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Virginia

Tech

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8453

VIRGLNIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY The Charle E. Via , Jr. Department of Civil Engineering Blacksburg, VA 24061

Structural Engineering

Behavior and Modeling of Mild and Reinforcing Steel

by

Clinton O. Rex

Research Assistant

W. Samuel Easterling, Ph .D., P.E.

Principal Investigator

Submitted to

The American Institute of Steel Construction

The American Iron and Steel Institute

The National Science Foundation

(MSS -9222064)

Innovative Steel Research For Construction Program

Report No. CE/VPI-ST 96/

October, 1996

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• • • • • • • • • Research Report

Behavior and Modeling of Mild and Reinforcing teel

by

Clinton O. Rex

Research Assistant

W. Samuel Easterling, Ph .D., P.E.

Principal Investigator

Submitted To

The American Institute of Steel Construction

The American Iron and Steel Institute

The National Science Foundation

(MSS-9222064)

Innovative Steel Research For Construction Program

Report No. CElVPI-ST 96/

October, 1996

Structures and Materials Research Laboratory

The Charles E. Via, J. Department of Civil and Environmental Engineering

Virginia Polytechnic Institute and State University

6. /.3 Remaining Key I'alue.• .. ........................................... .. ............................................................ U 6 .2 RENFORCING STEEL .... ... ........ .. .................. ................ ........................................... IS 6 .3 COMPAJUSOSOF MULTI-LINEAR ESTIMATETOMEAsUREDDATA. ...................................................... 16 7, UMMARY, CONCLUSION ,AN D RECOI\1I\1E DATIONS .................................................... 17 • 71 StJ\ IMARY ................................................................................................................................... , 17 7.2 CO. CLUSIONS .............................................................................................................................. 19 7 1 RE COMMENDATIONS .. .......................... ................. .......... .......... ....................... ...... ..... .. ... ........ ...... 19

REFERE CE ..................................................................................................................................... 20 APPE DIXA ....................................................................................................................................... 21 APPE DIX B ....................................................................................................................................... 2~^ •

APPENDIX C ....................................................................................................................................... 32

APPE DIX D ....................................................................................................................................... 76 ,.

111

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LIST OF FIGURES

• 1 OMlNAL^ DIMENSIO^ NS^ OF^ TENSILE^ COUl'ONS^ .....................................^ ..^ ............................... 8 2 M LTI-LINEAR APPROXlJ\tATlO FOR J\ULO STEEL STRESS- TRAI BEHAVIOR ...... 17 3 M ULTI- UNEAR APPROXIMATION FOR REINFORCING STEEL STRESS- TRAI
• BEBA^ VIOR^ .................^ ..^ .......................................................^ ..^ ........................................^ ..^ .................... 18
• • • • • •

IV

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TA BLE OF 0 1 EN LAT RE

F, = Yield stress

Fu = Ultimate tensile stress

(F» m,1I = Yield stress based on millteosile test (F ,).,. ". = Yield stress based on pseudo static tensile test

E = train rate

CO = oefficient of variatIOn

E = Modulus of elasticity

VI

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• • • • • • • • • A B TRA CT

An investigation of the stress-strain behavior of mild structural steel and

reinforcing steel is presented in this repon. Two grades of mild steel are included in the

investigation, ASTM A36 and A TM A572Gr50. The only reinforcing steel investigated

is Grade 60 and specifically #4 bars. Data from existing literature, tensile tests conducted

at Virginia Tech (VT), and mill test repons was used as a basis to develop approxtmate

methods for representing the stress-strain behavior of these steels

VII

The strain rate was not really known at the time but because the formula was fairly insensitive to the strain rate the value of 800 seemed reasonable. This strain rate results in approximately a 4 ksi difference. The results (of interest for this report) are summarized as follows:

• Mean elastic modulus = 29,000 ksi, Coefficient of Variation (COY) = 6%
• Mean yield stress for flanges in rolled shapes = 1.05 Specified Stress, COY = 10%
• Mean yield stress for plates and webs of rolled shapes = 1. 10 Specified Stress, COY = 11%
• Mean strain hardening modulus = 600 ksi , COY = 25% The large quantity of structural steel being produced from recycled steel in recent years, which is approximately 85% (Bell, 1995), has changed the characteristics of structural steel A mill survey was conducted (Read & Frank, 1993) to evaluate the properties of steel curre nt ly being supplied. Mill test data for rolled W sections from six steel companies was provided over a 12 month period. Table I summarizes the results of a statistical analysis of the data which included orne 57,930 mill tests. Only the results for A36 and A572GrSO steel have been included. Ta bl e I Results of Recent M ill Survey Steel Grade A36 AS Number of Data 36,570 13 , Yield (ksi) Mean 49.2 57. Standard Deviation 4.9 5. 1 Ultimate (ksi) Mean 68.5 75. Standard Deviation 4.6 6. YieldlVltimate Mean (^) .720. Standard Deviation .057.

• • • • • • • • • •

• (^) ..
• • • • • • • • • 1.2 Reinforcing teel

Standard defonned bar reinforcing steel is available in grade 40, 60 and 75 with

nominal yie ld stresses of 40 ksi. 60 k i, and 75 ksi respectively The most common

reinforcing steel used in buildings is grade 60 A review of mill test data by Mirza and

MacGregor (1979) determined the following results for Grade 60 reinforcing teel

• Yield Stress' Mean = 71 ksi , OY = 9.3%

itimate Stress' Mean = 110 .8 ks~ COY = 8 73% Elastic Modulus. Mean = 29,200 ksi , COY = 33%

The stress-strain behavior of reinforcing bars is usually taken a ela tic plastic

( ollins and Mitchell 1991); but, because #4 Grade 60 bars typically have a very short

Yield plateau, a more detailed representation of the stress-strain behavior I desired by the

wnter Four of the key points of an ideal stres -strain curve for grade 60 relOforcing bars,

a given by Wang and Salmon ( 1985), are shown in Table 2.

Table 2 Ideal tress train Points For Grade 60 Reinforcing teel

Point tress (ksi) tralO (mi lO)

Yield 60 0002

Begin Strain Hardening 60 0 0 1

Ultimate I 10 00

Rupture 95 o 125

2. Focus And Objecti e

The objective of this investigation is to develop an appro Imate method of

numerically representing the stress-strain behavior of mild and reinforcing teels The

stress-strain behavior will later be used in composite connection analysis

representation is probably the simplest method of representing the behavior

multi-linear

3. Mill Survey of Angles and Plates Mill tests reporting yield stress, ultimate stress, percent elongation, and chemical analysis for hot rolled angles and plates were supplied by a steel mill. These tests covered

approximately a six month time period from 6/ 25 / 95 to 12120 195. The mill that supplied

the mill test data uses electric arc furnaces and scrap steel to produce the angles and plates. Data from the mill test reports was entered into a commercial database program and then analyzed with a commercial spreadsheet program. The data included 15 angle shapes and 40 plate shapes, a summary of the shapes included in the analysis is presented in Appendix A Table A-I. The data also included 14 different grades of steel. Only A and A572Gr50 steels have been included in the analysis. A summary of steel property statistics including the mean, median, coefficient of variation, minimum values, maximum value, and number of data is presented in Appendix A Table A-2. These statistics are grouped by shape (plate or angle) and steel grade The mean values are also presented in Table 3 below. Table 3 Mean Values of Mill Survey Data

Fy F. %^ Elongation^ F.fFy

(ksi) (ksi) A36 Structural Angles 46. 1 67.3^ 34.9^ 1. A36 Plates 45 .7^ 67.2^ 32.0^ 1. AS72GrSO Structural Angles 57.7^ 79.3^ 30.4^ 1. AS72GrSO Plates 54.7^ 77.1^ 29.6^ 1. A36 Angles & Plates 45.8 67.2 32.7 1. AS72GrSO Angles & Plates 55 .8^ 77.9^ 29.9^ 1.

As can be seen in Table 3 the properties for A36 angles differed very little from

those for A36 plates Consequently, it does not seem necessary to distinguish between

angles and plates when considering A36 steel properties The properties for AS72GrSO

angles did differ some from those for AS72Gr50 plates There were only 50 mill test

reports available for AS72GrSO angles and plates. The small number of tests is the likely

reason for tbe difference seen in the properties between AS72Gr50 angles and plates.

Consequently, the writer be lieves distinguishing between angles and plates when

considering AS72Gr50 steel is also not necessary

4. Tensile Te t onducted at' ir ginia Tech

The following describes the collection and compilation of various tensile test data

available from recent work at VT. In addition, a description of special tensile tests which

reported the entire stress-strain behavior is presented

.t.1 1i ce llaneou Ten il e Te t Data o ll ec ted

Data from tensile tests that were performed at VT was collected and compiled.

The amount of stress-strain data available varied depending on the particular tensile test

The available data was analyzed to determine as many key points for the stress-strain

behavior as possible. Tensile tests for plates and angles made of A36 steel , wide flange

shapes made from AS72GrSO steel, and #4 Grade 60 reinforcing steel were found. T hi s

test data is summarized in Appendix B Tab le B-2 and Tab le B-4 for mild steel and for

reinforcing steel respectively

4.2 Te nsile T es ts With Full tr ess- train Data

Typical tensi le tests only measure enough strain data to determine the steel yie ld

stress and occasionally extend into the start of the strain hardening region To determine

additional strain values needed to define an adequate multi-linear representation of the

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Mild Steel Flat Plnte SpecImen

'-------':~;=_1_1/2" _~,----------,I J.

L^ k^ /Ik^ L 71

71 10' _ 20" ) Reinforcing Steel Round Specunen #4 Bar (^) O.3S0" Nominal Diameter

2" 71 k^ 3' 71 k^ 2" 71 k

Figure I Nominal Dimensions of Tensile Coupons

4.2.2 In trumentation

An Instron e>.1ensometer was used to measure the strain over a 2-in gage length.

This extensometer was capable of strain measurements up to 50% a1ipers were u ed to

measure initial and final gage lengths for purposes of calculating percent elongation. The

mild steel coupons had gage lengths of 8-in. and the reinforcing steel coupons had gage

lengths of 2-i n.

4.3 Re ult

Tabular summaries of all key stress-strain and statistical values for both mild and

reinforcing steel are presented in Appendix B Full stress-strain plots for the ten ile tests

described in Section 4.2 are presented in Appendix C and D for mild steel tests and

• • • • • • • • • •

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• • • • • • • • • reinforcing steel tests respectively. A discussion of these results IS reserved for the following sections.

5. ummary and Comparison of Data The purpose of this section is to summarize and compare the mean values of the steel properties determined from work described in Sections J and 4 as well as any pertinent ex.isting literature

5.1 Yield and Ultimate Stress Yield and ultimate stress values are probably the most important values for defining the stress-strain behavior. Data for these values was reported in ex.isting literature and in the work described In ections 3 and 4. A summary of this data is pre ented in Table 4.

Tabl e 4 lean Valu es of Y ie ld li nd Itimate tr ess Data

F) F. FJF, o.^ On", (ksi) (^) (ksi) A36 Mltd Steel Tensile Tests on Wide Flange Shapes Mill Survey (Read & Frank 1993) 49.2 (^) 68.5 1.39 36570 Tensile Tests on Plates & Angles Mill Survey 45 .8 67.2 147 760 Tensile Tests Conducted @ vr 459 678 148 90 A572 Gr 50 Mold Steel Tensile Tests on Wide Flange Shapes MillS ",vey (Read & Frank 1993) 57.6 75.6 1.31 13536 Tensile Tests Conducted @ vr 46.0 627 I 16 10 Tensile Tests on Plales & Ang les Mill S",ve' 558 779 140 50 Grade 60 Reinforcmg Steel Mill Survey (Mirza & MacGregor 1979) 71.0 110.8 1.56 3042 Tensile Tests Conducled vr^ (#4 Bars)^ 70.5^1146 1 63 25

• • • • • • • • •
  • Two stress-strain points between start of strain hardening and the ultimate stress
  • The strain at ultimate stress (percent elongation)
  • The stress and strain at rupture A summary of these key points is presented in Table 5. Based on the data, distinctions between steel grades and shapes does not r eq uired for the steel properties listed. Consequently, the data presented in Table 5 are the mean values without regard to steel grade or shape. Based on a visual inspection of the typical stress-strain behavior the writer choose the intermediate stress-strain values at 5% and 10% strain were chosen The stresses corresponding to these strains were determined and normalized by dividing the value by the ultimate stress. The stress at rupture was also normalized by the ultimate stress.

Tab le 5 Mean Val ues For Key Stress-Strain Strai n Points For Mild tee I

Modulus of elasllcll), (ksi) train @ stan of strain hardening (in .lin.) Stress @ 5% strain (nomlalized by F.) Stress @ 10% strain (nonnalized by F.) Strain @ ultimate stress (in .l in .) Stress @ rupture (nomlalized by F.) Strain @ rupture (in.lin.)

Galambos & (^) Plate & Angle Mtll Sun' e,

Tensile Tests Conducted a VT 30000 00219 0846

1. 957

2. 189-

The only values that can be compared between sources are the modulus of elasticity and the strain at rupture. The commonly accepted value of the ela tic modulus for mild steel is 29,000 ksi. The difference between this and what was determined from tensile tests at VT can be attributed to the small number of tests and the lack of accuracy with which the extensometer used can measure small strains. The difference in rupture strains is small and can easily be attributed to the wide variability seen in percent elongation measurements.

II

A summary of the mean values for the key points of the stress-strain behavior for reinforcing steel is presented in Table 6 Based on a visual inspection of the typical stress- strain behavior the intermediate stress-strain values at 3% and 7% strain were chosen. The tresses corresponding to these strains were determined and nonnalized by dividing the value by the ultimate stress. The stress at rupture was also normalized by the ultimate stress

Ta bl e 6 Me an Valu es F or Key tress- tr ain S tr a in Points F or Re inforcing te el

Modulus of clasllCIl) (ksi) tram u start of stram hardenmg (m.lm.) Stress ~ 3% stram (nonnahzed b) F. ) Stress (u 7"10 strall1 (nonnahled by F.) Strain (0, ullimate stress (m .lm.) Stress (ii, ru pture (normahzed by F.) Stram u rupture (in lin.)

M,rza & MacGrc or 1979) 29200

1. 01

3. 125

Tens,le Tests Conducted u VT 32500 () 0074 U

n.1 0 t

() 167 A comparison of the data presented in Table 6 reveals some minor differences between the three sources For the most pan these difference may be explained by the limited variety of reinforcing steel used in the tensile tests conducted at T However, the ource of the ideal stress-strain behavior given by Wang and Salmon (1985) is not known. onsequently, it is difficult to say which set of values is more accurate.

6. Multi-Linear Approximation The objective of this repon is to develop a method of representing the stress-strain

curves for typical mild structural steel and for #4 Grade 60 reinforcing bars In particular

a multi-linear representation of the stress- train curve is sought. For c1anty, methods to do this for mild steel and reinforcing steel are developed separately below After the methods are developed a comparison of the multi-linear representations to the measured stress-strain data is discussed.

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