

fluctuating wind loads and under one-minute constant loads. Such estimates will

then be used to illustrate a method for assessing current practices for the

design of glass cladding subjected to wind loads.

2
2. FRACTURE MECHANICS OF GLASS

The basic criterion for fracture is derived from the Griffith equilibrium

expression, which can be written as

Ki = Kic (2)

where Kj = stress intensity factor, and Kj^ = critical value of Kj . If

equation 2 holds, the system reaches the state of instability wherein the rate

of crack growth becomes for practical purposes infinite [5, 7] and failure

occurs. Kjc is a property of the material and is determined experimentally.

The stress intensity factor, Kj , is proportional to the actual stresses in

the material in the presence of cracks causing stress concentrations. % can

be expressed as follows [5, 7]:

Ki(t) = Ya(t) /c(t) (3)

where

Y = geometric shape factor

a = nominal stress (i.e., stress calculated by assuming the absence of

cracks

)

c = crack length

t = time

The geometric shape factor, Y, is assumed to be constant; this is equivalent

to assuming that the crack geometry does not change and can be characterized

by one dimension, c. According to experiments reported in references 5 and

22-26, the following relationship holds for the rate of subcritical crack

growth (figure 1):

^ = AK.(t)

dt I (4)

The parameters A and n depend upon ambient humidity and temperature and are obtained experimentally. Equation 4 expresses quantitatively the fact that the

cracks of an element of glass subjected to stress for some length of time

will grow - albeit not catastrophically - provided that the stress is contained

within a certain range. This phenomenon is referred to as static or dynamic

fatigue according to whether the stress is constant or time-dependent.

It follows from equations 2 and 3 that the strength of glass, S, i.e., the

value of the nominal stress at which failure occurs, is:

S(t) =-^M=^ (5) Y/c(t)

3
If Kj and c are eliminated from equations 3, 4, and 5 and the notation

S(0) = Si is used (S^ = initial strength), the following relationship is

obtained:

1 S(t) = [Si -i- / (t) dT] (6)

where 1/B = (n-2) AY^ [5]. It follows from the definition of S(t)

that failure occurs if

a(t) > S(t) (7)

In the calculations presented in this paper it is assumed that the variability

of A and n in equation 4 is small and that its effect upon the results being

sought can be neglected. As far as the variability of B is concerned, the

following comment is in order. Because B is a function of Y, which in turn

depends upon the flaw shape, its variability is difficult—if at all possible

to ascertain. If a deterministic value of B is assumed, based on a conventional value of Y, it is possible by using equation 6 to obtain values of Si

from experiments in which n. A, Kj^,, a(t) are known, and the time to failure,

tf, and the strength, S(tf), are measured. The empirical probability distributions of the initial strength estimated from the values S-^ so obtained

automatically reflect the actual shapes of the flaws.

The initial strength Si of an element with area, a, experiencing a uniform,

direction-independent state of tensile stress throughout one of its outer

faces can be described probabilistically by a Weibull distribution [21], i.e.,

, , Sj .m, P(si,a) = 1 - exp {-(—i—) } for m > 1 (8)

So(a)

where P(si,a) = probability that the random variable S^ < s^, So(a) = scale

parameter (characteristic strength), and m = shape (tail length) parameter.

The scale parameters, SQ(a) and SQ(aj), of two elements with areas a and aj,

respectively, each experiencing uniform direction-independent states of tensile

stress throughout one of its outer faces, can be written as [6]:

J_

a, m

S^(a) = S^(a,)(-J^) (9)

o o i a

This relation reflects the dependence of strength distribution upon the

distribution of flaw lengths. The larger the area of the panel, the larger will

be the number of flaws and, therefore, the larger the probability that the area will contain a severe flaw to which, by virtue of equation 5, there corresponds

a relatively low initial strength.

Consider now an element of glass with uniform but direction-dependent stresses

throughout one of its outer faces. In this case, shear stresses are present,

4
in addition to normal stresses. The effect of the normal stresses is by far

the strongest, however, as far as crack propagation is concerned [7, p. 52],

Therefore it may be assumed to a first approximation—as is done in

reference 2 —that the effects of the shear stresses can be neglected. In the case of the element now being considered failure will not necessarily be initiated by a flaw normal to the maximum principal stress - indeed, it may well

happen that all such flaws are relatively small. Neither will failure be

necessarily initiated by the largest flaw within the element, since that flaw

may well be perpendicular to a relatively low normal stress. Rather, failure

will be initiated by the largest of the flaws oriented along some direction, af

,

such that

an (t. Of) > ^ (10)

where (t, af) = normal stress perpendicular to direction af (equations

5 and 7) and Cj^^x ^^f) ~ length of largest flaw oriented along direction af

.

Under the assumption that the distribution of flaw orientation is uniform [2,

p. 84], equation 9 can be applied to the case of an element subjected to uniform but direction-dependent state of stress as follows. The probability of

occurrence within a certain area of flaws with crack length dimension less

than c and having orientation angles a^ < a < a2 is equal to (a2 ~ a^) times

the probability of occurrence within an area of flaws with dimension less than

c and having any orientation 0 < a <2tt. The following relation is therefore

consistent with equation 9 for any elemental circular area:

So(ai < a < a2) = 8^(0 < a < 2tt) ( H- ) ^2 ^1

(11)

5
3. STRESS ANALYSIS

Equations 6 and 7 clearly show that to Investigate the behavior of glass,

information is required on the time history of the stresses induced in the

glass by the external loads.

The out-of-plane deflections of glass plates subjected to lateral loads can be

large relative to the thickness of the plate. The plate develops substantial

mid-plane membrane stresses in this condition, and the von Karman

equations [18, 20] must be used to account for this effect. Based on these

equations, Vallabhan and Wang [19] have developed a program that uses the

finite difference method to determine the deflections and stresses in uniformly

loaded simply-supported thin glass plates having boundary conditions allowing

for in-plane movement. With the permission of the Institute for Disaster

Research, Texas Tech University, this program was employed in the present study

to determine the stresses at various locations on the plate. The results from

the program were non-dimensionalized as follows [9]

LF = pb^/Dh (12)

SF = ab2h/D (13)

where LF and SF = loading and stress factors, respectively, p = uniform pressure

loading, a = corresponding stress, b = smaller side of rectangular plate,

D = flexural rigidity, defined by

12(l-v^)

E = modulus of elasticity, v = Poisson's ratio, and h = thickness of plate.

For a square plate, the relationship between SF and LF for various locations

is shown in figure 2. Note that the relationship is closer to being linear

for the corner than for the center stresses.

Relationships for each location on the plate from the grid used for the finite

difference analysis were determined and represented analytically in terms of

piece-wise linear curves. On the basis of such relationships, given a timedependent loading, the plate dimensions, and the material properties, the

principal stresses and normal stresses corresponding to various directions can

be calculated as functions of time.

6
4. WIND LOADING

Wind loading on cladding has a fluctuating character. Because the dimensions

of cladding panels are relatively small (on the order of a few meters at most)

it is acceptable to assume that the fluctuating loads acting over the area of

the panel are uniformly distributed at any one instant and proportional to the

pressures at the panel center.

The wind loads depend upon the local extreme wind climate [16, 17], the features

of the oncoming air flow (which are in turn dependent upon the roughness of

the surrounding terrain and the possible presence of neighboring buildings),

and the aerodynamic characteristics of the building in question. These characteristics differ from point to point on the building facades and are, in

addition, dependent upon wind direction.

Wind loading time histories are obtained principally from wind tunnel tests.

Any given loading time history can be analyzed to determine its statistical

characteristics; e.g., mean, standard deviation and peak. Models of the loading

can be obtained in the frequency domain (using a spectral approach, for example,

see reference 17), or in the time domain, e.g., using a Box-Jenkins approach

[14], Knowledge of these models in turn allows the numerical simulation of

loading time histories that correspond to various reference wind speeds. In

the particular case of a mean wind speed normal to a building face and in the

absence of neighboring buildings which significantly alter the oncoming flow

field, at a point Q near the center of the building face the pressures may be

written approximately as

where p and p^ = mean and fluctuating pressure, respectively, p = air density,

Cp(Q) = pressure coefficient at point Q, z = elevation of point Q, v(z) = mean

wind speed, at elevation z and v^(z,t) = longitudinal fluctuating component of

wind speed. The fluctuating pressures can be simulated from spectral

information or v'(z,t) [17].

P (Q) =

2

P Cp(Q) V (z) (14)

p'(Q,t) = p Cp(Q) v(z)v'(z,t) (15)

7
5. PROPOSED PROCEDURE FOR INVESTIGATING GLASS BEHAVIOR

Earlier in this paper it was noted that a glass panel will not necessarily fail

at the point of maximum stress or of minimum strength. Rather, failure will

occur where the relationship between stress and strength is such that equation 7 is satisfied, where S(t) is given by equation 6, and S± is described probabilistically by equation 8 (recall that the effects of area and of stress

directionality are included in the procedure through equations 9 and 11).

With this background it is now possible to describe the proposed procedure for

investigating glass behavior. The procedure entails the following steps:

1. For any given mean wind speed and direction generate the time history

of the wind loading for the glass cladding panel of concern by Monte

Carlo simulation as outlined in the section "Wind Loading."

2. Using the procedure outlined in the section "Stress Analysis" obtain

from the time history of the wind loading the time histories of the

stresses normal to the directions = —, (k = 1, 2, ... r) at the

2r

center, , of each of the elements into which the panel is divided

for numerical computation purposes.

3. From equations 8 and 9 generate by Monte Carlo simulation initial

strengths Si (Mj » o^k.)* where a]f_ = kAa (k = 0, 1, 2, . . . n) - see figure 3.

4. Evaluate numerically the expression

S(M., o,^, t) = {Si ^(M., a^) -4- / [o'^in., a^, x)] dj}^ ^ (16)

B Q

J

for all j and k and t = mAt , where At = incremental time used in

numerical computations, and m = 1, 2, .., .

5. Computation is stopped if for at any set j, k,

a(Mj , aj^, mAt) >_ S(Mj, aj^ , mAt). (17)

At that point, failure of the general panel has occurred. ^

8
6. INPUT DATA FOR NUMERICAL CALCULATIONS

Numerical examples were carried out for the case of annealed float glass

panels simply supported on four sides with dimensions 4 ft x4 ft x 1/8 in

(1.2 mx 1.2 mx 3 mm). The following parameters were used: S^(a^ = 1 m ) n

= 35.2 MPa [4] , m = 6 [4] , A = 1.08 (MPa)-n ml-2 sec"! [23], n = 19.69 [23],

Ki = 0.75 MPa [23], v = 0.22 [2] , E = 0.0689 MPa [2]. The values A and n

C

correspond to 50 percent humidity and 20°C temperature (see figure 1). It was assumed that the geometric shape factor Y = 1.12 [see reference 10 for details.

It was further assumed that the glass panel is located near the center of a building facade at an elevation of z = 150 ft (46 m) , that it is subjected to

winds normal to the building face, that the building is located in open

terrain, and that Cp = 1.0 in equations 14 and 15.

For any given mean wind speed, v, the corresponding mean wind pressure was obtained by using equation 14. The fluctuating wind pressures were generated

by numerical simulation using equation 15 and the following expression for the

spectrum of the longitudinal velocity fluctuations v', [17]:

n S„ (n) v _ 200f

u2 (1 + 50f)5/3

(18)

where u = v(z)/[2.5 i!,n(z/zo)], n = frequency, f = nz/v(z) , z = elevation of

* panel in meters, and the roughness length corresponding to open terrain Zq = 0.07 m [17].

9
7. PROBABILITIES OF GLASS FAILURE

Failure of Glass Cladding Under Fluctuating Wind Loads . Consider the wind

load, p-i^(t), corresponding to a mean wind speed, v(z). The subscript, 1, indicates that p±(t) is the i-th realization of the specified stochastic process.

Let Xp, Yp be the coordinates of the centers of the elements into which the

glass panel is divided. The size of these elements is sufficiently small so that the variation of the stresses over each element is insignificant for practical purposes. Let o^. be the directions, perpendicular to the normal stresses,

being considered at each point. Obtain the stresses a-j^(xp, yq, a^- , t) corresponding to Pi(t) for all values p, q, r. Assume that the number of panels

(the sample size) is L. Simulate initial strengths Sqj^^ (xp, yq, aj-) for one given set of values p, q, r for all the panels of the sample (l = 1, 2, ... L).

Rank order these strengths beginning with the smallest. Denote this smallest

value by SqI (xp, yq, a^.). Compare (xp, yq, aj-, t) to S]^(t) by using

equation 6. If a-j^ ^ Sj^ for every t, then no panel will break at point Xp, yq

in the direction of a^.. However, if > for some t, the panel for wnich

the initial strength at Xp, y^, a^. is S^i will break. One breakage is recorded,

and the panel concerned is eliminated from further consideration. If a± > S2,

where S2 is derived from the second smallest initial strength for the given

p, q, r, then breakage initiated at Xp, yq, a^- will occur. Repeat the comparison until < Sj^. The number of failures initiated at Xp, yq, a^- will then

be N=N-1 , and the corresponding panels are eliminated from further consideration. Repeat the procedure for all values, p, q, r. The probability of failure

under load Pj:(t) is F[f allure | pj^(t)] = E(N/L)j^. Repeat the the procedure

for different realizations of the pressure. The probability of failure under

G

load p(t) is P[fallure | p(t)] = E Prob. [failure | pi(t)]/G, where the

1 summation is over the number of realizations, G, being considered.

A cumulative distribution function P[failure | p(t)] is derived indicating

that the strength of the plate is less than required to withstand the load p(t)

in 100 X P[fallure | p(t)] percent of the cases. Note that P[f allure | p(t)]

embodies both the characteristics of the material and the aerodynamic characteristics of the loading under consideration. These two types of characteristics

are inseparable owing to the dependence of glass strength upon load time

history.

For convenience, the load p(t) may be indexed by its mean value p, so that the

notation P[failure | p], or simply P^ (p) may be substituted for P[fallure

I p(t)]. Estimates of points of the cumulative distribution function Pf(p)

estimated for the conditions described in the section "Input Data for Numerical

Calculations" are shown in figure 4. These points were obtained for simulated

failure tests carried out on two sets of 1,000 panels, each set being subjected

to different realizations of the fluctuating pressure, p(t).

Typical time histories of pressure, stress, and strength at panel points where

failure was found to occur are shown in figure 5. Note the continuous strength

10
degradation under load. In certain instances a storm can cause significant

strength degradation without causing failure. The weakened panel could then

break under the action of subsequent, less intense storms, should such storms occur during its lifetime.

Failure of Glass Cladding Under 1-Minute Constant Load . Let the normal stress

induced by the 1-minute load, P60> the initial strength be denoted by

a5o(M, a) and S-j^(M, a), respectively, where M and a are the point and the

direction under consideration. It is assumed that the 60-second action of 059

(M, a) causes failure. It follov7s from equation 6 that, with negligible error,

the following relation holds:

S. (M, a)

^/'^

The procedure for obtaining pgQ is as follows: Generate initial strengths,

^ol (^p» yq> ^'r) ^ ~ ^' 2,... L panels. Use equation 19 to solve for 059

(M, a) at each Xp, yq, a^. for panel i. Calculate the value of P50 corresponding to each a^QvM, a). Find the minimum pgQ foi" panel i; it represents the

lowest 60-second pressure loading for which failure of panel i will occur. Repeat the procedure for i = I, 2, ... L panels. The results obtained can be

plotted in the form of a cumulative distribution function P [failure | P6oK

denoted as Pf(p5o)« Figure 6 shows a cumulative distribution P^Cp^q) for the

conditions described in the section "Input Data for Numerical Calculations,"

based results of obtained for a set of 4,000 panels.

Note that according to the PPG charts [2] the 1-minute load, P60» corresponding

to a probability of failure of 8 in 1,000 is 23 psf. The corresponding value

of p5o indicated by figure 6 is about 19 psf.

11
8. ASSESSMENT OF CURRENT PROCEDURES FOR DESIGNING GLASS CLADDING

The purpose of this section is to compare the current design loadings with the

present procedure.

Procedure Used in Refs. 12-13 . This procedure is based on the assumption that

the effect of wind loading is determined solely by the peak load averaged over

1 or 2 seconds that occurs during the storm. It is assumed that the loading

on the cladding which is subjected to a fluctuating wind pressure is equivalent

C

to a 1-minute constant pressure, P50> defined as

J_

P60 = Ppk (^>' (20)

where pp]^ = peak pressure averaged over the time, tp^, that occurs during the

storm being considered, and tp]^ = 1-2 seconds. According to this assumption,

then, provided that Pp^ is the same, it does not matter whether the mean

loading is large and the fluctuations are small or vice-versa. The probability

of failure of a panel subjected to a load, p(t), implicit in reference 12 is

thus equal to the probability of failure of that panel under the action of a 1-minute load, P^q, obtained from p(t) by using the above equation.

Procedure Proposed in Ref. 3 . This procedure assumes that the equivalent

1-minute pressure loading is given by

t D r ^ n

1/n

P60 = r P

eo''

^''^

where tg = duration of storm.

Comparison of Design Loadings Based on Various Procedures . The purpose of

C D

this section is to compare the loads p(t) , P50» and p^Q corresponding to various

probabilities of failure. These loads are obtained from the cumulative

distribution functions of figs. 4 and 6.

To the storm with mean speed v these corresponds a mean pressure p, a

C

1-minute load obtained in accordance with reference 12, PgQ* ^ 1-minute load

D

obtained in accordance with reference 3, PgQ* conditions described in

C _ D _ the section "Input Data for Numerical Calculations," the ratios P50/P P60^P

C were found to be approximately 1.08 and 1.26, respectively. Values of pgQ

D _

and pgQ corresponding to various values p, and the probabilities of failure

12
C D

Pf(p) = P[failure | p(t)], Pf (p^g = P60)' ^^^^ (P60 P60)' obtained from

figs. 4 and 6, are listed in table 1. It is seen that, in this instance, the

estimates based on the procedure of reference 12 appear to be overly optimistic,

i.e., they appear to underestimate the probability of failure of the panel

under any given storm and, therefore, the probability of failure of the panel

during its lifetime. The probability estimates based on the procedure of

reference 3 are somewhat closer to those based on the time history of the

stresses. Note that for storms causing rates of failure of about 8 in a 1,000

the probability estimates based on the stress time history and on the nominal

C D

1-minute loads p^g ^^'^ P60 happen in this case to be relatively close. The

respective discrepancies increase considerably in the case of stronger storms.

13
9. CONCLUSIONS

A procedure for investigating glass cladding behavior under arbitrary loads,

including fluctuating wind loads, was presented. The procedure accounts for

the fact that internal stresses are nonlinear functions of the external loads,

that initial glass strengths are random functions of position and direction,

and that the glass strength undergoes degradation under the action of external

loads in accordance with basic fracture mechanics laws that reflect subcritical

crack growth. Numerical examples were presented, and corresponding probability

distributions were calculated, indicating the probability of failure of a specified panel subjected to fluctuating wind loads and to 1-minute constant

loads. These curves are used to illustrate a method for assessing current

glass cladding design procedures. For the case considered in the paper it was found that procedures based on the transformation of the wind load averaged

over 1-2 seconds into an equivalent 1-minute load appear to result in overly

optimistic assessments of the probability of failure of glass cladding under

wind loads. The work reported in the paper is part of an ongoing window

cladding research program being conducted at the National Bureau of Standards.

Future work will consider the effect of fluctuating loads on corner and eave

panels, and the effect upon fracture load predictions of the variability of

the parameters that control glass behavior under load.

14
REFERENCES

1. American National Standards Institute, "Building Code Requirements for

Minimum Design Loads in Buildings and Other Structures," ANSI A58. 1-1972,

1972.

2. Beason, William L. , "A Failure Prediction Model for Window Glass,"

Institute for Disaster Research, Texas Tech University, Lubbock, Texas,

May 1980.

3. Dalgliesh, W. A., "Assessment of Wind Loads for Glazing Design," Practical

Experiences with Flow-Induced-Vibrations , lAHR - lUTAM Symposium,

Karlsruhe , Germany , Sept. 3-6, 1979, Springer-Verlag, pp. 696-708.

4. Fuller, E. , Wlederhorn, S. M. , Ritter, J. E., and Gates, P. B., "Proof

Testing of Ceramics: Part II: Theory," J. Materials Science , Vol. 15,

1980, pp. 2275-2281.

5. Hertzberg, R. W. , Deformation and Fracture Mechanics of Materials , John

Wiley and Sons, New York, N.Y., 1976.

6. Johnson, N. L. and Kotz, S. , Continuous Univariate Distributions , Vol. I,

John Wiley and Sons, New York, N.Y. , 1970.

7. Lawn, B. R. and Wilshaw, T. R. , Fracture of Brittle Solids , Cambridge

University Press, Cambridge, England, 1970.

8. L. 0. F. Technical Information - Strength of Glass Under Wind Loads , 805-109, Toledo, Ohio, Jan. 1980.

9. Moore, Donald M. , Proposed Method for Determining the Thickness of Glass

in Solar Collector Panels , JPL 80-34, Jet Propulsion Laboratory, Pasadena,

1980.

10. Newman, J..C., Jr. and Raju, T. S. , "Analysis of Surface Cracks in Finite

Plates Under Tension or Bending Loads," NASA Technical Paper 1578, Dec.

1979.

11. Peterka, J. A. and Cermak, J. E., "Wind Pressures on Buildings - Probability Densities," J. of the Structural Dlv. , ASCE, Vol. 101, No.

ST6, June 1975, pp. 1255-1267.

12. Peterka, J. A. and Cermak, J. E. , "Wind Tunnel Study of Atlanta Office

Building," Research Report of the Fluid Mechanics and Wind Engineering

Program, College of Engineering, Colorado State University, Ft. Collins,

CO, November 1978.

13. PPG Glass Thickness Recommendations to Meet Architects Specified 1-Minute

Wind Load, Technical Services/Flat Glass Division, PPG Industries, April

23, 1979.

15
14. Reed, D. A. and Scanlan, R. H. , "ARIMA Representation of Turbulence

Spectra and Longtudinal Integral Scales," to be published in Proceedings , U.S. - Japan Cooperative Program in Natural Resources, Tokyo, May 1981.

15. Ritter, J. E. , Jr., et al., "Proof Testing of Ceramics: Part I:

Experiment," J. Materials Science , 15, 1980, pp. 2282-2295.

16. Simiu, E., Changery, M. E., and Filliben, J. J., Extreme Wind Speeds at

129 Stations in the Contiguous United States , Building Science Series

Report BSS 118, National Bureau of Standards, Washington, DC, March 1979.

17. Simiu, E. and Scanlan, R. H. , Wind Effects on Structures: An Introduction to Wind Engineering , John Wiley and Sons, New York, N.Y., 1978.

18. Timoshenko, S. and Woinowsky - Krieger, S., Theory of Plates and Shells , 2nd Edition, McGraw-Hill: New York, N.Y. , 1968, pp. 415-428.

19. Vallabhan, C. V. G. and Wang, B. Y.-T., "Nonlinear Analysis of Rectangular

Glass Plates by Finite Difference Method," Institute for Disaster Reserach,

Texas Tech University, Lubbock, Texas, June 1981.

20. von Karman, Th. , "Encyklopadie der Mathematischen Wissenchaf ten.

Vol. IV, p. 349, 1910.

21. Weibull, W. , "A Statistical Theory of the Strength of Materials,"

Ingeniorsvetenskapsakademiens , Handlingar NR 151, Stockholm, 1939.

22. Wiederhorn, S. M. , "Influence of Water Vapor on Crack Propagation in

Soda-Lime Glass", J. Amer. Ceramic Society , 50, 1967, pp. 407-414.

23. Wiederhorn, S. M. , "Subcritical Crack Growth in Ceramics," in Fracture

Mechanics of Ceramics , Vol. 2, Bradt, R. C. , Hasselman, D. P. H. , and

Lange, F. F. , eds. , Plenum Publishing Corp, New York, 1974, pp. 613-646.

24. Wiederhorn, S. M. , "Strength of Glass - A Fracture Mechanics Approach,"

Proceedings, Tenth International Congress of Glass, The Ceramics Society

of Japan , Kyoto, Japan, July 1974.

25. Wiederhorn, S. M. , "Dependence of Lifetime Predictions on the Form of

the Crack Propagation Equation," Fracture 1979 , Vol. 3, ICF4, Waterloo,

Canada, June 19-24, 1977, pp. 893-901.

26. Wiederhorn, S. M. , and Ritter, J. E., Jr., "Application of Fracture

Mechanics Concepts to Structural Mechanics," Fracture Mechanics Applied

to Brittle Materials , ASTM STP 678, Freiman, S. W. , eds. ASTM, 1979, pp.

202-214.

16
APPENDIX I. NOTATION

a, aj = area under uniform tension

A = material constant relating rate of crack propagation to the stress

intensity factor Kj

B = material constant used in fracture mechanics analysis

b = length of side

c = flaw (crack) length

D = flexural rigidity

E = modulus of elasticity

f = Monin or similarity coordinate

G = total number of storm realizations

h = plate thickness

Kj = stress intensity factor

Kj = critical value of Kj

c LF = load factor

m = Weibull parameter

n = material constant

n = frequency in Hz

N = total number of panel failures /storm realization

p(t) = wind pressure loading at time t

p(Q) = mean component of the quasi-static pressure at point Q

p(Q,t) = fluctuating component of the quasi-static pressure at point Q

P50 ~ orie minute effective loading

C

P50 ~ oi^G minute effective loading defined by equation 20

D

P50 = one minute effective loading defined by equation 21

17
Pplj^ = peak pressure

= Internal velocity pressure

qp = effective velocity pressure for parts and portions

s = sample standard deviation

S(t) = strength at time t

Si = initial strength

So = Weibull location parameter

SF = stress factor

t = time

tpk = time duration of peak pressure

Vf = fastest mile wind speed

X = sample mean

Y = proportionality constant

y = parameter calculated in Type I distribution

z = elevation

Of = direction

V = Poisson's ratio

p = density of air

a(M,t) = nominal stress induced by a pressure load at point M and time t

Oj^Ct, Of) = normal stress perpendicular to direction af at time t

%0^^) ~ equivalent one-minute stress at point M

18
APPENDIX II. COMPUTER LISTING
c

C GLASS ANALYSIS PROGRAM

C

c

C THIS PROGRAM ESTIMATES THE PROBABILITY OF FAILURE

C OF SQUARE GLASS PANELS SUBJECTED TO ARBITRARY

C PRESSURE LOADINGS. THE PROGRAM CAN BE EASILY

C MODIFIED TO ACCOMODATE RECTANGULAR PANELS.

C THE LOADINGS CAN BE CONSTANT ONE-MINUTE LOADS,

C DETERMINISTIC TIME DEPENDENT LOADS, OR

C FLUCTUATING LOADS. THE LATTER ARE SIMULATED

C USING QUASI-STATIC THEORY AND AUTOREGRESSIVE MODELS,

C OR CAN BE READ IN AS FLUCTUATING OR CONSTANT.

C THE INITIAL STRENGTH VALUES FOR EACH LOCATION

C ON THE PANEL ARE GENERATED FROM INPUT WEIBULL

C PARAMETERS, OR CAN BE READ IN, OR SIMPLY INPUT

C AS CONSTANT. STRENGTH DEGRADATION IS DETERMINED

C AND IF DESIRED, THE STRESS AND STRENGTH TIME

C HISTORIES OF THOSE PANELS WITH DEGRADATION

C OF A CERTAIN PERCENTAGE CAN BE WRITTEN ONTO A C FILE. C

C

C THE SIXTY-SECOND LOADINGS GIVEN BY EQNS. 20 AND 21 ARE

C CALCULATED FOR EACH P(T) (FLUCTUATING LOADING).

C

C

c

C TO OBTAIN FAILURE STATISTICS, NUMERICAL EXPERIMENTS

G ARE CONDUCTED ... C UP TO 1000 PANELS CAN BE SUBJECTED TO AS MANY

C AS 10 STORMS, EACH HAVING THE SAME MEAN BUT

C WITH FLUCTUATINF TIME HISTORIES THAT ARE

C DIFFERENT ON ACCOUNT OF THE RANDOM NATURE OF

C THE FLUCTUATIONS. EACH STORM CAN BE OF DURATION

C 900 SECONDS OR LESS. TO SUMMARIZE...

C TEN STORMS CAN BE TESTED.

C 1000 PANELS/ STORM CAN BE TESTED.

C STORM DURATION CAN BE 900 SECONDS OR LESS.

C THESE PARAMETERS CAN BE CHANGED BY INCREASING

C OR DECREASING THE DIMENSION STATEMENTS BELOW...

C INPUT PARAMETERS ARE DEFINED BELOW

C

c

C THE STATEMENTS CONCERNING THE PRESSURE TIME

C HISTORY IN THIS PROGRAM CORRESPOND TO THE

C CASE WHERE ( 1 ) THE VELOCITY IS PERPENDICULAR

C TO THE PLANE OF THE FACADE AND (2) THE PANEL

C IS SUFFICIENTLY FAR FROM THE EAVE OF THE

C GROUND (SEE EQNS 1M AND 15 IN THE REPORT).

C FOR ANY OTHER POSITION OF THE PANEL, THE PRESSURES

C ARE DETERMINED IN ACCORDANCE WITH THE RELATION:

C

C P(Y,Z,T) = 0.5 RHO (U(H)»«2 ) CP(Y,Z,T)

CC WHERE P(Y,Z,T) = TIME DEPENDENT PRESSURE AT ELEVATION Z C AT DISTANCE Y FROM THE CENTERLINE OF

C THE FACADE AT TIME T C RHO = AIR DENSITY

C U(H) = MEAN WIND SPEED AT THE TOP OF THE

C BUILDING

20
C CP(Y,Z,T)= PRESSURE COEFFICIENT CORRESPONDING TO

C THE WIND TUNNEL OR FULL SCALE REFERENCED

C WITH RESPECT TO U(H)

Cc

c

c

c

C PARAMETER DEFINITIONS IN ORDER OF INPUT...

C

c

C NSTORM NUMBER OF STORMS

C NPANEL NUMBER OF PANELS

C NDUR STORM DURATION ( SECONDS ) C DT TIME STEP ( SECONDS ) C SIDEA LENGTH OF PANEL SIDE (INCHES)

C TH THICKNESS (INCHES)

C E MODULUS OF ELASTICITY (PSI)

C PR POISSONS RATIO

C KIC STRESS INTENSITY FACTOR (COMPATIBLE W/ MPA UNITS)

C A FRACTURE MECHANICS PARAMETER (SAME AS WITH KIC)

C RY GEOMETRIC SHAPE PARAMETER

C RN POWER USED IN EQN. 6 C SO UNITS = MPA, WEIBULL DISTRIBUTION PARAMETER

C CO Mrl/CG IN WEIBULL DISTRIBUTION, EQN, 8 IN

C THE REPORT

C SCONT CONSTANT STRENGTH VALUE ,UNITS=MPA

C STCONT CONSTANT STRESS VALUE, UNITS = MPA

C DAF(1) NAME OF FILE WHICH CONTAINS INITIAL

C STRENGTH VALUES, IF THIS OPTION IS

C CHOSEN

C ILOAD LOAD TYPE

C = 1 , SIMULATE FROM AR(2) MODEL

C = 2 , CONSTANT, READ IN FROM LOGICAL UNIT 5 C = 3 , READ IN FROM LOGICAL UNIT 10 C ISTREN INITIAL STRENGTH TYPE

C = 1 , WEIBULL DISTRIBUTION

C = 2 , CONSTANT, INPUT VALUE

C = 3 , READ IN FROM LOGICAL UNIT 11 C ISTRES STRESS TIME HISTORY TYPE

C = 1 , CALCULATE FROM P(T)

C = 2 , CONSTANT, INPUT VALUE

C IWRIT PRINTING OPTION

C = 1 .PRINT ONLY FINAL TABLE

C =2 .PRINT OUT FAILURE TIME & INITIAL STRENGTH

C AT LOCATIONS WHERE FAILURE OCCURS

0 & THE FINAL TABLE

C =3 .PRINT OUT FAILURE TIME & INITIAL STRENGTH

C AT LOCATIONS WHERE FAILURE OCCURS,

C AS WELL AS THE STRENGTH & STRESS TIME

C HISTORIES, & THE FINAL TABLE

C IRAT RATIO CHECK

C = 1 . CHECK FOR % DEGRADATION

C & PRINT OUT % AT LOCATION & DIRECTION

C = 2 .DO NOT CHECK

C =3 .CHECK AND PRINT OUT THE STRENGTH

C & STRESS TIME HISTORIES

C = 1 OR 3, INPUT RAT1.RAT2 %S BELOW

C NOTE RATI MUST BE .GE. RAT2

C

C

cc DOUBLE PRECISION DSEED,TERM1 .TERM2,RDIFF.RDIR .RATIO. SLOPE

DOUBLE PRECISION A1 ( 1 000) . A2( 6 )

, S( 900) , AI (6 , 1 000) ,RSIG( 36 . 6

)

REAL IT,PV(10),F(1000),PMEAN,PM(10),NFAIL2(216).FMAX.

21
•UMEAN ( 1 0 )

, PF ( 1 0 ), PCER (10), PDAG ( 1 0 ), RAT 1, RAT2

DOUBLE PRECISION P( 900 ), SIGMA (36, 900)

EQUIVALENCE( P(1),S(1) ) DOUBLE PRECISION M, COEF,D, SO , BP, A, KIC, TH, PR ,E, ROOT, RNM, RN DOUBLE PRECISION P60( 10) ,SCALE,FLEX,SC0NT,STC0N,SIGG2,

»SINT(1000),SU,Ry

INTEGER MRI , ISTREN , NCOUNT , NPANEL , NDUR , I 1

,

•ISEED , TIME ( 1 000 ), IWRIT , IRAT , K? , K6 ( 36

)

CHARACTER*16 DAF(1»)

CC ENTER PARAMETERS

C

C

C READ ( 5

, • ) NSTORM , N PANEL , NDUR , DT READ(5,*)SIDEA,TH

READ(5,»)E

READ(5,»)PR,KIC

READ(5,*)A,RN,RY

READ ( 5 ,*) ILOAD , ISTREN , ISTRES , IWRIT , IRAT

IF( ISTREN .EQ. 1 )READ(5,»)SU,S0,C0

IF( ISTREN .EQ. 2)READ(5,*)SC0NT

IF( ISTRES .EQ. 2)READ(5,*)STC0N

IF( ISTREN .EQ. 3 )READ(5,8)DAF( 1

)

IF( IRAT .NE. 2 )READ(5,»)RAT1 ,RAT2

C CALL TWRITE ( ILOAD , ISTRES , ISTREN , NDUR

)

C

C DEFINE POWERS FOR EQUATIONS

C RNN=RN+1

.

RNM=RN-2.

R00T=1./RNM

R00T2=1./RN

C

C CALCULATIONS

C BP=(RNM»A»RY»RY*(KIC*»RNM))/2.

FLEX= ( E »TH»TH »TH ) / ( 1 2

. • (

1 - PR »PR )

)

COEF=DT«BP/RNN

SCALE= ( SIDEA«»i| . ) / ( FLEX'TH

)

C

c

c CALL GWRITE ( SIDEA , TH , E , PR , A , KIC , NPANEL , RN , BP)

,0 DO 5555KK=1 , NSTORM

IF( IWRIT .NE. 1 )WRITE(6,7)KK

IF( IRAT .NE. 2 )WRITE(9,7)KK IF ( ILOAD .EQ. 2 ) GO TO 1111 IF ( ILOAD .EQ. 3 ) GO TO 1112

IF( ISTRES .EQ. 2 ) GO TO 2222

IF( ISTREN .GT. H )WRITE(6 ,9000)

IF( ISTRES .GT. k )WRITE(6 , 9000)

c

c

c

c

c PARAMETER DEFINITIONS FOR P(T) SIMULATION

c CP STATIC PRESSURE COEFFICIENT

c Z ELEVATION

c ZO FRICTION LENGTH

c UMEAN MEAN WIND VELOCITY

c MRI MEAN RECURRENCE INTERVAL

cc

22
READ(5,»)CP,Z,Z0,IT,MRI

DATA XMIN,XMAX,NDIV/0, 100, 1000/

UMEAN(KK)=IT

IT=IT«1.i»7

CC ICLOCK IS A FUNCTION WHICH RETURNS THE NUMBER OF SECONDS

C SINCE MIDNIGHT

C

c CALL ICLOCK ( 2, ISEED)

DSEED=DFLGAT ( ISEED

)

C

C

C GENERATE LOAD AND NON-DIMENSIONALIZE

C

C CALL PRES ( XMIN , XMAX , NDIV , DSEED ,DT,NDUR,Z,ZO,IT,CP, PMEAN , PVA , P

)

PV(KK) = 1i»4.«PVA

PM(KK) = 141|.*PMEAN

CALL PWRITE ( IT , MRI , DT , CP , PMEAN , P , NDUR

)

C

C

c GO TO

1111 CONTINUE

READ(5,»)P60(KK)

DO 3331=1, NDUR

333 P(I)=P60(KK)

GO TO HkH

1112 READ(10,»)( P(I), 1=1 ,NDUR ) CC

C FIND THE EQUIVALENT SIXTY-SECOND LOADINGS FOR P(T)

CCkkh CONTINUE

CALL PEQ(NDUR,DT,RN,P,P1,P2)

PCER(KK) = 1i<4.»P1 PDAG(KK)=141».»P2

C

C

C CALCULATE THE LOAD FACTOR FROM P(T)...

CC DO 301 11=1, NDUR

3011 P(I)=P(I)»SCALE

C

C FIND DIRECTIONAL MULTIPLIERS AND CALCULATE THE STRESS FACTORS...

C CALL DIR(RSIG)

CALL STRESS( FLEX , SIDEA , TH , NDUR , P , SIGMA

)

CC

c

C INITIAL STRENGTH DISTRIBUTION

C WEIBULL DISTRIBUTION ASSUMED

C2222 CONTINUE

IF ( ISTRES .NE. 2 .AND. ISTREN .NE. 2 )G0 TO 2223

J=1

JK=0

111=0

GO TO 60 2223 IF( ILOAD .NE. 2 .AND. IWRIT .NE. 1 )WRITE(6,3)

IF( ISTREN .EQ. 3 )OPEN( 1 1

, IOSTAT=ISTAT, FILE=DAF( 1 )

)

C

23
c DO 111J=1,36

111 K6(J)=0

DO 10J=1,36

IFdSTREN .EQ. 2) GO TO 50 IFdSTREN .EQ. 3) GO TO HO M=1./C0

C

C CALL ICL0CK(2,ISEED)

DSEED=DFLOAT(ISEED)

CALL GGUBS (DSEED.N PANEL, F)

CC DO 22K=1,6

DO 3011=1 ,NPANEL

30 A1(I1)=SU + S0«((-AL0G(F(I1)))»»M)

CC RANK THE INITIAL STRENGTH VALUES ...

CC ELIMINATE THOSE WHICH ARE TOO LARGE FOR FAILURE TO

C OCCUR...

CC CALL VSRTAD(A1,NPANEL)

C

C DO 3111=1, NPANEL

31 AI(K,I1)=A1{I1)

22 CONTINUE

DO 23K=1,6

A2(K)=AI(K,1)

23 CONTINUE

C

C VSRTAD IS AN IMSL SUPPLIED ROUTINE WHICH

C RANKS THE VALUES OF THE INPUT VECTOR FROM SMALLEST

C TO LARGEST

C

C

C RANK THE INITIAL STRENGTH VALUES ACCORDING TO DIRECTION.

C CALL VSRTAD (A2, 6) C

C

C CHECK TO SEE HOW MANY DIRECTIONS CAN BE ELIMINATED FROM

C COMPARISON BELOW...

CC DO 24K=1,6

IF( A2(1) .EQ. AI(K,1) )K5=K

K6(J)=K5

24 CONTINUE

GO TO 10 C

C READ IN INITIAL STRENGTH VALUES AND RANK AS ABOVE FOR

C GENERATED VALUES

CC

C40 CONTINUE

DO 26K=1,6

READ(11,44) ( A1(I1), 11=1, NPANEL ) CC RANK THE INPUT INITIAL STRENGTH VALUES ... C

24
c CALL VSRTAD(A1,NPANEL)

C

C

C DO 2711=1 ,NPANEL

AI(K,I1)=A1(I1)

27 CONTINUE

26 CONTINUE

DO 28K=1,6

A2(K)=AI(K,1)

28 CONTINUE

CC

C RANK ACCORDING TO DIRECTION

C

C CALL VSRTAD(A2,6)

C

C CHECK TO SEE HOW MANY DIRECTIONS MAY BE CRITICAL...

C

C

C DO 29K=1,6

IF(A2(1) .EQ. AKK.D) K5=K

K6(J)=K5

29 CONTINUE

10 CONTINUE

50 CONTINUE

C

C

C THE ICQ LOOP IS FOR EACH NPANEL CHECK

CC JK=0

NPOS=36

DO 110J=1,NPOS

K7=K6(J)

NCOUNT=0

DO 20K=1,K7

NCOUNT2=0

JK=JK+1

DO 100 11=1, NPANEL IFdSTREN .EQ. 2) GO TO 60

S(1)=A1(I1)

GO TO 70

60 S(1)=SC0NT

NCOUNT=0

JK=JK+1

111=111+1

70 CONTINUE

C

C EQUATION 6 IN REPORT

CC DO 200I=2,NDUR

IF( ISTRES .EQ. 2 ) D=1.0

IF( ISTRES .EQ. 2 )G0 TO 700

SLOPE=SIGMA ( J , I

) -SIGMA ( J , I- 1

)

IF( SLOPE .EQ. 0 ) GO TO 700

IF( RSIG(J,K) .LT. 0 )G0 TO 20 RDIR= (RSIG(J,K))»»RN

D=RDIR»((SIGMA(J,I)»«RNN) -(SIGMA(J,I-1 )«»RNN) )/SL0PE

SIGG2= SIGMA ( J , I

) "RSIG ( J , K

)

GO TO 800

700 IF( ISTRES .EQ. 2 )SIGG2=STC0N

25
IF( ISTRES .NE. 2 )SIGG2=SIGMA(J,I)»RSIG(J,K)

IF( ILOAD .EQ. 2 )D=1.0

IF( SIGG2 .LE. 0 ) SIGG2=0

IF( SIGG2 .EQ. 0 )D=0

IF( D .EQ. 0 ) GO TO 800

D=RNN»( SIGG2»»RN ) 800 TERM1=S(I-1 )»»RNM

TERM2=C0EF»D

C WRITE(6,»)' TERM1 ',TERM1

C WRITE(6,«)« TERM2 ',TERM2

RDIFF=TERM1 -TERM2

IF( RDIFF .LT. 0 ) GO TO 900

S(I)=RDIFF»»ROOT

200 IF( SIGG2 .GE. S(I) ) GO TO 900

C

CC FAILURE DOES NOT OCCUR IN THE GIVEN TIME PERIOD

C CHECK FOR DEGRADATION

C IF( IRAT .EQ. 2 )G0 TO 102

RATIO = (S(NDUR)/S(1))»100.

IF( RATIO .LT. RATI ) GO TO 901 102 CONTINUE

IF( ISTRES .EQ. 2 .AND. ISTREN .EQ. 2 ) GO TO 5555

IF( ISTREN .EQ. 2 ) GO TO 10 GO TO 902

900 NCOUNT = NCOUNT + 1 NC0UNT2=NC0UNT2+1

TIME (NCOUNT )= I SINT(NCOUNT)= S(1)

IF( IWRIT .EQ. 1 .OR. IWRIT .EQ. 2 ) GO TO 333^ NEND=I

IF( ISTRES .NE. 2) WRITE(6 , 6000) ( SIGMA(J,I) ,1=1 ,NEND)

WRITE(6,6000)( S(I), I=1,NEND ) IF(I1 .LT. NPANEDGO TO 100 IFdSTREN .NE. 2) GO TO 3334

DO l»Hi(3I=1 ,NEND

HHtiS SIGMA(1,I)= SIGG2

WRITE(6,6000)( SIGMA(J,I), I=1,NEND ) 3334 DO 99991= 1,NEND

9999 S(I)=0.0

GO TO 100

901 WRITE (9,*)' RATIO OF FINAL TO INITIAL S = '.RATIO,' %

' WRITE(9,»)' AT POSITION '

, J, ' AND DIRECTION ',K

IF( ISTRES .EQ. 2 .AND. ISTREN .EQ. 2 )WRITE(9,»)' PANEL # ',111

IF(ISTRES.NE.2 .AND. ISTREN. NE. 2)WRITE(9, •) ' PANEL # ',11

WRITE (9,*)' % CHECK VALUES ARE ',RAT1,' AND ',RAT2 IF ( RATIO .GE. RAT2 )G0 TO 101 IF( IRAT .EQ. 1 .OR, IRAT .EQ. 2 )G0 TO 101 IF( RATIO .LT. RAT2 )WRITE{9 ,6000) ( S(I )

, 1= 1 ,NDUR ) DO 88761=1, NDUR

8876 SIGMA(J,I)=SIGMA(J,I)»RSIG(J,K)

IF( RATIO .LT. RATI )WRITE(9 ,6000) ( SIGMA(J,I) ,1=1 ,NDUR)

DO 67881=1, NDUR

6788 SIGMA(J,I)=SIGMA(J,I)/RSIG(J,K)

101 CONTINUE

DO 99981=1, NDUR

9998 S(I)=0.

C

C

C FINISH OF 100 LOOP

C

C100 CONTINUE

CC

26
902 DO 99881= I.NDUR 9988 S(I)=0.

NFAIL2 ( JK ) =REAL ( NC0UNT2

)

IF( NCOUNT .EQ. 0 ) GO TO 20

IF( IWRIT .EQ. 1) GO TO 20

WRITE(6,3)

DO 700 11=1, NCOUNT

7001 WRITE(6,2)I,J,K,TIME(I),SINT(I)

IF( ISTRES .EQ. 2 .AND. ISTREN .EQ. 2) GO TO 5555

CC FINISH THE DIRECTION LOOP

C20 CONTINUE

C

C FINISH THE LOCATION / POSITION LOOP

110 CONTINUE

C

C

C CALCULATE THE NUMBER OF FAILURES PER STORM AND

C WRITE TO AN OUTPUT DEVICE

C FMAX=0.0

II=JK

DO 70021=1,11

7002 FMAX=AMAX1(FMAX,NFAIL2(I))

PF(KK)=FMAX/NPANEL

IF( ILOAD .EQ. 2 ) GO TO 5555

C

C

C GO TO NEXT STORM...

C

C CLOSE(II)

5555 CONTINUE

C IF( ISTREN .EQ. 2 .AND. ISTRES .EQ. 2 ) GO TO 5561

IF( ILOAD .EQ. 2 )G0 TO 5558

WRITE(6,6)

CC PRINT THE FINAL PROBABILITY ESTIMATES

C DEFINITIONS. .

.

C UMEAN(K) MEAN WIND SPEEDS

C PM(K) MEAN PRESSURES

0 PV(K) STANDARD DEVIATION OF P(T)

C PCER(K) 60-SECOND LOADING OF EQN. 20

e PDAG(K) 60-SECOND LOADING OF EQN. 21 C PF(K) # OF FAILURES FOR P(T)/# OF PANELS TESTED

C UNITS OF PRESSURE VALUES = PSF

C VELOCITY IN FT/ SEC

C

C DO 5556KK=1 ,NSTORM

5556 WRITE (6, 5) UMEAN ( KK ), PM( KK )

, PV ( KK ), PCER ( KK ), PDAG ( KK ), PF ( KK

)

GO TO 5559

5558 WRITE(6,9)

DO 55601= 1,NST0RM

P60(I) = 1HJ».»P60(I)

5560 WRITE(6,112)P60(I),PCER(I),PDAG(I),PF(I)

5561 CONTINUE

C6000 FORMAT(1X,5F10.4)

9000 FORMATdX,' THE VALUE OF ILOAD, ISTREN, OR ISTRES IS WRONG')

2 F0RMAT(1X,I5,6X,I5,7X,I5,5X,I5,2X,F12.4)

3 FORMATCIX, ' FAILURE # '.IX,' POSITION ',1X,' DIRECTION ', •IX,' TIME '.IX.'S INITIAL ') 5 FORMAT(1X,6F10.5)

27
6 F0RMAT(3X,' MEAN U ',3X,' MEAN P ',1X,' STAN P'.IX,

PI ',1X,' P2 ' ,1X, 'PF(PMEAN) ') 7 FORMATdX,' STORM NUMBER ',110)

8 F0RMAT(16C)

9 F0RMAT(3X, ' PRESSURE ',5X,' PI '.IX, • P2 • ,7X,

»' PF ') 112 FORMAT(1X,F10.2,5X,F10.2,5X,F10.5,5X,F10.5)

kH FORMATdX, 6F10. 4)

C

C5559 CONTINUE

STOP END

C SUBROUTINE DIR(RSIG)

C FIND DIRECTIONAL MULTIPLIERS FOR STRESSES AT VARIOUS

C ANGLES...

CC DOUBLE PRECISION PH,RSIG(36 ,6) ,C(6) ,SII(6) ,S2S1 (36) DATA S2S1/ 1.0,. 98,. 94,. 89,. 79,. 68,. 52,. 12,. 97,. 93,

*. 86,. 77,. 65,. 47,. 05,. 89,. 82,. 71,. 57,. 36, -.09,. 73,. 61,

•.45,. 21, -.24,. 47,. 28,. 02, -.38,. 83, -.17, -.52, -.39, -.66,

»-.8l/

DO 5K=1,6

PH=(K-1 )*3. 14159/10.

C{K)=DCOS(Ph)«DCOS(PH)

5 SII(K)=DSIN(PH)»DSIN(PH)

DO 10J=1,36

DO 11K=1,6

11 RSIG(J,K)=C(K) + S2S1(J)»SII(K)

10 CONTINUE

RETURN

END

C SUBROUTINE PEQ(NDUR,DT,RN,P,P1 ,P2)

C

C

C THIS ROUTINE CALCULATES THE 60- SECOND LOADINGS OF

C EQNS. 20 AND 21 C

CC DOUBLE PRECISION RN ,R00T2, PEFF( 2) , PMAX, P(»)

•,AREA,P1,P2,PD(900)

R00T2=1./RN

PMAX=0.0

IlrNDUR

DO 10001=1,11

PMAX=DMAX1(PMAX,P(I))

1000 CONTINUE

DO 2000K=1,2

PEFF( 1

) = ( ( DT/60 . ) *»R00T2 ) *PMAX

IF{K .EQ. 1) GO TO 3000 DO 25001= 1,NDUR

2500 PD(I)=P(I)»»RN

C

C

C INT IS AN INTEGRATION ROUTINE

C

C CALL INT ( PD , NDUR , 1 . 0 , AREA

)

C

C PEFF( 2) = ( AREA/60 . ) »»R00T2

P2=PEFF(2)

28
3000 P1=PEFF(1)

2000 CONTINUE

RETURN

END

C

C SUBROUTINE INT(P,NDUR,H,AREA)

C

C

C TRAPEZOIDAL RULE

C DOUBLE PRECISION AREA, P( 900)

N=NDUR-1

SUM=0.0

DO 501=2,

N

50 SUM=SUM+P(I)

AREA=0.5»H»( P(1) + 2.0»SUM + P(NDUR) ) RETURN

END

C

C SUBROUTINE PWRITE ( IT , MRI , DT , CP , PMEAN , P , NDUR

)

C

C

C SUBROUTINE TO PRINT INPUT PRESSURE SIMULATION PARAMETERS

C

C DOUBLE PRECISION P(900) REAL IT WFITE(6,1)

WRITE(6,2)IT,MRI,DT,CP

WRITE (6, 3) NDUR WRITE (6, 30) PMEAN WRITE(6,4)( P(I), 1=1, NDUR ) WRITE(6,1)

1 FORMAT(IHI)

2 F0RMAT(//,1X,' LOADING SIMULATION ',/,

•5X,' INPUT MEAN VELOCITY (FT/SEC) =',F10,4,/,

»5X, • MEAN RECURRENCE INTERVAL (YEARS) =',110,/,

»5X, ' TIME STEP IN SECONDS =',F10.4,/,

*5X, ' PRESSURE COEFFICIENT, CP =',F10.4)

3 F0RMAT(5X,' P(T), T=1, ',15,' SECONDS ') 30 F0RMAT(6X,' MEAN PRESSURE IN PSI = ',F10.4)

4 FORMAT (5F1 0.4)

RETURN

END

C SUBROUTINE GWRITE ( SIDEA , TH , E , PR , A , KIC , NPANEL , RN , BP

)

CC

C SUBROUTINE TO PRINT INPUT PLATE PARAMETERS...

C

c DOUBLE PRECISION KIC, A, PR, E,RN, BP, SIDEA

WRITE(6,1)

WRITE (6, 2) NPANEL WRITE(6,3)SIDEA,TH,E,PR,A,KIC,RN,BP

1 FORMAT(IHI)

2 FORMATdX,' •• GLASS PANEL CHARACTERISTICS • •2X,I5,' PANELS ARE TO-BE TESTED ',/)

FORMAT (/,5X,

• 5X,

• 5X,

• 5X,

• 5X,

• 5X,

LENGTH OF EACH SIDE

THICKNESS

MODULUS OF ELASTICITY

POISSONS RATIO

VALUE OF A STRESS INTENSITY FACTOR

II,

,F10.4,/,

,F10.4,/,

,E10.4,/,

,F10.i»,/,

,F10.4,/,

,F10.4,/,

29
• 5X,' POWER N IN EQUATION =',F10.1»,/,

• 5X, ' 1/B IS CALCULATED TO BE =

' , F1 0.4 , ///

)

RETURN

END

C SUBROUTINE TWRITE ( ILOAD , ISTRES , ISTREN , NDUR

)

C

c

c

C PROGRAM TO WRITE TEST PARAMETERS

CC

C WRITE(6,1) IF ( ILOAD .EQ. 1 )WRITE(6,2) IF ( ILOAD .EQ. 2 )WRITE(6,1») IF ( ILOAD .GT. 3 )WRITE(6,31) IF ( ILOAD .EQ. 3 )WRITE(6,32) WRITE (6, 3) NDUR WRITE(6,5)

IF ( ISTREN .EQ. 1 )WRITE(6,6)

IF( ISTREN .EQ. 2 )WRITE(6,7)

WRITE(6,8)

IF( ISTRES .EQ. 1 )WRITE(6,9) IF ( ISTRES .EQ. 2 )WRITE(6,10) WRITE (6, 3) NDUR

1 FORMATdX,TEST PARAMETERS *•»',//,

•2X, ' #1 PRESSURE LOADING ',/) 2 F0RMAT(7X,

SIMULATED P(T) ') 3 FORMAT (7X,

FOR ' ,15, ' SECONDS ' ,/)

31 F0RMAT(7X,

NOT CONSIDERED ') 32 F0RMAT(7X,

READ IN FROM FILE ') 4 F0RMAT(7X,

CONSTANT PRESSURE ') 5 F0RMAT(2X,

#2 INITIAL STRENGTH DESCRIPTION'

6 F0RMAT(7X,

TO BE GENERATED FROM A WEIBULL DISTRIBUTION •) 7 F0RMAT(7X,

CONSTANT VALUE ') 8 FORMAT (2X,

#3 ',' STRESS TIME HISTORY ',/)

9 F0RMAT(7X,

GENERATED FROM THE PRESSURE LOADING ') 10 F0RMAT(7X,

CONSTANT SIGMA VALUE •) RETURN

END

C SUBROU TINE PRES ( R 1

, R2 , NDIV , DS , DT , NDUR , Z , ZO , IT , CP , PM , PVAR , P

)

C

c

C THIS SUBROUTINE COMPUTES THE QUASI-STATIC LOADING

C AT THE STAGNATION POINT USING THE ARIMA-COMBINED

C TECHNIQUE AND THE SPECTRAL EXPRESSION IN EQN. 18

CC

CC

C

c REAL AO.IT.DENSTY.PJ ,Z,SUM,K1 ,C,UF

DOUBLE PRECISION P(900),DS

REAL U(900),NORM(900)

REAL UFS , DT , PH1 1

, PHI2 , ACOV ( 3 )

, ACF( 3 ), VARU , VARAU

PI=3. 14159

DENSTY=. 00258

XMAX=R2

XMINrRI POWER=5./3.

DX= ( XMAX-XMIN ) /NDIV

C

c

30
cC DEFINITIONS

C

(:C IT= MEAN VELOCITY

C Z=ELEVAT1()N

C 2.0=FRICTION PARAMETER

C UF=FRICTION VELOCITY

C ACOVrAUTOCOVARIANCE, ACF=AUTOCORRELATION

C VARU,VARAU= SCALING VARIANCES FOR VELOCITY

C U=GENERATED VELOCITY, P=GENERATED PRESSURES

C

C

C GGNML IS A PSEUDO-RANDOM # GENERATOR FROM IMSL

C

C

C FOR AN EXPLANATION OF THE METHOD, SEE "AUTOREGRESSIVE

C MODELING OF LONGITUDINAL TURBULENCE SPECTRA", J. OF

C INDUSTRIAL AERODYNAMICS AND WIND ENGINEERING, 1982,

C BY REED AND SCANLAN.

CC

c A0r50.»Z,/IT

UF=(0.4»IT)/(AL0G(12.»Z/Z0))

UFS=UF*UF

C=(200.»UFS»Z)/IT

C DO 10J=1,3

1=1 X=0.0

SUM=1.0

TAU=(2.«J)-2.

TAU=PI»TAU

2 X=X+DX FREQ=TAU»X

FX=C0S(FREQ)/((1 .+A0»X)«»POWER)

G=2.»FX

SUM=SUM4-G

1=1+1

IF(I .LT. NDIV)GO TO 2 FB=COS ( FREQ ) / ( ( 1 . +AO»XMAX) »»POWER

)

SUM=SUM+FB

AREA=SUM«(DX/2.)

10 AC0V(J)=(C/2.)*AREA

DO 20J=1,2

20 ACF(J)=AC0V(J+1)/AC0V(1)

C D=1.-(ACF(1)»»2.)

PHI1r(ACF(1)*(1 .-ACF(2)))/D

PHI2=(ACF(2)-(ACF(1)**2.))/D

WRITE(6,»)' AUTOREGRESSIVE MODEL PARAMETERS ARE ',PHI1,PHI2

VARU=AC0V(1)

VARAU=(((1.+PHI2)«((1 .-PHI2)«»2.-(PHI1«»2. )))/(1 .-PHI2))

1 "VARU SDEVA=SQRT(VARAU)

DO 30J=1,2

30 U(J)=0.

CCC CALL GGNML(DS,NDUR,NORM)

C

c

C SET UP GENERATION EQUATION FOR FLUCTUATING VELOCITY

31
C DEFINE PMEAN

PMEANr { 1 . / 1 41 . ) . 5»IT*IT»CP»DENSTY

RCON=PMEAN/IT

C DO 50J=3,NDUR

50 U(J)=PHI1»U(J-1) + PHI2«U(J-2) + SDEVA«NORM( J) DO 60J=1,NDUR

60 P(J)=PMEAN + RCON»U(J)

C

C

C

C THIS P REPRESENTS THE TOTAL LOAD, MEAN + FLUCTUATING COMPONENT

C UNITS OF P = PSI

C

C

C SUM=0.0

DO 5J=1,NDUR

5 SUM=SUM+P{J)

PM=SUM/NDUR

SUM=0.0

DO 6J=1,NDUR

6 SUM=SUM + (( P(J) - PM )«»2 ) PVAR=SQRT( SUM/(NDUR-1) ) C

C WRITE{8,70)(P(I),I=1,NDUR)

C70 FORMAT (5F10.i»)

C RETURN

END

C SUBROUTINE STRESS( FLEX, SIDEA , TH , NDUR , P , SIGMA

)

C

CC THIS PROGRAM CALCULATES THE STRESS FACTORS FOR A SQUARE

C PLATE , GIVEN A PRESSURE TIME HISTORY

CC DOUBLE PRECISION TH, FLEX, SIDEA, »R1(36),R2(36),R3(36),Ri»(36),S1(36),S2(36),S3(36),Si»(36)

DOUBLE PRECISION P(900) , SIGMA(36 , 900)

COEF= ( . 00689*FLEX) / ( SIDEA •SIDEA*TH

)

CC

C INPUT INTERCEPT AND SLOPE PARAMETERS FOR STRESS-PRESSURE

C LINEAR RELATIONSHIPS

C

c DATA R1/1H9.,151.,157.,163.,165.,157.,130.,78. J50.,155.,

•162., 165., 157., 131., 79., 151., 157., 162., 156., 13?., 82., 127.,

»1 27., 122., ion., 70,, 180., 181., 165., 120., 1 51., I4lt., 144.,

•144. ,143. ,157./ DATA SI / . 058 , . 060 , . 066 , . 077 , . 092 , . 1 00 , . 094 , . 06 1

, . 059 , . 066

,

*. 078,. 092,. 103,. 096,. 063,. 065,. 080,. 096,. 109,. 103,. 066,

«. 086 , . 1 06 , . 1 1 9 , . 1 1 3 , . 07 1

, . 070 , . 084 , . 085 , . 056 , . 089 , . 086

,

••063, .086, .080, .118/

C DATA R2/ 207. ,211. ,223. ,240. ,257. ,257. ,224. ,139. ,209.,

•221 . ,239. ,258. ,258. ,227. , 142. ,216. ,237. ,258. ,265.

,

•235., 148., 21 3., 233., 241., 217., 141., 250., 265., 250., 176.,

•238. ,230., 186. ,237. ,223. ,246./ DATA S2/ . 034 , . 036 , . 036 , . 043 , . 054 , . 067 , . 067 , . 047

,

•.037,. 039,. 045,. 055,. 068,. 069,. 048,. 044,. 048,. 059,

•. 072 , . 075 , . 053 , . 059 , . 07 1

, . 089 , . 095 , . 068 , . 062, . 087

,

••099,. 073,. 100,. 118,. 090,. 123,. 105,. 114/

C

32
DATA R3/310. ,319. ,333. ,370. ,420. ,i<57. ,426. ,279. ,320.

,

•337., 374., H25., 463., 435., 286., 349., 381., 436., 1)82.,

•460. ,307. , 392. ,445. ,507. ,502. ,345. ,436. ,525. ,549.

,

•396. ,539. ,583. ,457. ,607. ,607. ,587./ DATA S3/ . 0 1 9 , . 0 1 8 , . 0 1 9 , . 023 , . 032 , . 045 , . 053 , . 038 , . 022

,

•.023,. 025,. 034,. 047,. 053,. 039,. 028,. 031,. 037,. 049,. 055,

•.041 ,.038,. 042,. 052,. 060,. 046,. 050,. 057,. 070,. 058,. 058,

•.083,. 077,. 096,. 082,. 105/

DATA R4/407., 410., 430., 484., 581., 687., 689., 471., 428.

,

•454., 500., 593., 697., 700., 480. ,490. ,538. ,620. ,725. ,735.

,

•51 1. ,584., 656. ,769. ,803. ,576. ,688. ,812. ,901 . ,688. ,827.

,

•998. ,843., 1086. , 1016. , 1114./ DATA S4/ . 029 , . 029 , . 027 , . 026 , . 032 , . 042 , . 049 , . 036 , . 030 , . 03 1

,

». 029,. 032,. 041,. 048,. 037,. 033,. 034, .034,. 042,. 049,. 037,

••037,. 038,. 043,. 050,. 039,. 044,. 046,. 056,. 048,. 038,. 064,

•.064, .072, .085,. 110/

DO 200I=1,NDUR

IF(P(1).LE.1000)GO TO 3 IF(P(I) .GT. 1000 .AND. P(I) .LE. 2000) GO TO 4 IF( P(I) .GT. 2000 .AND. P(I) .IF. 5000) GO TO 5 IF(P(I) .GT, 5000 .AND. P(I) .LE. 10000) GO TO 6 IF(P(I) .GT. 10000) GO TO 7

3 CONTINUE

SIGMA(1,I)= COEF«(202 - DLOG(P(I))»( 99.6 - 13. 3*DL0G(P(I) ) )

)

SIGMA(9,I)=SIGMA(1 ,1)

SIGMA(16,I)=SIGMA(1,I)

SIGMA (22, I)=SIGMA( 1,1)

SIGMA(2,I)=SIGMA(1 ,1)

SIGMA(3,I)=SIGMA(2,I)

SIGMA(10,I)=SIGMA(2,I)

SIGMA(4,I)=C0EF»(267 - DLOG(P(I) )«( I3I -16.9*DL0G(P(I) ) ) ) SIGMAdI ,I) = SIGMA(4,I)

SIGMA(17,I)=SIGMA(4,I)

SIGMA(5,I) = C0EF»(441 - DL0G(P(I))^( 201 - 23- 5^DL0G( P(I) ) )

)

SIGMA(12,I)=SIGMA(5,I)

SIGMA(18,I)=SIGMA(5,I)

SIGMA(23,I)=SIGMA(5,I)

SIGMA(6,I)= C0EF»( 676- DLOG(P(I) )^(292-31 .6*DL0G{P(I) ) )

)

SIGMA(13,I)=SIGMA(6,I)

SIGMA(19,I)=SIGMA(6,I)

SIGMA(24,I)=SIGMA(6,I)

SIGMA(28,I)=SIGMA(6,I)

SIGMA(7,I)=C0EF»( 4.96 + .130^P(I) ) SIGMA(14,I)=SIGMA(7,I)

SIGMA(20,I)=SIGMA(7,I)

SIGMA(25,I)= C0EF»(27.4 + .0790*P(I) ) SIGMA(29,I)=C0EF»( 30.2 + .0885*P(I) ) SIGMA(32,I)= C0EF»( 36.1 + .0969^P(I) ) SIGMA(8,I)= COEF»( 1.93 + .0785^P(I))

SIGMA(15,I)=SIGMA(8,I)

SIGMA(21,I)=SIGMA(8,I)

SIGMA(26,I)= COEF»( 2.70 + .0384»P(I))

SIGMA(30,I)= C0EF*( 6.52 + 0.109^P(I))

SIGMA(33,I)= C0EF»( 8.37 + .120»P(I))

SIGMA(35,I)= COEF*( 7.93 + .142^P(I))

SIGMA(36,I)= C0EF»( 7.07 + 0.156^P(I))

SIGMA ( 27 , I ) =SIGMA ( 36 , I

)

SIGMA(31,I)=SIGMA(36,I)

SIGMA ( 34 , I ) = SIGMA ( 36 , I

)

33
c

c GO TO 200

C

c

k CONTINUE

DO 42J=1,36

42 SIGMA(J,I)= COEF»( R1(J) + S1(J)»P(I) ) C

C GO TO 200

CC

5 CONTINUE

DO 52J=1,36

52 SIGMA(J,I)=COEF*( R2(J) + S2(J)«P(I) ) GO TO 200

C

6 CONTINUE

DO 62J=1,36

62 SIGMA(J,I)= C0EF«(R3(J) + S3(J)»P(I) ) C

c GO TO 200

C

c

7 CONTINUE

DO 72J=1,36

72 SIGMA(J,I)= C0EF«(R4(J) + S1»(J)»P(I) ) C200 CONTINUE

C RETURN

END

$BEND

34
Table 1. Estimated Probabilities of Failure Based on Stress Time

History, and on l-Minute Loads Estimated in Accordance

with References 12 and 3. Units of pressure = psf.

p

C

P60

D

P60 Pf (P) Pf(P60 - P60^ Pf(P60 - P60)

10 10.8 12.6 0.001 0.002 0.003

15 16.2 18.9 0.015 0.004 0.008

20 21.6 25.2 0.050 0.012 0.022

25 27.0 31.5 0. 150 0.035 0.069

30 32.4 37.8 0.400 0.084 0.160

35
36
37
Principal

stress

directions

Figure 3. Schematic representation of angles a]^ = kAa

38
Figure 4. Cumulative distribution function for p(t)

39
0.20

TME, t (sj

Figure 5. Evolution of strength and stresses with time for breaking panel

40
41

NBS-n4A (REV. 2-8C)

U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publication Date BIBLIOGRAPHIC DATA

REPORT NO. May 1983 SHEET (See instructions) NBS BSS 154

4. TITLE AND SUBTITLE

Wind Loading and Strength of Cladding Glass

5. AUTHOR(S)

D. A. Reed and E. Simiu

6. PERFORMING ORGANIZATION (If joint or other thon NBS. see in struct/on s) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234 Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Same as in item 6 above.

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 83-600515

I I Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual sumnnary of most si gnificant information. If document includes a si gnificant

bibliography or literature survey, mention it here) A procedure for investigating glass cladding behavior under arbitrary loads,

including fluctuating wind loads, is presented. The procedure accounts for

the fact that internal stresses are nonlinear functions of the external loads,

that initial glass strengths are random functions of position and direction,

and that glass strength undergoes degradation under the action of external

loads in accordance with basic fracture mechanics laws. Numerical examples

are presented, and corresponding probability distribution curves are calculated,

indicating the probability of failure of a specified panel subjected to fluctuating wind loads and to 1-minute constant loads. These curves are used to

illustrate a method for assessing current glass cladding design procedures.

For the case considered in the paper, it was found that transformation of

the peak wind load averaged over 1-2 seconds into an equivalent 1-minute load

appears to underestimate the probability of failure of glass cladding. The

work reported in the paper is part of an ongoing window cladding research

program being conducted at the National Bureau of Standards.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

aerodynamics; buildings; deformation; engineering mechanics; failure; glass;

loads (forces); probability theory.

13. AVAILABILITY

[X| Unlimited

I I For Official Distribution. Do Not Release to NTIS

[X] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

[^31 Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

49

15. Price

$4.00

USCOMM-DC 6043-P80

-> U.S. GOVERNMENT PRINTING OFTICE ; t983 O—380-997 (5022)

NBS TECHNICAL PUBLICATIONS

PERIODICALS

JOURNAL OF RESEARCH—The Journal of Research of the National Bureau of Standards reports NBS research and develop- ment in those disciplines of the physical and engineering sciences in which the Bureau is active. These include physics, chemistry,

engineering, mathematics, and computer sciences. Papers cover a broad range of subjects, with major emphasis on measurement

methodology and the basic technology underlying standardization. Also included from time to time are survey articles on topics

closely related to the Bureau's technical and scientific programs. As a special service to subscribers each issue contains complete

citations to all recent Bureau publications in both NBS and non- NBS media. Issued six times a year. Annual subscription: domestic

$18; foreign $22.50. Single copy, $5.50 domestic; $6.90 foreign.

NONPERIODICALS

Monographs—Major contributions to the technical literature on

various subjects related to the Bureau's scientific and technical activities. Handbooks—Recommended codes of engineering and industrial practice (including safety codes) developed in cooperation with in- terested industries, professional organizations, and regulatory

bodies. Special Publications—Include proceedings of conferences sponsored by NBS, NBS annual reports, and other special publications

appropriate to this grouping such as wall charts, pocket cards, and

bibliographies. Applied Mathematics Series—Mathematical tables, manuals, and

studies of special interest to physicists, engineers, chemists,

biologists, mathematicians, computer programmers, and others engaged in scientific and technical work.

National Standard Reference Data Series—Provides quantitative data on the physical and chemical properties of materials, compiled from the world's literature and critically evaluated. Developed under a worldwide program coordinated by NBS under

the authority of the National Standard Data Act (Public Law

90-396).

NOTE: The principal publication outlet for the foregoing data is the Journal of Physical and Chemical Reference Data (JPCRD)

published quarterly for NBS by the American Chemical Society

(ACS) and the American Institute of Physics (AlP). Subscriptions,

reprints, and supplements available from ACS, 1 155 Sixteenth St., NW, Washington, DC 20056.

Building Science Series—Disseminates technical information developed at the Bureau on building materials, components,

systems, and whole structures. The series presents research results,

test methods, and performance criteria related to the structural and

environmental functions and the durability and safety characteristics of building elements and systems.

Technical Notes—Studies or reports which are complete in themselves but restrictive in their treatment of a subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of the subject area. Often serve as a vehicle for final reports of work performed at NBS under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under procedures

published by the Department of Commerce in Part 10, Title 15, of

the Code of Federal Regulations. The standards establish nationally recognized requirements for products, and provide all concerned interests with a basis for common understanding of the

characteristics of the products. NBS administers this program as a supplement to the activities of the private sector standardizing

organizations. Consumer Information Series—Practical information, based on NBS research and experience, covering areas of interest to the con- sumer. Easily understandable language and illustrations provide

useful background knowledge for shopping in today's technological marketplace. Order the above NBS publications from: Superintendent of Documents. Government Printing Office. Washington. DC 20402. Order the following NBS publications—FlPS and NBSIR's—from

the National Technical Information Service. Springfield. VA 22161.

Federal Information Processing Standards Publications (FIPS

PUB)—Publications in this series collectively constitute the Federal Information Processing Standards Register. The Register

.serves as the official source of information in the Federal Govern- ment regarding standards issued by NBS pursuant to the Federal Property and Administrative Services Act of 1949 as amended.

Public Law 89-306 (79 Stat. 1127), and as implemented by Executive Order 11717(38 FR 12315, dated May II, 1973) and Part 6 of Title 15 CFR (Code of Federal Regulations).

NBS Interagency Reports (NBSIR)—A special series of interim or

final reports on work performed by NBS for outside sponsors

(both government and non-government). In general, initial dis- tribution is handled by the sponsor; pub'.ic distribution is by the National Technical Information Service , Springfield, VA 22I6I,

in paper copy or microfiche form.
U.S. Department of Commerce

National Bureau of Standards

Washington, D.C. 20234

Official Business

Penalty for Private Use $300

US.MAIL

POSTAGE AND FEES PAID

U S DEPARTMENT OF COMMERC

COM-215

THIRD CLASS BULK RATE