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Static load tests for through-fastened metal roof and wall systems

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Title:
Static load tests for through-fastened metal roof and wall systems
Creator:
Kreiner, Jonathan Sabia
Publication Date:
Language:
English
Physical Description:
xii, 193 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Boxes ( jstor )
Buckling ( jstor )
Fasteners ( jstor )
Standard deviation ( jstor )
Steels ( jstor )
Stiffness ( jstor )
Stress tests ( jstor )
Structural deflection ( jstor )
Tensile stress ( jstor )
Test data ( jstor )
Civil Engineering thesis, Ph. D
Dissertations, Academic -- Civil Engineering -- UF
Materials -- Dynamic testing ( lcsh )
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bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1996.
Bibliography:
Includes bibliographical references (leaf 192).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Jonathan Sabia Kreiner.

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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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35765544 ( OCLC )

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STATIC LOAD TESTS FOR THROUGH-FASTENED
METAL ROOF AND WALL SYSTEMS










By

JONATHAN SABIA KREINER


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

1996





',!': ;.. .. I .- ', ..* IE S
I !- :. ..: ** r*ls
























Copyright 1996

by

Jonathan Sabia Kreiner









TABLE OF CONTENTS

page

SYMBOLS AND ABBREVIATIONS.................................... iv

ABSTRACT....... ............ .................. ....................... ............. ...... x

CHAPTERS

1 INTRODUCTION TO STATIC LOAD TESTING.............. 1

1.1 G eneral........................................................................ 1
1.2 Research Objectives..................................... .......... 3

2 TEN SILE TESTS.................................................................. 8

2.1 G eneral..... ..................................... ............................... 8
2.2 Procedure.................................... ............ .................. 8

3 STANDARD PULLOVER TESTS................................ 11

3.1 G eneral................ ............ ....................... .................... 11
3.2 Procedure............................................... .............. ...... 11
3.3 Results.......... ........................................................ 12

4 SIMULATED TESTS...................................................... 26

4.1 Components................................................................ 26
4.1.1 Concentric Loading.......................... ........... 26
4.1.2 Eccentric Loading................................ ....... ... 29
4.1.3 Revised Apparatus (Load Cell Development)....... 29
4.1.4 The Strain Gage Test................................ ...... 31

4.2 System s................................................................... ..... 34
4.2.1 Introduction To The Vacuum Box Test................. 34
4.2.2 Apparatus Design And Construction................... 35
4.2.3 Test Methods And Data................................. 37


iii









5 PULLOVER THEORY..................................................... 99

5.1 General ..................... ............................................... .... 99
5.2 Uniaxial Tension ......................................................... 100
5.2.1 AISI Specifications (Section E4.4.2).................... 100
5.2.2 The Actual Condition....................................... 101
5.3 Biaxial Tension...................... ........................................ 107
5.3.1 Biaxial Stresses................................................. 107
5.3.2 Concentric Loading.............................................. 111
5.3.3 Eccentric Loading.............................................. 114
5.4 Pullover Strength And Steel Strength.............................. 122

6 FIELD INSPECTIONS ............................... ........... 142

6.1 Existing Systems........................................................ 142
6.2 Catastrophic Failure................................................... 142

7 CONCLUSIONS AND RECOMMENDATIONS.................. 165

7.1 Reduction Factors For The Standard Test
And Equation E4.4.2.1............................. .................. 165
7.2 Summary Of Test Data And Theoretical Data................. 169
7.3 Recommendation For The Standard Pullover Test............ 171
7.4 Sample Problems......................................................... 173

REFER EN C ES................................................................................. 192

BIOGRAPHICAL SKETCH........ ................................................. 193








SYMBOLS AND ABBREVIATIONS


Aa Longitudinal Projected Area Of Hole Drilled From Fastener

Ap Transverse Projected Area Of Hole Drilled From Fastener

a Width Or Length Dimension

b Width Or Length Dimension

C The Ultimate Strength To Yield Strength Ratio For Steel

c Constant

d- Depth

da Longitudinal Projected Distance For Stress Distribution

dp Transverse Projected Distance For Stress Distribution

d Projected Distance For Stress Distribution

dh Hole Diameter

dw Washer Diameter By Definition Of AISI Specifications

E Modulus of Elasticity

Eea Longitudinal Elastic Modulus

Epa Longitudinal Plastic Modulus

Eep Transverse Elastic Modulus

Ep Transverse Plastic Modulus

Eeanmx Elastic Modulus For Shortest Longitudinal Span








Eeain Elastic Modulus For Longest Longitudinal Span

Ee,,,ax Elastic Modulus For Shortest Transverse Span

Eepmin Elastic Modulus For Longest Transverse Span

Epama Plastic Modulus For Shortest Longitudinal Span

Epamin Plastic Modulus For Longest Longitudinal Span

EppAx Plastic Modulus For Shortest Transverse Span

Eppmin Plastic Modulus For Longest Transverse Span

Fa Longitudinal In-Plane Tensile Stress

Fp Transverse In-Plane Tensile Stress

Fa Longitudinal Ultimate In-Plane Stress

Fa, Longitudinal In-Plane Yield Stress

F,. Transverse In-Plane Yield Stress

Famx In-Plane Tensile Stress For Shortest Longitudinal Span

Famin In-Plane Tensile Stress For Longest Longitudinal Span

Fpmx In-Plane Tensile Stress For Shortest Transverse Span

Fp,,n In-Plane Tensile Stress For Longest Transverse Span

fp Actual Bending Stress

Fp Allowable Bending Stress

F,- Stress For Longer Span In A Uniaxial, Eccentric Loading Condition








Fu Ultimate In-Plane Stress

Fui Ultimate In-Plane Stress By Definition Of AISI Specifications

f. Actual Shear Stress

F, Allowable Shear Stress

F, Yield Stress

I- Moment of Inertia

I- Length

la Longitudinal Span Length For Biaxial, Concentric Loading

lp Transverse Span Length For Biaxial, Concentric Loading

la,,a Shortest Longitudinal Span Length

larin Longest Longitudinal Span Length

I,,& Shortest Transverse Span Length

fi~i, Longest Transverse Span Length

M Moment

Po,. Pullover Strength By Definition Of AISI Specifications

P, Ultimate Axial Strength

qo Distributed Load

Q Shear Flow

R Reaction At Support








S Section Modulus

tl Thickness By Definition Of AISI Specifications

V- Shear

w Distributed Load

W Displacement

a Angle Of Deflection For Span a (Biaxial, Concentric Loading)

a, Ultimate Angle Of Deflection For Span a (Biaxial, Concentric Loading)

a,ax Angle Of Deflection For Shortest Longitudinal Span

qin Angle Of Deflection For Longest Longitudinal Span

a,, x Ultimate Angle Of Deflection For Shortest Longitudinal Span

a,minu Ultimate Angle Of Deflection For Longest Longitudinal Span

p- Angle of Deflection For Span b (Biaxial, Concentric Loading)

pu Ultimate Angle of Deflection For Span b (Biaxial, Concentric Loading)

pl,, Angle Of Deflection For Shortest Transverse Span

,mi, Angle Of Deflection For Longest Transverse Span

fPmx Ultimate Angle Of Deflection For Shortest Transverse Span

Pminu Ultimate Angle Of Deflection For Longest Transverse Span

8- Deflection

A Deflection









Aa, Ultimate Defelction For Longitudinal Span

Ap, Ultimate Deflection For Transverse Span

Aaaxu Ultimate Defelction For Shortest Longitudinal Span

Aarinu Ultimate Defelction For Longest Longitudinal Span

ApMu Ultimate Deflection For Shortest Transverse Span

Apninu Ultimate Deflection For Longest Transverse Span

c- In-Plane Strain

a Longitudinal In-Plane Strain

cE Transverse In-Plane Strain

,, Longitudinal In-Plane Yield Strain

ef Transverse In-Plane Yield Strain

,u Ultimate Longitudinal In-Plane Strain

eu, Ultimate Transverse In-Plane Strain

Earn, In-Plane Strain For Shortest Longitudinal Span

calin In-Plane Strain For Longest Longitudinal Span

eamax Ultimate In-Plane Strain For Shortest Longitudinal Span

camnuu Ultimate In-Plane Strain For Longest Longitudinal Span

pax In-Plane Strain For Shortest Transverse Span

E *n In-Plane Strain For Longest Transverse Span








Emu, Ultimate In-Plane Strain For Shortest Transverse Span

Elinu Ultimate In-Plane Strain For Longest Transverse Span

sana In-Plane Yield Strain For Shortest Longitudinal Span

Eminy In-Plane Yield Strain For Longest Longitudinal Span

cPum). In-Plane Yield Strain For Shortest Transverse Span

fminy, In-Plane Yield Strain For Longest Transverse Span

0 Angle Of Failure Mode Generated From Biaxial In-Plane Tension

S- Angle Of Deflection

B, Angle Of Deflection For Span a (Uniaxial, Eccentric Loading)

Op- Angle of Deflection For Span b (Uniaxial, Eccentric Loading)








Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillmemt of the
Requirements for the Degree of Doctor of Philosophy

STATIC LOAD TESTS FOR THROUGH-FASTENED
METAL ROOF AND WALL SYSTEMS

By

JONATHAN SABIA KREINER

AUGUST 1996


Chairman: Dr. Duane Scott Ellifritt, P.E.
Major Department: Civil Engineering

Self-drilling screws are used for attaching roof and wall panels to

structural framing and are often subjected to tensile loads caused by negative

wind pressures. A failure mode often associated with this loading condition

is pullover, which occurs when a fastener pulls through the sheet but remains

attached to the structural framework underneath.

The American Iron and Steel Institute (AISI) has developed several

standard tests for pullover. Previous research at the University of Florida has

focused on one particular test and has found that it is unconservative,

providing fastener load capacities 2.5 times greater than load capacities

measured in an actual installation. Given this discovery, a proposal was made

to AISI in 1993 requesting further study of pullover and its effects by testing








a wider range of variables and providing a reduction factor for the standard

test. The proposal was approved and research began in May 1994.

In order to determine the reduction factor for the standard test, simulated

tests were performed in addition to the standard tests. While initially using

the simulated testing apparatus, many difficulties were encountered and

adjustments were made to improve the simulated data. From these

adjustments a new and improved apparatus for the simulated test (the vacuum

box test) was developed and proposed to AISI in the summer of 1995. The

proposal was approved and a new series of simulated tests were included.

Rather than testing single components alone, this new series included system

testing, which modeled the actual conditions more realistically. For these

reasons, the system tests proved most valuable when determining reduction

factors for the standard test.

The purpose of the research was to provide a better understanding of

pullover. The first approach was to determine a reduction factor for the

standard test specified in the AISI Cold Formed Steel Design Manual. The

second approach was to develop both theoretical and empirical methods for

designing through-fastened metal panel systems that resist pullover.












CHAPTER 1
INTRODUCTION TO STATIC LOAD TESTING


1.1 General

Self-drilling screws are used for attaching metal roof and wall sheets to

structural framing (Figure 1-1). These screws are often subjected to tensile

loads caused by negative wind pressures. Two failure modes associated with

this loading condition are pull-out and pull-over. Pull-out is a fastener's

resistance to pulling out of the heavier framework underneath the sheet, and

pull-over occurs when a fastener pulls through the sheet, but remains attached

to the heavier framework. The primary focus of this discussion is pull-over.

The American Iron and Steel Institute (AISI) has developed several

standard tests for pull-over. One test is simple to conduct and requires only

small amounts of sheet material. A schematic of this Standard Pull-Over Test

is shown in Figure 1-2. This test does not attempt to simulate the action in a

real installation. In an actual building, the sheet is perpendicular to the screw

axis and in a state of biaxial membrane tension when pulled in a direction

parallel to the axis of the screw. This behavior differs from that of the








Standard Test, which provides the same loading condition, but does not

provide the same support conditions (Figure 1-1). A member used in the

Standard Test has a stable initial support condition, which remains stable

throughout the loading process. This has greatly affected the actual load

capacity of a given member. In fact, previous research at the University of

Florida has shown that the Standard Test produced a load approximately 2.5

times greater than the loads recorded from the test that simulated a real

installation. For this reason, the Standard Test may be very un-conservative

when used to determine the number of screws required to hold down a metal

sheet subjected to a given wind load.

Previous research was performed only on one roof sheet configuration,

one gauge, one steel grade, one screw position, and one simulated sheet span.

In order to accurately assess the differences between a Standard Test and a

simulated building test, many more simulated building tests must be

performed. For this reason, an expanded program of testing has been

established. This report describes the details of the research and provides

data relating to the effectiveness of the simulated test. One objective was to

be able to predict the performance of a through-fastened sheet in a real

building by performing the Standard Test and applying a reduction factor.








The reduction factor will depend on testing a wider range of variables than

those previously tested (Table 1-1).

All previous simulated tests have been set up to produce perfect axial

tension on the screw. This simulates the attachment of a continuous sheet at

an interior support, which is probably the most ideal of conditions (Figure 1-

3). In a real installation, many screws are eccentrically loaded and are more

likely to fail before a concentrically loaded screw. The Standard Test is

concentrically loaded, which tests the ideal state of attachment and is un-

conservative. Therefore, in order to obtain a more conservative reduction

factor, several of the simulated tests included eccentric loadings (Figure 1-4).



1.2 Research Objectives

The primary objective was to determine a reduction factor for the Standard

Test. However, a favorable objective was to revise the Standard Test

because the current testing procedure does not accurately model an actual

installation. Section E4.4.2 in the 1996 Draft AISI Specification provides a

standard equation for calculating pullover. Both the equation and the

Standard Test provide the same pullover values for a given system because

the equation was derived from a free body diagram of the standard testing








apparatus. Therefore, it was also necessary to revise Section E4.4.2 by

providing the appropriate design criteria for pullover. This was the most

difficult task in the research; however, pullover theory was derived

successfully and compared with the Standard Test data and the data

accumulated from the simulated tests.

After conducting all of the proposed tests, and deriving the pullover

theory, a reduction factor was recommended to AISI. Additional

recommendations included a revised Standard Test that models an actual

installation and an accurate design method for calculating the pullover

strength that would replace the current provision given in Section E4.4.2.








Standard Pull-Over Test


Performance in Building Installation


Figure 1-1 Initial Boundary Conditions










Center Lines For
1" Hole In Jig





Test Jig

12 Ga. C-Channel


Center Lines
For 1" Hole In
Flange



1/8" Stiffener




8" x 6" Base


Clamping Detail


1" Threaded
Rod


2 1/4" Bolts 4" Long










#12 Self Dilling Screw


Test Specimen


Figure 1-2 Schematic of the Standard Pull-Over Test








Table 1-1 Proposed Testing Program for Simulated Tests

Test Installation Supplier Gages Steel Number of Tests
Series Type Grade
1 component Pascoe 24& 26 55 18
2 component American 24 &26 80 18
3 component Pascoe 24 &26 55 10
4 component American 24 &26 80 10
5 component Pascoe 24 &26 55 14
6 component American 24 &26 80 14
1 system Pascoe 24& 26 55 4
2 system American 24 &26 80 4
3 system Pascoe 24 &26 55 4
4 system American 24 &26 80 4
5 system Pascoe 24 &26 55 4
6 system American 24 &26 80 4
7 Other Tests as Directed by Sponsor


IB


Figure 1-3 Attachment of Sheet at Interior Support (Concentric Concentric)


-J


Figure 1-4 Attachment of Sheet at End Support (Eccentric Condition)













CHAPTER 2
TENSILE TESTS


2.1 General

The tensile test, an essential part of the research, provides a stress/strain

relationship for each material specimen (Table 2-1). This data is later used in

a mathematical model for pullover. The developed theory assumes a bilinear

stress/strain distribution for each material specimen tested (See Figures 2-1

and 2-2 for illustrations).



2.2 Procedure

Three tensile coupons were constructed for each of the four selected

material specimens in accordance with the American Society of Testing

Materials (ASTM) A370 recommendations. Each coupon was subjected to

the tensile test where both load capacities and deformations were measured

during the loading process by means of a Tensile Test Apparatus. Average

load capacities and percent of elongations were later recorded as seen in

Table 2-1. See Figures 2-1 and 2-2 for bilinear stress/strain distributions.












Pascoe Steel Samples


70000

60000

50000

40000

30000

20000

10000

0
0


- 26 Gage
---24 Gage


--~- -- -- f
0.05 0.1 0.15

Strain (in.lin.)


0.2 0.25
0.2 0.25


Figure 2-1 Stress/Strain Distribution For Pascoe Steel






American Steel Samples


120000


100000


80000

60000


--26 Gage
-- 24 Gage


40000


20000

0 -4--
0 0.001 0.002 0.003 0.004 0.005 0.006

Strain (in.lin.)


Figure 2-2 Stress/Strain Distribution For American Steel


I-










Table 2-1 Tensile Test Results


Property Units 26 Gage 24 Gage 26 Gage 24 Gage
Pascoe Pascoe American American
Th. = (in.) 0.021 0.0234 0.018 0.022
Pu = (Ibs.) 2090 2040 925 1180
DLu = (in.) 1.2412 1.2279 0.01125 0.011
Py = (Ibs.) 1870 1775 857 1150
Epsilon y = (inin.) 0.0021 0.0017 0.0033 0.0036
Red. W= (in.) 1.3065 1.3367 0.483 0.483
Red. A= (in.) 0.0274 0.0312 0.0087 0.0106
Fy = (psi) 59300 50600 97400 106900
Fu = (psi) 66400 58000 105000 109800
%A Red. = (%) 12.9 10.9 1.23 1.28
% Elong. = (%) 24.125 22.788 0.564 0.552
Epsilon u = (in./in.) 0.24125 0.22788 0.00564 0.00552













CHAPTER 3
STANDARD PULLOVER TEST


3.1 General

The ultimate objective of the research was to predict the performance of a

through-fastened sheet in a metal building by performing the Standard Test

and applying a reduction factor. The reduction factor was determined from

the results obtained by both the simulated test and the Standard Test. A

comparison of the final results from both tests will be discussed later in

Chapter 7. Since the Standard Test is already in accordance with AISI

specifications, it was selected as the initial test for the analysis.



3.2 Procedure

All panels were cut into small sections, approximately 4.5 inches x 12

inches. The first data series (Pascoe, Fy = 55 ksi) contained 21 steel samples,

which are listed on Table 3-1 an illustration of the apparatus is also shown

on Figure 1-2.








The test was simple. After each sample was placed within the tensile

testing machine, an ultimate load was recorded along with the respective

failure mode.



3.3 Results

Table 3-9 represents data obtained from the previous research at the

University of Florida. It shows variations among the data with a calculated

standard deviation of +/- 254. The calculated mean load capacity for one

screw fastening 26 gage Dean steel (Fy = 80 ksi) was 1,962 pounds.

Table 3-1 shows variations among the data with a calculated standard

deviation of +/- 180.8 from the mean. The mean was 1,790.9 pounds. There

are many possibilities that may explain the variations. For one, the failure

modes changed at random. This may have been caused by the imperfections

of the material specimens. However, a more realistic possibility could be the

presence of an eccentric point load, since it is difficult to generate a perfect,

ideal concentric load with the apparatus used.

Despite the minor variations, a measurable value representing the ultimate

load capacity for one screw was obtained by taking a mean and comparing it

with the entire data series. This was performed in two ways: first, by








plotting a best fit curve as seen on Figure 3-1, and secondly, by calculating

the sorted composite and plotting the standardized normal distribution as

seen on Table 3-2.

The standardized normal distribution describes several characteristics of

the data series (Figures 3-3, 3-4, 3-7 and 3-8). Initially, it shows the

percentage of those data points that fall within the first standard deviation and

those that fall within 1.96 times the standard deviation. An acceptable data

series should have at least half the data points within the first standard

deviation. This was the case with the first data series, since 66.6% of the

data points fell within that range. Secondly, it shows which data points

should be rejected from the data series. The area of rejection is considered to

be 1.96 times the standard deviation or greater. Table 3-2 shows that only

one test (15) was greater or equal to 1.96. Since 21 tests were conducted,

only 1/21 or 4.76% of the tests were rejected and this is shown on the first

normal distribution curve.

This statistical analysis, better known as the Standard Z Test, was applied

to each data series. A total of four specimen types were analyzed and tested.

Tables 3-1 through 3-9 display the accumulated data, mean load capacity and

standard deviation for each specimen tested. A revised mean and standard






14

deviation was calculated for each composite that contained at least one data

point in the areas of rejection.










Table 3-1 Standard Test Results For 24 Gage Pascoe Steel (Fy = 55 ksi)

FASTENER DATA (Cold Form Steel Coupons):


FROM: 8/4/94


TO:


Supplier: Pascoe
Fy = 55 ksi


912/94


TEST # TL. LOAD COMMENTS PL. TH.
(Ibs.) (gage)
1 1920 Pullover 24
2 1650 Pullover 24
3 1800 Pullover 24
4 1750 Pullover 24
5 2110 Pullover 24
6 1720 Pullover 24
7 2040 Pullover 24
8 1590 Pullover 24
9 1930 Pullover 24
10 1870 Pullover 24
11 1920 Pullover 24
12 1550 Pullover 24
13 1800 Pullover 24
14 1720 Pullover 24
15 1430 Disregard-Misfire w/ screw gun. 24
16 1510 Pullover 24
17 2080 Pullover 24
18 1860 Pullover 24
19 1740 Pullover 24
20 1820 Pullover 24
21 1800 Pullover 24


* Eccentric Loading

Mean =
Standard Deviation =

Revised Mean =
Revised Standard Deviation =


1790.952
180.8288

1809
164.9848











Table 3-2


- Data Points For Standardized Normal Distribution
(Pascoe 24 Gage)


SORTED SORTED TEST#
CMPSTA LOADS
-1.9961 1430 15
-1.55369 1510 16
-1.33249 1550 12
-1.11129 1590 8
-0.77948 1650 2
-0.39237 1720 6
-0.39237 1720 14
-0.28177 1740 19
-0.22647 1750 4
0.050034 1800 3
0.050034 1800 13
0.050034 1800 21
0.160636 1820 20
0.38184 1860 18
0.437141 1870 10
0.713645 1920 1
0.713645 1920 11
0.768946 1930 9
1.377257 2040 7
1.59846 2080 17
1.764363 2110 5


TOTAL LOAD CAPACITY


2500

2000
1790.95
1500


* *


* *


* 4


1000 +


500


TEST


Figure 3-1 Best Fit Curve For 24 Gage Pascoe Steel (Fy = 55 ksi)


--










Table 3-3 Standard Test Results For 26 Gage Pascoe Steel (Fy = 55 ksi)

FASTENER DATA (Cold Form Steel Coupons):


FROM : 2/27/95


TO:


Supplier: Pascoe
Fy = 55 ksi


2/27/95


TEST # TL. LOAD COMMENTS PI. Th.
(Ibs.) (gage)
1 1520 Pullover 26
2 1820 Pullover 26
3 1700 Pullover 26
4 1830 Pullover 26
5 1620 Pullover 26
6 1580 Pullover* 26
7 1670 Pullover 26
8 1690 Pullover 26
9 1360 Pullover* 26
10 1810 Pullover 26
11 1950 Pullover 26
12 1570 Pullover 26
13 1450 Pullover *26
14 1620 Pullover 26
15 1880 Pullover 26
16 1400 Pullover* 26


* Eccentric Loading

Mean =
Standard deviation =


1654.375
173.3193











Table 3-4 Data Points For Standardized Normal Distribution
(Pascoe, 26 Gage)


SORTED SORTED TEST #
CMPSTA LOADS
-1.698454716 1360 9
-1.467666814 1400 16
-1.179181937 1450 13
-0.775303108 1520 1
-0.486818231 1570 12
-0.429121255 1580 6
-0.198333353 1620 5
-0.198333353 1620 14
0.090151524 1670 7
0.205545475 1690 8
0.263242451 1700 3
0.897909181 1810 10
0.955606157 1820 2
1.013303132 1830 4
1.301788009 1880 15
1.705666838 1950 11


TOTAL LOAD CAPACITY


2000
1800
1654.38
1600
1400
1200
0 D
O 1000
-I
800
600
400
200
0


TEST#


Figure 3-2 Best Fit Curve For 26 Gage Pascoe Steel (Fy = 55 ksi)
























4.8%


Percent of Cumulative
Probability


Area of Rejection


-3 -2 -1 0 +1 +2 +3


Figure 3-3 Standardized Normal Distribution For 24 Gage Pascoe Steel







Percent of Cumulative
Probability





62.Area of Rejection

/--- Area of Rejection


Figure 3-4 Standardized Normal Distribution For 26 Gage Pascoe Steel


-3 -2 -1 0 +1 +2 +3










Table 3-5 Standard Test Results For 24 Gage American Steel (Fy = 80 ksi)

FASTENER DATA (Cold Form Steel Coupons):

FROM: 2/22/95 Supplier: American
Fy = 80 ksi


2/22/95


TEST# TL. LOAD COMMENTS PI. Th.
(Ibs.) (gage)
1 2150 Pullover* 24
2 2160 Pullover* 24
3 2290 Pullover* 24
4 2010 Pullover 24
5 2030 Pullover 24
6 2220 Pullover 24
7 2190 Pullover 24
8 2190 Pullover 24
9 2020 Pullover* 24
10 1970 Pullover 24


* Eccentric Loading

Mean =
Standard deviation =


TO:


2123
107.3985










Table 3-6 Data Points For Standardized Normal Distribution
(American, 24 Gage)


SORTED SORTED TEST#
CMPSTA LOADS
-1.4246 1970 10
-1.05216 2010 4
-0.95904 2020 9
-0.86593 2030 5
0.2514 2150 1
0.344511 2160 2
0.623845 2190 7
0.623845 2190 8
0.903178 2220 6
1.554956 2290 3


TOTAL LOAD CAPACITY


2500 -r


2123
2000


1500


1000-


500


* *


TEST #


Figure 3-5 Best Fit Curve For 24 Gage American Steel (Fy = 80 ksi)










Table 3-7 Standard Test Results For 26 Gage American Steel (Fy = 80 ksi)

FASTENER DATA (Cold Form Steel Coupons):


FROM: 2/24/95


TO:


Supplier: American
Fy = 80 ksi


2124/95


TEST # TL. LOAD COMMENTS PI. Th.
(Ibs.) (gage)
1 1740 Pullover 26
2 1530 Pullover 26
3 1550 Pullover 26
4 2070 Pullover 26
5 1690 Pullover 26
6 2040 Pullover 26
7 1630 Pullover* 26
8 1610 Pullover* 26
9 1770 Pullover 26
10 1650 Pullover 26
11 1530 Pullover 26
12 1600 Pullover 26
13 1560 Pullover* 26
14 1690 Pullover* 26
15 1580 Pullover 26


* Eccentric Loading

Mean =
Standard Deviation =

Revised Mean =
Revised Standard Deviation =


1682.667
167.8633

1625.385
78.5934










Table 3-8 Data Points For Standardized Normal Distribution
(American, 26 Gage)


SORTED SORTED TEST #
COMPOSITE LOADS
-0.909470061 1530 2
-0.909470061 1530 11
-0.790325511 1550 3
-0.730753237 1560 13
-0.611608687 1580 15
-0.492464138 1600 12
-0.432891863 1610 8
-0.313747314 1630 7
-0.194602764 1650 10
0.043686335 1690 5
0.043686335 1690 14
0.341547708 1740 1
0.520264533 1770 9
2.12871595 2040 6
2.307432775 2070 4


TOTAL LOAD CAPACITY


1682.67-
1500


* *


*1*
~* .


1000


500


TEST#


Figure 3-6 Best Fit Curve For 26 Gage American Steel (Fy = 80 ksi)


2500


2000













Percent of Cumulative
Probability


Area of Rejection
20 % 10 .

I -1.960a +1.9607
-3 -2 -1 0 +1 +2 +3



Figure 3-7 Standardized Normal Distribution For 24 Gage American Steel









Percent of Cumulative
Probability





f 86. %7- 13.3%

/- Area of Rejection


Figure 3-8 Standardized Normal Distribution For 26 Gage American Steel


-3 -2 -1 0 +1 +2 +3










Table 3-9 Standard Test Results For 26 Gage Dean Steel (Fy = 80 ksi)


Test # Load % Deviation from Mean
(Ib.)
1 820 *
2 1740 11
3 950 *
4 1880 4
5 1640 16
6 2250 14
7 1680 14
8 1710 13
9 2170 10
10 1880 4
11 2180 11
12 2330 19
13 2120 8


Average =
STDEV. =


Note:


1962
254


* indicates tests that have been omitted from the calculation of the average and
standard deviation due to errors involved during testing.













CHAPTER 4
SIMULATED TESTS


4.1 Components

All the initial simulated tests were component tests. These tests included

multi-fastened systems that contain only one panel for any given test. The

tests represent the simplest model for typical through-fastened systems. The

general apparatus for component testing may be seen on Figures 4-1, 4-2, and

4-24.



4.1.1 Concentric Loading

Concentric loading has been selected as the initial test for the simulated

testing procedure. This simulates the attachment of a continuous sheet at an

interior support and is set up to produce perfectly axial tension on the screw

(Figures 4-1 and 4-2). Eccentric loading was applied later in the research.

The original apparatus was revised prior to testing. Figure 4-2 illustrates a

new support condition, which fixes all boundaries associated with the panel.

This change was necessary since deflections and angle of rotations are zero at








the supports in an actual building. A fixed boundary also eliminated the

installation of panel overlaps, which saved set up time and simplified the

testing procedure.

Each data series has been divided among suppliers and material type. The

corresponding data contains three separate data series representing Pascoe,

American, and Dean suppliers, respectively (Tables 4-1, 4-2 and 4-3). Each

data series contains a variety of conditions that change during the course of

the testing. However, note that all Dean steel data was obtained from

previous research and will not follow the same format. It is important to test

each panel type in a variety of diverse conditions in order to assess the

differences between the Standard Test and the simulated building test.

Therefore, variations of fastener spacing, span length and gage are tested in

each data series.

In order to minimize errors, four tests were performed for each specified

condition. There are many possible causes for error within this testing

procedure. They include lining up the screws on the panel, adjusting the

torque on the screw gun, calibrating the MTS and load cell and fastening the

panel to the framework. All of these variables are critical to the results.

Therefore, a mean total load capacity for each specified condition must be








calculated and later compared with the values obtained from the

corresponding Standard Test.

All concentric load tests were conducted with a fixed end boundary

condition. Figure 4-2 demonstrates an initial attempt to model this condition

using wood braces and C clamps. However, the over-all effect of the custom

brace was questionable, since it did not provide total resistance to lateral, in-

plane displacements. In fact, the brace relied on friction alone to resist lateral

movement in the panel. There were some indications of lateral movement

during testing and thus, a variation of the same test was conducted for each

panel type. This variation included the addition of self-drilling screws

centered at each valley and placed along the perimeter of the panel (Figure

4-13). This variation, called the Fixed End Concentric Load Test, insured

lateral resistance, which decreased the total load capacity of each screw

tested. Like both the Concentric Load Tests and the Eccentric Load Tests,

this data was later used to determine the reduction factor for the Standard

Test (Table 4-8).








4.1.2 Eccentric Loading

There are two ways to generate an eccentric load. The first method can be

achieved by offsetting the screws (Figure 4-3). The second method can be

achieved by offsetting the supports of the panel (Figure 4-4). In order to

determine the governing condition, data was obtained from both methods.

Data for each condition can be seen on Tables 4-4 through 4-7.

All fastener load capacities obtained from the Eccentric Loading Tests

were of lesser magnitude than those load capacities recorded from the

Concentric Tests. This was expected since concentric loads produce

perfectly axial tension on the screw and represent the most ideal of

conditions. Like the Concentric Tests, each data series has been divided

among suppliers and material type. A variety of span lengths and span offsets

were tested for both eccentric conditions (see Figures 4-5 through 4-12). The

lowest recorded load capacities were later used to determine the reduction

factor. Those values are identified, in bold, in Tables 4-4 through 4-7.



4.1.3 Revised Apparatus (Load Cell Development)

New load cells were constructed specifically for the simulated testing

apparatus and replaced the previous load cell. The original apparatus called








for only one load cell that rests directly between the two fasteners as seen in

Figure 4-14. This set up was sufficient, provided that the total load was

assumed to be equally distributed among the two fasteners present. However,

when LVDT's were attached to the individual fasteners, tests showed that

this assumption was not completely accurate. Even under the most carefully

installed conditions, slight differences of load occurred between the two

fasteners and in most cases, one fastener failed before the other.

The problem became a major concern and thus a revised set up was

necessary. In order to accurately record the precise ultimate load capacity for

one screw in a multi-fastener system, there must be a load cell placed under

each and every screw as seen in Figure 4-15.

All load cells were constructed out of 2024-T4 aluminum and contain four

strain gauges per cell (two vertical and two horizontal). Dimensions and a

circuit diagram are illustrated in Figures 4-16 and 4-17. Performance of the

revised load cells in a multi-fastener system is illustrated in Figure 4-18.

Lastly, each cell was calibrated. Table 4-9 shows a regression output for

each cell. Note the R-squared value. The closer to unity, the better the

response. Each cell reads up to 1,200 pounds of load.











4.1.4 The Strain Gage Test

In order to understand the effects of pullover, it is necessary to understand

the in-plane stresses and strains that develop within a panel that resists

pullover. The purpose of the stain gage test was to provide geometric profiles

and strain contours of a panel resisting pullover. The only other way to

accomplish this is to generate a finite element model of the system. An

extensive study was made prior to testing and it was determined that a finite

element model would not be helpful in determining these contours. Due to

the non-linearities of the system, theoretical modeling would be complex in

nature and very time consuming. A relatively fast and efficient method for

determining stress, strain contours was essential, particularly when an infinite

variety of panel configurations exist for through-fastened systems.

Specifically, such non-linearities include:

1.) the geometric non-linearities which primarily pertain to those stiffeners

within the panel which, in time, lose their effectiveness as the out-of-plain

load progresses. As a result, this constantly changes the panel's moment of

inertia.








2.) the elastic non-linearities, since pullover typically occurs within a highly

concentrated area that stresses well beyond the linearly elastic limit (i.e. the

yield point). Depending on the steel grade, such non-linearities may vary.

A 24 gage, 55 ksi steel panel was selected for the strain gage test. Figure

4-19 illustrates the strain gage configuration used. Since the highest

concentration of stresses existed along the center valley of the panel, all of the

gages were strategically placed in that area. In addition to the 2 load cells

that were placed underneath each screw, a total of 12 strain gages, capable of

measuring up to 10,000 .aE, were used. No strain gage was ever placed

closer than 2 inches from either screw for fear that elongation would surpass

the 10,000 pc limit. This was unfortunate, since it was later determined that

no gage ever exceeded the linear elastic limit. This proved that the pullover

area within the panel was very small and highly concentrated.

Since the dawn of the research, the strain gage test proved to be one of the

most valuable tests ever performed (Figures 4-25 and 4-26). For the very first

time a three dimensional view of the system was provided. Panel

deformations were generated at key phases which are displayed in Figures 4-

20 through 4-23. Table 4-10 shows the recorded data that generated both the

strain contours and the panel deformations (Figures 4-20 through 4-23, 4-27,








and 4-28). Like the component tests described earlier, a concentrated load

was applied directly to the purlin by means of a come-along (Figure 4-24).

Each strain value was recorded after one crank on the come-along.

Successive recordings followed in an identical manner until failure.

One of the most astonishing observations made was the abrupt change in

buckling modes from Figures 4-22 to 4-23. It was clear that the web stiffener

buckling behavior propagated through the valley area, and thus, disrupted the

continuity of the in-plane tensile stresses that existed within the valley. This

seems to indicate that the tensile stresses responsible for pullover are highly

concentrated and exist within a very small area around the screw. The

remaining in-plane stresses are very low in magnitude and virtually

insignificant by comparison. It is important to consider that a panel may

experience several buckling modes within a single load cycle. This depends

on the effective length and the amount of compressive stress it resists.

This test proved that the pullover strength of a panel is not effected by

bending, and thus, such variables relative to bending can be neglected. This

was a break-through discovery, because it greatly simplified the pullover

problem. The search for a theoretical model that accurately predicted the

pullover strength of a panel was now closer than ever before.









4.2 Systems

System tests include multi-fastener systems that contain more than one

panel for any given test. These tests are ideal for modeling through-fastened

installations and they provide the most accurate data for pullover. The

general apparatus used for component testing was replaced with the vacuum

box apparatus, which provided the most useful data for pullover (Figures 4-29

through 4-31, 4-35, 4-37, and 4-39 through 4-42).



4.2.1 Introduction To The Vacuum Box Test

In order to accurately simulate the effects of a screwed-down metal roof

subjected to a given wind load, both the supports and loading conditions must

be duplicated in a lab. In nature, the loading condition is random, distributed,

and time dependent. One way to simulate this is to construct an isolated

chamber that becomes the environment. Vacuum boxes are ideal for

simulating wind loads and are currently being used to test wind resistance on

glass doors, windows, and other cladding. In fact, several South Florida

counties have recently mandated vacuum box testing for specific building

components and there are testing facilities that cater to manufacturers who

need the testing performed. Figure 4-29 illustrates a typical vacuum box








assembly. The apparatus is quite simple; however, the solenoid, which shuts

the incoming air on and off, is itself air actuated. This requires an extra

supply of air (or a holding tank), which delivers constant air pressure to the

solenoid. An electrical switch box controlled by a CPU regulates the supply

of air.

For the purpose of the simulated pullover test, which is a static load test,

the assembly can be simplified by removing the solenoid, the holding tank,

and the electrical switch box. This revised set-up is illustrated in Figure 4-30.



4.2.2 Apparatus Design And Construction

The size of the vacuum box greatly depends on the size of the roofing

system. Standard spacing of purlins is typically 5 feet and initially, a single

span system was used with one foot of overhang per side of purlin. An

additional 4 inches of length insured proper fitting when placing the assembly

inside the chamber. This established a box length of 7 feet 4 inches.

Typically, a standard sheet width is 3 feet. An ideal model would provide a

seam (due to panel overlapping) in the middle of the chamber. With a few

extra inches to spare for fitting, a gross chamber width of 6 feet 7 inches was

established (Figure 4-31 illustrates the vacuum box detail).











Prior to constructing the vacuum box, a vacuum pump was selected for the

test. Previous tests showed that a single 5/8 inch diameter screw attached to

a 24 gage, grade E steel sheet, resisted a maximum load of 1500 pounds. The

overall surface area of the roofing system was 42 square feet. Each valley

within the roofing system required one screw and panel configurations

included 3 valleys. Therefore, 12 screws were required to fasten a single

span roofing system. From this information, it was determined that

approximately 430 psf (3 psi) of negative pressure would be necessary to

generate a failure. A factor of safety of at least 1.5 was included prior to

selecting a vacuum pump. This accounted for the loss of pump efficiency

with respect to time and the potential for leaks which were inevitable. A

vacuum pump with a maximum pressure of-5 psi and a volume rate of 117

cfm was selected. With a chamber volume of 70 cubic feet, a failure was

expected within the first minute of activation provided that leaks were kept to

a minimum.

The vacuum box was constructed entirely out of wood. Silicon was used

for caulking material which was critical since the chamber required an air

tight seal. Wood glue and dry wall screws insured proper connections. Each








side wall, standing 20 inches tall, was vulnerable to high pressures caused by

the internal vacuum (approximately 3 psi). Therefore, whalers were required

to increase the structural integrity of each wall. The side wall was designed

to 1991 National Design Specifications for Wood Construction and is shown

in Figure 4-32. In order to determine the amount of screws necessary for the

design, calculations of the fastener shear and tensile load capacities were

included (Figure 4-33).



4.2.3 Test Methods And Data

The initial test setup included the simplest representation of an actual

through-fastened metal roof system: the single span system, which contained

2 supports, 2 panels, and 12 fasteners. It was derived from a typical three

span system shown in Figure 4-34. The figure illustrates a three span metal

roof system subjected to a specified wind load. The center span, which

contains the maximum shear stresses and moments within the structure, was

considered the key model for the initial test. The moment diagram indicates

the key locations of the inflection points, which are located 1 foot away from

each interior support. This is how the 7 foot box length was determined

because, as noted earlier, standard spacing of purlins is typically 5 feet.











The first vacuum box test was constructed in this manner, but there were

several difficulties (Figure 4-35). Firstly, due to the inflection points, the

system was limited to 7 feet. At this specified length, where a 1 foot

cantilever existed on each side of the supports, a significant amount of shear

existed at each free end of the system (Figure 4-36). This shear was difficult

to model in the lab. Secondly, the 5 foot span appeared quite large when

placed within the small isolated chamber. Without the ability to apply shear

at the free ends, the panels were susceptible to buckling. Thirdly, the absence

of lateral braces caused both supports to roll, which, in addition to the span

length, contributed to the massive buckling behavior of both panels (Figure 4-

37).

Due to all of these difficulties, the first test never generated a pullover

failure and a number of revisions were implemented. The second test was a

tremendous improvement. In order to minimize panel buckling, it was

determined that the maximum positive moment, generated at mid-span, must

equal the maximum negative moments, generated at the supports. Figure 4-

38 shows the calculation for the span length which creates this condition. It

was determined that a span length of 4.1 feet was sufficient. Figures 4-39








and 4-40 illustrate the revised test setup. Note the addition of lateral braces

for both supports which eliminated the rolling action previously observed.

The revisions made on the single span system (Test 2) proved to be

satisfactory; however, the test required far more load cells than could be

provided (at least 8 at all times) and it was difficult to control the buckling of

the panels. Since the 5 foot standard span length was already reduced to 4.1

feet, it was decided that a two span system replace the existing single span

system (Figure 4-41). This system reduced the span length to 3.5 feet. Panel

buckling was no longer critical and the system required only six load cells for

any given test. This reduced setup time and greatly simplified the testing

procedure. Failures were generated along the center support where shear and

moment were both at a maximum (Figure 4-42). A theoretical model is

currently shown in Figures 4-43 and 4-44.

Deflections were recorded for each test. This data was necessary for

load-deflection curves and validating the theoretical data provided in Chapter

5. Deflection calculations for each system are provided in Figure 4-45.

No static load test ever produced better pullover data than the vacuum box

test. For the first time, subsequent pullover failures were observed in a

through-fastened metal system. Each screw within the system was monitored








independently. The pre-tensioning effects were recorded and the load

capacities were logged within quarter second intervals.

Typically, the initial pullover failures were concentric followed by two

distinct eccentric failures. The initial eccentric failures resulted from the

biaxial tensile stresses developed within the steel panel. This biaxial stressed

condition provided the lowest load capacities. Conversely, the highest load

capacities were generated from the secondary eccentric failures which

occurred at the free edges of the system. These locations developed uniaxial

in-plane stresses within the panel and consequently did not provide the typical

reduced pullover strength observed earlier in the component tests.

The grade E steel did provide slightly higher load capacities than the lesser

grade material. However, it did not provide a significant increase in pullover

strength because its brittle nature produces lower displacements and lower

deflection angles. Unfortunately, high strength steels do not always

contribute to pullover strength and in some cases, depending on the specific

conditions, may even reduce the pullover strength of a through-fastened

system. Chapter 5 explains in detail how steel strength affects pullover

strength. See Tables 4-11 through 4-13 for pressure box data.

























Figure 4-1 Original Apparatus For Simulated Test













LI


'::, ,'::-, ,, ,:,:::" i i; : 'i :: ,; ,,I':;ii ,,::j;

.. :.' .' .. .. .


y "....


rr
"" ... .. : .... ..;; : ,.;:: i "




Figure 4-2 Revised Apparatus For Simulated Test With Typical Panel
Deformations


.* bi,
,
.1












Table 4-1 Simulated Test Results For Pascoe Steel (Concentric)


FASTENER DATA (Concentric Loading):

Supplier: Pascoe F 1 screw placed at center of
Fy = 55 ksi each outer valley.
From: 6/8/94
To: 718194 C 2 screws placed in center valley.

TEST # SPACING SPAN TL LOAD LDJSCW. COMMENTS TH.
(in.) (Ibs.) (lbs./scw.) (gage)
1 F 17 1700 850 Uneven pullover. One side 24
buckled but no pullover.

2 C 17 1150 575 The entire panel buckled. 24
Pullover never occurred.

3 C 17 1300 650 The entire panel buckled. 24
Pullover never occurred.

4 F 17 2250 1125 Uneven pullover. One side 24
buckled but no pullover.

5 F 17 2400 1200 Uneven pullover. One side 24
buckled but no pullover.

6 C 13 2150 1075 Even pullover. Massive plate 24
buckling.

7 C 13 1960 980 Even pullover. Massive plate 24
buckling.

8 F 17 2300 1150 Even pullover. Massive plate 24
buckling.

9 F 17 2200 1100 Uneven pullover. No buckling. 26
Failure at both points.

10 F 17 2200 1100 Uneven pullover. No buckling. 26
Failure at both points.

11 C 17 2000 1000 Even pullover. Massive plate 26
buckling.

12 C 17 2150 1075 Even pullover. Massive plate 26
buckling.

13 F 17 1950 975 Uneven pullover. No buckling. 26
Failure at both points.

14 C 17 2100 1050 Even pullover. Massive plate 26
buckling.

34 C 13 2400 1200 Even pullover. Massive plate 24
buckling.

35 C 13 2000 1000 Even pullover. Massive plate 24
buckling.

36 F 17 2100 1050 Uneven pullover. No buckling. 26
Failure at both points.

37 C 17 2000 1000 Even pullover. Massive plate 26
buckling.












Table 4-2 Simulated Test Results For American Steel (Concentric)


FASTENER DATA (Concentric Loading):

Supplier: American F 1 screw placed at center of
Fy = 80 ksi each outer valley.
From: 11/1/94
To: 12/1/94 C 2 screws placed in center valley.

TEST # SPACING SPAN TL. LOAD LDJSCW. COMMENTS TH.
_(in.) Ibs.) (lbs./scw.) (gage)
15 F 21 1200 600 Minor plate buckling. 26
Uneven pullover.

16 F 21 2000 1000 Minor plate buckling. 26
Uneven pullover.

17 F 21 1900 950 Minor plate buckling. 26
Uneven pullover.

18 F 21 2000 1000 Minor plate buckling. 26
Uneven pullover.

19 F 21 2100 1050 Minor plate buckling. 26
Uneven pullover

20 & 21 C 21 & 17 Apx. 1500 Apx. 750 Massive plate buckling. 26
No failure. No pullover.

22 C 13 2000 1000 Massive plate buckling. 26
Even pullover.

23 C 13 2300 1150 Massive plate buckling. 26
Even pullover.

24 C 13 1900 950 Massive plate buckling. 26
Even pullover.

25 C 13 2500 1250 Moderate plate buckling. 24
Even pullover.

26 C 13 2400 1200 Moderate plate buckling. 24
Even pullover.

27 C 13 2400 1200 Moderate plate buckling. 24
Even pullover.

28 C 13 2100 1050 Moderate plate buckling. 24
Even pullover.

29 F 13 2200 1100 Minor plate buckling. 24
Uneven pullover.

30 F 13 1700 850 Poor Test Results. 24


31 F 13 2480 1240 Minor plate buckling. 24
Uneven pullover.
32 F 13 2460 1230 Minor plate buckling. 24
Uneven pullover.
33 F 13 2500 1250 Minor plate buckling. 24
Uneven pullover.












Table 4-3 Simulated Test Results For Dean Steel (Concentric)


Test No. Total Load Load I Screw % Deviation Deflection Of Deflection Of Load Rate
(Ibs.) From Mean Left Fastener Right Fastener (IbsJSec.)
(in.) (in.)

A 1553 777 *
B 1400 700 __ *
C 1350 675 *
1 1599 800 2 0.976 0.976 17.8
2 1773 887 11 1.201 1.422 17.2
3 1686 843 7 0.987 0.970 24.8
4 1241 620 26 0.774 0.773 8.6
5 1637 819 4 0.926 .931 12.6
6 1617 809 3 0.965 0.933 11.6
7 1652 826 5 0.956 0.876 14.9
8 1462 731 8 0.887 0.883 7.7
9 1501 751 5 0.870 0.887 8.8
10 1521 761 3 0.937 0.906 84.5
11 1515 757 3 0.972 0.918 7.3

Average = 1569 782
STDEV. = 148 70_




NOTES:

1) indicates tests that have been omitted from the calculation of the average and
standard deviation due to errors involved during testing.


2) Deflections that are underlined represent the fastener that failed.









Figure 4-3 Offsetting The Screws



r e n


Figure 4-4 Offsetting The Panel Supports










Table 4-4 Simulated Test Results (Eccentric Loading) For Pascoe Steel

FASTENER DATA (Eccentric Loading):
(Condition #1 Offsetting The Screws)

Supplier: Pascoe
Fy = 55 ksi
From: 4/3/95
To: 4/26/95


TEST SPACING SPAN TOTAL PANEL
NUMBER FROM CL LENGTH LOAD THICKNESS

(in (i) (in.) (Ibs.) (gage)

1 2 13 923 24

2 3 13 972 24

3 9 13 818 24

4 10 13 678 24

5 12 13 850 24

6 2 13 952 26

7 3 13 799 26

8 9 13 905 26

9 10 13 860 26

10 12 13 729 26









48






1000

900

800

A 700

600

S500

400

| 300

200 F

100

0
0 2 4 6 8 10 12
Distance From Fastener To Center Load (in.)




Figure 4-5 Eccentric Loading Condition 1 For 24 Gage Pascoe Steel









1000

900

800

700






S.
200

100
0
0 2 4 6 8 10 12
Distance From Fastener To Center Load (in.)



Figure 4-6 Eccentric Loading Condition 1 For 26 Gage Pascoe Steel












Table 4-5 Simulated Test Results (Eccentric Loading) For American Steel


FASTENER DATA (Eccentric Loading):
(Condition #1 Offsetting The Screws)

Supplier: American
Fy = 80 ksi
From: 5/1/95
To: 5/19195

TEST SPACING SPAN TOTAL .PANEL
NUMBER FROM CL LENGTH LOAD THICKNESS

(in.) (in.) (Ibs.) (gage)

1 2 13 507 24

2 3 13 530 24

3 9 13 385 24

4 10 13 701 24

5 12 13 660 24

6 2 13 535 26

7 3 13 605 26

8 9 13 290 26

9 10 13 356 26

10 12 13 347 26
















800

700

600


U 500
soo

400

300


3. 200

100

0
0 2 4 6 8 10 12
Distance From Fastener To Center Load (In.)




Figure 4-7 Eccentric Loading Condition 1 For 24 Gage American Steel










700


600





400


300


1 200


100



0 2 4 6 8 10 12
Distance From Fastener To Center Load (in.)




Figure 4-8 Eccentric Loading Condition 1 For 26 Gage American Steel











Table 4-6 Simulated Test Results (Eccentric Loading Condition 2) For
Pascoe Steel

FASTENER DATA (Eccentric Loading):
(Condition #2 Offsetting The Supports)

Supplier : Pascoe


Fy =
From:
To:


55 ksi
511/95
6/18/95


TEST ACTUAL SPAN PEAK LOAD PANEL
NUMBER DISTANCE LENGTH THICKNESS
MAX. MIN.
(#) (in.) (in.) (Ibs.) (Ibs.) (gage)

1 13.5 15 813 567 24

2 11.5 13 730 461 24

3 9.5 11 663 541 24

4 7.5 9 925 583 24

5 5.5 7 863 473 24
*
6 3.5 5 847 608 24
*
7 23.5 25 800 415 24

1 13.5 15 628 596 26

2 11.5 13 762 610 26
*
3 9.5 11 562 532 26
*
4 7.5 9 495 425 26

5 5.5 7 785 683 26

6 3.5 5 755 555 26

7 23.5 25 754 522 26
*


* Indicates Fastener Failure
















1000
900

0 800
700


o 400
-- M



S300
U 200
UIL
100


0 5 10 15 20 25
Distance From Fastener To Fixed Boundary (in.)




Figure 4-9 Eccentric Loading Condition 2 For 24 Gage Pascoe Steel


700

600

500

400

300

200

100


5 10 15 20

Distance From Fastener To Fixed Boundary (in.)


AX.
IN.


---MAX.
-- MIN.


Figure 4-10 Eccentric Loading Condition 2 For 26 Gage Pascoe Steel










Table 4-7 Simulated Test Results (Eccentric Loading Condition 2) For
American Steel

FASTENER DATA (Eccentric Loading):
(Condition #2 Offsetting The Supports)

Supplier: American
Fy = 80 ksi
From: 5/1/95
To: 5/19/95


TEST ACTUAL SPAN PEAK LOAD PANEL
NUMBER DISTANCE LENGTH THICKNESS
MAX. MIN.
(in.) (in.) (Ibs.) (Ibs.) (gage)

1 13.5 15 950 867 24

2 11.5 13 888 740 24

3 9.5 11 1001 859 24

4 7.5 9 1065 828 24

5 5.5 7 959 822 24
*
6 3.5 5 708 499 24

7 23.5 25 984 855 24

1 13.5 15 451 414 26

2 11.5 13 638 560 26

3 9.5 11 341 289 26

4 7.5 9 413 346 26

5 5.5 7 563 519 26

6 3.5 5 485 285 26

7 23.5 25 660 480 26


* Indicates Fastener Failure


















1000

800

o 600

400

S 200


--+--MAX.
- -MIN.


0 5 10 15 20 25
Distance From Fastener To Fixed Boundary (in.)





Figure 4-11 Eccentric Loading Condition 2 For 24 Gage American Steel









700 -

600

S00

Q 400 --MAX.
0 -i- -MIN.
S300


200

100


5 10 15 20 25
Distance From Fastener To Fixed Boundary (in.)


Figure 4-12 Eccentric Loading Condition 2 For 26 Gage American Steel










Table 4-8 Fixed End Concentric Load Test Data

FASTENER DATA (Concentric Loading I Edges Fastened):


From:
To:


6/8/95
6/17/95


Note: All Screws Failed Simultaneously.


One Screw Per Valley


Edge Stiffeners Were Clamped


Figure 4-13 Fixed End Concentric Load Test (Panel Layout)


COMPANY SPACING SPAN PEAK LOAD PANEL
Fy MAX. MIN. THICKNESS
(in.) (Ibs.) (Ibs.) (gage)

Pascoe C 13 560 504 24
55 ksi

Pascoe C 13 413 281 26
55 ksi

American C 13 644 570 24
80 ksi

American C 13 515 466 26
80 ksi













Fastener







Lead To Data
Acquisitionor


- Metal Panel





Purlin


Figure 4-14 Old Apparatus


I-11WI-

--- Treadd-Ro


Load Cell
-~-_ I-


Metal Panel


Threaded Rod
With Nut


Actuator


Figure 4-15 New Apparatus


Lead To
Acquisitic


Fastener







Data
nor


N._-- Purlin











2024-T4 Aluminum





Solder Pads d

Vertical
Strain Gage


S3/16 in.

5/8 in.


Horizontal
Strain Gage


Figure 4-16 New Load Cell


Solder Pad


White Lead
(+ Readout)


-Green Lead
(- Readout)


Figure 4-17 Load Cell Circuit











































Figure 4-18 Revised Load Cells For Multi-Fastener System









Table 4-9 Regression Output For Load Cells


Load Cell 001 Cell 002 Cell 003 Cell 004 Cell 005 Cell 006 Cell 007 Cell 008
(pounds) (my) (my) (mv) (my) (my) (mv) (mv) (my)
0 1.48 -33.51 -11.26 -0.487 3.41 -0.004186 0.041224 -0.001398
100 1.06 -34.02 -11.735 0.06 3.945 -0.004531 0.04169 -0.00186
200 0.06 -34.51 -12.2 0.632 4.345 -0.005045 0.042145 -0.0024
300 0.12 -34.97 -12.662 1.167 4.875 -0.00558 0.04255 -0.00292
400 -0.37 -35.44 -13.115 1.685 5.355 -0.006091 0.04296 -0.00345
500 -0.86 -35.92 -13.56 2.235 5.83 -0.0066 0.04338 -0.00399
600 -1.35 -36.38 -14.015 2.785 6.305 -0.007098 0.04381 -0.00453
700 -1.845 -36.84 -14.452 3.33 6.763 -0.007588 0.044255 -0.00506
800 -2.345 -37.3 -14.9 3.9 7.235 -0.00808 0.04469 -0.0056
900 -2.85 -37.78 -15.348 4.415 7.725 -0.00857 0.045185 -0.00613
1000 -2.35 -38.24 -15.785 4.95 8.206 -0.00907 0.045675 -0.00666
1100 -3.825 -38.7 -16.233 5.5 8.678 -0.00955 0.046175 -0.0072
1200 -4.33 -39.18 -16.69 6.034 9.158 -0.01005 0.04669 -0.00774

Regression Output:
Constant 319.6817 -7150.77 -2510.77 86.88819 -822.069 -9200.54 -250.968
Std. Error of Y Estimate 6.035464 3.179256 3.641473 2.094943 6.139784 13.7518 2.99223
R squared 0.999742 0.999928 0.999906 0.999969 0.99733 0.998662 0.999937
No. of Observations 25 25 25 25 25 25 25
Degrees of Freedom 23 23 23 23 23 23 23

X Coefficient(s) -204.343 -213.093 -222.223 184.1777 -200892 223359.7 -187731
Std. Error of Coefficients 0.684204 0.375809 0.448896 0.21403 684.2784 1704.957 311.6033











5.5 in.
2 in- 2 in


12 in 7in 12 in.

2.5 i. 2.5 in.










10000 pu
Strain Gage













Load Cell 2


Load Cell 1


24 Ga. Pascoe Steel
(Fy = 55 ksi)


6 in.


3 in.


3 in.




2 in.


2 in.


2 in.


Figure 4-19 Strain Gage Configuration


2.5 in. 2.75in 2.75 in.


2.5 in.


0.75 in
0.75 in.


I I


'0.75 in.


mm n --rt---~----------~



















S 165
*
30 30


190
50 50



205 8 20
310
220 22





-700 190 Ibs. 190 lbs. -700



Figure 4-20 Before Web Yields


190 lbs. 190 lbs.


571 lbs. 571 lbs.


-7000 571 lbs. 571 lbs. -7000




Figure 4-21 After Web Yields


W





























532 lbs. 532 lbs.


532 lbs. 532 Ibs.


Figure 4-22 After Web Buckling


677 Ibs. 677 Ibs.


677 lbs. 677 Ibs.


Figure 4-23 Ultimate Strain







































Figure 4-24 Apparatus For Strain Gage Test


























-e 4-25 Strain Gage Test Includes 2 Load Cells And 12 Strain Gages


Figure 4-26 Computer Used For Strain Gage Test







Table 4-10 The Strain Gage Test Data


T.Load SG 1 SG 2 SG 3 SG 4 SG 5 SG 6 SG 7 SG 8 SG 9 SG 10 SG 11 SG 12
(Ibs) (me) (me) (me) (me) (me) (me) (me) (me) (me) (me) (me) (me)

0.856 4.773 0.398 -5.569 -2.784 0.398 1.193 0 -0.796 -0.398 0 2.377 -0.396
813.24 6.762 46.541 5.967 47.336 48.928 22.673 42.961 93.484 -88.694 145.604 235.733 -185.734
760.978 11.138 39.38 -1.591 36.596 44.552 22.673 38.983 87.516 -89.092 141.625 224.241 -187.318
741.982 15.911 30.629 -2.387 27.049 38.187 25.855 33.016 78.764 -91.478 137.248 213.938 -192.465
945.41 28.64 165.896 47.336 187.383 204.096 85.527 221.605 308.763 130.087 407.878 75.66 -699.406
1142.024 63.249 170.273 117.753 181.812 415.442 93.484 518.959 449.68 514.18 777.447 188.973 -6847.145
1065.043 66.829 -3.182 142.819 -87.103 377.624 -2.784 431.764 173.058 337.42 742.788 -106.142_
1136.169 89.505 -120.508 187.383 -233.434 401.11 -40.173 410.665 58.077 246.278 725.659 -419.287
1120.427 83.538 -121.701 184.598 -235.819 396.732 -37.389 405.888 52.508 242.697 716.497 -421.662
1113.448 79.162 -122.894 183.006 -237.012 394.343 -36.593 403.101 49.325 240.707 711.717 -424.432
1106.79 79.957 -123.292 182.21 -237.807 392.751 -36.195 401.509 47.336 238.717 708.132 -424.432
1073.848 93.086 -132.836 161.519 -224.289 364.09 -31.025 358.915 91.097 156.347 776.65 -655.895
1073.109 92.29 -106.192 145.604 -174.986 329.062 -21.081 320.703 198.127 134.463 892.595 -828.729
1080.8 74.388 -90.682 115.366 -186.517 278.912 -38.184 261.401 185.792 118.548 879.844 -1026.801
1194.401 75.183 -51.707 122.925 -206.397 278.912 -66.025 261.401 198.525 142.421 918.099 -1260.352
1251.061 48.53 19.889 75.979 -157.888 151.572 -131.643 192.556 200.913 129.291 875.062 -1549.472
1277.385 26.651 73.99 -2.784 -85.512 46.541 -160.274 80.753 235.135 112.183 826.85 -1931.545
1294.982 21.48 127.301 -87.501 43.358 172.661 -133.631 -61.65 310.753 107.011 812.108 -2425.276
1353.701 17.502 173.456 -127.269 106.215 346.575 -93.466 -152.719 399.518 150.378 811.71 -2949.62
48.199 -17.899 -9.944 264.187 -49.321 274.137 -231.048 176.64 -102.215 -79.149 132.474 -1881.04













0 i

-2000

-4000


S-2000 -0
0 -4000 --2000
0 -6000 --4000
* -8000 --6000
S-10000 --8000


-6000


-8000


-10000

4 5


- Before Web Yielding


6 7


-2000

-4000

-6000

-8000

10000


4 5


V


S7
S6
?5


I -2000-0
O -4000 --2000
O -6000 --4000
S-8000 --6000
a -10000 --8000


\ fterWeb Yielding


6 7


SS7
S6
5


! 0-2000
S-2000 -0
S0 -4000 --2000

8 -8000 --6000
:*-10000 -8000


After Web Buckling


2000

0

-2000

-4000

-6000

-8000

-10000


S7
S6
3.5
Sl


5- Ultimate Strain


-"7
S5 6


Figure 4-27 Computer Generated Panel Deformations With Strain Contours Included


2000

0

-2000

-4000

-6000

-8000

-10000 -
1 2 .,


4 5 6 7


31


S0 -2000
i -2000 -0
0 -4000--2000
0 -6000 --4000
1 -8000--6000
*a-10000 --8000

















900

700

500

300

100

-100

-300 -- _
2 3 -- S
5 6


-- S2
2 ^5 6 3


700 -900
M 500 -700
0 300-500
S7
S 6 0100-300
55 *-100-100
5 4 -300--100
53

52 K tlre Web Yielding




I


800 -1000
3 600-800
7 *400-600

6 0200 -400
S5 00-200
$4 0 -200-0
N -400 --200


.'.fter Web Buckling


900oo

700

500

300

100
A
-100

-300 -


S3
52
2 3 S1
6


900

700

500

30

100

-100 S3

-300 ._ S2

2 -- ... .
3 51
4 5 6


700 -900

P 500 -700
SS7 3 300 -500
S6 ] 100 -300
. $5
5 *-100-100
54
S4 -300--100


.1, ner Web Yielding


700 -900
a *500-700
S7 0300-500
S6 0 100-300
S*-100-100
M -300 --100


Ultimate Strain


Figure 4-28 Computer Generated Valley Deformations With Strain Contours Included (Stiffeners Removed)





























Figure 4-29 Standard Vacuum Box Assembly



Vacuum Box


Figure 4-30 Revised Vacuum Box Assembly











Purlin


Vacuum Box



Whaler


Vacuum Pump








Bleeder Valve



Brace


S6' 7"
Tarp or Plastic
Sheathing Elevated View


1' 2"






5.






S- 2"


Seam Due To Panel
Overlapping


Lateral Braces


Purlin


Brace


Vacuum Pump-*


Plastic Sheathing




Box
Perimeter


;Whalers


Bleeder Valve


Side View


Figure 4-31 Vaccum Box Detail


1' 8"








70

54 Ib./in.

3 psi
Web --
4--


7' -.0'*

S' ..2268 Ib.
4"--
d
Flange V
1.5"

S47628 in. Ib.

M




M SM 6(47628) 190512
f --
h b b 2 b 2 2
bd 1.5d d
3V 3(2268) 2268 f 2268
fb < F,' where f -- ; '
2bd 2(1.)d d d
Fb'= Fb(0.9X1.15) = 1.035Fb

Fv'= F (0.9)(2) = 1.8Fv
190512 2268
Fb & F, ---
1.035(d2) 1.8(d)

Average Southern Pine Has Fv = 100 psi & Fb = 1500 psi

IF d = 8" Fb = 2876 psi & Fv = 157.5 psi

6(23814) 1134
Fb'> & F,'>-
1.5d2 d


190512
Fb F F 1438 psi OK
b 1.035(d2 )
1134
F, > ---F = 78.75 psi OK
1.8(d)
2 / 2x8's of Southern Pine is acceptible


Figure 4-32 Web Design (Neglecting Contribution From Flange):







71





A' A36 Steel F = 36ksi
V
*C 1 1 2
Y in. Diameter Screw Has A = p(- = 0.01227 in.
8 16
P = 36(0.01227)= 0.441 kips =441 Ibs.
u
F =0.4F = 14.4 ksi
v v



2
VQ nr 4r
14.4 ksi; Qmax = A'max Y where A'max -- &
Ib 2 3x
2 3 4
nr 4r 4r3 rr
Qmax =(- )(-)=-- b = 2r; I
2 3x 6 4
4r3 4r3
V(-) V( 3
6 6 2r 2 4
4 5 >(- )(-3 2
7r arr 3 Ir 3rr
(- )(2r) (- )
4 2
4V 3 r2 (14.4)
3 14.4 ksi ; V = 0.132 kips 132 lbs
3nr2- 4


Figure 4-33 Fastener Properties










1200


2400 lbs. 6600 lbs. 6600 lb 2400 1b




3000 3600 lb .
2400 Ibs. < 24
3 ft.- 2.5 ft. 2400

2 ft.

2.5. 25 ft. 3 ft.-










2f3 ft. 1 ff 21.
f2400
3600 Ibs. 3000 lbs.
M 240'0 750f. 1 240) f.






3000 ft. 300 ft.
2 ft. 2 ft. ft 1. .38 181ft. 1.81.1.381 f. 2ft. 2 ft.





18f.7f ________ -


-6000x
f(x) x +2400
5
Jf(x) dx = -600x2 + 2400x

x(-600x + 2400) = 0-- x = ,4


f(x) = -1200x + 3000

Jf(x)2dx = -600x2 + 3000x + c

600x2 3000x +3000= 0
3000 1342
x = = 1.38, 3.62
1200


Figure 4-34 Three Span System (ASD 2-308 & 36)




























Figure 4-35 The Vacuum Box Used For The Simulated Pullover Test











2400 lbs.


1200 lbs./ft.


V


2400 lbs.



M
Existing Shear
At Free End





6


240


Figure 4-36 Shear at Free Ends


\/ l' lUfl lAl f llif llA


6600 lbs. 6600 Ibs.
I lftl, 5ft. ft .


3000 lbs. 3600 lbs.


52.5 ft.




3600 Ibs. 3000 1
750 ft lbs.






3000 ft. lbs. 3000 ft. lbs.
lft. 1.38ft 1.81ft. 1.81ft. 1.38ft. Ift.





7 ft. Span


- --


0 lbs.





Additional Loads
Required In Model





2400 lbs.






bs.

















Opp"


Figure 4-37 Massive Panel Buckling
















(-x) (-x)
2 2


wx w(l-x)
2 2




w(l-x) \ wx
2. wl(2x l) 2
8


w(l- x)2
8


w(- x)2
8


wl(2x- 1) w(l- x)2
8 8
21x 12 = 21x+x2
x2 -41x+212 = 0 or x2 -28x+98= 0

28 282 -4(98)
2
x = 4.1 ft. or 49.2 in.


Figure 4-38 Balancing Positive And Negative Moments







































Figure 4-39 The Revised Single Span System


-- -- ~ ~
it~;
~u~y~E~
;: ;;;*.~.
i~;'"~*f~ifi~:~u.:--" ~~5~r


Figure 4-40 Lateral Braces And Decreased Span Length Minimized Panel
Buckling




























Figure 4-41 The Two Span System


Figure 4-42 Pullover Failures Occurred At The Center Support











f \ \\ \ \ \E \ f
EI


2

Vo


B.C.'s: w(O) = M(O) = 0 & w(-) = 0 & w(l) = M() = 0
2


O 2


I
-< x < l: w2 (x)
2


Unknowns: Vo, V,, R, 0o, 0,
0
o M Vo x3 qox4
'i (x) =X0o+ 0ox A 6 + -
6Ex 24E2
w,'(x) = o + q
2EI 6EI
"(x= qx2
2El El
w ,'(x)= q0x o
El El


I I Vl, qo14
2( )= 0= -0 V0 + q0
2 2 48El 384E/

wM (1) = 0 = vol 3 +R13
6El 24El 48El
,[-Vol +q 12
M(l) = -EIw2"(1) = 0= -E) +,2
Lf 215(


Vx2 R(x- )2
w2'()=9 -0 + 0x- 2
2El 6EI 2E1

x q0X2 R(x-2)
W2 "X) = _L+_ --2
El 2E1 El
Vo qox R
M'2 "(x) = +
El El El


RI
2X(_


3 Equations & Three Unknows: V0, 0o, R:

1. 90 012 q0 13
24El 192EI

2. 0o = 12 q13 + 2
6EI 24El 48El

3. Vol- + R = 0
2 2


Figure 4-43 Two Span System (Solved By Method Of Initial Parameters)


R


V,


Vox3
w2 (x)= 00x -
6El


4
qox
24El


1-
R(x- 2)
2
6E1









V2: 12 013 VX12 q013 R12
1 24E 192- 6E= 24E+ 48
24EI 192El 6EJ 24El 48El


3V12 RI2 7qo3 7qf 24E
+ -48 = & 92o )
34EI 48El 192EI 192EI 31


56qol R 56q12
Vo & into 3
192 6 192


RI qo12
3 2


RI
6
6


RI2 (24E0)
48EI I 312
RI go12
2 2


56ql2 3qol 168qol
&192 2
192 2 192


Check:

(36qol K12
4692 608 E

0 4608EJlOK


q,13
4El


5qol 36q 2Ei qf3 5q
S8 48Kl 1152El 24EK 384El


36qol
By Inspection. V = V, = q
192
Check: 36qo12 +5qol8 ____ __O
C 192, ) 8 1


Figure 4-43 -- Continued


R qol 8
2 8 8
56qol 5ql_ 36ql
192 48 192
36qo/0 q13 12qP13
192(24EI) 192EI 4608El











w


0.1875wl


0. 1875w/


0.3125w/

0. 81251


A


0.625wl


0.18751


0.18751 1 0.81251

-0.3125w -0.1875w



0.0176w/2 0.0176wt2






-0.109, wf

0.3751 0.1251 0.1251 0.3751
,-- -___


f(-wn +0.1875w f=0 --+05wx +0.1875w x =0
0
x(0.1875v 05cx)= 0-- x= 0.3751


Figure 4-44 Two Span System (Theoretical Model)


r


C3



llni
0.1R














I-a l-a
2 a 2

wa
2 W(- -2)

2


8 4 2


_ -wl wla wa
8 4 8


-_


wa
V(x)= -EI[-wx +w-]
2
M(x) = V(x)dx

M(x) = -EIW(x)"

.-wx2 wax
M(x) = -El -+
2 2


S-a3
0--
W(x) = W(x)'dx 48

1 WX4 wa3 wla
W(x)= -- +--+ --
El 24 12 8


1
W(x)"= -M(x) W(x)'= Jw(x)dx
El
1 -wx3 war wl2 wla
W(x)'= --+-+ --+-
El 6 4 8 4

a
W(x)'= 0 @ x = -
2


wl2a wla2 wa3 wl2a
-+--+c c= -+--
16 8 48 16


wla wa2 x2
+ -- -
4 8)2


Figure 4-45 Deflection Calculations


V




M


wl2 wla wa2
8 4 8


wa2}
-- x+
8


wla2
8


Swa3
+ -+
48


wl2a
16


wla2
8


- -


I








V(x) = -EI[-wx]
M(x) = fV(x)dx
M(x) = -EIW(x)"

M(x) = -wx +c
2

W(x)"= -M(x) :. W(x)'= J ix)"dx
El
1 -wx3
W(x)' I -EJ + c

-1 wa. wl2a wla2
From Previous Calculation: W(x)'= + @ x =
El 48 16 8



l-a
wa3 wl2a wla2 2 w3 wa2l
+ ---- = +=---
48 16 8 6 48 16
1 wI x3 w13 wa2l
W(x) -- --+----
)' El 6 48 16

S( wx4 w (wl3 wa 2
W(x) W(x)-- --- x+c
El 24 48 1 6




,E 1) -a6 2 2 4wl wa16 -aj

W24a
Swx4 (wl3 wa'1 W 2 )- W13 wa2l\1-a
W(x)=-- --+--- x+ --- -- ---- -
E El 24 48 16) 24 48 16


Figure 4-45 -- Continued









The Two Span System (Figure 16):

V(x) = -wx + 0.1875wl
M(x) = V(x)dx = -0.5Ox2 + 0.1 875l + c ; M(0) = 0 c

W(x)'= M(x)= [-0.167W3 +0.09375wlx2 +c]
El El
I wl'
W( = 0 .. c = 0 .0234wl ; c = -0.0026w3
2 48
W(x) = W(x)'dx = [0.0417,x4 0.03125wlx3 + 0.00261
W(0) = 0:. c = 0

W(x)L = I 0.0417wx4 -0.03125wlx3 + 0.0026wl3x]
Ef I X


Figure 4-45 -- Continued




























Figure 4-46 The Vacuum Pump And Ball Valve


Figure 4-47 The Pressure Transducer







Table 4-11 Vacuum Box Test Number 1


DATE TIME P.T. LVDT1 LVDT2 LCELL1 LCELL2 LCELL3 LCELL4 S LCELL5 LCELL6 LCELL7 LCELL8
S_(psi) (inches) (inches) (pounds) (pounds) (pounds) (pounds) (pounds) (pounds) (pounds) (pounds)
11/14/95 16:10 0 2.089 0.954 -3.774 -807.058 55.862 -4.741 -19.819 0.863 -24.522 0.899
11/14/95 16:10:25 0.03 1.964 1.075 -3.122 -715.436 57.148 -0.667 -16.795 1.729 -21.099 3.188
11/14/95 16:10:56 0.09 1.125 0.903 13.322 -966.786 104.919 47.154 12.070 33.961 26.130 29.006
11/14/95 16:11:27 0.19 -0.212 2.159 112.708 -562.648 257.305 113.129 142.358 115.239 190.245 101.461
11/14/95 16:11:56 0.29 -0.212 2.172 259.143 -493.476 322.603 194.220 210.464 205.551 278.466 123.327
11/14/95 16:12:50 0.38 -0.212 2.062 390.310 388.130 368.689 212.485 198.289 223.641 298.689 120.616
Test Number 1
Failed Cells: NA A
Peak Loads: NA ______ 1 5
Peak Pressures: 0.38 psiLVD
Peak LVDT 1 NA ___ 2 6
Peak LVDT 2 NA 6' LVDT 2
Elapsed Time: 02:50 ______ 1 3 7
Size: 26 Ga. _
Type: Pascoe________ I 4 8
Comments: Purlins lacked lateral support and rolled. Panels buckled at midspan. P I PV
A U-tube manometer filled with mercury was used instead of a ,
pressure transducer. 1 5' 1..






Table 4-12 Vacuum Box Test Number 2


DATE TIME LVDT1 LVDT2 LCELL1 P.T. LCELL3 LCELL4 LCELL5 LCELL6 LCELL7 LCELL8
(inches) (inches) (pounds) (pounds) (pounds) (pounds) (pounds) (pounds)
11/28/95 17:38:17.800 -0.064 -0.212 140.419 -0.202 -80.001 91.176 86.490 8.887 180.521 64.003
11/28/95 17:38:19.899 -0.065 -0.212 140.560 -0.191 -28.578 89.260 104.643 27.293 180.038 63.775
11/28/95 17:38:21.899 -0.065 -0.212 140.501 -0.207 -28.821 89.306 104.500 27.141 179.828 63.866
11/28/95 17:38:23.899 -0.065 -0.212 140.610 -0.240 -29.281 89.323 104.412 27.061 180.038 63.877
11/28/95 17:38:25.899 -0.065 -0.212 140.772 -0.007 -30.130 89.571 104.349 26.809 177.791 64.284
11/28/95 17:38:27.899 -0.064 -0.212 141.273 -0.008 -30.985 90.164 104.567 27.015 175.376 65.118
11/28/95 17:38:29.899 -0.065 -0.212 143.393 0.004 -34.707 92.279 105.486 27.491 165.380 69.501
11/28/95 17:38:31.899 -0.065 -0.212 153.055 0.041 -36.392 96.680 111.699 34.713 136.652 86.180
11/28/95 17:38:33.899 -0.065 -0.212 197.348 0.177 -9.245 123.951 148.352 89.317 142.826 154.699
11/28/95 17:38:35.899 -0.064 -0.212 259.258 0.333 51.712 202.241 207.880 165.517 229.430 263.988
11/28/95 17:38:37.899 -0.065 -0.212 329.193 0.469 114.218 287.295 265.160 233.513 300.683 363.038
11/28/95 17:38:39.899 -0.065 -0.212 428.787 0.642 260.675 394.084 386.087 283.543 430.946 481.263
11/28/95 17:38:41.899 -0.065 -0.212 490.819 0.748 324.404 460.120 406.429 326.873 510.557 534.358
11/28/95 17:38:43.899 -0.065 -0.212 550.549 0.852 386.815 533.946 433.427 362.769 563.477 596.026
11/28/95 17:38:45.899 -0.065 -0.212 598.880 0.838 287.413 15.275 416.035 356.567 590.945 539.886
11/28/95 17:38:47.000 -0.065 -0.212 617.461 0.878 278.954 15.641 434.274 363.619 587.963 539.695
Test Number 2
Failed Cells: #4 __
Failure Type: Pullover __ 1 5
Peak Loads: 442.770_ _
Peak Pressures: 1.054 _2 6
6' LVDT2
Peak LVDT 1 NA LVDT2
Peal LVDT 2 NA 3 7 ,
Elapsed Time: 00:29 4 _
Size: 26 Ga._____
Type: Pascoe __ P P V PT
Comments: Pressure Transducer Installed. Failures generated on second 1.45' 4.1' 1.45'
attempt. Load Cell #2 inactive. Supports laterally braced. Major 4 .4
panel buckling. Air leaks abundant.







Table 4-13 Vacuum Box Test Number 3


DATE TIME LVDT1 LVDT2 P.T. LCELL3 LCELL4 LCELL5 LCELL6 LCELL7 LCELL8
(inches) (inches) (psi) (pounds) (pounds) (pounds) (pounds) (pounds) (pounds)
11/30/95 19:59:52.000 2.423 2.080 -0.076 46.924 133.747 125.234 106.717 124.115 52.744
11/30/95 20:00:02.000 3.391 3.442 0.259 86.908 213.001 185.371 190.035 245.117 123.767
11/30/95 20:00:12.000 3.819 3.857 0.446 142.402 297.866 303.572 259.125 330.776 191.468
11/30/95 20:00:22.000 3.968 4.049 0.620 173.102 350.225 371.863 302.719 387.119 226.471
11/30/95 20:00:32.000 4.041 4.131 0.668 190.565 378.694 401.001 325.087 420.509 246.468
11/30/95 20:00:42.000 4.103 4.194 0.635 202.373 399.529 418.120 342.865 447.158 262.639
11/30/95 20:00:52.000 4.154 4.243 0.741 210.066 415.498 428.159 356.837 466.961 274.044
11/30/95 20:01:02.000 4.199 4.288 0.761 216.856 427.210 434.211 367.105 483.194 283.324
11/30/95 20:01:12.000 4.235 4.324 0.780 222.341 436.174 439.870 377.169 497.810 291.366
11/30/95 20:01:22.000 4.271 4.367 0.798 227.064 444.439 444.980 386.493 511.922 299.337
11/30/95 20:01:32.000 4.312 4.470 0.812 231.423 451.645 449.285 392.795 524.963 305.851
11/30/95 20:01:42.000 4.339 4.506 0.824 235.646 458.043 452.654 400.443 535.316 311.335
11/30/95 20:01:52.000 4.361 4.544 0.839 239.189 464.144 456.057 408.343 545.732 317.227
11/30/95 20:02:02.004 4.381 4.578 0.850 245.555 470.639 460.764 418.059 556.253 322.559
11/30/95 20:02:12.000 4.399 4.612 0.860 249.010 477.131 464.602 426.877 567.488 329.269
11/30/95 20:02:22.000 4.417 4.647 0.868 252.054 482.844 467.896 435.519 577.736 334.700
11/30/95 20:02:32.000 4.435 4.681 0.746 255.832 487.404 470.358 442.757 586.976 339.225
11/30/95 20:02:42.009 4.450 4.710 0.815 258.117 491.309 472.209 448.667 594.074 344.137
11/30/95 20:02:52.000 4.464 4.738 0.767 260.189 494.789 473.736 453.885 600.269 347.584
11/30/95 20:03:02.000 4.557 4.792 0.676 260.772 495.807 473.591 452.401 602.999 349.789
11/30/95 20:03:12.000 4.560 4.804 0.633 261.440 497.092 472.832 453.907 604.511 350.917
11/30/95 20:03:22.000 4.568 4.821 0.756 262.070 498.622 472.771 455.973 605.960 352.549
11/30/95 20:03:32.000 4.598 4.857 0.712 265.279 503.327 475.360 461.337 613.394 358.097
11/30/95 20:03:42.000 4.627 4.906 0.741 271.767 509.489 478.810 472.221 626.750 367.110
11/30/95 20:03:52.000 4.641 4.964 0.725 271.206 507.939 473.769 473.003 627.170 377.870
11/30/95 20:04:02000 4.663 4.969 0.811 274.886 511.833 466.315 478.643 633.953 379.918
11/30/95 20:04:12.000 4.711 5.047 0.847 283.653 518.034 435.830 492.909 649.913 390.739
11/30/95 20:04:20.899 4.725 5.101 0.846 282.506 518.029 342.693 498.099 650.060 392.072
11/30/95 20:04:22.000 5.625 5.704 0.697 246.192 502.130 -4.393 404.623 547.769 334.754
Test Number 3
Failed Cells: #5 A
Failure Type: Pullover ,3_
Peak Loads: 353.575 < 4 LVDT 2
Peak Pressures: 0.817 LVDT 1 5
Peak LVDT 1 2.204 6' 6
Peal LVDT 2 2.827 PT
Elapsed Time: 04:29 7
Size: 26 Ga ___ 8
Type: Pascoe PV
Comments: Air leaks around perimeter. Failure generated on third attempt. 3
Minor panel buckling. Big improvement. 55 3.




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