Flexural strength and ductility of HPS-100W steel I-girders

Lehigh UniversityLehigh Preserve

Theses and Dissertations

1998

Flexural strength and ductility of HPS-100W steelI-girdersLarry Alan FahnestockLehigh University

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Fahnestock, LarryAlan

Flexural Strength .and Ductility ofHPS-1 OOWSteel 1-Girders

May 13,1998

Flexural Strength and Ductility ofHPS-100W Steel I-Girders

by

Larry Alan Fahnestock

A ThesisPresented to the Graduate and Research Committee

of Lehigh Universityin Candidacy for the Degree of

Master of Science

ill

Civil Engineering

Lehigh University

May 6, 1998

Acknowledgments

The author acknowledges the support provided by the American Iron and Steel

Institute (AISI) for the experimental portion of this research. The research was

conducted at the Center for Advanced Technology for Large Structural Systems

(ATLSS) at Lehigh University. Financial support for the author was provided by the

ATLSS Center. The author thanks the technical and support staff of the ATLSS .

Center and the Fritz Engineering Laboratory at Lehigh University.

The author gratefully acknowledges the advice, guidance, and direction given

by his research advisor, Dr. Richard Sause, not only regarding academics and research,

but also concerning personal and professional development.

The opinions, findings, and conclusions expressed in this thesis are those of the

author and do not necessarily reflect the views of those acknowledged here.

Finally, the author thanks Dad, Mom, Lisa, Lauren, and Anne for all of their

love, support and encouragement.

All praise, glory, and honor to Jesus Christ the Lord.

iii

Table of Contents

Page

Title PageAcknowledgmentsList of TablesList of Figures

Abstract

Chapter 1 - Introduction1.1 Objectives1.2 Approach1.3 Thesis Outline

1

iiivi

vii

1

3455

Chapter 2 - Background 72.1 AASHTO LRFD Bridge Design Specifications 7

2.1.1 Slenderness Limits 82.1.2 Alternative Formula for Flexural Resistance 10

2.2 Ductility of I-Girders 122.3 Previous Research 15

2.3.1 McDermott (1969) 152.3.2 Croce (1970) 172.3.3 Holtz and Kulak (1973) 192.3.4 Holtz and Kulak (1975) 202.3.5 Grubb and Carskaddan (1979) 212.3.6 Grubb and Carskaddan (1981) 222.3.7 Schilling (1988) 232.3.8 Schilling (1990) 232.3.9 Barth (1996) 252.3.10 White, Ramirez, and Barth (1997) 262.3.11 Green and Sause (1997) 292.3.12 Summary of Previous Research Relevant to the Present Study30

Chapter 3 - Test Design and Set-Up3.1 Test Specimen Design

3.1.1 Specimen 13.1.2 Specimen 2

iv

40404144

spacing to radius of gyration (4/ry) is limited to 21 for uniform moment regions and

36 for regions of moment gradient.

2.3.2 Croce (1970)

Eight specimens were tested at the University of Texas at Austin in a study

investigating the web slenderness required for use in plastic design. The specimens

were welded I-girders fabricated from ASTM A36 steel, a steel with a nominal yield

stress of 36 ksi (248 MPa). The specimens were three-span continuous I-girders with

varying span lengths and loading configurations.

Flange slenderness values ranged from O.l3tJE/Fyc to 0338~E/Fyc' Web

slenderness values ranged from 2.04~E I Fyc to 4.07~E I FyC . Table 2.2 summarizes

the flange slenderness and web slenderness values for the specimens. The specimens

failed by flange and web local buckling and carried loads greater than those predicted

by simple plastic theory. The study concluded that plastic design can be permitted for

A36 steel members with web slenderness up to 125, provided that the maximum shear

stress is less than the critical web buckling stress assuming pinned boundary

conditions for the web.

Several of the web slenderness values considered by Croce are in the range of

interest of the present study. However, the flange slenderness values were much less

than those considered in the present study. In addition, the loading conditions imposed

on the test specimens were much different than those used in the present study and all

17

other similar studies. The specimens were tested as three-span girders with side spans

of 4.5 ft. (l.48 m) or 7.5 ft. (2.46 m) and center spans of 20 ft. (6.56 m) or 30 ft. (9.84

m). The short side spans were included to provide continuity at the ends of the center

spans, and as a result, the test specimens were indeterminate to the second degree.

Ductility of the specimens was quantified in terms of the midspan deflection. The

ductility limit was reached when the applied load dropped below the theoretical plastic

collapse load for the continuous I-girder. The ductility of the plastic hinges was not

provided by Croce, but can be estimated from the test results. The failure modes for

the majority of the tests involved shear buckling of the web rather than local buckling

of the compression flange and/or the web due to longitudinal bending stresses.

For Croce's Specimen 1, an elastic-plastic analysis was performed to estimate

the inelastic rotation that occurred at each of the three plastic hinges. Specimen 1 was

chosen because it developed local buckling of the compression flange and the web at

the plastic hinge locations and its failure mode did not involve shear buckling of the

web. The values of maximum inelastic rotation through which the plastic moment was

sustained, 8inel,u, are plotted in Figure 2.2. The results show that different levels of

maximum inelastic rotation were estimated for the three hinges of the specimen, ~hich

has only a single value of web slenderness.

18

2.3.3 Holtz and Kulak (1973)

Ten specimens were tested at the University of Alberta to determine the web

slenderness limit for an I-shaped member expected to reach the plastic moment as its

ultimate flexural strength. The specimens were welded I-shaped beams fabricated

from CSA G40.12 steel, a steel with a nominal yield stress of 44 ksi (196 kN). The

beams were simply-supported and loaded symmetrically in four-point loading.

Eight specimens had a flange slenderness of 0388~EI Fyc , and two specimens

had slightly stockier flanges with a slenderness of 0321~E I Fyc • The web

slenderness values for the specimens ranged from 3.00~E I FyC to 554~E I Fyc •

Table 2.3 lists the flange slenderness and web slenderness for each specimen

(Specimens WS-l through WS-l1). The study concluded that I-shaped beams with

flange slenderness not exceeding 0388~E I FyC and web slenderness not exceeding

3.05~E I Fyc are capable of reaching the plastic moment as their ultimate flexural

strength. The study concluded that flexural ductility should not be expected for

specimens meeting the above criteria.

Four of the specimens tested by Holtz and Kulak exceeded the plastic moment.

For these specimens, the rotation capacity, R, is plotted in Figure 2.3. This figure

shows a wide range of rotation capacities for similar levels of normalized web

slenderness, and no clear trend is observed. Figure 2.4 shows a plot of normalized

ultimate flexural strength versus normalized flange slenderness for the ten specimens

19

tested by Holtz and Kulak (1973). This figure shows a clear trend of decreasing

normalized ultimate flexural strength with increasing normalized web slenderness.

2.3.4 Holtz and Kulak (1975)

Two specimens were tested in an experimental program at the University of

Alberta to determine the web slenderness limit for an I-shaped member expected to

reach the yield moment as its ultimate flexural strength. Both specimens were welded

I-shaped beams fabricated from CSA G40.12 steel. The beams were simply-supported

and loaded symmetrically in four-point loading.

Both specimens had a flange slenderness of 0589~E I FyC • The web

slenderness values for the specimens were 4.l8~E I Fyc and 454~E I Fyc • Flange and

web slenderness information is listed in Table 2.3 (Specimens WS-12-N and WS-13

N). The experimental program concluded that specimens with flange slenderness not

exceeding 0388~E I Fyc and web slenderness not exceeding 452~E I Fyc are capable

of reaching the yield moment as their ultimate flexural strength. The two specimens

tested by Holtz and Kulak (1975) are not relevant to the present study because the web

slenderness values are too high.

20

2.3.5 Grubb and Carskaddan (1979)

Three welded I-girders with the same cross-section but different span lengths

were tested by the United States Steel Corporation to examine their flexural ductility.

The I-girders were simply-supported and tested in three-point loading to simulate the

condition of negative flexure at an interior pier of a continuous-span bridge. To

account for the contribution of steel reinforcement in the slab to the behavior in

negative flexure, cover plates were welded to the tension flanges. As a result, the

neutral axis was shifted and more than one-half of the web was in compression. The

girders were fabricated from ASTM A572 Grade 50 steel, a steel with a nominal yield

stress of 50 ksi (345 MPa).

The flange slenderness value for the three specimens was 0351~E I Fyc • The

actual web slenderness value was D/tw = 254~E I Fyc ' To account for the shift of the

neutral axis, twice the depth of the web in compression at the plastic moment, 2Dcp, is

used in place of the actual depth, D, to quantify the web slenderness. Therefore, the

effective web slenderness is Dcp/tw = 3.45~E I Fyc •

The specimens did not provide the flexural strength and ductility that were

expected. One specimen slightly exceeded the plastic moment, one just reached the

plastic moment, and the third specimen did not reach the plastic moment. The study

concluded that a larger depth of web in compression and a more shallow moment

gradient cause a decrease in flexural ductility. Figure 2.2 shows the maximum

inelastic rotation, 8inel,u, versus normalized web slenderness for the two specimens that

21

reached the plastic moment. The normalized ultimate flexural strengths of all three

specimens are plotted versus normalized web slenderness in Figure 2.5.

2.3.6 Grubb and Carskaddan (1981)

The three specimens described in the previous section provided flexural

strength and ductility that were less than expected, and, as a result, four additional I

girders were tested by the United States Steel Corporation. These I-girders were

unsymmetrical and were designed to account for the depth of web in compression of

unsymmetrical sections. The specimens were fabricated from ASTM A572 Grade 50

steel. The I-girders were simply-supported and tested in three-point loading to

simulate the condition of negative flexure at an interior pier of a continuous-span

bridge.

The compression flanges of the specimens were ultra-compact, with

slenderness ranging from 0.249~E I Fyc to 0303~E I Fyc ' The effective web

slenderness values at the plastic moment ranged from 1.99~E I FyC to 2.63~E I Fyc •

These specimens performed much better than those of the previous study (Grubb and

Carskaddan, 1979). All four specimens exceeded the plastic moment and exhibited

significant rotation capacity. However, the web and flange slenderness values

considered by Grubb and Carskaddan (1981) are much less than those considered in

the present study.

22

2.3.7 Schilling (1988)

Three steel I-girders were tested by Schilling to obtain full moment-rotation

curves for use in the autostress design of continuous-span bridge I-girders. The

specimens were fabricated from ASTM A572 Grade 50 steel. The I-girders were

simply-supported and tested in three-point loading to simulate the condition of

negative flexure at an interior pier of a continuous-span bridge.

The flange and web slenderness values were nearly identical for all three

specimens tested. Flange slenderness was 0.409~E I Fyc and web slenderness was

7.1O~E I Fyc for two specimens and 7.22~E I Fyc for the third specimen.

Intermediate transverse stiffeners were used between the load bearing and reaction

bearing stiffeners. The study varied several parameters which affect rotation capacity:

section symmetry, span length, initial web out-of-flatness, and shear stress level. The

ultimate flexural strength of each I-girder was very close to the yield moment. From

the test results, Schilling proposed a lower-bound relationship between the moment

and inelastic rotation for I-girders with stiffened webs. The high slenderness values of

the specimens considered by Schilling (1988) ate outside the range of interest of the

present study.

2.3.8 Schilling (1990)

Three I-girders were tested to determine moment-rotation characteristics. The

specimens were fabricated from ASTM A572 Grade 50 steel. The I-girders were

23

simply-supported and tested in three-point loading to simulate the condition of

negative flexure at an interior pier of a continuous-span bridge.

The flanges of the test specimens were ultra-compact, with slenderness

approximately equal to 0300~E I Fyc ' The web slenderness values ranged from

3.6tJE I Fyc to 6.89~E I Fyc ' Table 2.4 lists the flange and web slenderness values

for each specimen. In an effort to restrain local buckling and improve flexural

ductility, intermediate transverse stiffeners were welded on each side of midspan at a

distance of one-half of the section depth away from the load bearing stiffeners at the

midspan. Schilling observed that all specimens failed by an interaction of local flange

buckling, web buckling, and lateral-torsional buckling, and that the additional

stiffeners in the plastic hinge region prevented significant cross-sectional distortion at

their locations while forcing buckling away from midspan. The specimen with the

most slender web failed to reach the plastic moment as its ultimate flexural strength

and the two specimens with less slender webs had ultimate flexural strengths

exceeding the plastic moment. From the test results, Schilling concluded that flexural

ductility increases as the web slenderness decreases.

The tests performed by Schilling (1990) provide useful results to compare with

the flexural strength and ductility of the I-girders tested in the present study. The

maximum inelastic rotation values, 8inel,u, of the two specimens that exceeded the

plastic moment are plotted versus normalized web slenderness in Figure 2.2. The

variation of normalized ultimate flexural strength with normalized web slenderness is

24

shown in Figure 2.5. The two plots show clear trends of decreasing nonnalized

ultimate flexural strength and ductility with increasing normalized web slenderness. In

both figures, the test results are labeled with UCF to indicate that the compression

flange slenderness is much less than the AASHTO LRFD specifications require for a

compact section (Le., ultra-compact flange), and with CSB to indicate that the

compression flange brace spacing is less the AASHTO LRFD specifications require

for an I-girder designed to reach the plastic moment (Le., closely-spaced bracing).

2.3.9 Barth (1996)

Six I-girders were tested at Purdue University to study the effects of flange

slenderness, web slenderness, compression flange brace spacing, and moment gradient

on moment-rotation behavior. The specimens were fabricated from ASTM A572

Grade 50 steel. The I-girders were simply-supported and tested in three-point loading

to simulate the condition of negative flexure at an interior pier of a continuous-span

bridge.

Four test specimens had flange slenderness values near 0390~E I Fyc and two

specimens had ultra-compact flanges with slenderness values near 0.290~E I Fyc • The

web slenderness values ranged from 451~E I Fyc to 5.86~E I Fyc • Table 2.5 lists the

flange and web slenderness values for each specimen. Intermediate transverse

"""""-stiffeners were used between the load bearing and reaction bearing stiffeners. In an

effort to restrain local buckling and improve flexural ductility, intermediate transverse

25

stiffeners were welded on each side of midspan at a distance of one-third of the section

depth away from the load bearing stiffener at the midspan. Only one of the six

specimens reached the plastic moment as its ultimate flexural strength. This specimen,

P6 (Table 2.5), had ultra-compact flanges and a web that was the least slender of all

the specimens tested by Barth (1996). The maximum inelastic rotation, 8inel,u, of

Specimen P6 is plotted in Figure 2.2. Figure 2.5 shows four specimens on a plot of

normalized ultimate flexural strength versus normalized web slenderness. In both

figures, the test results are labeled with UCF to indicate that the compression flange

slenderness is much less than the AASHTO LRFD specifications require for a compact

section (Le., ultra-compact flange).

2.3.10 White, Ramirez, and Barth (1997)

A study was conducted at Purdue University to develop simple comprehensive

moment-rotation relationships for steel I-girders for use in inelastic bridge design.

Previous experimental and analytical. studies were reviewed and compiled into a

uniform data set and a finite element study was conducted to fill major gaps in the

existing data.

The finite element I-girder models had a steel yield stress of 50 ksi (345 MPa).

A wide range of flange and web slenderness values were considered. Flange

slenderness ranged from 0.29 tJE I FyC to 0382~E I Fyc ' Web slenderness ranged

from 357~E I Fyc to 6.77~E I Fyc • The finite element models were simply-supported

26

I-girders loaded in three-point loading to simulate the condition of negative flexure at

an interior pier of a continuous-span bridge.. The experimental program carried out by

Barth (1996), described in Section 2.3.9, was designed to confirm key portions of the

finite element study. As a result of the study, expressions for nominal moment

capacity and inelastic rotation at the nominal moment were developed. The expression

for nominal moment capacity is:

where:

Mn =the nominal moment capacity,

Mp =the plastic moment,

Dcp =the depth of web in compression at the plastic moment,

tw=the thickness of the web,

My =the yield moment.

The parameter arp is defined as:

27

(2-16)

(2-17)

where:

br=the width of the compression flange,

tr =the thickness of the compression flange.

Equation 2-17 is based on steel with compression flange yield stress Fyc =50

ksi (345 MPa). This expression can be rewritten in a form that is valid for steel with

yield stress other than 50 ksi (345 MPa):

M_D =1+Mp

0.73 +_1__ 0.4 Mp ~I.O

2D ~ lOarp My~~

t w E

(2-18)

Fyc =the specified minimum yield stress of the compression flange,

E =the modulus of elasticity of steel.

The expression developed for inelastic rotation, the rotation through which the

nominal moment capacity is sustained, is:

where:

D =the depth of the web.

28

Like Equation 2-16, Equation 2-19 is based on steel with compression flange

yield stress Fyc =50 ksi (345 MPa). This expression can be rewritten in a form that is

valid for steel with yield stress other than 50 ksi (345 MPa):

9RL =0128-0287 b, ~F" -0.0216E.+0.0482.EL~F"E. (2-20)2t f E b f 2t f E b f

2.3.11 Green and Sause (1997)

A finite element study was conducted at Lehigh University to evaluate the

flexural strength and ductility of I-girders fabricated from HPS-70W steel, a newly

developed high performance steel with a nominal yield stress of 70 ksi (483 MPa).

Two I-girders were studied. The finite element models were simply-supported 1-

girders loaded in three-point loading to simulate the condition of negative flexure at an

interior pier of a continuous-span bridge. Both I-girders had ultra-compact flanges

with slenderness equal to0.288~E / Fyc ' The web slenderness values of the two

specimens were 3.84~E / Fyc and 5.76~E / Fyc •

The specimen with the less slender web reached a peak moment equal to the

plastic moment and the specimen with the more slender web reached a peak moment

of 96 percent of the plastic moment. The maximum inelastic rotation, Sinel,u, and the

rotation capacity, R, for the specimen that reached the plastic moment are plotted in

Figures 2.2 and 2.3, respectively. The normalized ultimate flexural strengths of both

specimens are plotted in Figure 2.6. In all three figures, the test results are labeled

29

with UCF to indicate that the compression flange slenderness is much less than the

AASHTO LRFD specifications require for a compact section (Le., ultra-compact

flange). The normalized web slenderness range of the specimens considered by Green

and Sause (1997) is very close to the range considered in the present study.

2.3.12 Summary of Previous Research Relevant to the Present Study

Research results most relevant to the present study are those for I-girders with

compression flange slenderness at or slightly below the slenderness limit for compact

sections in the AASHTO LRFD Bridge Design Specifications (AASHTO, 1997), and

with web slenderness near and above the slenderness limit for compact sections.

Research conducted to investigate the behavior of the negative moment region at the

pier of a continuous-span bridge I-girder is particularly useful because the loading

conditions and the methods of quantifying the results are similar to those of the present

research. The relevant research results are: Grubb and Carskaddan (1979), Schilling

(1990), Barth (1996), and Green and Sause (1997). The tests carried out by Holtz and

Kulak (1973) involved specimens with flange and web slenderness in the ranges of

interest. However, different loading conditions create some difficulty in comparing

test results. The tests conducted by Croce (1970) are of limited interest because the

loading conditions were quite different than those used in the present study and

inelastic rotation data had to be estimated from the test results presented by Croce

(1970).

30

Table 2.1 Properties of ASTM A514 Steel Beams Tested by McDennott (1969)

Jlt~ D"t ~Specimen

2t f E t w E ryR

1 0.777 1.61 11.6 -2 0.533 1.34 9.0 -3 0.381 1.12 7.3 4.84 0.321 1.15 6.0 8.45 0.258 1.14 5.4 6.36 0.205 1.69 24.9 2.47 0.307 1.62 23.9 3.6A 0.208 2.01 37.5 -B 0.309 1.98 35.4 -

Table 2.2 Properties of ASTM A36 Steel Beams Tested by Croce (1970)

Specimen Jlt~ D~!i2t f E t w E

1 0.338 3.232 0.200 2.993 0.200 2.984 0.131 3.035 0.200 2.23

'6 0.205 2.047 0.205 2.908 0.204 4.07

31

Table 2.3 Properties of CSA G40.12 Steel Beams Tested by Holtz and Kulak(1973, 1975)

Specimen ~t' D"t2t f E t w E

WS-1 0.388 3.07WS-2 0.388 3.84WS-3 0.388 4.63WS-4 0.388 5.54WS-6 0.388 3.67

WS-7-P 0.321 3.28WS-8-P 0.321 3.63WS-9 0.388 3.00WS-lO

-0.388 3.27

WS-11 0.388 3.58WS-12-N 0.589 4.18WS-13-N 0.589 4.54

Table 2.4 Properties of ASTM A572 Grade 50 Steel Beams Tested by Schilling(1990)

Specimen ~t" DcpiFyc

2t f E t w E

S .300 3.61M .297 5.27D .295 6.89

32

Table 2.5 Properties of ASTM A572 Grade 50 Steel Beams Tested by Barth (1996)

Specimen Jlt" D~t~2t f E t w E

PI 0.391 5.85P2 0.388 5.86P3 0.296 5.68P4 0.387 5.55P5 0.390 4.51P6 0.291 4.52

33

M

p

4- ~e1 1;~ Lp

. >1

compact

e

Figure 2.1 Typical Moment versus End Rotation Plot for an Adequately Braced Flexural Member

34

6.505.504.503.50

+UCF = Ultra-Compact Flange ICSB = Closely-Spaced Lateral Bracing

A/~HTO

UCF, IISlenderness

CSBLimit

_c

UCF A

X

·UCF,CSB

0

0 :: UCF•

o2.50

0.07

0.06

0.05

0.02

0.08

0.01

Jg 0.04.:3-.a

CD

0.03

Nonnalized Web Slenderness

II Schilling (1990), Specimen S• Schilling (1990), Specimen MA Barth (1996), Specimen P6o Croce (1970), Specimen 1 (estimated)D Croce (1970), Specimen 1 (estimated)4 Croce (1970), Specimen 1 (estimated)o Grubb and Carskaddan (1979), Specimen 1• Grubb and Carskaddan (1979), Specimen 2:: Green and Sause (1997), FE Specimen 1• Holtz and Kulak (1973), Specimen WS-l- Holtz and Kulak (1973), Specimen WS-9+Holtz and Kulak (1973), Specimen WS-I0X Holtz and Kulak (1973), Specimen WS-ll

Figure 2.2 Maximum Inelastic Rotation versus Nonnalized Web Slenderness

35

Rotations were measured by seven rotation meters along the length of the

girder. The rotation meters were placed at midspan, east and west bearings, 12 in.

(305 mm) east and west of midspan, and 54 in. (1370 mm) east and west of midspan,

as shown in Figure 3.10.

Linear strain gages were used to measure longitudinal web and flange strains.

Strain gages were placed near midspan on the web and compression flange in expected

locations of local buckling. Strain gages intended to detect local distortion of the web

and flange plates were placed in pairs, one on each side of the plate at a given location.

In addition, strain gages were placed at the center of the compression and tension

flanges to measure primary bending strains. Strain gage locations are shown in Figure

3.11.

To measure lateral deflection of the compressIon flange, displacement

transducers were placed on the compression and tension flanges within the first and

second unbraced lengths both east and west of midspan. Also, measurements from

strain gages near opposite tips of the compression flange were compared to observe

lateral bending of the compression flange between brace points.

3.6 TestProcedure

The procedure used for both I-girder tests was composed of the same two

steps: (1) two elastic loading cycles to 100 kips (445 kN), and (2) loading until failure.

The initial loading cycles to 100 kips (445 kN) were used to align and seat the test

50

specimen, che~l' the instrumentation, and monitor possible lateral or longitudinal

movement of the load fixture. Load was initially applied at a rate of 10 kips per

minute (44.5 IQJ per nllnute). This load rate corresponds to a displacement rate of

approximately 0·2 in. per minute (5 mm per minute). In the inelastic range, this

displacement fqte was maintained until the test was terminated and the specimen was

unloaded. At ~~vera1 points during the test, the loading was stopped temporarily so

photographs c()\.11d be taken. Loading at the displacement rate of 0.2 in. per minute (5

mm per minut~) \Vas then resumed.

3.7 Steel Str~,"StraiI1 Properties

The ~G"lOOW steel used to fabricate the I-girder specimens has a nominal

yield stress of 100 ksi (690 MPa). The HPS-100W steel was produced at the Gary

Works of United States Steel Corporation. Plates with nominal thickness of 3/4 in.

(19 mm) and 3/~ in. 00 nun) were used for the I-girder flanges and webs, respectively.

After the girders were tested, tensile coupons were cut from regions of the

flange and w~b plates that were subjected to elastic-range stresses during the tests.

The coupons ~~ gage lengths of 8 in. (203 mm), and were fabricated according to

ASTM E8 (AS1'M, 1994). The tensile coupons were tested at the ATLSS Center,

Lehigh Univel's'ty in a Satec 600 kip (2700 kN) hydraulic universal testing machine.

Tests were petfOlll1ed on six flange coupons and four web coupons.

51

_____________ .. ....J

1O!94J69~69~ 94 II" (2388) 'I( (1753) ~1(1041)1(1041)1~ (1753) >r:-(='23~8-8)~)

(10360)

Note: Primary dimensions in inches; secondary dimensions in millimeters.

Figure 3.5 Specimen 1Lateral Brace Locations

~ (l~~5) f 115~ 77~ 77 f 115 f 75

~(2921) (1956) 838 83 «1956) (2921) (1905)

[J DC )( )( li )( )( )(

lfJ~

600~(15240)


Figure 3.6 Specimen 2 Lateral Brace Locations

60

S\0 00\0 \0.....

'-"

~l~ _<t Girder & Brace

Tefon (Typical)

All connections between anglesand baseplates are made using3/16 in. (5 mm) fillet welds.

All bracing membersare 5 x 5 x 3/4 angles.


Figure 3.7 Typical Lateral Brace Arrangement

61

MachineHead

Yb ~

(a) Test Specimen in Fixture With No Load Applied

p

!Machine

Head

fI; ~

(b) Test Specimen in Fixture During Loading

Figure 3.8 Test Fixture

62

Figure 3.9 Specimen 1in Test Fixture Prior to Testing (Looking Northeast)

63

[Q==.=.~.=.=PJ~ L ~

Figure 3.10 Location ofRotation Meters

S3 82 81 81 81 81 82 83

I I I I I I I I~

36 +8+6~6+8+ 36~

~(914) (203) (152) 102 102«152) (203) (914)

~[I

~L

~

81 82 83


Figure 3.11 Location of Strain Gages

64

140

120

100

,-.....80g

til

§ 60CI)

40

20

0

0 20000 40000 60000 80000 100000 120000 140000 160000

Strain (microstrain)

Figure 3.12 Stress versus Strain for HPS-1ooW Steel 3/4 in. (19 mm) Thick Flange Plate

140

120

100

,-..g 80tiltil

~ 60CI)

40

20

0

0 20000 40000 60000 80000 100000 120000 140000 160000

Strain (microstrain)

Figure 3.13 Stress versus Strain for HPS-100W Steel 3/8 in. (10 mm) Thick Web Plate

6S

640

fF;c

Specimen 2•

f(Specimen 1

3.76 ; 1----------------. •yc

.382J; .yc

65

[F;:

Figure 3.14 Web Slenderness versus Flange Slenderness

66

-

Chapter 4

Test Results for Specimen 1

Specimen 1 is a compact section according to the AASHTO LRFD Bridge

Design Specifications (AASHTO, 1997), therefore the ultimate flexural strength of

Specimen 1 was expected to reach or exceed the plastic moment. In addition, the

failure of Specimen -1 was expected to be ductile. In particular, the rotation capacity

was expected to be greater than or equal to three.

Based on the measured section dimensions and steel yield stress, the theoretical

plastic moment, Mp, is equal to 2257 kip-ft (3060 kN-m), occurring at a theoretical

plastic load, Pp, equal to 265.5 kips (1181 kN). Figure 4.1 presents a plot of midspan

moment versus average end rotation. Specimen 1 reaches a peak midspan moment,

Mu, equal to 2329 kip-ft (3158 kN-m). Figure 4.2 presents a plot of applied load

versus vertical midspan deflection. As shown, the peak load, Pu, is equal to 274.1 kips

(l219kN).

,Test results for Specimen 1 are discussed in the following five sections.

Section 4.1 discusses test results in the elastic range. Section 4.2 discusses the

behavior of Specimen 1 at yielding of the extreme fibers of the flange. Section 4.3

discusses distortion and buckling of the compression flange and web. Section 4.4

discusses the behavior of Specimen 1 after the peak load is reached. Section 4.5

summarizes the test results.

67

-12000 -10000 -8000 -6000 -4000 -2000 oLongitudinal Strain in Compression Flange (microstrain)

--Top-South (TS)

- - -Top-North (TN)

........... Bottom-South (BS)

- - -'- Bottom-North (BN)

Figure 4.5 Load versus Longitudinal Strain 10 in. (254 mm) West of Midspan inCompression Flange

-12000 -10000 -8000 -6000 -4000 -2000 o

Longitudinal Strain in Web Compression Zone (microstrain)

1--North South IFigure 4.6 Load versus Longitudinal Strain 10 in. (254 mm) West ofMidspan in

Web Compression Zone

89

TN,BNTS, TN 250

-14000 -12000 -10000 -8000 -6000 -4000 -2000 oLongitudinal Strain in Compression Flange (microstrain)

--Top-South (TS)- - -Top-North (TN)

........... Bottom-South (BS)

- - - .- Bottom-North (BN)


-14000 -12000 -10000 -8000

i"'"250

\I

\\

\\,i\i\\\\\

-6000 -4000 -2000 0


1--North South I

Figure 4.8 Load versus Longitudinal Strain 4 in. (102 mm) West of Midspan in


90

indicates local buckling. At the peak load Pu =287.4 kips (1278 leN), the strain

separation at 4 in. (102 mm) east of midspan is 535 Il£ in the north flange tip and 931

J.1£ in the south flange tip.

At lOin. (254 mm) east of midspan, the local curvature in the north and south

flange tips remains small up to an applied load of 100 kips (448 kN), then increases

steadily as the load increases (Figure 5.16). Both north and south flange tips are

concave upward until a load of 150 kips (667 kN), when the south flange tip reverses

curvature. Near a load of 250 kips (890 kN), the curvatures in the north and south

flange tips begin increasing more rapidly. Figure 5.13 shows strain separation in both

north and south flange tips at the peak load. At the peak load Pu =287.4 kips (1278

kN), the strain separation at 10 in. (102 mm) east of midspan is 1695 J.1£ in the north

flange tip and 1111 Il£ in the south flange tip.

Figures 5.7 and 5.9 show load versus longitudinal strain in the compression

flange at 10 in. (254 mm) and 4 in. (102 mm) west of midspan, respectively. The

compression flange on the west side of the girder did not buckle, but it did distort

locally. At the peak load, the strain separation in the compression flange on the west

side of the girder is: 519 Il£ in the north flange tip 10 in. (254 mm) from midspan, 690

J.1£ in the south flange tip 10 in. (254 mm) from midspan, 626 Il£ in the north flange tip

4 in. (102 mm) from midspan, and 1574 J.1£ in the south flange tip 4 in. (102 mm) from

midspan.

111

5.3.4 Interaction of Web and Flange Distortion and Buckling

Specimen 2 was designed with a web slenderness that is more critical than the

flange slenderness. Therefore, web distortion begins first and eventually drives the

flange distortion. At locations where web distortion begins· early and grows as the

load increases, early flange distortion occurs. At locations where early distortion of

the web does not occur, the compression flange distortion does not occur until the web

distortion begins. For example, significant local curvature is not observed in the web

at 4 in. (102 mm) east of midspan early in the test, and local curvature of the flange at

this location is small until the peak load is reached (Figure 5.15). However at 10 in.

(254 mm) east of midspan, local curvature of the web begins early in the test and local

curvature of the compression flange is significant before the peak load is reached

(Figure 5.16).

Two types of interaction occur between the web and compression flange. First,

as the web distortion increases, the web carries less longitudinal bending stress than

expected from beam theory. As the web sheds bending stresses, the neutral axis drops,

and the bending strains in the compression flange increase. Shedding of bending

stresses from the web and the presence of residual stresses in the compression flange

cause the compression flange to yield at an applied load less than the theoretical yield

load Py =269.7 kips (1200 kN). The yield strain of 3954 J.1E is first observed in the

compression flange at an applied load of 265.1 kips (1179 kN). Figures 5.5 and 5.6

show strains in the compression flange beginning to increase significantly at an

112

applied load of 250 kips (1112 kN). Second, the compression flange partially restrains

the distortion of the web. Yielding of the compression flange reduces the restraint

provided to the web, and the web distortion increases more rapidly. As the web

distortion increases, the web sheds more stress into the compression flange. As a

result of these interactions, local flange distortion tends to be greatest at locations

where web distortion is greatest.

5.4 Post-Peak Behavior

When the peak load Pu = 287.4 kips (1278 kN) was reached, the testing

machine was held at a constant displacement to inspect the specimen and take pictures.

Although the displacement was held constant, the load began to decrease. This event

appears as the straight vertical portion of the load-deflection curve immediately after

the peak load (Figure 5.2). The displacement was held constant until the load on the

girder stabilized. Then the displacement was increased until the end of the test.

When the peak load was reached, and the load decreased while the

displacement was held constant, the flange and web local buckles were growing.

Figures 5.17 and 5.18 are photographs of the north side of the web east of midspan,

taken while the displacement was being held constant and the load was decreasing.

These figures show the rapid growth of flange and web local buckles immediately after

the peak load was reached. Figure 5.19 is a plot of moment versus inelastic girder

113

rotation. After the peak moment, inelastic rotation increases rapidly, largely due to the

growth of the flange and web local buckles.

Figure 5.20 shows moment versus curvature for the regions immediately east

and west of midspan. As seen in this plot, the inelastic deformation is concentrated in

the east side of the girder in the region of local buckling. While inelastic rotation is

increasing at the girder midspan, the remainder of the girder is unloading elastically.

Loading of the girder continued until a midspan deflection of 9.53 in. (242 mm) was

reached, then the load on the girder was removed.

5.5 Summary

Specimen 2 reached a peak applied load Pu = 287.4 kips (1278 kN)

corresponding to a peak midspan moment Mu = 3592 kip-ft (4870 kN-m). The peak

moment is three percent below the theoretical plastic moment. Figure 5.21 shows a

plot of normalized midspan moment (MlMp) versus normalized end rotation (S/Sp).

Figure 5.22 shows a plot of normalized load (PlPp) versus normalized midspan

deflection (Mlip). The sequence of events that lead to a decrease in resistance (Le.,

unloading from the peak load) of Specimen 2 was: local distortion of the web, local

distortion of the compression flange, local buckling of the web, and local buckling of

the compression flange.

Specimen 2 does not have a rotation capacity, R, defined by Equation 2-12, a

maximum inelastic rotation, Sinel,u, defined by Equation 2-14, or a displacement

114

ductility, 1.1, defined by Equation 2-15, because it does not reach the theoretical plastic

moment,Mp•

115

Table 5.1 - West Side Longitudinal Strains at P = 100.0 kips (445 leN)

10 in. (254 mm) West of Midspan 4 in. (102 mm) West of Midspan

Experimental Theoretical % Error Experimental Theoretical % Error(J.I.£) (J.I.£) (~£) (J.I.E)

Top of North -1358 -1413 3.9 -1394 -1442 3.4Top Flange Center -1310 -1413 7.3 -1304 -1442 9.6

South -1279 -1413 9.5 -1279 -1442 11.3Bottom of North -1336 -1355 1.4 -1421 -1383 -2.7Top Flange South -1252 -1355 7.6 -1265 -1383 8.6Compression North -839 -903 7.1 -872 -922 5.4Zone ofWeb South -914 -903 -1.1 -777 -922 15.7Bottom of Center 1352 1413 4.3 1333 1442 7.6Bottom Flan~e

Table 5.2 - East Side Longitudinal Strains at P =100.0 kips (445 kN)

10 in. (254 mm) East ofMidspan 4 in. (102 mm) East ofMidspanExperimental Theoretical % Error Experimental Theoretical % Error

(J.I.£) (J.I.£) (J.I.£) (J.I.£)Top of North -1373 -1413 2.8 -1376 -1442 4.6Top Flange Center -1299 -1413 8.0 -1307 -1442 9.4

South -1268 -1413 10.3 -1218 -1442 15.6Bottom of North -1326 -1355 2.1 -1414 -1383 -2.2Top Flange South -1236 -1355 8.8 -1287 -1383 6.9Compression North -929 -903 -2.8 -885 -922 4.0Zone of Web South -845 -903 6.4 -829 -922 10.1Bottom of Center 1370 1413 3.0 1341 1442 7.0Bottom Flange

116

4000

'0 3500Jj

I 3000g2500...

~§ 2000~ 1500~

~ 1000~ 500

0

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Average End Rotation (radians)

Figure 5.1 Midspan Moment versus Average End Rotation

300 ...,--------------------------,

250

,.... 200enQ.

;g 150

~100

50

108642

O-f------r-----1----..t!.:::.....---f-----+------lo

Midspan Deflection (inches)

Figure 5.2 Load versus Deflection

117

-6000 -5000 -4000 -3000 -2000 -1000 oLongitudinal Strain in Web Compression Zone (microstrain)

--10" West North (tOWN) -----·lO"WestSouth (lOWS)

- -4"WestNorth(4WN) - - -4" West South (4WS)

Figure 5.3 Load versus Longitudinal Strain in Web Compression Zone West ofMidspan

-6000 -5000 -4000 -3000 -2000 -1000 oLongitudinal Strain in Web Compression Zone (microstrain)

--4" East North (4EN) - - - - -·4" East South (4ES)

- - 10" East North (tOEN) - - - 10" East South (lOES)

Figure 5.4 Load versus Longitudinal Strain in Web Compression Zone East of Midspan

118

IiI !I //1

I !

/ .II ;I :, I

250

-15000 OOסס1- -5000 o 5000 ooסס1 15000

Longitudinal Strain in Flange (microstrain)

1--Compression Flange Tension Flange I

Figure 5.5 Load versus Longitudinal Strain 4 in. (102 mm) West of Midspan atCenter ofFlange

t"""'"\

/ I/ \/ )I "/ ;'

, I

I !/ I

I /

250

-15000 OOסס1- -5000 o 5000 10000 15000

Longitudinal Strain in Flange (microstrain)

1--Compression Flange - - - - _. Tension Flange IFigure 5.6 Load versus Longitudinal Strain 4 in. (102 mm) East ofMidspan at

Center ofFlange

119

-12000 -1()()()() -8000 -6000 -4000 -2000 o 2000

Longitudinal Strain in Compression Flange (microstrain)

--Top - South (TS) - - - - - . Bottom - South (BS)

- - - Top - North (TN) - - - - Bottom - North (BN)

Figure 5.7 Load versus Longitudinal Strain 10 in. (254 rom) West of Midspan inCompression Flange

{--_._-~

\\ ,,

\\

-12000 -1()()()() -8000 -6000 -4000 -2000 o 2000


1--North South I

Figure 5.8 Load versus Longitudinal Strain 10 in. (254 rom) West of Midspan in


120

r"--=-..-:::I"'r---.-

\/

B~\",,\

,'.",

",,,,,,".'---""

250

200

150

\

-12000 -10000 -8000 -6000 -4000 -2000 o 2000


--Top - South (TS) - - - - -. Bottom - South (BS)

- - - Top - North (TN) - - - - Bottom - North (BN)


(-----·\1

\ 2~0

~4\ I

\ 1'0

Qo~

-12000 -10000 -8000 -6000 -4000 ·2000 o 2000


1--·North - -- - _. South IFigure 5.10 Load versus Longitudinal Strain 4 in. (102 mm) West of Midspan in


121

TS

TN

-30000 -25000 -20000 -15000· -10000 -5000 o 5000 10000


--Top - South (TS)

- - - Top - North (TN)

- - - - _. Bottom - South (BS)

- - - - Bottom - North (BN)

Figure 5.11 Load versus Longitudinal Strain 4 in. (102 mm) East of Midspan inCompression Flange

.....................,/_ ...r-----' --

\II

\\\

-30000 -25000 -20000 -15000 -10000 -5000 o 5000 10000


1--North .....: ..... SouthI

Figure 5.12 Load versus Longitudinal Strain 4 in. (102 mm) East of Midspan in


122

OOסס3- -25000 OOסס2- -15000 OOסס1- -5000 oo5000סס1

TS

o

~ I

~;./-- .._.-// -_._.--_._ .. --

\ \BN\ \BS

\ \I \


--Top - South (TS)

- - - Top - North (TN)

- - - - _. Bottom - South (BS)

- - - - Bottom - North (BN)

Figure 5.13 Load versus Longitudinal Strain 10 in. (254 mm) East of Midspan inCompression Flange

III

i

IOOסס3- -25000 OOסס2- -15000 OOסס1- -5000 o 5000 ooסס1

Normal Strain in Web Compression Zone (microstrain)

\--NOrth -----·SouthI

Figure 5.14 Load versus Longitudinal Strain 10 in. (254 mm) East of Midspan in


123

W- - - - - - - - - - ------::::.S_····:...~2c:!--N

25~1

200

Note:Only data up to peak

load (PJ is shown

150

100

50

-0,01 -0.008 -0.006 -0.004 -0.002v

o 0.002 0.004

1--North Tip Average (N) - - - - - . South Tip Average (S) - - - Web (W)1Figure 5.15 Load versus Local Curvature 4 in. (102 mm) East of Midspan in

Compression Flange and Web

N--

50

_--------- - --W

Note:Only data up to peak

load (PJ is shown

-0.004 -0.002 o 0.002 0.004 0.006 0.008 0.01

1--North Flange Tip (N) South Flange Tip (S) - - - Web (W)1Figure 5.16 Load versus Local Curvature 10 in. (254 mm) East ofMidspan in

Compression Flange and Web

124

Figure 5.17 Northeast Side of Specimen 2 at P = 281 kips (1250 kN) Post-Peak

Figure 5.18 Northeast Side of Specimen 2 at P = 271 kips (1205 kN) Post-Peak

125

4000 -r-------------------------,

-=- 3500

~ 3000Q.

;g 2500

=S 2000

~ 1500

! 1000

~ 500

0+------i1---t----/---+----i---1---<-t----i

o 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Total Inelastic Rotation (radians)

Figure 5.19 Midspan Moment versus Total Inelastic Rotation

--.,"'-.,.-...... ............. ._- ....---_·__·__··_-_·--····7

//

I,I,

3500

3000

-=- 2500eu~,

2000g... 15005

~ 1000

500

0

0 0.0005 0.001 0.0015

"//

0.002 0.0025

1--12" West .. ·· .. ·· .. · 12" East IFigure 5.20 Average Moment versus Curvature in Section 12 in. (305 rom) on Either

Side of Midspan

126

i1

0.9

0.8...§

0.7

~ 0.6§ 0.5~ 0.4~

~OJ

1 0.2

0.1Z 0

0 0.2 0.4 0.6 0.8 1 1.2

NonnalizedEnd Rotation (9/9p)

Figure 5.21 Normalized Midspan Moment versus Nonnalized End Rotation

1.41.20.4 0.6 0.8 1

Nonnalized Midspan Deflection (MIIp)

0.2

1-.-------------------------,0.90.80.70.60.50.40.30.20.10-f----1---+---+-"""""--+----+----+----l

o

Figure 5.22 Normalized Load versus Normalized Midspan Deflection

127

Chapter 6

Summary, Discussion of Test Results, and Conclusions

This chapter briefly summarizes (Section 6.1) the test results presented in

Chapters 4 and 5. The test results are then discussed (Section 6.2) in the context of the

current AASHTO LRFD Bridge Design Specifications and previous research on the

flexural strength and ductility of steel I-girders. Conclusions are then given (Section

6.3). Finally, recommendations for future research are given (Section 6.4).

6.1 Summary

This thesis investigated the flexural strength and ductility of bridge I-girders

fabricated from HPS-lOOW steel, and compared them with the flexural strength and

ductility expected from the AASHTO LRFD Bridge Design Specifications (AASHTO,

1997). The HPS-lOOW steel is a newly developed high performance steel with a

nominal yield stress of 100 ksi (690 MPa). This steel has stress-strain characteristics

that are significantly different than those of conventional ~teel (e.g., ASTM A709

Grade 50), on which the current provisions of the AASHTO LRFD specifications are

based. Two one-half scale I-girder specimens were fabricated from HPS-100W steel

and tested to failure under three-point loading which simulated the condition of

negative flexure at an interior pier of a continuous span bridge. The test results for the

two specimens are summarized in the following two sections.

128

6.1.1 Specimen 1

Specimen 1 was a compact section according to the AASHTO LRFD Bridge

Design Specifications (AASHTO, 1997). The flange slenderness and web slenderness

were at the AASHTO LRFD limits for compact I-girders and the compression flange

brace spacing was designed according to the AASHTO LRFD compact section

criteria; therefore, the ultimate flexural strength of Specimen 1 was expected to reach

or exceed the plastic moment. Specimen 1 was expected to have a ductile failure with

a rotation capacity, R, greater than or equal to three, according to the AASHTO LRFD

specifications. ,

Specimen 1 had a test span of 34 ft. (l0.4 m) and was simply-supported and

loaded at midspan. The girder reached a peak moment, Mu, equal to 2329 kip-ft (3158

kN-m), three percent above the theoretical plastic moment, Mp• The rotation capacity,

R, was equal to 0.28 and the maximum inelastic rotation through which Mp was

sustained was Sinel,u =0.019 radians. The sequence of events that lead to a decrease in

resistance (Le., unloading from the peak load) of Specimen 1 was: lateral distortion of

the compression flange, local distortion of the compression flange, local distortion of

the web, local buckling of the web, and local buckling of the compression flange.

6.1.2 Specimen 2

Specimen 2 was a non-compact section according to the AASHTO LRFD

Bridge Design Specifications (AASHTO, 1997). The flange was compact and the web

129

was non-compact. The compression flange brace spacing satisfied the AASHTO

LRFD specifications for compact sections. According to the alternative formula for

flexural resistance in the AASHTO LRFD specifications, the ultimate flexural strength

of Specimen 2 was expected to reach the plastic moment, but no significant flexural

ductility was expected.

Specimen 2 had a test span of 50 ft. (15.2 m) and was simply-supported and

loaded at midspan. It reached a peak moment, Mu, equal to 3592 kip-ft (5604 kN-m),

three percent below the theoretical plastic moment, Mp• The sequence of events that

lead to a decrease in resistance (Le., unloading from the peak load) of Specimen 2 was:

local distortion of the web, local distortion of the compression flange, local buckling

of the web, and local buckling of the compression flange.

6.2 Discussion of Test Results

6.2.1 Specimen 1

For Specimen 1, the AASHTO LRFD Bridge Design Specifications

(AASHTO, 1997) correctly predicted that the ultimate flexural strength would reach or

exceed the theoretical plastic moment, Mp• Specimen 1 exceeded the theoretical

plastic moment, Mp, by three percent. This result suggests that I-girders fabricated

from HPS-1DOW steel which meet the web and flange slenderness limits for compact

sections in the current AASHTO LRFD specifications can be expected to have a

flexural strength equal to the theoretical plastic moment.

130

While the ultimate strength of Specimen 1 was correctly predicted by the

AASHTO LRFD specifications (AASHTO, 1997), the rotation capacity, R, of 0.28

was well below the expected value of three. The maximum inelastic rotation through

which the plastic moment was sustained was 8inel,u = 0.019 radians. The AASHTO

LRFD specifications do not quantify the expected inelastic rotation and little

information on the expected inelastic rotation of I-girders similar to Specimen 1 exists

in the published literature.

I-girders which satisfy the web and compression flange slenderness criteria of

prior versions of the AISC plastic design specifications (AISC, 1978) are assumed to

provide a maximum inelastic rotation, 8inel,u, of approximately 0.06 radians (Grubb

and Carskaddan, 1981). However, this maximum inelastic rotation is not a reasonable

basis for comparison with Specimen 1 because the slenderness limits of the plastic

design specifications in AISC (1978) are more strict than the slenderness limits in

current specifications. According to AISC (1978), the web slenderness limit for 1-

shaped members designed by the plastic design method is:

(6-1)

131

0- _

~AASHTOLRFD

+ SlendernessLimit

6.50

•

5.50

......-..."'X

4.50

:1(- _

-----..... - ........

IJ

3.50

.............

...0, .... "

" ... III, ..., ...A ' ............

... ... ... ... ............ ... ... ...

............ ... ...

1.2

1.15

1.1

1.05

~ 1

0.95

0.9

0.85

0.82.50

NormalizedWeb Slenderness

• Holtz and Kulak (1973), Specimen WS-l

II Holtz and Kulak (1973), Specimen WS-2

• Holtz and Kulak (1973), Specimen WS-3

• Holtz and Kulak (1973), Specimen WS-4

c Holtz and Kulak (1973), Specimen WS-6

o Holtz and Kulak (1973), Specimen WS-7-P

AHoltz and Kulak (1973), Specimen WS-8-P

o Holtz and Kulak (1973), Specimen WS-9

+ Holtz and Kulak (1973), Specimen WS-IO

- Holtz and Kulak (1973), Specimen WS-ll

XFahnestock and Sause (1998), Specimen 1

XFahnestock and Sause (1998), Specimen 2

Figure 6.3 Nonnalized Ultimate Moment versus Nonnalized Web Slenderness

144

1.2..------,.------------------,

1.15

1.1

1.05

0.95

0.9

UCF,CSB

+

•"

UCF =Ultra-Compact FlangeCSB =Closely-Spaced Lateral Bracing

0.85

/~HTOSlendernessLimit

UCF,CSB

6.505.504.503.500.8 +-----+-....l...----!------f------t-------J

2.50

Nmmalized Web Slenderness

• Schilling (1990), Specimen S• Schilling (1990), Specimen M• Schilling (1990), Specimen D• Barth (1996), Specimen PIc Barth (1996), Specimen P3o Barth (1996), Specimen P511 Barth (1996), Specimen P6• Grubb and Carskaddan (1979), Specimen 1- Grubb and Carskaddan (1979), Specimen 2+Grubb and Carskaddan (1979), Specimen 3:II: Fahnestock and Sause (1998), Specimen 1X Fahnestock and Sause (1998), Specimen 2


145

6.505.504.503.50

IUCF =Ultra-Compact Flange I

--

:tC ~~....... _-

~~

~~

A-- ________.....................

~~~~~---

-------===~UCF

UCF

V~HTOSlendernessLimit

0.8

2.50

0.9

1.1

1.2

0.85

0.95

1.05

1.15

Normalized Web Slenderness

A Green and Sause (1997), FE Specimen 1• Green and Sause (1997), FE Specimen 2X Fahnestock and Sause (1998), Specimen 1X Fahnestock and Sause (1998), Specimen 2


146

References

AASHTO (1997). AASHTO LRFD Bridge Design Specifications -1997 Interim,American Association of State Highway and Transportation Officials, Inc.,Washington D.C.

AISC (1978). Specifications for the Design, Fabrication, and Erection of StructuralSteel Buildings, American Institute of Steel Construction, Chicago, IL.

ASTM (1994). E8 - Standard Test Methods/or Tension Testing o/Metallic Materials,1994 Annual Book of Standards, American Society of Testing Materials, Philadelphia,PA.

AWS (1988). Bridge Welding Code, American Welding Society, Miami, FL.

Barth, K. E. (1996). Moment-Rotation Characteristics for Inelastic Design of SteelBridge Beams and Girders, Ph.D. Dissertation, Purdue University, West Lafayette, IN.

Croce, A. D. (1970). The Strength of Continuous Welded Girders with UnstiffenedWebs, Structures Research Laboratory Report No. 70-2, Department of CivilEngineering, University of Texas at Austin.

Green, P. S. and R. Sause (1997). Personal communication, Lehigh University.

Grubb, M. A. and P. S. Carskaddan (1979). Autostress Design of Highway Bridges,Phase 3: Initial Moment-Rotation Tests, Research Laboratory Technical Report,United States Steel Corporation, Monroeville, PA, April 18.

Grubb, M. A. and P. S. Carskaddan (1981). Autostress Design of Highway Bridges,Phase 3: Moment-Rotation Requirements, Research Laboratory Technical Report,United States Steel Corporation, Monroeville, PA, July 6.

Holtz N. M. and G. L. Kulak (1973). Web Slenderness Limits for Compact Beams,Structural Engineering Report No. 43, Department of Civil Engineering, University ofAlberta.

Holtz N. M. and G. L. Kulak (1975). Web Slenderness Limits for Non-CompactBeams, Structural Engineering Report No. 51, Department of Civil Engineering,University of Alberta.

147

McDermott, J.F. (1969). Plastic Bending ofA514 Beams, Journal of the StructuralDivision, American Society of Civil Engineers, Vol. 95, No. ST9, September, pp.1851-1871.

Nickerson, Robert L. (1997). Girder Fabrication Report #3: HPS-l00W for LehighUniversity by High Steel Structure~ report to the American Iron and Steel Institute.

Sooi, T. K., P. S. Green, R. Sause, 1. M. Ricles (1995). Stress-Strain CharacteristicsofHigh-Performance Steel and the Implications for Civil-Structure Design,Proceedings of the International Symposium on High Performance Steels forStructural Applications, Cleveland, Ohio, November, pp. 35-43.

Schilling, C. G. (1988). Moment-Rotation Tests ofSteel Bridge Girders, Journal ofStructural Engineering, American Society of Civil Engineers, Vol. 114, No.1, pp.134-149.

Schilling, C.G. (1990). Moment-Rotation Tests ofSteel Girders with Ultra-CompactFlanges, SSRC Annual Technical Session Proceedings, Structural Stability ResearchCouncil, St. Louis, MO, April, pp. 63-71.

SSRC (1988). Technical Memorandum No.7, Guide to Stability Design Criteria forMetal Structures, Structural Stability Research Council, Fourth Edition.

White, D. W., 1. A. Ramirez, K. E. Barth (1997). Moment Rotation Relationships forUnified Autostress Designs of Continuous-Span Bridge Beams and Girder~ FinalReport, Joint Transportation Research Program, West Lafayette, IN, November 17.

148

Vita

Larry Alan Fahnestock was born to James Richard and Nancy Geib Fahnestock

on June 21,1973, in Washington, DC. In June 1996, he graduated summa cum laude

from Drexel University, Philadelphia, PA, with the degrees of Bachelor of Science in

Architectural Engineering and Bachelor of Science in Civil Engineering. In July 1996,

he began graduate study at Lehigh University, Bethlehem, PA. He expects to receive

the degree of Master of Science in Civil Engineering in May 1998. Following

graduation, he will be employed as a structural engineer at Kling Lindquist,

Philadelphia, PA.

149

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Documents

Flexural strength and ductility of HPS-100W steel I-girders