Comparison and evaluation of web crippling prediction formulas

(1)

Comparison and evaluation of web crippling prediction

formulas

Citation for published version (APA):

Bakker, M. C. M., & Peköz, T. (1986). Comparison and evaluation of web crippling prediction formulas. (EUT report. B, Dept. of Architecture Building and Planning; Vol. 86-B-01). Technische Universiteit Eindhoven.

Document status and date: Published: 01/01/1986 Document Version:

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Afdeling Bouwkunde Vakgroep Konstruktie EUT-reports 86-B-01 ISBN 90-6814-301-8 Mei 1986

-.-

• =

Technische

Hogeschool

Eindhoven

Comparison and evaluation of web crippling prediction formulas. Monique Bakker Teoman Pekoz, Ph.D. pro~essor of structural engineering March 1985

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TABLE OF CONTENTS

Summary 3

Notation 5

Chapter 1 Introduction 7

1.1. General 7

1.2. Objective and scope 7

1.3. Outline 8

Chapter 2 Formulations evaluated 9

2.1. ECCS appro,ach 9

2.2. AISI approach 9

2.3. Waterloo approach 10

Chapter 3 Differences in web crippling formulations 11

Chapter 4 Testresults used 16

4.1. Stockholm test 16

4.2. Cornell tests 22

4.3. Missouri-Rolla tests 26

4.4. Waterloo tests 30

4.5. Eindhoven tests 34

Chapter 5 Comparison of experimental and computed results 36

Chapter 6 Conclusions 55

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SUMMARY

Since the use of end and load stiffeners is frequently impractical in thin-walled cold-formed steel construction, the webs of beams and deck may cripple due to the high local intensity of the load or reaction.

In this report three different web criI'pling prediction formulations are compared with experimental results from five different sources.

It is found that these web crippling formulas show considerable differences and do not give satisfactory results consistently.

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-r

hw

\

b

_o

_b

_o

I

bo

I I I

~

\

/

\

I

_I

_I'

I

bu

2 bu

bu

b

I

0 I I

b

u

Figure 1

(6)

NOTATION

The most frequently used symbols are given below. Other symbols, defined in the text, are used in particular cases.

b

o b

u B

width of element in compression (mm) width of element in tension (mm) modulus of elasticity in this report 210 000 (N/mm2) yield stress (N/mm 2) depth of profile (mm) depth of stiffener (mm) span length (mm) length of bearing (mm) bending moment (Nmm)

ultimate bending moment (Nmm) bending radius (mm)

web crippling load (N)

ultimate web crippling load (N)

ultimate web crippling load according to the BCCS - 1983 Recommendations (N) ultimate web crippling load according to the AISI - 1980 Specification (N)

ultimate web crippling load according to the Waterloo Method (N)

width of web measured along the web between the points of intersection of the system lines (mm)

clear distance between flanges measured along the plane of web (mm) thickness of sheet (mm)

acute angle between web and flange (degrees) For a designation of symbols see Figure L

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I /

I.T.

F.

l~ing

-

... \ /

~1.5sw(A)

<

1.5s

_w

(A}

n

E1 F.loadin

/- 1\1

LO.F.lca:Jing

/' 1 \

/

"

. /

I

I.T~F.loading

E.D.t loading

. 1."[

F.loading

<1.5S

w

(A)

< tSsw(A)

1.0 -.---"""'1

I

MINd

I

U

<

1. 5s

w(A)

l.o.F : Interior One-Flarge

E.o.F: End One-Flarge

1.1F : Interior Two-Flange

ElF: End Two-Flange

Figure 2

OJ

_{- - .}

-,---I

I

o

+-~--~_r--~_r--~~--r__~~

o

0.3 to

Figure 3

(8)

1. INTRODUCTION 1.1. General

A concentrated load induced into the web of a cold formed steel member can cause web crippling, i.e. localized crushing or crippling of the web.

A simply supported member loaded with a concentrated load or a continuous member over interior supports is subjected to the combined action of web crippling and bending. This combined action can cause fallure at a load less than if the member was subjected to web crippling alone.

1.2. Objective and scope

This report presents the results of a study comparing three different web crippling prediction formulations with 194 test results from five different sources.

The study is restricted to the investigation of the ultimate capacity of cold formed steel members (sections and decks) subjected to a web crippling load only.

This is not a very realistic problem because in practice most cold formed members are subjected to a combination of web crippling and bending. However, the allowable web crippling load in such a case is determined by means of an interaction formula using the ratios R/Rd and MlM

d. The interaction formulas currently in use do not give satisfactory results consistently.

Assuming that the calculation of the moment capacity is sufficiently accurate. the results of the interaction formulas can possibly be improved by a more accurate determination of the web crippling load.

In practice a number of different loading cases which can cause web crippling are encountered.

In this study only the case of single (unreinforced) webs loaded on one flange away from the end of the member (to be referred to as Interior One Flange loading) is considered. (see Figure 2). For an IOF loading the distance from the edge of the interior bearing plate to the interior edge of the exterior bearing plate has to be 1.5 sweA) or larger. This restriction is the result of tests conducted by Winter in the 1940's and insures that there is a one flange loading, not a two flange loading.

In any IOF web crippling test it is impossible to avoid a bending moment. Research reported by Baehre (10) has shown that there is negligible interaction for MlMd

<

0.3 (see Figure 3), Hetrakul, Yu and Wing (4 and 8) adopted this criterion for their work, apparently assuming that the European and American methods for calculating the moment capacities give the same results. In the BCCS-1980 Recommendations the moment ratio MlMd for negligible moment interaction was increased to 0.52, but in the ECCS-1983 Recommendations the ratio was decreased to 0.25. In this study all the test results used (except the Stockholm tests, see chapter 4) have a moment ratio less than or equal to 0.3. For certain members it is impossible to determine the IOF web crippling load. When for example the span length is taken large enough to get an IOF loading, the moment at failure will be larger than 0.3 times the ultimate moment. For these members the web crippling load is determined with test specimens having shorter spa.ns.

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1.3. Outline

Chapter 2 of this report describes the three web crippling formulations evaluated. Chapter 3 states the differences in these web crippling prediction formulas.

Chapter 4 gives the necessary information of the test series used to compare the web crippling prediction formulas with the test results.

Chapter 5 contains the comparison between the test loads and the ultimate web crippling loads computed with the three web crippling formulations.

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2. FORMULATIONS EVALUATED

The three formulations evaluated have been based on test results, not on theoretical analysis.

This is due to the complexity of the theoretical analysis. A theoretical analysis involves

Nonuniform stress distribution under the applied load and the adjacent portions of the web

Elastic and inelastic stability of the web element

Local yielding in the immediate region of load application

The effect of the inside bend radius (bending of the webs out of the plane) The web crippling prediction formulas evaluated are:

2.1. The ECCS approach

In the ECCS-1983 Recommendations (1 and 2) the web crippling load is predicted by the equation

The use of the equation is subject to the following limitations:

r

<

lOt

1s

<

200 (mm)

9> 500

When the support consists of a round tube, z- or c-purlin, so that the nominal bearing length becomes very small,

t.

may be taken equal to 10 mm.

s

The equation applies to both sections and deck.

The BCCS approach is based on the testing of profiled sections performed at the Royal Institute of Technology in Stockholm (3). Baehre (10) reported that the testing involved 78 specimens, but it is doubtful whether all these tests can be seen as lOP web crippling tests (see the description of the Stockholm tests in chapter 3).

The empirical formula for the ultimate web crippling load given in References 5 and 10 has been modified slightly to make it applicable to aluminium also.

The original formula (5) included a limitation sW(E)

<

l70t. 2.2. The AISI approach

In the AISI-1980 Specification (3) the web crippling load is obtained by the equation Rd

=

1.85*.f tl33·C

1

Ca'C

e

(291 - 0.40 swCAlt)(1+0.007 1/t>** where C 1 = (1.22 - 0.22 f tl228) C 2 = (1.06 - 0.06 r/t) :i 1.0 2 C

_e

= 0.7 + 0.3 (9/90) * Safety factor

** When 1 It

>

60 the factor (1 + 0.007 1 It) may be increased to (0.75 + 0.011

t.

It>

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The formula applies to beams when rlt ~ 6 and to deck when i/sw(A)

<

3.5.

Further limitations applied to the use of the equation are:

e

~ 45 0

swCA) ~ 200 t

The AISI approach is based on the evaluation of 58 lOF tests (8).

rlt ~ 7, i It ~ 210 and s

The tests included 28 tests performed at the University of Missouri-Rolla and 30 tests performed at Cornell University.

Some additional tests have been conducted for the purpose of determining the effect of large bearing lengths on web crippling.

2.S. The University of Waterloo approach

A modification of the AISI approach was reached in a research project conducted at the University of Waterloo (4).

The web crippling formula is:

*

2 sw(A)

-Rd = 1.85' 9.0 t f

ty(sin6)(1.0-0.00l -t-)(1.0+0.005 i/t)(1.0-0.075h!t)(1.0-0.lftI228)

*

Safety factor

The use of the equation is subject to the following limitations sw(A/t ~ 200

rlt ~ 10

The University of Waterloo approach is based on the evaluation of 90 lOF tests (4).

These tests included 59 tests performed at the University of Waterloo and 31 tests performed at Cornell University.

The University of Waterloo approach was developed for deck (multi-web cold formed steel sections). In this study it is also applied to sections.

This is reasonable because the AISI and BCCS use the same equations for sections and deck too.

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3. DIFFBRBNCBS IN WEB CRIPPLING FORMULATIONS The three web crippling prediction formulas can be written as

2 Rd'" t·C· Cft; Cr/t ' C II./t· C SW(A/t ' C

e

where C C f ty C r/t and is a constant

is a term depending on fty is a term depending on rlt etc.

2

= 1 for fty :: 400 (N/mm )

= 1 for rlt ::: 0

=

1 for

1s/t :::

200 CSW(A{t = 1 for sweAtt = 40 C

_e

=

1 for

e :::

900

In the three web crippling formulas these terms have different forms.

1. BCCS approach C :: 0.15 ./ 210 000

aOO·

2.5 . 3.4

=

11686 (N) C r/t 1 - 0.1 ,/ r/t (0.5 -+ C ::: 1 sw(A) It (2.4 -+ (e1901') C

_{e ::}

3.4 It) rlt

<

10 !I.

<

200 (mm) s

(13)

12

2. AISI approach C

=

1.:: .

3336· 2.95 • 275

=

15172 (N) 2 (1.22 f t

_Y

- 0.22 f t

_Y

I 228) 333.6 C r/t = (1.06 - 0.06 rlt) ~ 1 (1 + 0.007 2. It) C _ ~ __________ s __ _ 2. It - 2.95 s (0.75 + 0.011 It) 2.95 C _ (291 - 0.40 sw(A/t ) S W(Alt - 275 2 C

_e

= 0.7 + 0.3 (e/90) 3. Waterloo approach when 2. It ~ 60 s when !lIt > 60 s C = 1.85,9.0 • 329.8 ·2 • 0.96 = 10543 (N) 2 (f ty - 0.1 f ty 1228) 329.8 0.075

J"r/t

(1.0 + 0.005 It It ) S C sw(A{t

=

C

_e

= sin

e

n.o

0.96 beams: r/t

<

6, deck rlt

<

7 deck: 2. / < 210 s t rlt ~ 10

(14)

to

0.8

0.6 t

0.4 ~01

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250

300

350

400 fty

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2]

-1D

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0.6 I

OJ.

/"'

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....

..

¢

,/ ~.' , /

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.

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200

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50

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70

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... t.,;. • .:... :.,:.. .. .::.:..~.~

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40

80

120

160

200 Sw(A)

It

c:a - - E((S

approach

(=11686 [N]

..,..-- AISI approach

(=15172[Nl

... Waterloo approach

(=

10543[N]

Figure 4

(15)

For a comparison of the terms see Figure 4.

The most striking difference between the three web crippling prediction formulas is that the BCCS approach, unlike the AISI and Waterloo approaches, does not contain a web slenderness term.

The values of the term C

r/t of the AISI approach decrease at a much greater rate than

the values of the BCCS and Waterloo approach.(See Figure 4).

The values of the terms C2.s/t of the BCCS and Waterloo approach are almost identical

for 2. It

>

50.

s

The values of the term C

e do not show big differences.

In the Waterloo approach sine was used because it is simpler to compute on a hand calculator and has physical meaning as demonstrated in Figure 5.

The constants C show rather big differences.

The constant C of the AISI approach is about 45% higher than the constants C of the BCCS and Waterloo approach.

This may be caused by the relatively large reduction of the web crippling load according to the AISI approach for increasing rlt and swCA/t and decreasing !tit.

Peose

(16)

150

I

100

100 I

qf

J2

0

G)

,50 I

100 r\~OCD

150 I

-J, I

( )

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150 ,

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150

J.,

strip'

o

Q

I

65 _{'tt(E) If}

_{Sw(E) -}

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(E)= 100

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,50 I

100 ~~

_,50

®

,50

t-

150 Figure 6

\lr I

/\

f i l l !

Is

Figure 7

(17)

4. TESTRESULTS USED 4.1. STOCKHOLM TESTS (5) 1. Properties of test specimens

The configuration of the test specimens is shown in Figure 5. The dimensions and properties are given in table 1.

2. Test setup See figure 7.

To prevent spreading the tension flanges were connected with a strip in the middle of the span. It is assumed that the central bearing plate and the end supports had the same bearing length.

3. Load application

The loading speed was 196 N (20 kp) per minute. After a load increment of 981 N (l00 kp) the load was kept constant for about 20 seconds to read the dial indicators (used to measure the deformations). Circa 2942 N (300 kp) before failure the dial indicators were read after load increments of 490 N (50 kp).

4. Determination of the test load

The test load was taken as the largest load the section was able to sustain.

This criterion was suitable for the sections (with small bending radii) showing small deformations at failure. Sections with large bending radii failed with large deformations. These deformations were too large to be accepted in practice.

Yet, lacking a better failure criterion, for these tests too the test load R

test was taken as the largest load the section was able to sustain.

Each type of test was performed twice.

When the test loads differed more than 5% a third test was performed. 5. F allure mode

Several types of iailure occurred during the testing: failure in the middle of the span (type M figure 8) failure at the end supports (type E figure 8)

failure by sway of the whole section (type 5, figure 8)

failure of the top flange over the whole length of the section (type V Figure 8)

failure in the middle of the span after failure at the end supports and stiffening the section at the end supports with a wooden block between the top flange and the bearing plate (type M )

o

The failure types 5 and V do not occur in practice

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I

J

I

l

--( '

...

I I I I I I I

-

....

-

...

-~

...

"'"

...

-I 1\ I

I

'I

j I

I

....

... I I

I

I :L: f OJ Cl.. >.

...

QJ c.... .3 ~

>

OJ Cl.. ~ QJ c.... ::J ro '4-I..U OJ 0->.

...

OJ c.... ::J

-~

(19)

6. Moment ratio

The moment ratio MtestlMd is not given in Reference 5.

It is reported that the span length was taken so short that the influence of the bending moment on the ultimate web crippling load was negligible. However, using the BCCS-1983 to calculate the ultimate moment capacity Md it appears that the moment ratios MtestlMd range from 0.28 to 0.48.

eM

t es t was computed by the equation Mt es t;: Rt es t (R. - R. s )/4).

According to Baehre (10) interaction is negligible for MlMd ( 0.3. Hence it is doubtful whether all the Stockholm tests are web crippling tests. Some tests are probably interaction tests.

Since the Bces approach was based on the Stockholm tests. the tests with moments ratios larger than 0.3 are also included in this study.

7. Test results

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HR. TESTCO(lE fty Is t, l' 0 sw(E) 5w(A) bo bl.! hs 1 t OF WEBS 1 1-2-1 366 40 1.02 10.4() 90 50 49 100 50 0 2(;0 2 2 1-3-1 366 40 1.02 10.40 90 50 4'1 100 50 0 260 :> 3 1-'4-2 366 40 1.02 10.40 90 100 99 100 50 0 460 2 4 1-5-2 366 40 1.02 10.40 91 100 99 100 ~.=;O 0 460 :> 5 1-6-2 366 40 1.02 10.50 88 100 99 100 50 0 460 2 6 1-10-5 366 40 1.02 10.40 70 100 99 100 50 0 460 2 7 1-11-5 366 40 1. 0::' 10.40 70 100 99 lOO 50 0 4(,() 2 8 1-13-8 366 40 1.02 10.40 ~jO lOO 9<1 100 50 0 460 2 9 1-'3.4-8 366 40 1.02 10.40 49 lOO 99 100 50 0 460 2 10 1-15-8 366 40 1.02 10.40 50 100 99 tOO 50 0 460 2 11 2-1-5 366 40 t.02 1..40 72 100 9" 100 50 0 460 2 12 2-2-0 361., 4() 1.02 1.30 71 100 99 100 50 0 4e,O 2 13 2-3-5 3(,6 40 1.02 1.20 71 100 99 lOO 50 0 460 14 2-4-5 366 40 1.02 ::;.30 71 l,()O 99 lOO 50 0 460 2 " ~ _2-5-5 ₃₆₆ ₄₀ _1.02 _5.20 7~) 100 99 100 50 0 4bO 2 h J 16 2-7-8 366 40 1.02 1. 60 50 IOO 99 lOO 50 0 "1M 2 17 2-9-8 366 40 1.02 1.10 50 lOO '19 lOO 50 0 460 2 18 2-10-8 366 40 1.02 5 .. 50 49 IOO 99 lOO 50 0 460 2 19 2--11-'8 3b6 40 l.O2 ~i. 40 50 lOO 99 100 ~iO 0 460 ;~

20 3-1-4 384 40 0.50 1. 30 69 50 49 100 50 0 260 :? 21 3-3-4 384 40 0.58 1.30 70 50 49 100 50 0 260 2

22 3-5--4 384 40 O.5S 2.70 70 50 4'i' 100 50 () ₂₆₀ 2

n 3-6--4 384 4() 0.58 2.70 70 50 49 100 ~,:jO () ₂₆₍₎ ₂ ... _'-D

24 3-'1-4 384 40 0.50 5 .. 20 7() 50 49 :lOO 50 () 260 2

25 3-·8-4 384 40 0.58 ~;. 00 69 ~;o 4<1 lOO 50 0 2bO ~.~

26 3 .... 9·-4 384 40 0.5E! 5 .. 20 1:>9 50 49 lOO 50 0 260 2 27 3-10-5 384 4() 0.::;8 1.30 70 100 99 100 50 0 460 2 ~~8 3-11-5 384 40 0.58 L30 71 100 99 100 50 0 460 2 2<1 3-'13-5 384 40 0.58 2.80 60 100 99 100 50 0 460 2 30 3-14-5 384 40 0.58 2.90 71 100 9<1 100 50 0 41.,0 2 31 3-"16-,5 384 4() o . ;';0 4.60 6f.l 100 99 100 ~.)o () 46() :~ 32 3-17-5 384 40 0.58 4.90 71 100 99 100 ~;O () ₄₆₀ 2 33 4'-1-5 274 40 0.93 5.3(} 71 100 99 100 50 0 46() 2 34 4-2-5 274 40 0.95 5.30 70 100 99 100 50 {) 460 2 35 4-4-5 274 70 0.93 5 .. 20 71 100 9<1 100 50 0 430 2 36 4-5-5 274 70 0.94 5.30 70 100 99 100 50 0 430 2 37 4-6-5 274 70 0.95 5.40 69 100 99 100 50 0 43() 2 38 4-7-5 274 100 0.92 5.30 70 100 99 100 50 0 400 2 39 4-8-5 274 100 0.97 5.30 '70 100 99 100 ~jO 0 400 2 40 4-9-5 274 100 0.93 5.3() 70 100 99 100 50 0 400 2 41 4--10-5 366 70 1.02 5.50 70 100 99 100 50 0 430 2 42 4-11-5 366 70 1.02 5.40 71 100 99 100 50 0 430 2 43 4-12-5 366 100 L02 5.40 71 tOo 99 100 50 0 400 :2 44 4-13-5 366 100 L02 5.30 72 lOO 9'7 100 50 0 400 :-45 4'~·15-·5 366 100 1.02 ::; .30 69 tOO 99 JO() :;() 0 400 2

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PROPERTIES OF TEST SPECIMENS; STOCKHOLM TESTS

Nf\. TEST CODE fty ls t r 0

46 4-17-7 384 40 O.5B 3.30 50 47 4-22·-7 384 100 0.513 3.50 51 48 4-24-7 ~m4 lOO 0.58 3.60 51 49 4-25-7 244 40 0.52 2.60 52 50 4-26-7 244 40 o _{.. oJ.:..}C"'" 1.40 ₅₂ 51 4-28--7 244 70 0 .. 52 2.40 50 52 4-29-7 244 70 o .. tj2 2.70 ;,iO 53 4-33-7 244 100 0 .. 52 2.40 51 5w(E) sw(A) bo bl.! 50 49 100 50 50 4'1 tOo 50 ~'i0 49 100 50 50 49 100 50 50 4'; 100 50 50 49 100 50 :jO 49 100 50 50 49 tOO 50 hs 0 260 0 200 0 200 0 260 0 260 0 no 0 230 0 200 t OF WEBS 2 :; 2 2 2 2 ;2 2 N o

(22)

37

75

37

I I I

149 I

100

r-N N en

o

en

prof

i

les

13 to

24 _{profiles 25}

_to

₃₆

_{profi les 37}

_to

₄₈

Figure

9

r~id

central plate

~

Figure 10

(23)

4.2. CORNELL TESTS

A complete description of these tests is reputed to have been given in Reference 8. Since this Reference was not available References 4, 5 and 9 have been used.

1. Properties of test specimens

The test sections used in the Cornell Study are shown in Figure 9. The dimensions and properties are given in Table 2. Only the overall length of the stiffeners is given, the dimensions of the curved and straight portures of the stiffeners were not available.

2. Test setup See figure 10. 3. Load application No information available.

4. Determination of the test load No information available.

5. Failure mode

During the progress of a test at moderately high loads but still before failure the webs deflected inwards out of their plane (see Figure 11).

This deflections were relatively small and extended throughout the depth of a web in the vicinity of the external load. At failure, there was a sudden bulging of the web with large deflections under and in the immediate vicinity of the central bearing plate, as shown in Figure 12.

6. Moment ratio

According to Reference 4 the moment ratio MtestIMd was less than 0.3.

The AISI-1980 Specification was used to compute the ultimate moment capacity Md' The test moment M

test was computed by the equation M

test

=

Rtest (~ - is) I 4. 7. Test results

(24)

Figure 12

(25)

PROPERTIES OF TEST SPECIMENS; CORNELL TESTS

NF( • TESTCO[lE ftlJ ls t r 0 sw(E) ~;w (A) bo b'l hs 1 4 OF

WEBS 54 1,3 234 19 1.54 1.54 90 151 149 49 100 ,.,~ 610 2 .... ,J 55 14 254 38 1 C'''"') _1.52 ₉₀ ₁₅₁ ₁₄₉ 49 tOO ">"- 610 2 • ..1 .... "",,.J ~j6 16 255 19 1.52 4,,~5 90 1,51 149 49 100 25 610 2 57 17 225 38 1.53 4.60 90 151 149 49 tOO 25 6tO 2 58 18 225 64 1.54 4.61 90 151 1.49 49 100 :?5 610 :2 59 19 372 19 1.64 1..64 90 151 149 49 100 25 610 2 60 20 370 38 1.66 L6{, 90 151 149 49 100 25 610 2 61 21 371 64 1.65 l.65 90 151 149 49 100 .,~ 610 2 ",-, 62 22 372 19 1.64 4.92 90 151 149 49 lOO ')" ~.J ₆₁₀ ₂ 63 23 365 38 1.b5 4.95 90 151, 149 49 lOO '">.,- _b10 2 .: ..• J {,4 24 367 64 1.67 ~' .. O2 90 151 14'9 49 100 "1" .' .. .J 610 2 65 25 260 19 1.53 1.53 '10 227 226 37 75 0 914 2 66 26 247 38 1.51 l.51 90 227 226 37 7'" ,J 0 914 2 67 28 21'7 19 1.53 4.58 90 227 22b 37 75 0 914 2 68 29 228 38 1. 51 4.53 90 227 22b 37 7'" -! 0 914 2 N 69 30 223 64 1.4'1 4.47 90 227 226 37 75 0 914 :2 .j:::o. 70 31 376 19 1.65 1.b5 90 227 225 37 75 0 9],4 ;! 71 34 377 j,9 1.62 4.85 90 227 225 37 75 0 914 2 72 35 374 38 1.63 4.08 90 227 225 37 75 0 914 2 73 3b 373 b4 1.61 4.82 90 227 225 37 75 () 914 2 74 :57 221 1,9 1. ~;3 1.53 90 303 302 3-) 75 0 1219 2 75 38 229 38 1.56 1.56 90 30:3 302 37 75 0 1219 2 76 39 2b3 b4 l .. 5~i 1 .. 55 90 303 302 37 7" _," 0 1219 2 77 40 213 19 1 • 50 4. ~;l 90 303 302 37 75 0 1219 ::.: 78 41 224 30 1.54 4.63 90 303 302 37 75 0 1219 ;! 79 42 223 64 l .. 55 4.64 90 303 301 37 75 0 121 '1 :2 SO 43 371 19 1.69 1.69 90 303 301 37 75 0 1219 2 81 44 374 38 L6'1 1.69 90 303 :~()1 37 75 0 1219 2 82 46 385 19 1.68 5.03 90 :~03 301 37 75 0 1219 2 83 47 373 :38 1.70 5.1 () 90 3()3 301 37 75 () ₁₂₁₉ ."

--H4 4EJ 368 ~)4 1.6EJ 5.04 90 303 301 37 75 0 1219 2

(26)

37

37 to--+- ____

~

37

37 t7-+ ____

+--4

~

40

8 - - - -

+--I-

-8

0

'"

...

-:r

rn N

8

m t:o

...-177

₁₇₇

(27)

4.3. MISSOURI-ROLLA TESTS (8) 1. Properties of test specimens

Three different types of cross-sectional configurations of beam specimen were used. The first type consisted of two channel sections (section SU, Figure 13). The channels were braced by 19.05 x 19.05 x 3.175 mm angles at the compression flange and 3.175 x 19.05 rectangular bars at the tension flange.

Self tapping screws were used for connections. The intervals of braces were provided such that the lateral buckling of each individual channel section was prevented.

The second type of beam specimens (section MSU, Figure 13) was fabricated in the same manner as the first type except that the beam flanges were connected to the bearing plates by machine bolts. The purpose of this arrangement was to evaluate the possible improvement of web crippling loads resulting from the restraint provided by beam flanges when they are connected to bearing plates by machine bolts.

The third type consisted of two channel sections with unstiffened flanges (sections USU, Figure 13). The braces of the tension and compression flanges were provided in the same manner as the first type. The dimensions and properties are given in Table 3.

2. Test setup See Figure 14. Q. Load application

During the test the loads were applied by an increment of 15% of the predicted ultimate load. The duration for each load increment was approximately five minutes.

After failure of each specimen the ultimate load for web crippling was recorded. 5. Failure mode

All failure modes were consistent. Failure occurred in the web underneath the bearing plate.

However, the maximum deformation is located at about lj4 of the depth measured from

the top flange of the specimen. See Figure 15. 6. Moment ratio

The moment ratio M

test / Md was less than 0.3.

The AISI-1968 Specification was used to compute the ultimate moment capacity Md' Backcalculating from the tables in Reference 8 it appears that M

test was computed by the equation

M

test '" Rtest 2./4. 7. Test results

(28)

brae ing angle

-...

/

bracing strip

Figure 14

" f f t i

Figure 1S

(29)

PROPERTIES OF TEST SPECIMENS; MISSOURI-ROLLA TESTS

NH. TESTCO!lE ft"y Is t r 0 sw([) sw(A) bo hI.! hs 1 t OF

WEBS 85 BUI-IOFt 302 "" ...:. ... 1 1.22 :5.38 90 ::'48 250 37 37 16 965 2 86 SU1-l0F2 302 25 1.21 3.H) 90 250 2~2 37 37 16 965 :: 87 SU1-10F5 302 76 1.23 ~LH) 90 249 250 36 36 16 966 2 BS SUI--IOF6 302 71.. 1.22 3.18 90 249 250 37 37 16 965 2 89 8U2-IOFl 302 25 1.24 3.1H 90 310 311 36 36 16 111H 2 90 SU2-IOF2 302 '">" ... .J _1.27 _3.18 90 309 310 36 36 17 lll8 2 91 SU2-IOFS 302 76 1 .. :~2 3.18 90 309 310 :57 37 17 11.18 2 92 SU2-10F6 30;2 76 1.24 3.18 90 310 311 36 36 16 1118 :: 93 8LJ2'-IOF3 254 76 1.26 2.38 90 lEl2 184 40 40 15 1,7:5 ~~ 94 SI.J2'-IOF4 254 76 1.29 2.3B 90 183 184 4() 40 15 673 2 95 SU2'-JOrS 254 76 1.29 2.38 90 lfi3 184 4() 4() 15 52l 2 96 8U2'-IOF6 254 76 I • ~~9 2.3B 90 Hl3 Hl~j 40 40 15 521 2 97 BU5-10FI 325 ..,,,-.. '-l 1.26 2.38 '?() 1~'j4 155 66 66 15 635 2 98 S1l5-IOF2 325 2!:5 1.213 2.38 90 1.53 154 66 b6 15 6>35 2

99 8U5-IOf3 325 ~;1 1.27 2.48 90 154 1~i5 66 lI6 1'" ,J 635 :? N

100 SUe;-IOF4 325 51 1.28 2.3H 90 1~j3 154 66 1..6 15 635 2 ():) 101 5U5-IOF5 325 76 1.28 :?:2fJ 90 i_53 155 66 lie. l~i 635 :'

102 SU5-IOF6 325 ?b 1.28 2.38 90 153 1 !3~; 66 66 15 635 :2 103 SU6' -- IOFl 325 25 1.27 2 .. 38 <~o 1113 18~5 78 78 l5 635 2 104 SU6' - IClF2 325 2~5 1.27 2.18 90 1134 11'16 78 78 1" - _I 635 :?

105 SU6'-IOF3 ",~.J 3 "'1 c· _~:j_:t _1.26 _::.20 ₉₀ 1<14 1.85 "lB 7f:! 1.5 63'5 :? 106 SlJ6'-IOF4 325 51 1.26 ~~. 38 90 Hl5 106 78 78 15 63:; :?

107 SUb' --!OFS 325 76 1.25 2.38 9() 184 185 78 78 t :; 6:5~; 2

108 StJ6'-IOF6 325 7f> 1.28 2.28 90 1134 185 7!3 7B 15 635 2 109 MS1l6'-IClFl 325 2~) 1.28 2.38 ')0 184 HI:5 78 7 I:! :1.5 635 :2 110 MSU6'-IOF2 325 2~~ 1.27 2.38 90 184 185 7B 78 15 635 2 111 MSU6'-IOF5 325 76 1.28 2.3B ')0 184 lB5 I'D 78 15 635 2 112 MSU6'-IOF6 325 76 1.26 2.38 90 lB3 185 78 78 15 635

..

'1 H3 lISlI17-IOF5 250 76 L24 1..19 90 121 122 35 35 () :;59 2 114 1.l5U:l7-IOF(' 25() 76 1.24 1.19 90 121 122 35 35 0 ~j59 ::. 115 USU18-IOF5 25() 76 1.24 1.19 'to 2:5'~ 24() ~;;~5 55 0 914 2 116 USU1B-xor6 250

n.

1.24 1.19 (,0 240 242 55

.-.,.

_"J () 915 2

(30)

\/\100

~V,7~

~50

I

_"'50

I I

1.,50

I

"'100

'",

50 I

V'\

100 0~'

7/,50

~50

I

Sw{E)

=

85 - 200

Figure 16

R

1 ls

I

Figure

17

I",SO

I

Figure 18

(31)

4.4 WATERLOO TESTS (4) 1. Properties of test specimens

The test specimens consisted of profiles specially fabricated at the University of Waterloo, as shown in Figure 16. They were brake-formed using ASTM A611 Grade C steel with a minimum garanteed yield stress of 228 (N/mm2). Their dimensions and properties

are given in Table 4. 2. Test setup

See Figure 17.

Relatively large end bearing plates were used to insure that failure would occur at the interior load position. Spreading was prevented by bolting the lower flanges to the bearing plate.

3. Load application

The load was appUed to the test specimens by means of a 45 kN capacity hydraulic jack through a hand operated hydraulic pump. The rate of load application was uniform up to the failure load.

4. Determination of the test load The test load R

test was taken as the largest load the specimen was able to sustain after which a sudden decrease in load was experienced.

5. Failure mode See Figure 18.

The failure region for the tests was a localized failure which was restricted to the area under the bearing plate and immediately adjacent to it.

6. Moment ratio The moment ra.tio M

test I Md was less than 0.3.

The AISI-1980 Specification was used to compute the ultimate moment capacity Md' M

test

=

Rtest 01. 2) I 4. 7. Test results

(32)

HR. 117 118 119 l20 1.21 :1.22 12~~ 124 125 126 127 128 129 130 131 132 133 134 1.35 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 1.5l 152 153 154 il::·;;:-.1. oJ..J 156 157 1'58 159 160 161 TESTCODE '5W-IOF 6\.1-IOF 7W-IOF OW-IOF 14W-IOF 15W-IOF 16W-IOF 17W-·1/)F 23W-·IOF 24W-IOF 25W-IOF 2bIJ-IOF 34W-IOF 35W-IOF 3bW-IC1F 5\W·· 101" 52W-IOF 54W-IOF 55W-IOF 56W-IOF 57W-IOF 60W-WF 61W-IOF 62W'-IOF 69W-IOF EI9W-IOF 91W-·IOF 101W--IOF 103W-IOF 1241J- lOF 125W-·lOF 12f:lW-IOF 134W-·IC1F 135W-·IOF 13bW-IOF 13?W-IOF l.39W-·IQF 3WR·- I OF 12Wf\-IOF 1. SWR-·IOF 21WR-IOF 24WR-IOF 30Wf'i:-IOF 33WR·-IOF 39WR-IOF fty 274 265 231 274 274 265 231 274 274 265 231 274 265 265 265 274 265 274 274 274 231 253 253 253 274 265 274 265 274 265 2£,5 ~~65 274 274 274 274 265 318 318 284 279 299 318 284 318 Is 25 25 25 25 25 25 '>'" .:... ~.; .. ,t::. ,:".,J ,.,,,,.

'"'"

t;.:-~'" 25 25

.,,,

... CJ 51 76 ,>'" •. V 25 25 2'5 -'''' •• ...! 25 25 51 76 76 .,,, " .• J .,'" iO-",,' 25 25 J27 102 1 ()~'. 102 127 25 51. 25 51, 51 51 51 51 51 51 51 t 0.97 0.b1 1 .. 52 0.97 0.97 0.61 1 .-I.e c'''' 0.97 0.99 0.64 1 .. 55 1. O:~ 0.61 0.61 0.61 0.'11 0.61 0.91 0.97 0.91 1 .. 52 1.14 1.14 1.14 0.97 0.61 0.97 O.6! O.S'7 0.61 0.61 ().61 0.'1'7 0.97 0.97 0.97 0.61 0.63 0.63 0.B5 O"S5 1.00 0.63 0.85 0.63 r 2.38 2.313 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.3El 2.38 2.38 2.38 ~~.38 2.38 2.38 2.38 2.38 2.38 2.30 2.38 2.38 2.38 2.38 2.38 2.7:113 2.38 2.3B 2.38 2.38 2.38 ;.'.38 2.38 2.38 2.38 2.38 2.3f:l 4.76 6.35 6.35 c~ .53 9.13 4.76 4. U, 6.35 o 90 90 90 90 70 70 70 70 50 50 50 50 90 90 90 70 70 50 50 50 90 90 90 90 90 70 70 50 50 90 90 90 90 90 90 90 90 90 90 90 90 90 70 70 70 sw([) 101 l01 201 203 101 102 202 202 lO? 1(>3 202 203 101 100 100 105 lOb 130 1~~9 130 lOl 1()0 100 I01 101 108 109 132 133 102 102 101 102 102 102 l01 101 86 B8 f:!5 n~' <"I 87 106 l04 106 sw(A) 100 lOl 199 202 l.OO 101 201 201 101 102 200 202 100 100 lOO 104 105 129 128 1,2'1 99 99 99 100 tOO 10? OB 131 132 10l. 101 100 t01 1.0l 10l. 100 100 f:l5 07 84 84 86 105 103 lOS bo 100 101 to:? 100 lOO 101 99 100 cl9 99 100 101 lOt 101 101 100 1()0 101 127 75 100 103 103 103 103 lO() lOt t02 102 102 102 102 103 103 103 103 101 101 101 101 10l lOO 102 101 lOO bu ~jo 51 50 50 50 51 50 50 50 50 49 50 50 50 ~jO 49 50 50 49 50 :so 50 50 50 50 50 49 ~;o ~;O 51 51 51 ~jl 51 51 51 51 53 49 53 55 51 53 54 53 tis o () o o o o o () o o o o () o o o o o o o o o o o o o o o o o () o () o o o o o o o () () o o o 4l>O 4M 559 ~;59 508 511 508 508 508 50B 50B 508 315 318 315 :'.08 50B 50B SOB 508 31E1 3lB 318 318 305 516 521 533 533 483 470 318 305 305 .305 305 521 50S 508 508 508 508 50S 50B 50S • OF WEBS 2 2 2 2 2 ::.~ 2 2 2 :.~ 2 2 2 .2 2 ;2 2 2 2 .2 2 2 2 2 .2 2 .2 :::: 2 2 2 2 2 .2 .2 2 4 .2 2 2 2 2 .2 2 2 w ...

(33)

PROPERTIES OF TEST SPECIMENS; WATERLOO TESTS

Nt, • TESTCCltlE ft'l ls T' 0 sw(E) 5w(A) bo btl hs t

or

WEBS 162 42WR-IOF 299 51 1.00 6.35 ;70 105 104 106 54 0 ~;08 2 163 48WR-ItlF 279 51 () .. ~;5 7. 1~) ?O 106 105 99 54 0 S08 :: 164 ~'i1 WF,-l OF 299 5l 1.00 8.74 . 70 107 106 103 52 0 508 2 165 57WR-IOF 318 ~1 0.63 4.76 50 130 129 103 55 0 SOB 2 166 60WR-IOF 284 51 0.85 7.15 50 126 125 lOS 56 0 508 2 167 66WR-IOF 318 51 0.63 6.35 50 134 133 103 53 () SOB 2 168 69WH-IOF 299 ~}l 1.00 6.35 ~,!;O ₁₂₇ LU. 105 54 0 508 2 169 75WR-IOF 279 51 0 .. 55 7.15 50 1'·)1::" ₁₂₄ ₁₀₄ ₅₇ ₀ ₅₀₈ ₂ .. "_..J 170 78UR-IOF 299 51 1.00 '1.53 ~:jO 13~j 133 100 52 0 508 2 171 81UR-lor 302 51 1.S4 '1.53 50 132 130 102 53 0 508 2 172 131Wf(- IOF 318 102 0.63 6 .. 35 90 88 B;7 101 49 0 508 2 173 137WF\-IOF 318 102 0.63 4.76 70 lOt, 105 102 53 0 5013 2 174 140WR-IOF 318 102 0.63 l,.35 70 106 105 100 53 0 508 ::> 175 1441JR- IOF 299 102 1.00 El.74 70 107 106 103 52 0 508 2 w N

(34)

wood

2Ox20

14-4 I

,44,

n

F\

188

188 R

screw

>

2h

_w

,44 I

n

~5

188

I

Figure 19

steel

barZ12

I

C

for

ls =0

steel plate

t=

6

III

(

for

15=25

50

70 Figure

20 __ '-_ .... _-_-' __ f

6 _~d

\~--Figure

21

(35)

4.5. EINDHOVEN TESTS (9)

L Properties of test specimens

All the test sheets consisted of three full corrugations as shown in Figure 19.

The dimensions and properties of the sheets are given in Table 5. The sheets were roll-formed by Hoesch (Germany): type PC 750 - 55 - 0.71; distributor Prince Cladding. 2. Test setup.

See Figure 20.

t

=

is + swen)"

The clear distance between the bearing edges of the central bearing plate and the end supports is smaller than 1.5 sweAr This was necessary for the limitation of the bending moment.

3. Load application

For each sheet the load was applied in more than 5 equal steps upto 90% of the ultimate load. When the deflection in the middle of the span was increasing at constant load at least 2 minutes were taken before the new load was applied.

The sheets A-3, B-3. B-3 and D-1 were loaded upto the characteristic load (ultimate load devided by 1.5). Then the load was removed and afterwards the sheets were loaded to failure as described a.bove.

Because of the large deformation of the compression flange at failure (up to 17 mm) the test load was corrected to be the load causing a flange deformation 6 of hwllO (see Figure

21.)

5. Failure mode See Figure 2 L

6. Moment ratio

The maximum moment ratio M

test / Md was 0.24. The BeeS - part 1 - draft - 1980 was used to calculate the ultimate moment capacity Md'

The test moment M

test was calculated by the equation

7. Test results

(36)

NR. TESTCDtIE ft.y 1$ t r 0 176 4-Al 297 0 0.79 c>.35 Ell 177 4'-A2 304 0 0.79 6.35 1:12 178 4-A3 305 0 0.79 6.35 8~> 179 4·-A 323 0 0.71 5 .. 65 81 180 4-£1 324 0 0.71 5.65 8l. 181 4-Bl 302 25 0.78 6.35 1:10 182 4-82 303 25 0.78 6.35 82 183 4-l'l3 309 25 0.78 0.35 BO 184 4-K 320 25 0.71 ~;.6::j 8l 185 4-El 302 50 0.79 6.35 79 186 4-E2 309 50 0.79 6.35 81 187 4-E3 307 50 0.80 b.35 BO 188 4-D 327 50 0.72 5.65 81 189 4-F 324 50 0.72 5.65 81 190 4-C1 305 70 0.78 {, .35 80 191 4-C2 304 70 0.79 6.35 79 192 4-C3 304 70 0.79 6.35 81 193 4-6 327 70 0.72 5.65 B1 l.94 4-H 324 70 0.72 5.65 81 sw(E) 5w(A) bo blJ 56 55 44 63 56 55 44 62 55 55 44 63 C ' " ".J 54 44 63 5~5 54 44 63 55 54 44 63 56 55 45 63 ~j6 56 44 63 56 55 44 63 ~57 56 43 62 56 56 43 63 :i6 56 44 62 co,::-.Jd 54 44 63 ;:15 54 44 63 56 55 44 63 56 56 44 63 56 5;:.) 42 62 55 54 44 b3 ~5 54 44 6~' hI> 0 55 0 55 0 55 0 55 0 55 0 80 () 80 0 80 0 80 0 105 0 105 0 1 0~5 0 105 0 105 0 125 0 125 0 125 0 125 0 125 '" OF WEBS 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 {, w U"I

(37)

~. COMPARISON OF EXPERIMENTAL AND COMPUTED RESULTS The test loads R

test are compared with the computed ultimate web crippling loads R ECCS' RAISI and RWat:

The test loads 1<test and the load ratios RteslRECCS' RteslR AISI and RteslRWat are listed in the Tables 6,7,8,9 and 10.

A load ratio Rtest/Rd less than 1 means that the applied web crippling formulation gives an unsafe prediction for the ultimate web crippling load Rd'

For each test series the mean, standard deviation and coefficient of variation of the load ratios were calculated. A load ratio marked with

*

means that the test is not within the limits of the applied web crippling prediction formula. These load ratios are not included in the computation of the mean, standard deviation and coefficient of variation. In order to include tests that only just fail the limitations (as given in Chapter 2) these limitations are enlarged by 5%. The limitations consist of restrictions to the ratios 2./s

w(A), 2./t, rlt and sw(a{t.

These ratios are also shown in the Tables 6, 7, 8. 9 and 10.

An overview of the computed means, standard deviations and coefficients of variation is given in Table II.

The load ratios RteslRECCS' RteslRAISI and RteslRWat. are plotted against some test parameters in Figures 22 to 30.

The dashed line CRteslR

d

=

1) represents perfect correlation between Rtest and Rd'

The plots shown in Figures 22 to 30 are a selection of the available plots. Similar plots can be made for every parameter.

From Figure 22 it can be seen that the ECCS approach can probably be improved by introdUcing a web slenderness term.

For the comparison of the web crippling formulations the coefficient of variation is the most important.

The coefficient of variation, which can be seen as the standard deviation for a mean of 1, is a measure for the scattering of the load ratios. The mean of the load ratios can easily be corrected by multiplying the web crippling prediction formulas with a constant.

The AISI and Waterloo approaches have the same coefficient of variation for all the test results together.

The ECCS approach has a larger coefficient of variation. Since the Waterloo approach has a wider range of application it can be concluded that the Waterloo approach gives the best average results. The Waterloo approach does not give the best results for each test series individually.

From Table 11 it can be seen that there are significant differences between the test series.

The Waterloo tests show the lowest mean of the ratios Rtest'R

d for all the web crippling formulas evaluated This may be due to the test setup or load application.

Because the Stockholm tests had relatively large bending moments the EeCS approach was expected to give a relatively safe prediction of the web crippling load for the other test series. This is not the case. Nor do the AISI and Waterloo approaches give a relativel~ unsafe prediction of the web crippling load for the Stockholm tests.

Apparently the web crippling prediction formulas give a prediction of the mea.n web crippling load.

When a characteristic web crippling load is required (Le. a web crippling load lfJ"hich ha.s a certain specified probability of being achieved), the web crippling equations should be multiplied by a constant K.

(38)

Assuming a normal distribution of the load ratios, this constant K can be calculated from the given mean m and standard deviation s by the equation

K = m - x.S

(39)

TEST RESULTS; STOCKHOLM TESTS

NR. TESTCDrlE Rtest Rtest Rt,est Is r sw(Al

RECCS f(W,~t. sw(A) t t -1-2-1 4291 0.98 1.49* 0.93 0.82 39 10.20 48 2 1-3--1 4085 0.93 1.42* 0.89 0.82 3'1 10.20 48 3 1-4-2 4379 1.00 1.64-1( 1.00 0.40 39 10.20 97 4 1-5-2 4~j75 1.05 1 . 7~~* 1.05 0.40 3'1 10.20 97 5 1-6-2 4546 1.05 l.ni* 1.04 0.40 39 10.29 97 6 1-10-5 3942 1.02 1.1.)8* (). 'f<; 0.40 39 10.20 97 7 1-11-5 402l 1.04 1. 71* 0.9f:J 0.40 39 10.20 97 8 1-13--8 3481 1.00 1. 6~ilE 1.04 ().4l 39 10.20 97 9 1-14-8 3697 1.06 1.76* 1.12 O.4l 39 10.20 97 10 1-15-8 3697 1. .06 1.75* L10 0.41 39 10.20 97 11. 2-1-5 4771 0.94 0.92 0.96 0.40 39 1.37 97 12 2-2-5 5355 1.05 1.03 1.08 0.40 39 1.27 97 l_ 3 2-3-5 5134 1.01 0.913 1.03 0.40 39 1.18 97 l.4 2-4-·5 4237 0.96 1.07 0.94 0.40 39 5 .. 20 97 15 2--5-5 4090 0.93 1.03 0.91 0.40 39 5.10 97 l.6 2-7-8 4295 0.96 0.94 1.08 0.41 39 1.57 97 17 2-8-8 4281 0.93 0.91 1.05 0.41 39 1.08 97 18 2-10--8 3633 0.93 1.05 1.01 0.41 3';> 5.39 97 19 2--11-0 3678 0.93 1.05 1. 01 0.41 39 5 .. 29 97 20 3-1-4 2010 L04 1.04 1.10 0.81 6'1 2 .. 24 85 21 3-3-4 2010 1.04 1.03 1.09 0.81 69 2 .. 24 85 22 3-5-4 1755 0.98 1..07 1.01 0.81 69 4.66 05 23 3-6-4 1790 1.00 1.09 L03 0.81 69 4.66 85 W 24 3--7-4 1471 0.92 1.34* 0.92 O.Bl 69 8.97 85 CO 25 3-8-4 1574 0.98 1.39* 0.98 0.81 6'1 B.62 85 26 3-9-4 1520 0.96 l..39* 0.95 0.8l. 69 8.9/ 85 27 3-10-5 2001 1.03 1.19 1.20 0.40 69 2.24 171 28 3-11-5 1.966 1.01 1.16 1.17 0.40 69 2 .. 24 171 29 3-13-5 1687 0.96 1.22 1.09 0.40 6'1 4.83 171 30 3-14-5 1692 0.95 1 ,.,-, , .. .;.. ... i.OS 0.40 b'Y ~," ()() j ;? 1 31 3-16-5 1652 1.02 1.57* 1.1:3 ().40 69 7.93 171 32 3-17-5 1603 0.99 1. .50* 1.09 0.40 69 8. 4~'i 1,71 33 4-1-5 2922 0.90 1.12 1.00 0.40 43 5.70 106 34 4-2-5 2932 0.88 L07 0.97 0.40 42 5 .. 58 104 35 4-4-5 3516 0.90 1.l.0 l.O6 0.71 75 5 .. 5(7 106 36 4 .... 5-5 3658 0.92 1.14 1.09 0.71 74 5.64 105 37 4-6-5 3756 0.94 1.16 1_.10 0.71 74 5.68 104 38 4-7-5 3776 0.87 1. no 1.05 1.01 109 5.76 108 39 4-8-5 4153 0.B7 0.99 1.04 L01 103 5.46 t02 40 4-9-5 3957 O.B9 1.03 1.08 1.01 108 5.70 106 41 4-10-5 5286 1.00 1.16 1. ()6 0.71 69 5.39 97 42 4-11-5 5350 l.()t 1.1.6 1.06 0.71 69 5 ... 29 97 43 4-12--5 6634 1.10 1.18 1.18 1.01 98 5 .. 29 97 ".1\ 4-13-5 6257 1.03 1.tO loll 1..01 98 5 .. 20 97 45 4-15-5 6002 1.00 1.07 l.OB 1..01 98 5.20 97

(40)

NR. TEST CODE Rtest Rtest Rtest Rtest Is Is RECCS RAISI RIJ'lt. .w(A) t

46 4-l,7-7 1486 0.95 1.09 1.07 0.81 69 5.69 85 47 4-22-'7 2403 1.10 1.03 1.24 2.03 172 6.03 85 48 4-24-7 2555 1.17 1.11 1.33 2.03 172 6.21 85 49 4-25-7 1079 1.01 1.21 1.34 0.81 77 5.00 95 50 4-26-7 1005 0.B7 0.95 1.18 0.81 77 2.69 95 51 4-28-7 1427 1.08 1.12 1.49 1.42 135 4.6<! 95 52 4-29-7 1437 1.10 1.18 1 .. 52 1.42 135 5.19 95 53 4-33-7 1594 1.04 0.97 1.40 2.03 192 4.62 95 MEAN 0.9'7 1.08 1.08 STANDARD IIEVIATION 0.07 0.08 0.13 COEF. OF VARIATION 0.07 0.08 0.12

Value. followed bV

*

not included in computation of mean, standard deviation and coef'i~ient of variation.

(41)

TEST RESULTS; CORNELL TESTS

NR. TESTCOtlE Rtest Rtest Rt.ef.4 t ls Is sw(A)

f(ECCS F(AISI 5w(A) t

-t-.-54 13 9030 1.19 1.07 1.23 0.13 12 1.00 97 55 14 8363 0.90 0.138 1.03 0.26 25 1.00 '?9 56 16 7651 1.0B 0.99 1 .06 0.13 13 3.00 99 57 17 8a07 1.07 1.14 1.26 0.26 25 3.00 97 5B 18 8496 0.88 0.'19 1.12 0.43 41 3.00 97 59 19 15569 1.45 1.1.7 1 .. 25 0.13 12 1.00 91 60 20 15079 1.15 1 "03 1.13 0.26 23 1.00 90 61 21 16681 1.10 L06 1.1 <I 0.43 3'1 1.00 91 62 22 13834 1.40 1.18 1.18 0.13 12 3.00 91 63 23 13967 1.18 1.1J. 1.14 0.26 23 3.00 90 64 24 14902 1.0S 1. 05 1.10 0.43 38 3.00 89 65 25 6895 0.87 O.tl3 0.92 0.08 12 LOO 148

66 26 e,B41 0.75 O.Bl 0.92 O.l7 25 LOO 149 67 28 5783 0.87 0.90 0.96 0.08 12 3.00 148 68 29 6272 0.78 0.90 0.97 ().17

..

~ ... ..J 3.00 149 6'1 30 ,,784 0.74 0.92 L02 O.2B 43 3.00 151. 70 31 10676 0.98 0.85 O.8'? 0.08 12 1.00 136 71 34 10676 1.10 1.01 0.98 O.OB 12 3.00 139 72 35 10511 0.90 0.92 o.n 0.17 23 3.00 139 73 36 10734 O.SO <l.87 <l.89 0.28 39 3.00 140 74 37 6450 0.013 0.95 1.05 O.Ot. 12 i.OO 197 75 3fJ 6895 0.74 <l.Bf:! 0.98 0.1.3 24 1. 00 193 76 39 7562 0.65 0.80 0.90 0.21 41. 1.00 1.94 77 40 6116 0.96 loll. 1.14 0.06 13 3.00 201 +:> 78 41 6228 0.75 0.95 0.99 () .13 25 3.00 196 0 79 42 6450 0.66 0089 0.95 0021 41 3.00 1. '?5 SO 43 10631 0.95 (l.af:! 0.90 O.Of., 1l. 1.00 179 81 44 10231 0.75 0.79 0.H2 0.13 23 LOO 179 02 46 1000B 0.96 0.93 0.89 0.06 11 3.00 180 03 47 1.1236 OoBS' 0.97 0.94 0.1.3 22 3,,00 177 84 4B 11459 0.80 0.93 0.93 0.21 38 3.00 laO MEAN 0.94 0.96 1..02 STANDARD DEVIATION 0.20 0.11 0.12 COEF. OF VARIATION 0.21 0.11 0.12

Values followed by • not included in computation of mean, st.andard deviation and coefficient of variation.

(42)

NR. TESTCODE Rtest F<test Rtest r,test Is 1s r 5w(A) RECCS RA1S! F<Wol'- • sw(A) t t t -135 SU1-10Fl 5605 0.97 1.12 1..12 0.10 21 2.77 205 86 SU1-l0F2 :;227 0.92 1.06 1.07 0.10 21 2.6:5 209 87 SU1-·IOF5 6450 0.77 1.00 1.06 0.30 62 2.58 203 88 SLJ1-IOF6 6161 0.75 0.97 1.04 0.30 6~' 2.60 205 89 SLJ2-lOFl 5093 0.85 1.06* 1.04* 0.()8 20 2 .. 55 250 90 SLJ2-IOF2 5805 0.93 1.14* 1.13* 0.08 20 2 .. 50 244 91 t;U2-IOF5 6161 (). 7~5 1.07i< 1.10* -0 .. 2~) 1..2 2.1..0 254 92 SLJ2-IOF6 6472 0.76 1.08* 1.. 11l~ 0.24 61 2 .. 5~) 2~,() 93 SU2'-IOF3 7784 0.95 1.13 1.30 0.41 t.o 1.89 145 94 SLl2'-IOF4 760t. 0.90 1. 0~5 1 ~'? 0.41 59 l. 8~:; 143 95 SU2'-IOF5 7028 0.83 0.97 1.13 0.41 59 1.85 143 96 SU2'-IOF6 6850 0.81 0.9::; 1.10 0.41 :;';> 1.f:l5 143 97 SU5-IOFl 624l. 0.96 0.92 O.9B O.lt. 20 1.89 123 98 SLJ5-IOF2 6583 0.98 0.94 l.Ol o .1t. 20 1.B/ 1.21 99 SU5-IOF3 7784 0.96 1.00 1.10 0.3:3 40 1.95 122 .+:>0 100 SU5-·l0F4 8140 0.98 1.02 1.1~~ 0.33 40 l.86 120 >-' 101 SU5-IOF5 9252 0.97 1.04 1.19 0.49 60 1. 78 121 102 SU5-·IOF6 8162 0.86 0.93 1.05 0.4'? 60 1.B6 l21 103 SLJ6'-·IOFl 6583 0.9'7 0.98 1.04 0.14 20 1.88 14'5 l04 SU6'-·IOF2 7028 1.05 1.04 1.11 0.14 20 1.72 146 105 SLJ6'-IOF3 8407 1.04 1.14 1.24 0.27 40 1.81 147 106 SLJ6'-IOF4 8074 l.OO 1.09 1.l9 0.27 40 1.09 148 107 SU6'-IOF5 9275 1.02 1.1.6 1.29 0.41 t.1 1.91. 148 108 SLJb'-IOF6 8407 0.B9 0.99 1..11 0.-41 60 1.79 145 109 MSU6'-IOFl 7340 1.10 1.09 1.15 0.14 20 1.87 145 110 MSU<,,'-IOF2 7308 1.10 1.09 1.16 0.14 20 l.B8 l46 111 MSLl6'-IOF5 9097 0.96 1.07 l. • ~·O 0.41 5(J 1.86 144 112 MSU6'-IClF6 9519 1.02 1..:1.6 l.29 0.41 60 LBO 146 113 USLJ17-IOF5 6672 0.80 O.H8 1 .. 06 0.62 61 0.96 98 114 USLl17-·IOFb 1..784 O.B2 0 .. 09 1.01'1 0.62 1..1 O.ru. 91'1 115 USU18···IOF5 7517 0.91 LIb 1.. :~4 0.32 bl. 0.96 193 1.l.6 U~)UJB-IOF6 6517 0.79 1..01 1.l6 () .. ~~2 6:1. (). 'i6 194

MEAN 0.92 1.03 1.14

STANDARD DEVIATION 0.10 O.OB 0.09 COEF. OF VARIATION O. 1.1 O.OB 0.08

Volues followed by * not included in computation of meon, stondard deviotion ond coefficient of voriation. (See Cholpter 5)

(43)

TEST RESULTS; WATERLOO TESTS

NF< • TESTCOtrE ,<test Rt .. st Rtest f(t,e~; t l' 5w(A)

RECCS HAISI HWGt. sw t t -117 :514- lOF 2700 0.72 0.73 O.IH O. ~:5 26 2.47 104 118 t.W-IOF 1254 0.78 0.98 1.01 0 .. 25 42 3.91 165 119 7W-IOF 6895 0.89 0.89 1.01 0.13 17 1..56 1.31 120 aW-IOF 3145 0.84 1.03 1.06 0.13 26 2.47 209 121 14W--IOF 2504 0.76 0.77 0.80 0 .. 25 26 2.47 103 l22 15W-IOF 921 0.65 0.82 0.79 0.25 4'> 4 3.91 166 123 16W-IOF 6392 0.93 0.94 0.99 0.13 17 1.56 132 124 17W-IOF 2811 0.85 1.04 1. 01 0.13 26 2.47 20'1 125 23W-IOF 2113 0.68 0.68 O.nl 0 .. 25 26 2.41 102 126 24W-"IOF 974 ().71 0.88 0.94 0.25 40 3.75 161 127 25U-IOF 5338 0.84 0.84 ().98 0.13 16 1.54 129 128 26W"-IOF 2002 0.62 0.73 0.79 ().13 25 2.34 198 129 34W-IOF 1392 0.87 1.09 1.12 0.25 42 3.91 165 130 3~;W-IOF 1726 O.EIS 1.04 1.18 0.51 83 3.91 164 1.31 36W'-IOF 2002 0.B5 O. '15 L 1'1 0.76 1 '")c.M 3.91 164 h.;J 132 51W-TOF 2375 0.80 0.83 O.BS 0.24 28 2.6l 114 133 52W-IOF 1152 0.81 1.04 0.99 O. ~~4 42 3.91 173 134 54W-IOF 1877 0.70 0.76 0.85 0.20 28 2.61 141 135 S5W-IOF 1948 0.66 0.70 0.78 0.20 26 2.47 133 136 56W--IOF 1890 0.70 0.77 O.BS 0.20 28 2.61 141 137 5'7W'- IOF 6508 0.84 O."?6 <l.8S 0.26 17 1 .. 51.. 65 138 60W-IOF 4395 0.91 O.Ba 0.99 0.26 2~! 2.08 B7 139 61W-IOF 5271 0.88 0.93 L08 O.5t 44 2.00 87 140 62W-IOF 5729 0.83 0.89 1.Ot) 0.76 67 2.013 87 .j:>. _N 141 69W-IOF 4226 0.79 0.84 1.02 0.76 79 2.47 104 142 El9W-IClF j 1l.2 O.7B 1.01 0.96 0.24 4':' 3.91 175 143 91W-IOF 2558 O.7f.l 0.130 0.82 0.24 26 2.47 112 144 lOlW-'IOF 836 0.65 0.91* 0.93* 0.19 42 3.91 215 145 lO3W-IllF 233~j 0.79 0.84 0.94 ().1,9 26 2.47 137 146 124W-IOF 1779 0_62 0.59 O. El5 1 .. 25 ;:Otl 3.'11 166. 147 125W-IOF 1779 O • .!>? O. }() 0.94 J".Ol U,7 3.91 166 14f.l 128W-IOF 18b8 0.71 0.73 0.99 1. Ol 167 3.91 16,5 149 134W-IOF 4942 0.83 0.83 L09 1.0l 105 2.47 104 ISO 1.35W-"IOF 5422 0.84 0.79 1..:11 1 . k ; , } '1~ _1.32 _2.47 ₁₀₅ 151 136W-IOF 3314 0.89 0.90 0.99 0 .. 25 26 2.47 104 152 137W-IOF 3914 0.84 0.92 1.05 ().51 :53 2.47 104 153 139W-IOF 1045 0.65 0.82 0.84 o .,.~ "' .... .,.} 42 3.91 165 154 3WR-IOF 1352 0.64 0.90* 0.78 0.60 81 7.59 lU. 155 12WR-IOF 1366 0.69 1.22* 0.83 0.:;8 61 10.12 139 156 15WR-"IOF 2113 0.64 0.89* 0.76 0.60 60 7.49 99 157 21WR-IOF 1090 0.86* 32.75* 1.04* 0.60 93 17.36 154 158 24WR-IOF 27l.3 0.63 0.97* 0.70 0.59 51 9.10 86 159 30WH-IOF 1472 0.79 1.17* 0.94 0.413 81 7.59 168 160 33WR-IOF 2246 0.74 0.94 0.85 0.4'1 60 5.61 121 161 39WR-IOF 1579 0.90 1.68* 1.05 0.413 81 10.12 168

(44)

NR. TESTCQIIE Rtest Rtest Rtest 1s r RAISI RW.).t. sw(A) t 162 42WR-IOF 3207 0.79 1.01 0.86 0.4'} 51 6.33 104 163 48WR-IOF 1179 0.96* 2.83* 1.19* 0.48 93 13.0:! 192 164 51WR-IOF 3105 0.81 1.24* 0.87 0.48 51 fl.71 106 165 57IJR-IOF 1463 0.87 1.39* 1.20 0.39 81 7.59 206 166 60WR-IOF 2U3 0.83 1.35* 1.07 0.41 60 8.42 147 167 66IJR-IOF 1330 0.B4 1.71* 1.15* 0.38 81 10.12 212 168 69lJR-IOF 3074 0.84 1.11 1.04 0.40 51 6.33 126 169 75WR-IOF 1001 0.90* 2.86* 1.29* 0.41 93 13.02 22b 170 713lJR-IOF 2,}80 0.88 1.51* 1.07 0.38 51 9.49 133 171 BlWR-lOF b606 0.87 1.03 0.96 0.3'7 33 6.19 85 172 131WR-IOF 1646 0.64 0.95* 0.77 1.16 162 10.12 139 l.73 137WR-IOF 1913 0.79 0.99* 0.95 0.97 162 7.59 168 174 140WR-IOF 1913 0.B4 1.32* 0.99 0.96 162 10.12 168 175 144WR-IOF 3781 0.78 1.09* 0.B8 0.96 101 8.71 106 ~ MEAN 0.713 O.B7 0.94 w STANDARD DEVIATION 0.09 0.13 0.12 COEF. OF VARIATION 0.11 0.14 0.13

Values followed by

*

not included ~n co~putation of ~ean. standard deviation and coefficient of variation. (S.e Chapter 5)

(45)

TEST RESULTS; EINDHOVEN TESTS

NR. TESTCDrIE Rtest Rtest Is ls sw(A) r,wo t. Sw<A) t -t-,-176 4-Al 1.967 1.15 1.41* 1.01 0.00 0 13.04 70 177 4-A2 2017 1.16 1.42* 1.02 0.00 0 8.04 70 178 4-A3 2017 1.16 1..41~ 1.01 0.00 0 8.04 b9 179 4-(\ 1650 1.12 1.39* 0.99 0.00 0 7. cl6 76 180 4-B 1617 1.09 1.36"· 0.96 0.00 () 7.96 76 181 4-£11 1967 0.91 1.19* 0.89 0.46 32 8.14 70 tEl 2 4-B2 2150 O.9B 1.28)< 0.96 0.46 32 8.14 70 183 4"1<3 2267 1.04 1.36* 1.00 (). 4~3 3'> <. B .14 71 Hl4 4-K 1967 1.03 1.34* 1.01 0.45 35 7.96 78 185 4-[1 2533 0.92 1.26* 0.98 ().90 63 13.04 71 186 4-[2 2633 0.94 1.28l(· 1.00 0.90 63 8.04 70 187 4-[3 2633 0.92 1 .. 2:i* O.'1B 0.90 63 7.94 69 188 4-D 2200 0.88 1..17* 0.94 0.92 69 7 .. 85 76 189 4-F 2217 0.89 1.18* 0.95 ().92 69 7.B5 76 190 4··Cl 2'133 0.96 1 .. 25* 1.05 1.27 90 8.14 71 191 4-C2 2883 0.93 1.20* 1.02 1.26 89 8.04 70 192 4-C3 2833 0.90 1 • .16. 0.99 1.26 89 8.04 70 193 4-'G 2500 0.89 1. 10. 0.97 1.29 97 7.85 76 194 4-H 2450 0.87 1.09. 0.95 1.29 97 7.85 76 MEAN 0.99 0.00 0.98 STANDARD DEVIATION 0.10 (l.00 0.04 COEF. OF VARIATION 0.11 0.00 0.04 ~ ~

Volues followed by • not included in CDMputotion of Neon, stondord deviatlon and coefficient of variotion.

(46)

Eees APPROACH AlSI APPROACH MEAN S.D. C.V. tiEAN S.D. STOCKHOLM TESTS 0.99 0.07 0.07 1. OS o.oa

CORNELL TESTS 0.94 0.20 0.21 0.'?6 0.11

MISSOURI-ROLLA TESTS 0.92 0.10 0.11 1. 03 0.08

WATERLOO TESTS 0.78 0.09 0.11 0.07 0.13

EINDHOVEN TESTS 0.99 0.10 0.11 o.()() 0.00

ALL TESTS 0.91 0.14 0.1 C. <l.98 0.1 :~ C.V. 0.00 ().11 0.08 0.14 0.00 0.1.3 WATERLOO APPROACH MEAN

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(47)

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(48)

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