NIST Technical Note 1714

High-temperature tensile constitutive data and

models for structural steels in fire

William Luecke

Stephen W. Banovic

J. David McColskey
NIST Technical Note 1714

High-temperature tensile constitutive data and

models for structural steels in fire

William E. Luecke

Stephen W. Banovic

Metallurgy Division

Material Measurement Laboratory

J. David McColskey

Materials Reliability Division

Material Measurement Laboratory

Nov 2011

U.S. Department of Commerce

John E. Bryson, Secretary

National Institute of Standards and Technology

Patrick D. Gallagher, Director
Certain commercial entities, equipment, or materials may be identified in this

document in order to describe an experimental procedure or concept adequately.

Such identification is not intended to imply recommendation or endorsement by

the National Institute of Standards and Technology, nor is it intended to imply that

the entities, materials, or equipment are necessarily the best available for the

purpose.

National Institute of Standards and Technology Technical Note 1714

Natl. Inst. Stand. Technol. Technical Note 1714, 135 pages (Nov 2011)

CODEN: NTNOEF
2

Abstract

This report documents a model to represent the true stress-strain, σ − ,

behavior of structural steel. It is based on combination of data from the

NIST World Trade Center collapse investigation and many other evaluated

literature sources. Unlike other models for stress-strain behavior of structural steel, such as the Eurocode 3 formulation [1], the model explicitly describes the time-dependent nature of the strength of steel at high temperature.

For untested steels, it predicts the stress-strain behavior using only the measured room-temperature yield strength, Sy. The relative deviation between

the model of this report and the actual data for the steels is generally less than

25 %, and is always less than 50 %. On subset of eight steels, the model predicts the stress-strain behavior slightly better than the equally complicated

Eurocode 3 model. For three literature structural steels, not analyzed as part

of the model, the model of this report and the Eurocode 3 model predict

stress-strain behavior with similar quality.

Keywords: steel, World Trade Center, tensile, strain rate, constitutive model
3

Contents

1 Introduction 6

2 Experimental Methods 6

3 Results 7

3.1 Microstructure and Chemistry of the steels . . . . . . . . . . . . . 7

3.2 Tensile deformation . . . . . . . . . . . . . . . . . . . . . . . . . 7

4 Discussion 8

4.1 Retained Yield Strength . . . . . . . . . . . . . . . . . . . . . . . 8

4.2 Modeling stress-strain curves . . . . . . . . . . . . . . . . . . . . 11

4.2.1 Yield strength . . . . . . . . . . . . . . . . . . . . . . . . 13

4.2.2 Elastic Modulus . . . . . . . . . . . . . . . . . . . . . . 14

4.2.3 Modeling the strain hardening . . . . . . . . . . . . . . . 14

4.2.4 Including strain-rate sensitivity . . . . . . . . . . . . . . . 14

4.2.5 Final form of the stress-strain behavior . . . . . . . . . . 17

4.3 Comparison with Eurocode recommended values . . . . . . . . . 19

5 Summary 28

A Symbols and Definitions 29

B Experimental Methods 30

B.1 Materials and Microstructural Characterization . . . . . . . . . . 30

B.2 Tensile testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

C Microstructure and chemistry of the steels 32

D Supporting data, plots, and analysis 36

D.1 Tensile data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

D.2 Stress-strain plots . . . . . . . . . . . . . . . . . . . . . . . . . . 39

D.3 Retained Yield Strength Analysis . . . . . . . . . . . . . . . . . . 50

D.4 Calculation and analysis of strain rate sensitivity, m . . . . . . . . 52

D.4.1 Calculation . . . . . . . . . . . . . . . . . . . . . . . . . 52

D.4.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 52

D.5 Calculation of the strain-hardening parameters . . . . . . . . . . . 54
4

E Literature Data 56

E.1 Descriptions of steels from the literature used in this report . . . . 56

E.1.1 Brockenbrough . . . . . . . . . . . . . . . . . . . . . . . 56

E.1.2 Borvik . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

E.1.3 Chen . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

E.1.4 Chijiiwa . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

E.1.5 Fujimoto . . . . . . . . . . . . . . . . . . . . . . . . . . 59

E.1.6 Gowda . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

E.1.7 Harmathy . . . . . . . . . . . . . . . . . . . . . . . . . . 60

E.1.8 Holt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

E.1.9 Holt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

E.1.10 Hu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

E.1.11 Jerath . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

E.1.12 Kirby . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

E.1.13 Kirby . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

E.1.14 Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

E.1.15 Lou . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

E.1.16 Manjoine . . . . . . . . . . . . . . . . . . . . . . . . . . 64

E.1.17 Outinen . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

E.1.18 Poh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

E.1.19 Sakumoto . . . . . . . . . . . . . . . . . . . . . . . . . . 65

E.1.20 Skinner . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

E.1.21 Smith, ASTM DS11 . . . . . . . . . . . . . . . . . . . . 66

E.1.22 Spaeder . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

E.1.23 Stevens . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

E.1.24 United States Steel 1972 elevated temperature handbook . 68

E.2 Tabular data for the literature structural steels . . . . . . . . . . . 69

E.3 Retained strength . . . . . . . . . . . . . . . . . . . . . . . . . . 88

E.4 Elastic Modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

E.4.1 Recommended value . . . . . . . . . . . . . . . . . . . . 88

E.4.2 Other determinations and representations of elastic modulus 90

E.4.3 Notes on literature reports of recommended values for elastic modulus . . . . . . . . . . . . . . . . . . . . . . . . . 92

E.4.4 Notes on literature reports of elastic modulus measurements 96

E.5 Strain rate sensitivity of literature steels . . . . . . . . . . . . . . 103

E.5.1 A model for m(T) for structural steel . . . . . . . . . . . 103
5

F Eurocode stress-strain model 108

F.1 Shape of the stress-strain curve . . . . . . . . . . . . . . . . . . . 108

F.2 Computing the yield strength . . . . . . . . . . . . . . . . . . . . 111

F.3 Comparison to Eurocode prediction . . . . . . . . . . . . . . . . 113

G ECCS stress-strain model 124

Bibliography 127
6

1 Introduction

Modeling the response of steel structures to fire requires accurate constitutive models for the behavior of the steels in the beams, columns, and connections. Finiteelement or other analytical models require the entire stress-strain curve, rather

than just the summary data like yield and tensile strengths, which are common

in the technical literature, for example the ASTM data series [2] that dates back

to the 1950s. Unfortunately, some high-quality data sets that form the basis of

high-temperature deformation models were produced as technical committee reports [3, 4] or as internal industry reports [5, 6] that were not widely circulated and

are difficult to obtain.

For structural steels in conditions relevant to fire, the majority of effort to develop full constitutive laws began in the 1980s in Europe [3, 7–9] and culminated

in the stress-strain model of the Eurocode 3 [1]. Even so, full high-temperature

stress-strain data sets for structural steels used in buildings are much less common

than summary data. The National Institute of Standards and Technology, as part of

its report on the collapse of the World Trade Center, characterized many important

steels recovered from the buildings to provide stress-strain models to analyze the

impact, fires, and resulting collapse. Those tests represent a large additional data

set that can be used for modeling the response of steel structures to fire. The nine

steels of the present report represent a selection of the steel most likely to have

been involved in the fires in the World Trade Center.

This report has four goals.

1. Summarize and reanalyze the high-temperature tensile behavior of steels recovered from World Trade Center collapse.

2. Evaluate the temperature dependence of their strength, stress-strain behavior,

and strain rate sensitivities to provide useful constitutive data for modelers

who need data for structural steel.

3. Present a method for modeling the high-temperature stress-strain behavior of

structural steel that is suitable for determining the response of steel structures

to fire.

4. Compare the high-temperature retained strength and the stress-strain model

to the Eurocode 3 [1] recommended values.

2 Experimental Methods

The steels were characterized for chemistry and microstructure using standard metallographic techniques. Room-temperature tensile testing at room temperature followed ASTM E8 [10], and high-temperature tensile testing followed ASTM E21
7

Table 1: Summary of the nine steels in this report.

Abbreviation Specimen Fy Description of shape

ksi

C65 C65-f1-1 36 12WF161 flange t = 37.7 mm

C80 C80-f1-1 36 14WF184 flange t = 35 mm

C128 C128-T1 36 core truss seat channel

HH HH-f1-1 42 12WF92 flange t = 22 mm

C53BA C53-ba3 36 76 mm × 50 mm angle t = 9.4 mm

C132 C132-ta-3 50 50 mm × 28 mm angle t = 6.35 mm

C40 C40-c2m-iw-1 60 t = 6.35 mm plate

N8 N8-c1b-f-1 60 t = 7.9 mm plate

C10 C10-c1m-fl-1 100 t = 6.35 mm plate

Notes: Fy : specified yield strength see Appendix A

[11]. Appendix B summarizes the experimental methods in greater detail. Appendix A summarizes the symbols used in this report. The data reported here

are abstracted from the NIST World Trade Center collapse investigation report on

structural steel properties. [12].

3 Results

3.1 Microstructure and Chemistry of the steels

The nine steels, summarized in Table 1, represent a cross-section of the steels that

were important to modeling the fire response of the World Trade Center. To facilitate cross-reference with the original report [12], this report retains the same

specimen nomenclature. The set comprises specimens from Fy = 36 ksi hotrolled wide-flange shapes, Fy = 60 ksi hot-rolled plates, a quenched-and-tempered

Fy = 100 ksi plate, and hot-rolled bar and angle taken from the floor trusses. The

lower-strength steels were generally supplied to ASTM A36 and ASTM A242.

The higher-strength plates were generally supplied to proprietary Japanese specifications, but are similar to contemporaneous U.S. specifications. Appendix C

summarizes the sources of the nine steels and their chemical and microstructural

characterization in greater detail.

3.2 Tensile deformation

Figure 1 summarizes the true stress-strain behavior of the nine steels. In Figure 1,

the true stresses are normalized to the room-temperature  = 0.002 offset yield
8

strength, Sy(0.002 offset), which are listed in Table 6 in Appendix D.1. Figure 1

omits several true stress-strain curves for clarity, but Table 6 contains entries for

them. Appendix D.2 plots the un-normalized curves.

4 Discussion

The goal of this report is to produce a model of the stress-strain behavior of structural steel that can predict the behavior of generic structural steels. It is based on

as much publicly available, critically evaluated data as possible, to ensure that it

represents the behavior of all structural steels, rather than just a few from a single

manufacturer or region. It breaks the behavior into three parts:

1. the general behavior of the retained yield strength as a function of temperature, which includes all the available literature data;

2. the behavior of the strain hardening post-yield, which is based on the behavior of the steels evaluated as part of the NIST World Trade Center collapse

investigation [12];

3. the behavior of the significant sensitivity of the strength of steel to the deformation rate at elevated temperature, which includes all the available literature data.

Basing the behavior on the retained yield strength allows us to include many more

steels than would be possible if the model were limited to literature reports that

included full stress-strain behavior.

4.1 Retained Yield Strength

A common method to represent the high-temperature strength of steel is to plot the

retained yield or tensile strength as a function of temperature, normalized to the

room-temperature value [1, 2, 9, 13–23]. A commonly voiced but undocumented

rule of thumb is that the yield strength of structural steel drops to one half its roomtemperature value at 538 ◦C (1000 F). Figure 2 plots retained-strength data from

this study, as well as from many literature sources [6, 12, 18, 23–35] , which are

summarized in Appendix E.1. The data in the figure and in the analysis are limited

to tests whose strain rate lies within or just slightly outside the ranges specified in

ISO [36], JIS [37], and ASTM [11] high-temperature tensile test standards. The

spread of the data demonstrates the variability in the response of structural steel to

elevated temperature deformation.

The shape of the decrease in retained yield strength with temperature is complicated. The NIST WTC collapse report [12] represented it with a five-parameter

phenomenological fit where the parameters were constrained and adjusted to visually provide the best representation of the data in the temperature region, (400 <
9

True strain

Normalized true stress

0.0

0.5

1.0

1.5

2.0

2.5

0.00 0.10 0.20

 226 MPa C65_FL

0.00 0.10 0.20

 233 MPa C80_FL_L

0.00 0.10 0.20

 234 MPa C128

0.0

0.5

1.0

1.5

2.0

2.5

 362 MPa HH_FL_1 386 MPa C53BA 406 MPa C132

0.0

0.5

1.0

1.5

2.0

2.5

 436 MPa C40_C2M_IW 473 MPa N8_C1B1A 760 MPa C10_C1M_FL

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 1: True stress-strain tensile curves for all steels, where stresses are normalized to the measured room-temperature yield strength, Sy(0.002 offset), shown in

the strip for each plot.
10

T /°C

R

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 200 400 600 800 1000

R= 0.5

538 °C

Literature

This study

full fit

WTC fit

Eurocode 3

(a) full temperature range

T /°C

R

0.0

0.2

0.4

0.6

0.8

1.0

450 500 550 600 650 700

538 °C

Literature

This study

full fit

WTC fit

Eurocode 3

(b) temperature range where strength drop is largest

Figure 2: Normalized, retained yield strength, R, as a function of temperature. The

strength is the 0.2 % offset yield strength, Sy(0.002 offset) normalized to its roomtemperature value. Data are from structural steels tested in the strain-rate range

(3.30 × 10−5 <  < ̇ 1.35 × 10−4) 1/s. (a) full temperature range. (b) temperature

range where strength drop is largest.
11

Table 2: Parameters for Eq. (1) shown in Fig. 2. Rightmost column is the predicted

value of the normalized retained strength, R, evaluated at 538 ◦C (1000 F).

Fit A2 r1 r2 r3 r4 R(T = 538◦C)

◦C◦C

Full 5.708 1.000 590 919 0.595

WTC 0.075 8.07 1.00 635 539 0.568

Eurocode 3 0.461

ECCS 0.405

See Appendix D.3 for discussion of the form of WTC fit.

T < 650)

◦C. The reported values [12] were based on a subset of the literature

data available here. This report modifies that representation to include more literature data, to require the retained strength to evaluate to unity at T = 20 ◦C, and to

asymptotically approach zero for high temperatures. The retained yield strength,

R, depends on temperature through a four-parameter model:

R =

Sy

Sy(T = 20◦C)

= exp −

1

2



T

∗

r3

r1

−

1

2



T

∗

r4

r2

(1)

where T

∗ = T −20, measured in ◦C. Figure 2 plots three representations of Eq. (1).

The curve labeled “WTC fit” uses the parameters that appeared in Ref. 12. The

curve labeled “full fit” was computed using a constrained, non-linear least-squares

fit to the literature data combined with data of this report, see Appendix E.1, from

tests with strain rate (3.30 × 10−5 <  < ̇ 1.35 × 10−4) 1/s. Figure 2 also shows

a curve of retained strength computed for the Eurocode 3 model [1]; details are

in Appendix F.2. The European Convention on Constructional Steelwork [9] also

recommended values for retained strength, described in Appendix G. Table 2 summarizes the parameters for both fits to the data. The last column of Table 2 shows

the predicted values of R for T =538 ◦C (1000 F). Both the original prediction

from the NIST WTC report [12] and the new prediction are slightly higher than

the commonly accepted value R = 0.5, while the predictions of other models are

lower.

4.2 Modeling stress-strain curves

Analyses often require more than simply the behavior of the yield strength as a

function of temperature. Finite-element analyses require the entire stress-strain

curve, rather than just an estimate of the yield strength. The Eurocode 3 [1] model

uses a multi-parameter model evaluated at fixed temperature points to describe

the stress-strain curve, see Appendix F, but does not document the origins of the
12

choices of the parameters. This report presents an alternative method to describe

the high-temperature steel stress-strain behavior and describes the method and data

by which the parameters were calculated.

Dozens of stress-strain-strain-rate models of different complexity exist. In preparing this report we examined and evaluated a number of them and tried to balance

the fidelity of the model against the number of parameters and the ease of calculation. The stress-strain model in this report uses a power-law (or Hollomon) strainhardening, and a simple power-low strain rate sensitivity that scales the entire true

stress-strain curve:

σ =



Sy(T) + K(S

0

y

, T)

n

p



f( ̇) (2)

Equation (2) can be broken into several independent terms.

• Sy(T) is the behavior of the yield strength as a function of temperature, T.

• p is the plastic true strain, as opposed to the total true strain.

• K(S

0

y

, T) is the behavior of the so-called strength coefficient, as a function

of temperature and room-temperature yield strength, S

0

y

.

• Together Kn

p

form the familiar power-law stress-strain equation.

• f( ̇) is the function that describes the strain-rate sensitivity of the stressstrain behavior.

For reasons of familiarity, and to create a model that was similar across all temperatures, elastic behavior is included up to the yield strength at all temperatures.

Each stress-strain curve has an elastic region up to the yield strength and a plastic

region post-yield.

σ =







E for  < Sy/E

Sy + K( − Sy/E)

n

for  ≥ Sy/E

(3)

See also Figure 3. The total strain, , is the sum of the elastic, e, and plastic, p,

strains:

 = e + p =

σ

E

+ p (4)

The following sections demonstrate the functional dependence and computation

of the individual terms.
13

Figure 3: Schematic diagram of the stress-strain model used in this report.

4.2.1 Yield strength

Most of the literature on high-temperature strength of structural steel reports only

the yield and tensile strength, and not the full stress-strain behavior. Those yieldstrength data were used in computing the retained strength behavior of the previous

section: Eq. (1) and Figure 2. Greater fidelity to actual stress-strain behavior can

be achieved by incorporating that large body of literature data, Figure 2, on the

behavior of the yield strength of structural steel. In Eq. (2) the high-temperature

yield strength is

Sy = RS0

y

(5)

One limitation of this approach is that the reported yield strength, Sy(0.2 % offset)

does not occur in the stress-strain curve at the point where stress deviates from

a linear increase with strain. However, the small difference that using the yield

strength as the end of the elastic region creates is outweighed by the utility of

using the large body of literature data to set the yield behavior of the stress-strain

curve.
14

4.2.2 Elastic Modulus

The temperature dependence of the elastic modulus is taken from the NIST World

Trade Center Collapse report [12]:

E = E0 + e1T + e2T

2 + e3T3

(6)

Table 3 summarizes the values of the parameters. Appendix E.4 discusses the

sources and limitations of elastic modulus data and expressions.

4.2.3 Modeling the strain hardening

The stress-strain behavior, Figure 1, demonstrates the general relation that steels

with high yield strength generally strain harden less than steels with low yield

strength. Figure 4a demonstrates this observation by plotting the ratio of the stress

evaluated at  = 0.075 to the yield strength, Sy, as a function of the measured

room-temperature yield strength, S

0

y

. The four panels show the data in different

temperature ranges. The effect is strong at temperatures up to 450 ◦C, but is weaker

at higher temperatures, where time-dependent effects are more significant. The

stress-strain model should capture this behavior.

In addition to the slight dependence on the room-temperature yield strength,

the amount of strain hardening decreases with increasing temperature for most

steels. Figure 4b plots the ratio of the stress evaluated at  = 0.075 to the yield

strength, as a function of temperature. The panels separate the steels into three

groups by room-temperature yield strength, S

0

y

. This ratio, which represents the

amount of strain hardening after yield, drops off with temperature for all but the

two highest-strength steels.

A model for stress as a function of plastic strain that captures the two requirements above, but that does not use too many parameters, is

σ =







E for  < Sy/E

RS0

y + (k3 − k4S

0

y

) exp −(

T

k2

)

k1



( − Sy/E)

n

for  ≥ Sy/E

(7)

The strength coefficient, K in Eq. (2), depends linearly on the room-temperature

yield strength. In addition, it drops off with increasing temperature through the

extra exponential term. That term causes the amount of strain hardening decrease

with increasing temperature, as seen in Figure 4b. The retained yield strength, R,

is computed from Eq. (1).

4.2.4 Including strain-rate sensitivity

At elevated temperature the strength of steel measured in a tension test increases

significantly as the strain rate at which it is deformed increases. At temperatures
15

S y

0

 /MPa

σ

(ε = 0.075

)

S

y

1.2

1.4

1.6

1.8

2.0

2.2

200 300 400 500 600 700

[20,300] °C

200 300 400 500 600 700

(300,450] °C

1.2

1.4

1.6

1.8

2.0

2.2

(450,600] °C (600,701] °C

(a) in different temperature ranges

T /°C

σ

(ε = 0.075

)

S

y

1.2

1.4

1.6

1.8

2.0

2.2

0 200 400 600

[222,300] MPa

0 200 400 600

(300,450] MPa

1.2

1.4

1.6

1.8

2.0

2.2

(450,761] MPa C65_FL

C80_FL_L

C128

HH_FL_1

C53BA

C132

C40_C2M_IW

N8_C1B1A

C10_C1M_FL

(b) in different room-temperature yield strength ranges

Figure 4: Ratio of the stress evaluated at  = 0.075 to the yield strength (a) as

a function room-temperature yield strength, S

0

y

. Sub-plots show four temperature ranges. (b) as a function of temperature. Sub-plots show different roomtemperature yield strength ranges. The notation in the strips of the panels denotes

a range of conditions, e.g. “(20,300] ◦C” denotes the range (20 ≤ T < 300)

◦C.
16

above about 500 ◦C increasing the strain rate by ten times can increase the measured strength 25 %; see for example Figure 36. In a constant-load test, this behavior manifests itself as creep, see for example Williams-Leir [38] for creep models

for structural steels. During creep at constant load, continuous deformation occurs.

The steel no longer requires an increase in stress to produce an increase in strain as

it does at room temperature. Some literature reports have recognized that this behavior is important [9,39,40], but most [9,39] have not incorporated it into models

in a transparent manner.

The strain rates in standard high-temperature tensile tests [11, 36, 37] produce

about 5 % strain in ten minutes. Therefore, the strengths measured in those tests

represent an upper limit to the load-carrying capacity at that temperature. It is

important, then, to be able to account for the time- or rate-dependent strength of

steel. The increase in stress, σ, relative to a reference stress, σ0 that results from

an increase in strain rate at constant temperature can be expressed through another

power-law relation:

σ

σ0

= f( ̇) = 

 ̇

 ̇0

m

(8)

The exponent, m, is termed the strain-rate sensitivity. The normalizing parameter,

 ̇0, ensures that the multiplier is unity at the strain rate at which the stress-strain

behavior was measured. For the data of this report  ̇0 = 8.33 × 10−5 1/s, the rate

used in ASTM E8 [10].

The strain-rate sensitivities m, for the steels of this report, which were determined from the tensile tests, see Appendix D.4.1 and Table 6 for details, increase

strongly with increasing temperature, Figure 5.

No one, simple, materials-science-based equation can describe behavior of the

strain rate sensitivity for all temperatures and strain rates, because the mechanism

responsible for deformation changes as temperature increases. Chapter 8 of Frost

and Ashby’s book [41] describes the deformation-mechanism-map approach for

understanding the behavior of ferrous alloys. It breaks the temperature and strainrate space into regimes where different deformation mechanisms dominate, and

presents the governing equations for each regime. The deformation-mechanismmap approach, which is based on fundamental mechanisms, is too complicated for

a simple representation. However, the general behavior of the mechanisms should

be retained even in a phenomenological approach, so that the material response

behaves well outside the range of the data. One important limitation is that strainrate sensitivity for power-law creep of ferrous alloys has a maximum [42]: mplc ≤

0.2, so any expression for the temperature dependence of the strain rate sensitivity

should never exceed that maximum. A convenient, phenomenological expression
17

that meets that requirement is

m(T) = m0 + m3



1 − exp −



T

m2

m1 (9)

Widely used, materials-science-based models for temperature and strain rate

dependence of the stress-strain behavior, such as the Johnson-Cook [43] and ZerilliArmstrong [44] models, employ temperature-independent strain-hardening exponents, n, and strain rate sensitivities, m. Of course, the data in Table 6 and the

model, Eq. (3), could be used to generate the parameters of these models as well.

Figure 5 also compares the strain rate sensitivity, m, data of the steels of this

study to literature data for structural steels, which are summarized in Appendix E.1.

Although the strain rate sensitivities of the steels of this study were evaluated near

an engineering strain, e ≈ 0.02, the literature data in Figure 5 were calculated

from the yield strength, since that parameter is most commonly reported. Figure 5

demonstrates that the strain rate sensitivities of the steels of this study are similar

to other low-alloy structural steels, however.

To compute the most appropriate values for parameters in the the strain rate

sensitivity relation, Eq. (9), the data of this report, Figure 27 were combined with

existing literature data. The entire data set was fit using Eq. (9). Appendix E.5

details the procedure, and Table 3 summarizes the values. The solid line in Figure 5

is the Eq. (9) evaluated with the best-fit parameters.

4.2.5 Final form of the stress-strain behavior

The expressions for the retained strength R, the elastic modulus, E, strain-rate

sensitivity, m, and the strain-hardening behavior can be combined into the final

form of the stress-strain model.

σ =







E for  < Sy/E



RS0

y + (k3 − k4S

0

y

) exp −(

T

k2

)

k1



( − RS0

y /E)

n

   ̇

 ̇0

m

for  ≥ Sy/E

(10)

where

E = E0 + e1T + e2T

2 + e3T3 Eq. (6)

R = exp −

1

2



T

∗

r3

r1

−

1

2



T

∗

r4

r2

Eq. (1)

m = m0 + m3



1 − exp −



T

m2

m1 Eq. (9)
18

T /°C

m

0.00

0.05

0.10

0.15

0.20

0 200 400 600 800

This study

0 200 400 600 800

Literature

This study Literature 

100 ksi plate C10

50ksi A242 angle C132

60ksi HSLA plate C40

60ksi HSLA plate N8

A36 12WF161 C65

A36 14WF184 C80

A36 angle C128

A36 angle C53BA

A572 12WF92 HH

ASME-SA516 Ref. 25

mild steel Ref. 62

AS3679.1 Ref. 31

AS A186:250 Ref. 33

AS187:WR350/1 Ref. 6

AS A186:250 L0 Ref. 6

AS A186:400 L15 Ref. 6

A992 Ref. 40

CSA G40.21 350AT Ref. 29

CSA G40.21 350WT Ref. 29

Figure 5: Strain rate sensitives, m, of WTC steels compared to literature data for

structural steels.

For strain rates other than the reference strain rate,  ̇0, the high-temperature yield

strength, RS0

y

should also be scaled by the strain rate sensitivity.

The five parameters, ki and n, in Eq. (7) were estimated by a non-linear leastsquares regression of the stress-strain data for 43 individual stress-strain curves,

excluding the Fy = 100 ksi steels. Appendix D.5 summarizes details and the results of the fit. Table 3 summarizes the values. Figure 6 plots the relative deviation,

Dr =

σˆ − σ

σ

(11)

between the plastic true stress predicted by Eq. (7), σˆ, and the measured plastic
19

Table 3: Values of the parameters in the stress-strain equation.

Parameter Value Equation

r1 5.708 Eq. 1

r2 1.000 Eq. 1

r3 590 ◦C Eq. 1

r4 919 ◦C Eq. 1

k1 8.294 Eq. 7

k2 538 ◦C Eq. 7

k3 959 MPa Eq. 7

k4 0.766 Eq. 7

n 0.483 Eq. 7

m0 0.0108 Eq. 9

m1 7.308 Eq. 9

m2 613 ◦C Eq. 9

m3 0.126 Eq. 9

 ̇0 8.333 × 10−5 1/s Eq. 9

E0 206.0 GPa Eq. 6

e1 −4.326 × 10−2 GPa/◦C Eq. 6

e2 −3.502 × 10−5 GPa/◦C

2 Eq. 6

e3 −6.592 × 10−8 GPa/◦C

3 Eq. 6

true stress, σ. The agreement is usually within 20 % and is frequently better. Appendix D.2 plots other comparisons.

4.3 Comparison with Eurocode recommended values

The Eurocode 3 standard for structural fire design [1] defines, for design purposes,

the stress-strain behavior of structural steel at elevated temperatures. Its model uses

four temperature-dependent parameters to describe the engineering stress-strain

(S − e) curve:

• the Young’s modulus (E ̄

a,θ),

• the proportional limit (fap,θ),

• the stress at e = 0.02 (famax,θ), and

• the tensile strength fau,θ.
20

An ellipse connects the stress-strain point at the proportional limit to the maximum

stress, famax,θ. The temperature dependence of each parameter is expressed in a

form normalized to a room-temperature value. The form is not a smooth function;

instead it specifies fixed values at 100 ◦C increments. The stress at e = 0.02,

famax,θ, is normalized to the room-temperature e = 0.002 offset yield strength,

Sy(0.2 % offset), from the mill-test report. This normalizing value is neither the

room-temperature proportional limit, fap,θ, nor the room-temperature stress at e =

0.02, famax,θ = Sy(2 % extension). Appendix F explains the Eurocode 3 stressstrain model in greater detail.

True strain

Relative deviation

-0.4

-0.2

0.0

0.2

0.4

0.00 0.10 0.20

 226 MPa C65_FL

0.00 0.10 0.20

 233 MPa C80_FL_L

0.00 0.10 0.20

 234 MPa C128

-0.4

-0.2

0.0

0.2

0.4

 362 MPa HH_FL_1 386 MPa C53BA 406 MPa C132

-0.4

-0.2

0.0

0.2

0.4

 436 MPa C40_C2M_IW 473 MPa N8_C1B1A T /°C

20

300

400

431

500

539

600

647

650

701

Figure 6: Relative deviation, Dr, between true stress predicted by Eq. (7) and the

measured stress.
21

T /°C

Retained 2% extension strength

0.0

0.5

1.0

1.5

0 200 400 600 800

Literature

This study

Figure 7: Normalized e = 0.02 yield strengths as a function of temperature. Solid

line is the Eurocode 3 recommended value. Data are from appropriate steels of this

study (C10 C1M FL, C128, C132, C40 C2M IW, C53BA, C65 FL, C80 FL L,

N8 C1B1A ) and literature [6, 12, 18, 23, 25, 28, 30–33] .

Figure 7 compares the rate-appropriate data of this study and literature data

[6, 12, 18, 23, 25, 28, 30–33] to the Eurocode 3 recommended value for famax,θ. All

the data in Figure 7 are from tests in the strain-rate range 3.30 × 10−5 <  < ̇

1.35 × 10−4. All the data for the steels of this study lie above the Eurocode 3

line at room temperature because they all strain-harden: Sy(2 % extension) >

Sy(0.2 % offset). Most lie above the recommended value for temperatures up to

650 ◦C. Appendix E.1 summarizes the literature steels in Figure 7.
22

It is also possible to compare the prediction of the Eurocode 3 stress-strain

model to the stress-strain data. Figure 8 plots the relative deviation, Dr between

the data and the Eurocode 3 stress-strain prediction. The figure is is directly comparable to Fig. 6. Note that the Eurocode prediction for the five lowest strength

steels is consistently lower than the actual data. Appendix F.3 compares the preTrue Strain

Relative deviation

-0.4

-0.2

0.0

0.2

0.4

0.00 0.10 0.20

 226 MPa C65_FL

0.00 0.10 0.20

 233 MPa C80_FL_L

0.00 0.10 0.20

 234 MPa C128

-0.4

-0.2

0.0

0.2

0.4

 362 MPa HH_FL_1 386 MPa C53BA 406 MPa C132

-0.4

-0.2

0.0

0.2

0.4

 436 MPa C40_C2M_IW 473 MPa N8_C1B1A T /°C

20

300

400

431

500

539

600

647

650

701

Figure 8: Relative deviation, Dr between true stress predicted by the Eurocode 3

stress-strain model, Eq. (20), and the observed behavior.

dictions of the model of this report, Eq. (10) and the Eurocode 3 model to the actual

stress-strain data for each steel individually.

Another method for understanding the utility of the model is to compare its

predictions on steels not analyzed as part of this report. Relatively few [13, 33,
23

40, 45] open-literature sources exist that report full stress-strain data for structural

steels in a form suitable for graphical comparison. Of these, three literature reports

that document stress-strain behavior were chosen:

• Hu [40] 2009 (ASTM A992) see App. E.1.10,

• Harmathy [13] 1970 (ASTM A36), see App. E.1.7, and

• Skinner [33] 1973 (Australian AS A186:250 see App. E.1.20).

Figures 9, 10, and 11 compare the reported true stress-strain behavior, the prediction of the model of this report, Eq. (10), and the prediction of the Eurocode 3

model [1], Eq. (20). Both models capture the trends of the stress-strain data. The

model of this report tends to overpredict the reported behavior of the A36 [13]

steel at high temperature, while the Eurocode 3 model significant underpredicts

it at intermediate tepmperature. Both models undepredict the behavior of the AS

A186:250 steel [33] at intermediate temperatures. Figure 12 summarizes the comparisons of Figures 9, 10, and 11 by plotting the residual standard deviation of the

predictions of the two models as a function of temperature for  > 0.02. The lack

of clear trend in the predictions of stress-strain is apparent here as well. Only for

the AS A186:250 steel [33] does the model of this report consistently predict the

behavior better than the Eurocode 3 model. Overall, in 12 of 24 cases , the model

of this report makes a better absolute prediction than the Eurocode 3 model.
24

True Strain

True Stress /MPa

0

100

200

300

400

500

0.00 0.04 0.08

T=200°C

0.00 0.04 0.08

T=20°C

0.00 0.04 0.08

T=300°C

0

100

200

300

400

500

T=400°C T=500°C T=600°C

0

100

200

300

400

500

T=700°C T=800°C

A992 Ref. 40

This report

Eurocode 3

Measured

Figure 9: Comparison of reported stress-strain data, prediction of Eq. (10) and

the Eurocode 3 [1] stress-strain model for 2000-era A992 steel [40] with Fy =

345 MPa (50 ksi). Individual panels show test temperatures.
25

True Strain

True Stress /MPa

0

100

200

300

400

500

0.00 0.04 0.08

T=204°C

0.00 0.04 0.08

T=21°C

0.00 0.04 0.08

T=316°C

0

100

200

300

400

500

T=427°C T=482°C T=535°C

0

100

200

300

400

500

T=593°C T=649°C

A36 Ref. 13

This report

Eurocode 3

Measured

Figure 10: Comparison of reported stress-strain data, prediction of Eq. (10) and

the Eurocode 3 [1] stress-strain model for 1970s-era A36 steel [13] with Fy =

248 MPa (36 ksi). Individual panels show test temperatures.
26

True Strain

True Stress /MPa

0

100

200

300

400

500

0.00 0.04 0.08

T=200°C

0.00 0.04 0.08

T=20°C

0.00 0.04 0.08

T=300°C

0

100

200

300

400

500

T=400°C T=500°C T=550°C

0

100

200

300

400

500

T=600°C T=650°C

AS A186:250 Ref. 33

This report

Eurocode 3

Measured

Figure 11: Comparison of reported stress-strain data, prediction of Eq. (10) and

the Eurocode 3 [1] stress-strain model for Australian 1970s-era AS A186:250 steel

with Fy = 250 MPa. Individual panels show test temperatures.
27

T /°C

RSD /MPa

0

50

100

150

0 200 400 600 800

A36 Ref. 13

0 200 400 600 800

A992 Ref. 40

0

50

100

150

AS A186:250 Ref. 33

This report

Eurocode 3

Figure 12: Comparison of absolute average deviation of the reported stress-strain

data for  ≥ 0.02 from the prediction of Eq. (10) and the Eurocode 3 [1] stressstrain model

.
28

5 Summary

This report documents a model to represent the true stress-strain, σ − , behavior

of structural steel. It is based on combination of data from the NIST World Trade

Center collapse investigation and many other evaluated literature sources. Unlike

other models for stress-strain behavior of structural steel, such as the Eurocode 3

formulation [1], the model explicitly describes the time-dependent nature of the

strength of steel at high temperature. For untested steels, it predicts the stressstrain behavior using only the measured room-temperature yield strength, S

0

y

. The

relative deviation between the model of this report and the actual data for the steels

is generally less than 25 %, and is always less than 50 %. On subset of eight

steels, the model predicts the stress-strain behavior slightly better than the equally

complicated Eurocode 3 model. For three literature structural steels, not analyzed

as part of the model, the model of this report and the Eurocode 3 model predict

stress-strain behavior with similar quality.

Acknowledgements and contributions

WEL performed the tensile tests for C53BA, C132, and HH, analyzed the data for

discussion section, and wrote the manuscript. JDM performed the tensile tests of

C65, C80, C128, C40, N8, and C10. SWB characterized the microstructures and

managed the chemical analysis, Appendix 3.1.
29

A Symbols and Definitions

Table 4 below summarizes the symbols used in this report.

Table 4: Symbols used in this manuscript.

Symbol Definition

 true strain; natural log of the current length, l over original length, l0:

 = loge(

l

l0

)

e engineering strain: e =

l − l0

l0

 ̇ true strain rate

σ true stress: force, P, over current area, A: σ =

P

A

S engineering stress: force, P over original area, A0: S =

P

A0

Sy measured yield strength as defined in ASTM E6 [46]. Sometimes denoted

YS in other sources. Can be qualified with the type of yield strength. For

example Sy (0.2 % offset) is the traditional offset yield strength in mill

test reports.

Fy in this report, Fy denotes the specified, as opposed to measured, yield

strength, for example, a “Fy = 36 ksi steel.” This usage is consistent with

the AISC [47] Steel Design Manual.

S

0

y measured yield strength at room temperature.

Su tensile strength as defined in ASTM E6 [46]. Often called “ultimate

tensile strength,” and defined as the maximum force over the original

specimen area: Pmax/A0. Often abbreviated in the literature as TS.

Elt Total elongation to failure as defined in ASTM E6 [46]

RA Reduction of area at failure, a measure of the ductility, as defined in

ASTM E6 [46]

K prefactor that defines the strength of the steel in the stress-strain curve,

defined in Eq. (13), and often called the strength coefficient.

n strain-hardening exponent defined in Eq. (13)

m strain rate sensitivity defined in Eq. (8) and (9)

R retained strength, usually yield strength, Sy, normalized to its

room-temperature value, S

0

y

.

Dr relative deviation of stress from model, Eq. (11)

continued on next page
30

Table 4: Symbols used in this manuscript

Continued from the previous page

Symbol Definition

Da absolute deviation of stress from model, Eq. (16)

E ̄

a,θ Young’s modulus in the Eurocode 3 standard, Eq. (20)

fap,θ the proportional limit in the Eurocode 3 standard, Eq. (20)

famax,θ stress at  = 0.02 in the Eurocode 3 standard, Eq. (20)

fau,θ stress at  = 0.04 in the Eurocode 3 standard for capturing strain

hardening, Eq. (20)

kE,θ non-dimensional reduction factor for Young’s modulus in the Eurocode 3

standard, Eq. (25)

kp,θ non-dimensional reduction factor for the proportional limit in the

Eurocode 3 standard, Eq. (26)

kmax,θ non-dimensional reduction factor for the stress at  = 0.02 in the

Eurocode 3 standard, Eq. (27)

ku,θ non-dimensional reduction factor for the stress at  = 0.04 in the

Eurocode 3 standard for capturing strain hardening, Eq. (28)

RSD residual standard deviation of a fit, defined in Ref. 48

RSD =

 

1

ν

X

i=n

i=1

(y − yˆ)

2

!0.5

(12)

where yˆ is the predicted value from the model, and ν is the number of

degrees of freedom of the fit to n data points. Smaller values represent

better fits.

ν Number of degrees of freedom in a regression

B Experimental Methods

B.1 Materials and Microstructural Characterization

A commercial testing laboratory characterized the chemistry of the nine specimens

using optical emission spectroscopy. Tests followed ASTM E415 [49] for all elements except C, which was analyzed in accord with ASTM E1019 [50].

Standard metallographic procedures were used to prepare the samples for optical microscopy. Specimens were ground with SiO2 papers to 800 grit and then

polished with diamond pastes of 6 μm, 1 μm, and 0.25 μm. The final, hand-
31

polishing step used a colloidal mixture of 0.05 μm SiO2 and Al2O3 particles. The

microstructures were revealed using a combination of 4 percent picral (4 g picric

acid, 96 mL ethyl alcohol) followed by 2 percent nital (2 mL concentrated nitric

acid, 98 mL ethyl alcohol).

The volume fraction of pearlite, f

p

v , in the hot-rolled steels was determined

using an area-detected measurement by automatic image analysis techniques using

seven measurements along the plate centerline at 200x or 500x magnification.

B.2 Tensile testing

High-temperature tensile tests employed two different machines. One was an electromechanical testing machine with a contact extensometer that had a 12.5 mm

gage length. The furnace was a split, MoSi2-element design. The specimen for

this machine, designated Flat C3 in Figure 13, conformed to Fig. 1 of ASTM

E 21. [11] The uniform cross-section was 32 mm long and 3.175 mm by 6.0 mm

wide. They were loaded using pin-aligned, superalloy, wedge grips. The specimen

temperature was monitored using a K-type thermocouple mounted within 1 mm

of the specimen surface. The specimens were loaded as soon as possible after the

furnace temperature stabilized at the test temperature, which was generally within

20 minutes. During the temperature stabilization step, the specimen temperature

was always within 5 ◦C of the desired temperature. The actuator displacement

rate in these tests was 0.0325 mm/s, which produced a strain rate after yielding of

approximately 0.001 s−1, measured using the extensometer. Prior to yield, the actuator displacement rate produced a specimen stressing rate of (4±2) MPa/s. These

rates meet the requirements of ASTM E 8 [10] and E 21. [11]

Most other tests used a second electromechanical testing machine with a hightemperature extensometer with a 25.4 mm gage length. The furnace was a split

design in which quartz lamps heated the specimen. This test frame employed two

specimen types. The round specimens, designated Rd 1 in Fig. 13, had a 38 mm

uniform long cross section 6.35 mm in diameter. The flat specimens, designated

Flat C1 in Fig. 13, had a uniform cross-section 28 mm long and 6.35 mm wide.

The thickness was that of the original plate, typically also 6.35 mm. These tests

followed the loading protocol of ASTM E 21. [11] The initial actuator displacement rate was 0.00167 mm/s. At about  = 0.02, the operator increased the actuator displacement rate to 0.0167 mm/s, as required by E 21. The extension rate

jump produces a discernible step in the flow stress, ∆σ, for elevated temperature

tests. The presence of this stress jump, ∆σ, made it possible to evaluate the strain

rate sensitivity of the stress for each temperature. Appendix D.4.1 summarizes the

method used to estimate the strain rate sensitivity from the stress jump. Tests on

three of the nine steels employed only a single extension rate, so it was impossible

to evaluate their strain rate sensitivity.
32

Figure 13: Tensile test specimens used in high-temperature tests.

C Microstructure and chemistry of the steels

Table 5 summarizes the origin and chemistry of the nine steels. All of the recovered steels are low-carbon alloys with carbon contents below 0.25 percent by mass,

strengthened by common elemental alloying practices. Carbon and Manganese are

the main strengthening elements in the wide flange core columns, floor trusses, and

floor truss seat. The floor truss angles and higher strength core column, HH, also

have minor additions of V for carbide formation. The two lower-strength perimeter

column plates, C40 and N8, originated from an inner web and a flange respectively.

Specimen C40 contains V, while flange plate N8 contains Nb. Their significantly

different chemistries, e.g., Si, Cu, V, Nb, suggest that different mills supplied the

two plates. Contemporaneous construction documents indicate that domestic mills
33

Table 5: Chemistry and description of the steels

Abbreviation C65 C80 C128 HH C53BA C132 C40 N8 C10

Specimen C65-f1-1 C80-f1-1 C128-T1 HH-f1-1 C53-ba3 C132-ta-3 C40-c2m-iw-1 N8-c1b-f-1 C10-c1m-fl-1

Fy (ksi) 36 36 36 42 36 50 60 60 100

Description

of shape

12WF161

flange

14WF184

flange

channel 12WF92

flange

(76×50) mm

angle

(50×28) mm

angle

plate plate plate

Source

† 904:86-89 603:92-95 unknown 605:89-101 unknown unknown 136:98-101 142:97-100 451:85-88

t 37.7 mm 35 mm ND 22 mm 9.4 mm 6.35 mm 6.35 mm 7.9 mm 6.35 mm

f

p

v

∗ 0.282 (0.019) 0.366 (0.027) 0.244 (0.022) 0.247 (0.018) 0.266 (0.009) 0.288 (0.007) 0.264 (0.032) 0.256 (0.019) NA

Chemistry

Element

‡ xi xi xi xi xi xi xi xi xi

% % % % % % % % %

C 0.23 0.23 0.19 0.17 0.17 0.19 0.15 0.16 0.17

Mn 0.74 0.90 0.83 1.08 0.60 0.82 1.10 1.50 0.89

P 0.006 0.008 0.010

<0.005 0.013 0.010 0.006 0.023 0.015

S 0.015 0.008 0.005 0.014 0.040 0.029 0.023 0.016 0.012

Si 0.02 0.03 0.04 0.03 0.02 0.07 0.03 0.44 0.24

Ni 0.02 0.01 0.01 0.02 0.09 0.08 0.08 0.01 0.01

Cr 0.02 0.02 0.02 0.02 0.08 0.10 0.06 0.02 0.90

Mo 0.01 0.01 0.02

<0.01 0.01

<0.01

<0.01

<0.01 0.43

Cu 0.05 0.05 0.03 0.24 0.32 0.32 0.23 0.05 0.28

V

<0.005

<0.005 0.002 0.065 0.039 0.038 0.052 0.005 0.007

Nb

<0.005

<0.005 ND

<0.005

<0.005

<0.005

<0.005 0.064

<0.005

Ti

<0.005

<0.005 ND

<0.005

<0.005

<0.005

<0.005 0.007

<0.005

Zr

<0.005

<0.005 ND

<0.005

<0.005

<0.005

<0.005

<0.005

<0.01

Al

<0.005

<0.005 ND

<0.005 ND 0.032

<0.005 0.042 0.081

B

<0.0005

<0.0005 ND

<0.0005

<0.0005

<0.0005

<0.0005

<0.0005

<0.0005

N 0.0041 0.0040 0.0099 0.0090 0.0080 0.0057 0.0033 0.0040

Notes: ND = not determined; NA = not applicable.

‡Chemical composition,

xi expressed in mass fraction. t is the original thickness

∗

f

p

v : Volume fraction of pearlite. Uncertainty listed in parentheses is the standard deviation of 7 measurements.

†Source . all identified sections from WTC 1 ; “904” identifies the column line; .“86-89” identifies the range of floors.
34

supplied the inner web plates and Yawata Iron and Steel (now Nippon Steel) supplied all the flange plates [51]. The higher strength flange plate, C10, contains

elevated levels of Cr and Mo for increased strength and hardenability.

Figures 14 g-i show the microstructures from the three hot-rolled, wide-flange

columns. The ferrite (white) and pearlite (gray-black) are uniformly distributed

across the sections, although lower magnification images revealed some localized

banding of the two phases. The ferrite morphology is a combination of polygonal

and irregular. Some Widmanstatten morphology is present, though not shown,  ̈

in the two Fy = 36 ksi∗columns, C65 and C80. The ferrite grain size in the

Fy = 42 ksi column is finer than that in the two lower-strength core columns,

which appears to have a larger effect on the strength of the material than the volume

fraction of pearlite, f

p

v , see Table 5.

The microstructures of the truss seat and the two floor truss angles are shown in

Figures 14 d–f. All three steels are hot-rolled. The ferrite and pearlite are uniformly

distributed across the sections. The ferrite morphology is primarily irregular or

polygonal. The pearlite volume fractions, f

p

v , are similar, Table 5. Although the

same mill produced the two angles, the ferrite grain size and volume fraction of

Widmanstatten morphology are larger in the lower strength angle, C53, than in the  ̈

higher strength angle, C132.

Figures 14 a–c show the microstructures from the perimeter column plates.

Both Fy = 60 ksi plates, inner web C40 and flange N8, plates are hot-rolled

steels with a ferrite-pearlite microstructure. Although different mills rolled the

plates, their microstructures are similar. Both the ferrite and pearlite are moderately banded, particularly near the centerline of the plate. This gradient in banding usually arises from compositional gradients present in the original ingot. The

ferrite morphology is a mixture of polygonal, irregular, and Widmanstatten. The  ̈

ferrite grain sizes of the two plates are similar, and volume fractions of pearlite,

f

p

v , are statistically equivalent. Two pearlite morphologies exist, depending upon

the local banding characteristics. In unbanded areas the pearlite colonies contain

dense, but distinguishable, lamellar plates. In the more heavily banded regions, the

pearlite appears mottled. The lamellar spacing of this pearlite could not be resolved

in the optical microscope. Some areas may be degenerate pearlite, but it was not

possible to be certain using only the optical microscope. Occasionally, the pearlite

morphology is granular. Bainite may also be present in regions where the ferrite is

associated with small cementite particles, but again, optical microscopy does not

permit definitive identification.

∗This manuscript identifies several steels by their strength grade, expressed in English, rather than

SI, units. The term “36 ksi” describes the strength class of the steel, rather than an exact measure

of its strength. This manuscript reports measured strengths in units of MPa as required by the NIST

Administrative Manual, Subchapter 4.09 Appendix D.
35

(a) C40 (b) N8 (c) C10

(d) HH (e) C53BA (f) C132

(g) C65 (h) C80 (i) C128

Figure 14: Light optical micrographs of representative microstructures of the nine

steels at the same magnification. Images were taken near the centerline of the plates

on the transverse plane. The rolling direction is horizontal. Steels are ordered leftto-right and bottom-to-top by increasing measured yield strength. All steels except

(c) C10 have ferrite-pearlite microstructures.
36

The Fy = 100 ksi flange plate C10, Fig. 14c, is a quenched-and-tempered steel.

In the optical microscope, the microstructure appears to be a tempered martensite.

Prior austenite grain boundaries and distinct remnants of ferrite lath boundaries are

visible. Cementite carbides lie on the prior austenite grain boundaries and the lath

boundaries.

D Supporting data, plots, and analysis

D.1 Tensile data

Table 6 summarizes the data used in this report. The footer of the table describes

the symbols. The reported total elongations, Elt should be interpreted with some

care. In general, they are measured over a gauge length G = 25.4 mm for hightemperature specimens, see Fig. 13. Room-temperature tests generally employed a

specimen with G = 50.8 mm. Reductions of area, RA, for rectangular specimens

were calculated by averaging the thicknesses, using the procedure in ASTM E8

[10]. Table 6 includes columns for the parameters of a power-law fit to the true

stress-strain data:

σ = Kn(13)

The fit for K and n used the total, as opposed to plastic, true strain. The method

for computing the strain-rate sensitivity, m, is summarized in Appendix D.4.1.

The final column, labeled “lm” indicates whether the stress-strain curve was used

in computing the parameters of the stress-strain model, Eq. (10).

Table 6: Data for steels of this study.

Specimen T  ̇0 S

002

y S

02

y Su Elt RA K n m lm

◦C 1/s MPa MPa MPa % % MPa

C65 20 8.75 × 10−5 225 320 461 43.0 62.7 815 0.234 0.0078 0

C65 20 8.75 × 10−5 210 305 448 42.0 61.4 802 0.241 0.0069 0

C65 20 8.75 × 10−5 215 313 483 43.0 62.2 817 0.239 0.0081 0

C65 20 8.75 × 10−5 264 370 469 38.0 63.1 771 0.187 0.0074 0

C65 20 8.75 × 10−5 240 334 455 42.0 61.8 777 0.212 0.0066 1

C65 20 8.75 × 10−5 202 298 441 43.0 61.6 792 0.244 0.0087 0

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

Su = tensile strength; Elt = total elongation; RA = reduction of area

lm: used in calculation of stress-strain model. 1=used, 0=not used

continued on next page
37

Table 6: Data for WTC steels of this study.

Continued from the previous page

Specimen T  ̇0 S

002

y S

02

y Su Elt RA K n m lm

◦C 1/s MPa MPa MPa % % MPa

C65 20 2.19 × 10−3 223 308 452 42.0 62.0 808 0.236 NA 0

C65 431 4.37 × 10−5 194 302 392 42.0 71.8 685 0.212 0.0091 1

C65 539 4.37 × 10−5 158 197 231 43.0 74.4 304 0.112 0.0391 1

C65 647 4.37 × 10−5 85 98 128 91.0 96.5 141 0.087 0.0981 1

C65 701 4.37 × 10−5 54 59 76 NA 96.6 68 0.040 0.1303 1

C80 20 8.75 × 10−5 233 307 464 38.0 68.5 864 0.256 0.0047 1

C80 431 4.37 × 10−5 190 300 407 37.0 73.1 881 0.276 0.0082 1

C80 539 4.37 × 10−5 166 205 255 42.0 72.1 272 0.074 0.0604 1

C80 647 4.37 × 10−5 86 105 135 61.0 97.6 146 0.088 0.1082 1

C80 701 4.37 × 10−5 58 NA 88 83.0 98.0 78 0.050 0.1419 1

HH 20 1.71 × 10−4 362 394 512 38.0 70.3 840 0.185 NA 1

HH 400 1.71 × 10−4 270 374 449 NA 75.2 734 0.172 NA 1

HH 500 1.71 × 10−4 239 315 352 NA 64.0 528 0.133 NA 1

HH 600 1.71 × 10−4 158 200 208 NA NA 268 0.078 NA 1

HH 650 1.71 × 10−4 136 164 166 NA 84.0 214 0.072 NA 1

C128 20 4.37 × 10−5 234 313 459 40.0 67.5 844 0.252 0.0088 1

C128 431 4.37 × 10−5 190 298 401 37.0 70.6 608 0.192 0.0648 1

C128 539 4.37 × 10−5 134 176 221 46.0 79.2 286 0.127 0.0603 1

C128 647 4.37 × 10−5 72 80 108 68.0 97.1 112 0.084 0.1177 1

C128 701 4.37 × 10−5 44 51 68 79.0 91.6 62 0.051 0.1421 1

C53BA 20 5.80 × 10−5 413 498 560 26.0 58.1 805 0.126 0.0021 1

C53BA 20 1.57 × 10−3 360 452 519 24.0 58.5 811 0.152 NA 0

C53BA 300 1.57 × 10−3 370 468 579 NA NA 947 0.176 NA 1

C53BA 400 1.02 × 10−3 284 370 427 NA 54.3 658 0.146 NA 1

C53BA 500 1.02 × 10−3 284 326 332 11.0 NA 445 0.080 NA 1

C53BA 600 1.02 × 10−3 186 208 205 8.0 29.6 246 0.045 NA 0

C53BA 600 1.02 × 10−3 183 186 183 16.0 28.1 207 0.026 NA 1

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

Su = tensile strength; Elt = total elongation; RA = reduction of area

lm: used in calculation of stress-strain model. 1=used, 0=not used

continued on next page
38

Table 6: Data for WTC steels of this study.

Continued from the previous page

Specimen T  ̇0 S

002

y S

02

y Su Elt RA K n m lm

◦C 1/s MPa MPa MPa % % MPa

C53BA 650 1.02 × 10−3 126 140 138 20.0 NA 162 0.040 NA 1

C132 20 9.02 × 10−4 398 403 528 38.0 NA 861 0.180 NA 0

C132 20 6.19 × 10−4 432 491 NA NA NA 819 0.128 NA 0

C132 20 3.28 × 10−5 396 461 549 33.0 65.0 850 0.152 NA 1

C132 20 1.02 × 10−3 399 403 528 NA NA 861 0.180 NA 0

C132 500 1.02 × 10−3 297 341 349 16.0 NA 465 0.080 NA 1

C132 600 1.02 × 10−3 192 215 212 NA NA 257 0.047 NA 0

C132 650 1.02 × 10−3 160 168 165 NA NA 181 0.020 NA 1

C132 400 8.38 × 10−5 339 423 483 32.0 NA 731 0.149 0.0079 1

C132 600 3.28 × 10−5 138 190 190 NA NA 223 0.085 0.0741 0

C132 600 8.40 × 10−5 161 199 202 NA NA 239 0.067 0.0634 1

C40 20 1.19 × 10−4 436 495 572 33.0 63.0 831 0.128 0.0060 1

C40 20 1.19 × 10−4 436 508 574 36.0 65.0 828 0.123 0.0080 0

C40 300 5.97 × 10−5 379 481 544 27.0 53.0 847 0.149 0.0060 1

C40 431 5.97 × 10−5 350 431 466 32.0 60.0 653 0.115 0.0070 1

C40 539 5.97 × 10−5 230 296 305 28.0 41.0 392 0.095 0.0300 1

C40 647 5.97 × 10−5 137 190 187 44.0 78.0 191 0.065 0.0830 1

C40 701 5.97 × 10−5 89 127 125 55.0 86.0 123 0.054 0.0960 1

N8 20 1.19 × 10−4 476 498 627 39.0 65.0 965 0.156 NA 0

N8 20 1.19 × 10−4 471 486 634 39.0 68.0 987 0.159 NA 1

N8 300 5.97 × 10−5 363 494 645 36.0 60.0 1096 0.204 0.0030 1

N8 431 5.97 × 10−5 323 435 496 37.0 73.0 848 0.177 0.0050 1

N8 539 5.97 × 10−5 233 321 340 45.0 80.0 465 0.121 0.0316 1

N8 647 5.97 × 10−5 129 174 174 48.0 80.0 205 0.082 0.0590 1

N8 701 5.97 × 10−5 86 122 123 54.0 84.0 150 0.101 0.0703 1

C10 20 1.19 × 10−4 759 809 860 27.0 67.0 1091 0.074 0.0064 0

C10 20 1.19 × 10−4 761 805 858 23.0 66.0 1095 0.076 0.0049 0

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

Su = tensile strength; Elt = total elongation; RA = reduction of area

lm: used in calculation of stress-strain model. 1=used, 0=not used

continued on next page
39

Table 6: Data for WTC steels of this study.

Continued from the previous page

Specimen T  ̇0 S

002

y S

02

y Su Elt RA K n m lm

◦C 1/s MPa MPa MPa % % MPa

C10 300 5.97 × 10−5 589 751 801 24.0 60.0 1234 0.134 NA 0

C10 431 5.97 × 10−5 613 708 712 23.0 64.0 946 0.080 0.0024 0

C10 539 5.97 × 10−5 515 606 598 25.0 72.0 800 0.081 0.0203 0

C10 593 5.97 × 10−5 343 506 498 30.0 79.0 1033 0.202 0.0423 0

C10 593 5.97 × 10−5 378 508 498 29.0 79.0 966 0.185 0.0359 0

C10 593 5.97 × 10−5 373 516 506 27.0 80.0 904 0.164 0.0385 0

C10 647 5.97 × 10−5 181 353 356 37.0 76.0 662 0.227 0.1086 0

C10 701 5.97 × 10−5 86 142 199 44.0 75.0 302 0.217 0.1574 0

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

Su = tensile strength; Elt = total elongation; RA = reduction of area

lm: used in calculation of stress-strain model. 1=used, 0=not used

D.2 Stress-strain plots

Figure 15 plots the un-normalized true stress-strain behavior for the nine steels on

identical axes. In each case, the curves are truncated at the tensile strength in the

engineering stress-strain curve. Figures 16- 24 plot the measured true stress-strain

data.
40

True strain

True stress /MPa

0

200

400

600

800

0.00 0.10 0.20

 226 MPa C65_FL

0.00 0.10 0.20

 233 MPa C80_FL_L

0.00 0.10 0.20

 234 MPa C128

0

200

400

600

800

 362 MPa HH_FL_1 386 MPa C53BA 406 MPa C132

0

200

400

600

800

 436 MPa C40_C2M_IW 473 MPa N8_C1B1A 760 MPa C10_C1M_FL

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 15: Stress-strain behavior of the nine steels.
41

True strain

True stress /MPa

0

100

200

300

400

500

600

0.00 0.05 0.10 0.15 0.20 0.25

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 16: Stress-strain behavior of steel C65. Sy(0.2 % offset) = 226 MPa.
42

True strain

True stress /MPa

0

100

200

300

400

500

600

0.00 0.05 0.10 0.15 0.20 0.25

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 17: Stress-strain behavior of steel C80. Sy(0.2 % offset) = 233 MPa.
43

True strain

True stress /MPa

0

100

200

300

400

500

0.00 0.05 0.10 0.15 0.20 0.25

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 18: Stress-strain behavior of steel C128.Sy(0.2 % offset) = 234 MPa.
44

True strain

True stress /MPa

0

200

400

600

0.00 0.05 0.10 0.15 0.20 0.25

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 19: Stress-strain behavior of steel HH. Sy(0.2 % offset) = 362.1 MPa.
45

True strain

True stress /MPa

0

200

400

600

0.00 0.05 0.10 0.15 0.20 0.25

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 20: Stress-strain behavior of steel C53BA. Sy(0.2 % offset) = 386 MPa.
46

True strain

True stress /MPa

0

200

400

600

0.00 0.05 0.10 0.15 0.20 0.25

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 21: Stress-strain behavior of steel C132. Sy(0.2 % offset) = 406 MPa.
47

True strain

True stress /MPa

0

200

400

600

0.00 0.05 0.10 0.15 0.20 0.25

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 22: Stress-strain behavior of steel C40. Sy(0.2 % offset) = 436 MPa.
48

True strain

True stress /MPa

0

200

400

600

800

0.00 0.05 0.10 0.15 0.20 0.25

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 23: Stress-strain behavior of steel N8. Sy(0.2 % offset) = 473.4 MPa.
49

True strain

True stress /MPa

0

200

400

600

800

0.00 0.05 0.10 0.15 0.20 0.25

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 24: Stress-strain behavior of steel C10. Sy(0.2 % offset) = 760 MPa.
50

Table 7: Regression statistics for the fit of Eq. (1) to the retained strength data.

Parameter Estimate Standard Error t

r1 5.70839 1.29926 4.39357

r2 1.00000 0.88480 1.13020

r3 590.30863◦C 42.56178◦C 13.86945

r4 918.72252◦C 907.33326◦C 1.01255

RSD: 0.08476 on 211 degrees of freedom

D.3 Retained Yield Strength Analysis

The parameters in Table 2 were calculated using the R statistical language [52],

version 2.11, function nls with the “port” algorithm. Only data from Tables 6

and 10 with strain rates in the range were used. In addition the fit used only a

subset of the data and was constrained:

Temperature range: (300 ≤ T ≤ 800)

◦C,

Strain-rate range: 3.30 × 10−5 <  < ̇ 1.35 × 10−4,

1 ≤ r1 ≤ 10,

1 ≤ r2 ≤ 10,

200 ≤ r3 ≤ 1500,

200 ≤ r4 ≤ 1500.

Table 7 summarizes the regression output. Constraining the values of r1 ≥ 1 and

r2 ≥ 1 ensures that the shape of the retained strength does not become “S-shaped.”

Two of the parameters of the regression summarized in Table 7, r2 and r4 have

large standard errors and correspondingly low values of t. In addition, the value

of r2 reached the lower limit of the constraint. Normally, this would be evidence

that they should be omitted from the regression. However, using a two-parameter

model produces very poor fidelity for temperatures, T > 600 ◦C, so the parameters

have been retained.

The form of Figure 2 makes it difficult to assess the deviations of the data from

the different fits. Figure 25 plots the difference between the prediction of the fit, Rˆ

and the reported the retained strength, R, for each of the three fits shown in Figure 2. The solid lines in Figure 25 are a moving regression that represents the trend

of the data. The fit of Eq. (1) is quite accurate up to 750 ◦C; it deviates by only

about 1 % from the general trend of the data. Because the fit is required to asymptotically approach zero at high temperature, it systematically deviates from the data

for the very highest temperatures. At these temperatures, the retained strength is

extremely small, so the error is correspondingly small in absolute terms. Because
51

T /°C

^

R

−

R

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0 200 400 600 800 1000

(a) Eq. (1)

T /°C

^

R

−

R

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0 200 400 600 800 1000

(b) Eurocode 3

T /°C

^

R

−

R

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0 200 400 600 800 1000

(c) Eq. (14)

Figure 25: Deviations from the fitted retained strength models. (a) This report,

Equation (1) (b) Eurocode 3, see Appendix F.2 (c) Original WTC report, Eq. (14).

the value of R is used in calculating the stress-strain behavior, it is important to

ensure fidelity across as much of the temperature range as possible. Figure 25b

shows that the retained yield strength predicted by the Eurocode 3 formulation, see

Appendix F.2, deviates significantly from the reported behavior in the mid-range
52

of the temperatures. Figure 25c shows the retained yield strength behavior, R,

predicted by the original World Trade Center report [12]

R =

Sy

Sy(T = 20◦C)

= A2 + (1 − A2) exp −

1

2



T

r3

r1

−

1

2



T

r4

r2

(14)

using the parameters of Table 2.

D.4 Calculation and analysis of strain rate sensitivity, m

D.4.1 Calculation

The high-temperature tensile tests to determine stress-strain behavior of this study

were conducted according to ASTM E8 [10] and E21 [11]. These tensile test standards allow the user to increase the strain rate after yield. In strain-rate sensitive

materials, increasing the strain rate increases the measured stress. The size of the

stress jump can also be used to estimate the strain rate sensitivity, m from the

change in initial and final strain rates:

m =

loge σ1 − loge σ2

loge ̇1 − loge ̇2

(15)

where the subscripts “1” and “2” denote before and after the strain rate jump.

Figure 26 describes the procedure graphically. To estimate the the stresses, the

center point of the stress jump in the stress-strain curve was identified graphically,

and the stress-strain points in the transition region were deleted. The slopes of the

stress strain curves were estimated by linear regression of a short section of stressstrain data before and after the jump. These linear fits were evaluated at the strain

corresponding to the center of the transition region to calculate σ1 and σ2.

D.4.2 Analysis

To model the behavior of the strain-rate sensitivity of the individual steels as a

function of temperature the parameters of Eq. (9) were fit using non-linear least

squares method, subject to the constraints listed below.

m0 not fit

(1 ≤ m1 ≤ 15),

(100 ≤ m2 ≤ 2000)

◦C,

0.1 ≤ m3 ≤ 0.2

T ≥ 390 ◦C

The value of m0, which is effectively the strain rate sensitivity at room temperature was not fit. Instead, it was set to the mean value of the room-temperature

measurements. In the case of specimen N8 C1B1A, where no room-temperature
53

value existed, it was set to the average of all the room-temperature values. In addition, only data for T ≥ 390 ◦C was included in the fit to help ensure that the

function evaluated to small values of m for low temperatures. Table 8 summarizes

the results of the fits. The uncertainties of the parameter m3 are large in several

cases, even when the overall quality of the fit is good. They are high in these cases

because the value of m3 controls the limiting, high-temperature value of the strainrate sensitivity. Steels whose data do not exhibit a limiting value will have large

uncertainty associated with this parameter. Note that for the two steels, C128 and

C65 FL, the value of m3 = 0.2, which is the maximum allowed in the fit. Figure 27 shows the strain rate sensitivity for each steel, which is plotted in a single

plot in the left-hand panel of Figure 5 as well. Insufficient data existed for several

steels to compute a strain rate sensitivity, but Figure 27 contains entries for these

steels to facilitate comparison with the other figures. The solid line in each panel

is the fit of Eq. (9) with the parameters of Table 8.

Figure 26: Illustration of the method for estimating the stress jump necessary to

calculate the strain rate sensitivity.
54

Table 8: Parameters of fits plotted in Figure 27.

Specimen m0 m1 m2 m3 RSD

◦C

C65 FL 0.007583 8.1±1.3 645.1±25.5 0.142±0.022 0.004

C80 FL L 0.004700 6.4±2.9 632.0±95.8 0.158±0.073 0.013

C128 0.008800 3.2±5.4 699.9±1392.3 0.200±0.750 0.027

HH FL 1 NA NA±NA NA±NA NA±NA NA

C53BA NA NA±NA NA±NA NA±NA NA

C132 NA NA±NA NA±NA NA±NA NA

C40 C2M IW 0.007000 10.4±1.0 608.6±7.8 0.090±0.004 0.003

N8 C1B1A 0.006646 8.2±3.4 599.6±40.5 0.064±0.012 0.007

C10 C1M FL 0.005650 15.0±1.6 648.9±7.4 0.159±0.010 0.005

NA: not available, data not calculated

D.5 Calculation of the strain-hardening parameters

The five parameters for the strain-hardening model, k1, k2, k3, k4, and n, Eq. (10),

were calculated by a non-linear least-squares regression of the entire set of fortythree stress-strain curves comprising about 32 000 individual points, using the R

statistical language [52], version 2.11, function nls with the “port” algorithm.

The parameters of the fit were constained:

Temperature range: (300 ≤ T ≤ 800)

◦C,

Strain-rate range: 3.30 × 10−5 <  < ̇ 1.35 × 10−4,

1 ≤ k1 ≤ 10,

(100 ≤ k2 ≤ 1000)

◦C

(100 ≤ k3 ≤ 2000) MPa,

200 ≤ k4 ≤ 1500.

200 ≤ n ≤ 1500.

The fit did not approach the constraints. The individual curves used are identified

in Table 6 by the entry “lm.” The data set excluded the Fy = 100 ksi steel (C10) because this steel is not common in building construction. Although Table 6 reports

all the tests, some of which replicated conditions, only one temperature condition

was used for each specimen, to avoid biasing the results toward one specific condition. The individual stress-strain curves did not, however, contain equal numbers

of stress-strain pairs, so a small bias may exist toward the stress-strain curves with

the most individual points. In fitting the parameters, the strain data were limited
55

T /°C

m

0.00

0.05

0.10

0.15

0 200 400 600

C65_FL

0 200 400 600

C80_FL_L

0 200 400 600

C128

0.00

0.05

0.10

0.15

HH_FL_1 C53BA C132

0.00

0.05

0.10

0.15

C40_C2M_IW N8_C1B1A C10_C1M_FL

Figure 27: Dependence of the strain-rate sensitivity, m, on temperature. Solid lines

are the fits of Eq. (9).

to the range (0.01 <  < 0.15. When the maximum strain was less than the upper limit, the maximum strain was used. Choosing this upper limit constrained the

fit to regions where the stress-strain data was appropriate to fire modeling. The

retained strength, R, Eq. (1) was computed for each temperature using the values

in Table 3. The measured room-temperature yield strength, S

0

y

, was used for each

the steel. The effect of strain rate was included via the expression for the strain

rate sensitivity, Eq. (9), with the parameters for the mi summarized in Table 3. Table 9 summarizes the output of that regression. Note that the elastic modulus is not

relevant in the regression, because the strain range only includes plastic strain.
56

Parameter Estimate Standard Error t

k1 8.29390 0.07215 114.95378

k2 537.64846 0.42718 1258.59509

k3 959.43380 7.74224 123.92201

k4 0.76632 0.01457 52.59578

n 0.48337 0.00212 227.71218

RSD: 30.09051 on 32252 degrees of freedom

Table 9: Output from the regression to determine the strain-hardening parameters

for Eq (7).

Figure 28 corresponds to Figure 6, except that it plots the absolute deviation,

Da

Da = ˆσ − σ (16)

of the global fit to the steel data, Eq. (7). The model is only evaluated for the plastic

strain:  > Sy/E. The largest deviation is about 100 MPa, and it is typically less

than 50 MPa.

The large absolute deviations at small strain are caused by the difference between the elastic behavior as modeled, and the low-strain behavior in the individual tests. The poorest overall agreement of the model with the data is around

T = 300 ◦C. This region is also where the spread in the retained yield strength, R,

is the largest, Figure 2. It is also the region in which dynamic strain aging (DSA)

effects are most prevalent in steels [53, 54].

E Literature Data

E.1 Descriptions of steels from the literature used in this report

This report uses data assembled from many literature sources. In many cases the

data were taken from tables in the individual references, but in others they were

digitized directly from plots. This section summarizes the data sources. Table 10

compiles all the literature data used in creating the plots and conclusions of this

report. This section also summarizes some of the other notable studies [5, 13, 21,

55–57] on high-temperature stress-strain behavior of structural steel that do not

appear in plots or Table 10, typically because they were obtained at unconventional

strain rates.

E.1.1 Brockenbrough

Year: 1968

Reference: [58]
57

Steel description Data for ASTM A36, and four grades of United States Steel

structural steels: T1, COR-TEN, TRI-TEN, and MAN-TEN (ASTM A440). T1

was a quenched-and-tempered construction steel with Fy = 100 ksi, supplied to

ASTM A514, “High-Yield-Strength, Quenched and Tempered Alloy Steel Plate,

Suitable for Welding.” COR-TEN steels were intended as steels with improved

atmospheric corrosion resistance, and could be supplied to ASTM A242 “ HighStrength Low-Alloy Structural Steel” and ASTM A588 “ High-Strength LowAlloy Structural Steel, up to 50 ksi [345 MPa] Minimum Yield Point, with Atmospheric Corrosion Resistance.” TRI-TEN was a high-strength low-alloy steel with

True strain

Absolute deviation /MP

a

-200

-100

0

100

200

0.00 0.10 0.20

 226 MPa C65_FL

0.00 0.10 0.20

 233 MPa C80_FL_L

0.00 0.10 0.20

 234 MPa C128

-200

-100

0

100

200

 362 MPa HH_FL_1 386 MPa C53BA 406 MPa C132

-200

-100

0

100

200

 436 MPa C40_C2M_IW 473 MPa N8_C1B1A T /°C

20

300

400

431

500

539

600

647

650

701

Figure 28: Absolute deviation, Da between true stress predicted by Eq. (7), σˆ, and

the measured stress, σ.
58

Fy ==50 ksi, that was produced to ASTM A441 “High-strength low alloy Structural Manganese Vanadium Steel.” That standard was withdrawn and replaced by

ASTM A572 in 1988. ASTM A440, “High Strength Structural Steel” was another

Fy = 50 ksi steel intended to “provide high strength at a price slightly less than

that of TRI-TEN steel” [58] was withdrawn in 1979 without replacement.

Notes Data for the USS grades appear in Holt [26, 27], Sections E.1.8 and E.1.9.

E.1.2 Borvik

Year: 2005

Reference: [55]

T range: (20 ≤ T ≤ 500)

◦C

Chemistry: C 0.08 Si 0.26 Mn 1.40 S 0.002 P 0.008 Nb 0.028 V 0.04 Ti 0.01 Cr

0.02 Ni 0.04 Mo 0.007 N 0.006 Al 0.032

Steel description Weldox 460 E is a thermomechanically rolled, weldable, finegrained t = 12 mm plate with V, Nb, Ti. The minimum Fy = 460 MPa.

Notes The manuscript describes tests to establish impact properties, but contains low strain-rate data. High-rate tests were conducted in a split-Hopkinson

bar test machine. The strain-rate sensitivity, m, is based on the measured stress

σ at  = 0.02. Figure 8 in the manuscript [55] shows stress-strain behavior at

 ̇ = 5 × 10−4 1/s. The report only presents data for the effect of strain rate on

stress measured at e = 0.02, and not for the effect of strain rate on the yield

strength, Sy. It shows no stress-strain curves for low-rate tests.

E.1.3 Chen

Year: 2006

Reference: [23]

T range: (22 ≤ T ≤ 940) ◦C

Chemistry: C 0.22 Si 0.55 Mn 1.7 P 0.04 S 0.03 Cr 0.30 Ni 0.5 Cu 0.4

Steel description Chen et al. describe the steel as “XLERPLATE Grade 350”

which is delivered to Australian AS3678 (“Structural Steel–Hot-rolled plates, floor

plates, and slabs”). Specimens were fabricated from t = 5 mm plate.

Notes The manuscript contains test results, but not stress-strain curves, for hightemperature tensile tests conducted at  ̇ = 1 × 10−4 1/s. It also contains results

temperature-ramp tests, in which the load is held constant while the temperature

is increased. In addition to the data for AS3678, the manuscript also reports data

for a high-strength steel, with Sy(0.002 offset)=780 MPa. The manuscript reports

strength reductions for other yield strengths, up to e = 0.02.
59

E.1.4 Chijiiwa

Year: 1993

Reference: [24]

T range: (20 ≤ T ≤ 700)

◦C

Chemistry: NA

Steel description The conventional steel was a Japanese SM490A steel plate.

SM490A is delivered to JIS G 3106 “Rolled steel for welded structures.” The

“490” in SM490A refers to the minimum tensile strength in MPa. The minimum

yield strength is Fy = 325 MPa. JIS G 3106 specifies composition limits for C,

Si, Mn, P, and S, and “an alloying element other than the above-mentioned can be

added as needed.”

Notes The manuscript compares conventional SM490A steel to fire-resistive steel

designed to meet the SM490A standard. In addition to high-temperature tensile

test results, the manuscript also contains creep data and microstructural analysis. The fire-resistive steel tensile tests were conducted to the Japanese hightemperature tensile test standard [37] JIS G 0567, which prescribes a strain rate,

 ̇ = 0.00005 1/s. Presumably the conventional steel tests were also conducted to

that standard. The manuscript contains only plots of retained strength, and does

not show stress-strain curves.

E.1.5 Fujimoto

Year: 1980

Reference: [56]

T range: (20 ≤ T ≤ 600)

◦C

Chemistry: C 0.18 Mn 0.73 Si 0.24 P 0.016 S 0.017

Steel description The steel is a Japanese SS41, t = 25 mm plate. SS41 is structural steel plate delivered to Standard JIS 3101, “Rolled Steels for general structure.” The “41” refers to the minimum tensile strength measured in kg/mm2

. The

minimum yield point is Fy = 285 MPa. A recent version of JIS G 3101 set composition limits for P and S only.

Notes Figure 5 in the manuscript shows tensile stress-strain curves conducted to

 = 0.03 in the range, but lacks evidence for any specific strain rate.

E.1.6 Gowda

Year: 1978

Reference: [25]

T range: (25 ≤ T ≤ 927)

◦C

Chemistry: C 0.13 Mn 0.82 Si 0.21 P 0.014 S 0.006
60

Steel description The steel was ASME SA 516 pressure vessel plate for moderate-temperature service from a t = 9.5 mm plate. This steel is specified to

have a minimum yield strength Fy = 207 MPa. ASME SA 516 is equivalent to

ASTM A516, “Standard specification for Pressure Vessel Plates, Carbon Steel, for

Moderate- and Lower-Temperature Service.”

Notes The strain rate sensitivity calculated was based on the tensile strength, T S.

The manuscript contains a long data table of all the tensile test results as well as

stress-strain curves for low-strain and higher strain as Figures 2 and 3.

E.1.7 Harmathy

Year: 1970

Reference: [13]

T range: (20 ≤ T ≤ 650)

◦C

Chemistry: A36: C 0.19 Mn 0.71 Si 0.09 P 0.007 S 0.03

Chemistry: CSA G40.12: C 0.195 Mn 1.4 Si 0.022 Cu 0.08 Ni 0.08 Cr 0.01

Steel description The ASTM A36 is described as Si semi-killed, open-hearth,

hot-rolled t = 12.7 mm. The Canadian CSA G 40.12 is described as Si semikilled, basic oxygen process, hot-rolled t = 12.7 mm plate. Canadian standard

CSA G 40.12, “General Purpose Structural Steel,” has a specified yield strength

Fy = 44 ksi. [59].

Notes The manuscript contains graphs of full stress-strain curves (Figure 3) as

well as creep curves. Tensile tests were conducted at a single strain rate, which is

higher than typical high-temperature tensile test rates. In addition, the manuscript

contains data for ASTM A 421 pre-stressing steel, at three different strain rates.

E.1.8 Holt

Year: Unknown

Reference: [27]

T range: (27 ≤ T ≤ 1038)

◦C

Chemistry: C 0.17 Mn 0.86 Cu 0.03 Ni 0.03 Cr 0.46 Mo 0.19 V 0.040

Steel description USS T-1A, ASTM A514 quenched and tempered. See further

description under Brockenbrough, Section E.1.1.

Notes The manuscript is an undated technical report from United States Steel,

Corp. Tests were conducted according to ASTM E21-58T, so  ̇ = 8.33 × 10−5 1/s.

The manuscript also contains data for USS T1, which appear in Brockenbrough

[58], Figure 1.5.
61

E.1.9 Holt

Year: 1964

Reference: [26]

T range: (27 ≤ T ≤ 1038)

◦C

Chemistry: A36: C 0.24 Mn 0.96 P 0.011 S 0.027 Si 0.043 Cu 0.058

Chemistry: Cor-ten t = 70 mm: C 0.17 Mn 1.00 P 0.018 S 0.030 Si 0.22 Ni 0.022

Cr 0.48 V 0.042 Cu 0.3

Chemistry: Tri-ten t = 12.7 mm: C 0.20 Mn 1.09 P 0.054 S 0.025 Si 0.025 V 0.038

Cu 0.26 N 0.005

Chemistry: Tri-ten t = 25 mm: C 0.20 Mn 1.16 P 0.016 S 0.035 Si 0.04 Ni 0.015

Cr 0.035 N 0.006 V 0.056 Cu 0.22

Chemistry: Tri-Ten t = 50 mm: C 0.21 Mn 1.25 P 0.017 S 0.028 Si 0.09 Ni 0.028

Cr 0.064 N 0.006 V 0.056 Cu 0.25

Chemistry: A440 t = 12.7 mm: C 0.29 Mn 1.54 P 0.026 S 0.038 Si 0.05 Cu 0.31

Chemistry: A440 t = 50 mm: C 0.20 Mn 1.60 P 0.017 S 0.018 Si 0.20 N 0.006

Cu 0.23

Chemistry: A440 t = 25 mm: C 0.26 Mn 1.48 P 0.017 S 0.036 Si 0.035 N 0.007

Cu 0.24

Steel description The steels were plates of different thicknesses, t, of USS CorTen, Tri-Ten and ASTM A440 and ASTM A36 steels. Cor-ten is a weathering

steel. See other description under Brockenbrough, Section E.1.1.

Notes This manuscript is an unpublished US Steel technical report. Much of

the data in this USS Technical Report appear in Spaeder [34], Sec. E.1.22, and

were identified by comparing the chemistry and plate thicknesses. In addition,

Brockenbrough [58], Sec. E.1.1, Fig.1.5 shows the average values for the steels.

The report shows only retained strengths, and no stress-strain curves.

E.1.10 Hu

Year: 2009

Reference: [40]

T range: (20 ≤ T ≤ 800)

◦C

Chemistry: NA

Steel description The steel was taken from the web of a W30x99 shape supplied

to ASTM A992 (‘Standard Specification for Structural Steel Shapes”) structural

steel.

Notes The manuscript contains the stress-strain behavior out to failure as well as

expanded views up to e = 0.1. The tests employed two rates, both of which are
62

greater than the standard ASTM E21 test rate. Tests also included determination

of the static yield strength via a load-relaxation method.

E.1.11 Jerath

Year: 1980

Reference: [5]

T range: (20 ≤ T ≤ 800)

◦C

Chemistry: see manuscript

Steel description The manuscript describes fifteen different structural steels produced by the British Steel and supplied to BS4360 (“Weldable Structural Steels.”)

Grades 43A, 43E, 50B, and 50D, as well as several other steels.

Notes This report does not appear in any library. Tests were conducted at a strain

rate  ̇ = 2.78 × 10−4 1/s, which is higher than the usual testing rate. For each steel,

a page describes the chemistry, and tabulates the retained yield and tensile strength,

the reduction of area and elongation for temperatures up to 800 ◦C and sometimes

1000 ◦C. No stress-strain curves are shown.

E.1.12 Kirby

Year: 1988

Reference: [18]

T range: (20 ≤ T ≤ 700)

◦C

Chemistry: NA

Steel description British BS4360 Grade 50B from flanges of notch-tough structural sections. Specification BS4360, “Weldable Structural Steels” was the common structural steel specification in Britain at the time.

Notes The manuscript contains a figure that shows retained strength determined

from tensile tests, denoted as “steady-state conditions.” The manuscript also contains data for constant-load, ramping-temperature tests, denoted as “transient state

conditions.” The tensile tests were conducted according to the British standard

BS3688, which was superseded by BS EN 10002-5:1992 “Tensile testing of metallic materials. Method of test at elevated temperatures.” That standard re-quires

 ̇ = 5 × 10−5 1/s.

E.1.13 Kirby

Year: 1993

Reference: [60]

T range: (20 ≤ T ≤ 800)

◦C

Chemistry: BS15 9J/428/H t = 14 mm: C 0.14 Si 0.04 Mn 0.70 P 0.017 S 0.060

Cr 0.03 Ni 0.09 Cu 0.19 N 0.0046 Sn 0.087
63

Chemistry: BS15 OJ055/JFP t = 15.9 mm: C 0.21 Si 0.04 Mn 0.53 P 0.021 S 0.031

Cr 0.02 Ni 0.04 Cu 0.03 N 0.0028

Chemistry: BS15 OJ/072/J t = 25.4 mm: C 0.22 Si 0.04 Mn 0.53 P 0.055 S 0.037

Cr 0.03 Ni 0.04 Cu 0.02 N 0.0025

Chemistry: BS4360Gr43A NA

Steel description The manuscript reports data from three historical steels taken

from a structure built in 1939, and presumably supplied to BS15:1936 “Standard

Specification for Structural Steel for Bridges and General Building Construction,”

which only specified the tensile strength. These three steels were complemented

by three more modern steels supplied to BS4360:Grade 43A “Weldable Structural

Steels.” The three BS4360 steels were taken from 73 kg/m, 240 kg/m, and 54 kg/m

rolled sections.

Notes The data are also published in Ref. 28. Tests were conducted according to

the British standard BS3688. which was superseded by BS EN 10002-5:1992 “Tensile testing of metallic materials. Method of test at elevated temperatures.” That

test requires  ̇ = 5 × 10−5 1/s. The manuscript contains plots of various strength

measures as a function of temperature for the six steels. However,it is not explicit

on which steel is assigned which symbol in the figures. I have assigned them based

on their order in the data tables. No stress-strain curves are shown.

E.1.14 Li

Year: 2003

Reference: [21]

T range: (20 ≤ T ≤ 700)

◦C

Chemistry: NA

Steel description The manuscript describes the steel as “constructional steel

widely used in China. . . used in steel frameworks.”

Notes Tests were conducted at  ̇ = 6.7×10−4 1/s, which is about ten times higher

than rates specified in the usual high-temperature tensile standards. Even at this

high rate, the retained strength is somewhat low. The authors report an expression

for the retained yield and tensile strength that is only valid in the temperature range

of the tests, because it decreased to below zero at high temperature. The manuscript

also contains information for a low-carbon steel used for bolts.

E.1.15 Lou

Year: 1995

Reference: [29, 61]

T range: (20 ≤ T ≤ 300)

◦C
64

Chemistry: CSA G40.21 350 WT plate t = 12.7 mm C 0.19 Si 0.17 Mn 1.07

P 0.006 S 0.010 Cr 0.02 Ni 0.02 Cu 0.06 N 0.0042 V<0.01

Chemistry: CSA G40.21 350 AT plate t = 17.8 mm C 0.12 Si 0.22 Mn 1.12

P 0.007 S 0.009 Cr 0.42 Ni 0.37 Cu 0.27 N 0.0059 V 0.046

Steel description The authors described the steels as produced in fine-grain condition using fully killed steelmaking practice. The plate was supplied to Canadian

standard G40.21, “General Requirements for Rolled or Welded Structural Quality Steel/ Structural Quality Steel” The “W” denotes weldable. The “A” denotes

a high-strength-low-alloy steel with improved corrosion resistance. The “T” indicates that Charpy tests for toughness are required. The “350” denotes the yield

strength in units of MPa.

Notes Tensile tests were conducted over a two-decade strain rate range.

E.1.16 Manjoine

Year: 1944

Reference: [62]

T range: (20 ≤ T ≤ 600)

◦C

Steel description The manuscript describes the steel as “mild steel,” a commercial low-carbon open hearth steel annealed 1 h at 920 ◦C in dissociated ammonia.

Notes The manuscript contains stress-strain curves for the entire temperature

range at different strain rates, as well as graphical representation of the decrease

in strength with temperature. The data in included here primarily for historic

value, since this was one of the first determinations of the rate dependence of steel

strength.

E.1.17 Outinen

Year: 2001

Reference: [30]

T range: (20 ≤ T ≤ 950)

◦C

Chemistry: S355 NA

Steel description The steel is described as S355, which is a European EN SFSEn 10 025(1993) hotrolled t = 4 mm sheet. The report contains no microstructure

or chemistry information for the steel.

Notes Most of the yield and tensile strength data presented in the report, Tables 6

and 8, are derived from the so-called transient state tests, in which the specimen

is heated at constant temperature ramp rate under fixed load. The tensile tests

reported in Figure 12 are also summarized in Appendix 2 as distinct stress-strain
65

points. All the true tensile tests were conducted to EN 10 002-5, which prescribes

a strain rate,  ̇ = 5 × 10−5 1/s, though the report does not explicitly state this rate.

The report also contains data for steel from structural steel tubes and cold-rolled

steel sheet. The data calculated from temperature-ramp test, called “transient state

tests,” also were published in 1997 [19], and are not included here.

E.1.18 Poh

Year: 1998

Reference: [31]

T range: (20 ≤ T ≤ 800)

◦C

Chemistry: C 0.16 P 0.018 Mn 1.46 Si 0.15 S 0.006 Ni 0.003 Cr 0.009 Cu 0.013

Sn 0.002 Mo 0.003 V 0.004 Ti 0.001 Nb 0.001 Al 0.024

Steel description The steel, from a heavy, hot-rolled shape, was supplied to Australian standard AS3679.1 Grade 300, “Hot-rolled structural steel bars and sections.” Kotwal [63] describes Australian steel specifications in detail. Grade 300

designates the nominal specified minimum yield strength measured in MPa.

Notes The report is a very detailed Ph. D. thesis. It contains stress-strain curves

for the steels. Some of the material was later published in 2001 [45]. The 2001

paper contains a very detailed, 42-parameter model for representing the stressstrain curve as a function of temperature.

E.1.19 Sakumoto

Year: 1999

Reference: [32]

T range: (20 ≤ T ≤ 800)

◦C

Chemistry: NA

Steel description The steel was supplied to Japan JIS 3106 SM400A, hot-rolled

steel. JIS Standard 3106 is titled “Rolled steel for welded structures.” Grade SM

400A refers to the minimum tensile strength measured in N/mm2. The specified minimum yield strength is Fy = 245 N/mm2

. Takanashi [64] describes the

Japanese structural steel specifications in detail.

Notes The manuscript contains stress-strain curves up to e = 0.04 as a function

of temperature for steels SM400A, fire-resistive steel NSFR400A, and SUS304, an

austenitic stainless steel. The testing rate  ̇ = 5 × 10−5 1/s is inferred from the

citation of Japanese tensile test standard, JIS G 0567 [37].

E.1.20 Skinner

Year: 1973
66

Reference: [33]

T range: (20 ≤ T ≤ 650)

◦C

Chemistry: NA

Steel description The steel was supplied to Australian AS A186:250 steel “Structural Steels (Ordinary Weldable Grades.” Kotwal [63] describes the Australian

steel grades in greater detail, and indicates that A186:250 was intended to be similar to ASTM A36. The “250” refers to the nominal specified yield strength, Fy,

measured in MPa.

Notes The manuscript contains much of the information that appears in a BHP

report [6]. Skinner includes includes data for for five different structural steels, but

only stress-strain curves for the A186 steel. The manuscript also contains graphic

representation of the decrease in strength with temperature, the effect of strain rate

on strength and temperature, creep curves, and constant-load temperature-ramp test

data.

The actual values for stress and strain in Figure 11 of this report were taken

from the tables in the BHP report [6]

E.1.21 Smith, ASTM DS11

Year: 1970

Reference: [2]

T range: (21 ≤ T ≤ 1038)

◦C

Chemistry: see manuscript

Steel description This ASTM report contains data for 37 different plate materials for pressure vessels, supplied to ASTM Standards A201, A212, A285, A299,

A442, A515, and A516.

Notes The report is a supplement to ASTM STP 180 [65], often called DS 11.

Relatively little data are reported for T > 538 ◦C. It also contains extensive data

tables that summarize the chemistry and processing of the steels, but does not show

any stress-strain curves. Because the report is essentially a table of data, it is unethical to simply reprint the table here. Figure 29 replots the data from the report

on the same scale with the same overlays as Figure 2. Although the fit to Eq. (1)

represents the data reasonably well, unlike the structural steel data, some of the

data drop below the R = 0.5 line at 538 ◦C. The report also contains a similar

quantity of data obtained on the same grades made into tubes, as well as some data

from wrought bar. None of the data from the report are used in the analysis of this

report, however.
67

T /°C

R

0.0

0.2

0.4

0.6

0.8

1.0

0 200 400 600 800 1000

R= 0.5

538 °C

Grade

A201

A212

A285

A299

A442

A515

A516

Figure 29: Normalized, retained yield strength,R, as a function of temperature for

different ASTM grades of pressure vessel steels reported in Ref. [2] Table III-P.

The strength is the 0.2 % offset yield strength, Sy(0.002 offset) normalized to its

room-temperature value. Solid lines have the same meaning as in Figure 2.

E.1.22 Spaeder

Year: 1977

Reference: [34]

T range: (27 ≤ T ≤ 649)

◦C

Chemistry: see manuscript

Steel description The manuscript contains data for eight different USS Cor-ten

A and Cor-ten B weathering steels. Both production and experimental heats are

included.

Notes Some data from this paper also appear also appear in Holt [26]. The

manuscript contains excellent data tables for test results and chemistry, but no

stress-strain curves. The identification of the plate thicknesses allowed correlation with the data in Holt [26]. Strain rates were assigned based on reference to

ASTM E21 [11],  ̇ = 8.33 × 10−5 1/s. .
68

E.1.23 Stevens

Year: 1971

Reference: [6]

T range: (27 ≤ T ≤ 650)

◦C

Chemistry: NA

Steel description The report contains extensive data for four Australian structural steels: AS A186:250 L0, AS A186:250, AS187:WR350/1, and AS A186:400

L15. Kotwal [63] describes Standard AS A186 “Structural Steel-Ordinary Weldable Grades” as an omnibus specification similar to ASTM A36. The numerical

designations 250 and 400 refer to the minimum yield stress measured in MPa,

rounded to the nearest 50 MPa. The designations “L0” and “L15” referred to additional Charpy test requirements for T = 0 ◦C and T = −15 ◦C. AS A187, “Structural Steels-Weather-resistant Weldable Grades,” was a specification for weathering steels supplied by BHP as their “AUS-TEN” series. Again, the designation 350

referred to the yield strength in MPa, rounded to the nearest 50 MPa. The “/1”

identified the lower carbon variant: maximum C=0.12 % mass fraction.

Notes Information about the steels was correlated by comparing the steel descriptions to those in Skinner [33]. This report contains data for AS A186:250 steel that

Skinner [33] published later. Tables of stress and fixed strain points are included

for all four steels.

E.1.24 United States Steel 1972 elevated temperature handbook

Year: 1968

Reference: [35]

T range: A36: (27 ≤ T ≤ 704) ◦C

Chemistry: A36: NA

T range: A514: (27 ≤ T ≤ 1038) ◦C

Chemistry: A514: C 0.14 Mn 0.76 Cu 0.3 Ni 0.86 Cr 0.55 Mo 0.45 V 0.03

Steel description ASTM A36 Steel, from United States Steel. It is not the same

A36 steel that appears in Holt [26] and Brockenbrough [58], see Sections E.1.9 and

E.1.1, based on examination of retained strengths and temperature increments. The

A514 steel is USS T1 Steel, quenched-and-tempered steel plate. Its chemistry was

not specified in the report, but was assigned based on comparison with data from

Holt [27], which contains graphical and tabular data, but not stress-strain curves.

Notes The introduction to the report states that tests were conducted to ASTM

E21, so  ̇ = 8.33 × 10−5 1/s. The report contains retained strengths, and not stressstrain curves.
69

E.2 Tabular data for the literature structural steels

Table 10 summarizes the mechanical property data taken from the literature sources,

that appear in Figures 2, 7, 5, and 36.

Table 10: Data for structural steels from literature sources.

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[23] E.1.3 AS3678 XLERPlate 22 1.00 × 10−4 401 465

[23] E.1.3 AS3678 XLERPlate 60 1.00 × 10−4 385 446

[23] E.1.3 AS3678 XLERPlate 120 1.00 × 10−4 381 446

[23] E.1.3 AS3678 XLERPlate 150 1.00 × 10−4 377 446

[23] E.1.3 AS3678 XLERPlate 180 1.00 × 10−4 369 446

[23] E.1.3 AS3678 XLERPlate 240 1.00 × 10−4 361 488

[23] E.1.3 AS3678 XLERPlate 300 1.00 × 10−4 381 516

[23] E.1.3 AS3678 XLERPlate 360 1.00 × 10−4 345 484

[23] E.1.3 AS3678 XLERPlate 410 1.00 × 10−4 361 479

[23] E.1.3 AS3678 XLERPlate 460 1.00 × 10−4 325 432

[23] E.1.3 AS3678 XLERPlate 540 1.00 × 10−4 313 400

[23] E.1.3 AS3678 XLERPlate 600 1.00 × 10−4 285 344

[23] E.1.3 AS3678 XLERPlate 660 1.00 × 10−4 225 256

[23] E.1.3 AS3678 XLERPlate 720 1.00 × 10−4 140 144

[23] E.1.3 AS3678 XLERPlate 830 1.00 × 10−4 60 60

[23] E.1.3 AS3678 XLERPlate 940 1.00 × 10−4 36 40

[24] E.1.4 SMA490 20 5.00 × 10−5 334 NA

[24] E.1.4 SMA490 100 5.00 × 10−5 321 NA

[24] E.1.4 SMA490 200 5.00 × 10−5 271 NA

[24] E.1.4 SMA490 300 5.00 × 10−5 229 NA

[24] E.1.4 SMA490 400 5.00 × 10−5 217 NA

[24] E.1.4 SMA490 500 5.00 × 10−5 188 NA

[24] E.1.4 SMA490 600 5.00 × 10−5 117 NA

[24] E.1.4 SMA490 700 5.00 × 10−5 56 NA

[25] E.1.6 ASME-SA516 25 1.00 × 10−4 307 319

[25] E.1.6 ASME-SA516 25 1.00 × 10−4 297 NA

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
70

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[25] E.1.6 ASME-SA516 315 1.00 × 10−4 208 328

[25] E.1.6 ASME-SA516 315 1.00 × 10−4 208 NA

[25] E.1.6 ASME-SA516 427 1.00 × 10−4 192 289

[25] E.1.6 ASME-SA516 427 1.00 × 10−4 192 NA

[25] E.1.6 ASME-SA516 537 1.00 × 10−4 164 215

[25] E.1.6 ASME-SA516 537 1.00 × 10−4 169 NA

[25] E.1.6 ASME-SA516 649 1.00 × 10−4 107 121

[25] E.1.6 ASME-SA516 649 1.00 × 10−4 108 NA

[25] E.1.6 ASME-SA516 760 1.00 × 10−4 38 41

[25] E.1.6 ASME-SA516 760 1.00 × 10−4 40 NA

[25] E.1.6 ASME-SA516 815 1.00 × 10−4 34 NA

[25] E.1.6 ASME-SA516 815 1.00 × 10−4 40 NA

[25] E.1.6 ASME-SA516 871 1.00 × 10−4 35 NA

[25] E.1.6 ASME-SA516 871 1.00 × 10−4 38 NA

[25] E.1.6 ASME-SA516 927 1.00 × 10−4 26 NA

[25] E.1.6 ASME-SA516 927 1.00 × 10−4 30 NA

[25] E.1.6 ASME-SA516 25 5.00 × 10−3 308 NA

[25] E.1.6 ASME-SA516 315 5.00 × 10−3 221 NA

[25] E.1.6 ASME-SA516 427 5.00 × 10−3 205 NA

[25] E.1.6 ASME-SA516 537 5.00 × 10−3 179 NA

[25] E.1.6 ASME-SA516 537 5.00 × 10−3 187 NA

[25] E.1.6 ASME-SA516 649 5.00 × 10−3 138 NA

[25] E.1.6 ASME-SA516 649 5.00 × 10−3 141 NA

[25] E.1.6 ASME-SA516 760 5.00 × 10−3 62 NA

[25] E.1.6 ASME-SA516 760 5.00 × 10−3 66 NA

[25] E.1.6 ASME-SA516 871 5.00 × 10−3 49 NA

[25] E.1.6 ASME-SA516 871 5.00 × 10−3 52 NA

[25] E.1.6 ASME-SA516 25 1.00 × 10−1 339 NA

[25] E.1.6 ASME-SA516 315 1.00 × 10−1 244 NA

[25] E.1.6 ASME-SA516 427 1.00 × 10−1 204 NA

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
71

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[25] E.1.6 ASME-SA516 537 1.00 × 10−1 198 NA

[25] E.1.6 ASME-SA516 537 1.00 × 10−1 200 NA

[25] E.1.6 ASME-SA516 649 1.00 × 10−1 166 NA

[25] E.1.6 ASME-SA516 649 1.00 × 10−1 169 NA

[25] E.1.6 ASME-SA516 760 1.00 × 10−1 82 NA

[25] E.1.6 ASME-SA516 760 1.00 × 10−1 83 NA

[25] E.1.6 ASME-SA516 871 1.00 × 10−1 67 NA

[25] E.1.6 ASME-SA516 871 1.00 × 10−1 67 NA

[26] E.1.9 A36 27 8.33 × 10−5 248 NA

[26] E.1.9 A36 93 8.33 × 10−5 228 NA

[26] E.1.9 A36 204 8.33 × 10−5 239 NA

[26] E.1.9 A36 316 8.33 × 10−5 216 NA

[26] E.1.9 A36 427 8.33 × 10−5 219 NA

[26] E.1.9 A36 538 8.33 × 10−5 181 NA

[26] E.1.9 A36 649 8.33 × 10−5 90 NA

[26] E.1.9 A36 760 8.33 × 10−5 50 NA

[26] E.1.9 A36 871 8.33 × 10−5 37 NA

[26] E.1.9 A36 1038 8.33 × 10−5 11 NA

[26] E.1.9 A440 27 8.33 × 10−5 414 NA

[26] E.1.9 A440 93 8.33 × 10−5 414 NA

[26] E.1.9 A440 204 8.33 × 10−5 442 NA

[26] E.1.9 A440 316 8.33 × 10−5 436 NA

[26] E.1.9 A440 427 8.33 × 10−5 396 NA

[26] E.1.9 A440 538 8.33 × 10−5 332 NA

[26] E.1.9 A440 649 8.33 × 10−5 185 NA

[26] E.1.9 A440 760 8.33 × 10−5 61 NA

[26] E.1.9 A440 871 8.33 × 10−5 27 NA

[26] E.1.9 A440 1038 8.33 × 10−5 9 NA

[26] E.1.9 A440 27 8.33 × 10−5 341 NA

[26] E.1.9 A440 93 8.33 × 10−5 318 NA

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
72

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[26] E.1.9 A440 204 8.33 × 10−5 309 NA

[26] E.1.9 A440 316 8.33 × 10−5 310 NA

[26] E.1.9 A440 427 8.33 × 10−5 276 NA

[26] E.1.9 A440 538 8.33 × 10−5 247 NA

[26] E.1.9 A440 649 8.33 × 10−5 112 NA

[26] E.1.9 A440 760 8.33 × 10−5 37 NA

[26] E.1.9 A440 871 8.33 × 10−5 17 NA

[26] E.1.9 A440 1038 8.33 × 10−5 11 NA

[26] E.1.9 A440 27 8.33 × 10−5 334 NA

[26] E.1.9 A440 93 8.33 × 10−5 313 NA

[26] E.1.9 A440 204 8.33 × 10−5 314 NA

[26] E.1.9 A440 316 8.33 × 10−5 322 NA

[26] E.1.9 A440 427 8.33 × 10−5 292 NA

[26] E.1.9 A440 538 8.33 × 10−5 272 NA

[26] E.1.9 A440 649 8.33 × 10−5 157 NA

[26] E.1.9 A440 760 8.33 × 10−5 73 NA

[26] E.1.9 A440 871 8.33 × 10−5 42 NA

[26] E.1.9 A440 1038 8.33 × 10−5 14 NA

[26] E.1.9 Cor-Ten 27 8.33 × 10−5 354 NA

[26] E.1.9 Cor-Ten 760 8.33 × 10−5 62 NA

[26] E.1.9 Cor-Ten 871 8.33 × 10−5 43 NA

[26] E.1.9 Cor-Ten 1038 8.33 × 10−5 13 NA

[26] E.1.9 Cor-Ten 27 8.33 × 10−5 318 NA

[26] E.1.9 Cor-Ten 93 8.33 × 10−5 302 NA

[26] E.1.9 Cor-Ten 204 8.33 × 10−5 300 NA

[26] E.1.9 Cor-Ten 316 8.33 × 10−5 291 NA

[26] E.1.9 Cor-Ten 427 8.33 × 10−5 273 NA

[26] E.1.9 Cor-Ten 538 8.33 × 10−5 221 NA

[26] E.1.9 Cor-Ten 649 8.33 × 10−5 130 NA

[26] E.1.9 Cor-Ten 760 8.33 × 10−5 54 NA

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
73

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[26] E.1.9 Cor-Ten 871 8.33 × 10−5 36 NA

[26] E.1.9 Cor-Ten 1038 8.33 × 10−5 22 NA

[26] E.1.9 Tri-Ten 27 8.33 × 10−5 364 NA

[26] E.1.9 Tri-Ten 93 8.33 × 10−5 319 NA

[26] E.1.9 Tri-Ten 204 8.33 × 10−5 297 NA

[26] E.1.9 Tri-Ten 316 8.33 × 10−5 267 NA

[26] E.1.9 Tri-Ten 427 8.33 × 10−5 252 NA

[26] E.1.9 Tri-Ten 538 8.33 × 10−5 205 NA

[26] E.1.9 Tri-Ten 649 8.33 × 10−5 121 NA

[26] E.1.9 Tri-Ten 760 8.33 × 10−5 50 NA

[26] E.1.9 Tri-Ten 871 8.33 × 10−5 30 NA

[26] E.1.9 Tri-Ten 1038 8.33 × 10−5 12 NA

[26] E.1.9 Tri-Ten 27 8.33 × 10−5 325 NA

[26] E.1.9 Tri-Ten 93 8.33 × 10−5 312 NA

[26] E.1.9 Tri-Ten 204 8.33 × 10−5 281 NA

[26] E.1.9 Tri-Ten 316 8.33 × 10−5 278 NA

[26] E.1.9 Tri-Ten 427 8.33 × 10−5 254 NA

[26] E.1.9 Tri-Ten 538 8.33 × 10−5 192 NA

[26] E.1.9 Tri-Ten 649 8.33 × 10−5 126 NA

[26] E.1.9 Tri-Ten 760 8.33 × 10−5 58 NA

[26] E.1.9 Tri-Ten 871 8.33 × 10−5 32 NA

[26] E.1.9 Tri-Ten 1038 8.33 × 10−5 11 NA

[26] E.1.9 Tri-Ten 27 8.33 × 10−5 321 NA

[26] E.1.9 Tri-Ten 93 8.33 × 10−5 306 NA

[26] E.1.9 Tri-Ten 204 8.33 × 10−5 288 NA

[26] E.1.9 Tri-Ten 316 8.33 × 10−5 283 NA

[26] E.1.9 Tri-Ten 427 8.33 × 10−5 268 NA

[26] E.1.9 Tri-Ten 538 8.33 × 10−5 212 NA

[26] E.1.9 Tri-Ten 649 8.33 × 10−5 128 NA

[26] E.1.9 Tri-Ten 760 8.33 × 10−5 55 NA

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
74

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[26] E.1.9 Tri-Ten 871 8.33 × 10−5 31 NA

[26] E.1.9 Tri-Ten 1038 8.33 × 10−5 12 NA

[27] E.1.8 USS T1a 27 8.30 × 10−5 816 NA

[27] E.1.8 USS T1a 93 8.30 × 10−5 779 NA

[27] E.1.8 USS T1a 204 8.30 × 10−5 723 NA

[27] E.1.8 USS T1a 316 8.30 × 10−5 671 NA

[27] E.1.8 USS T1a 427 8.30 × 10−5 634 NA

[27] E.1.8 USS T1a 538 8.30 × 10−5 514 NA

[27] E.1.8 USS T1a 649 8.30 × 10−5 198 NA

[27] E.1.8 USS T1a 760 8.30 × 10−5 66 NA

[27] E.1.8 USS T1a 871 8.30 × 10−5 43 NA

[27] E.1.8 USS T1a 1038 8.30 × 10−5 18 NA

[18] E.1.12 BS4360 Gr 50B 20 5.00 × 10−5 395 422

[18] E.1.12 BS4360 Gr 50B 100 5.00 × 10−5 367 401

[18] E.1.12 BS4360 Gr 50B 200 5.00 × 10−5 336 422

[18] E.1.12 BS4360 Gr 50B 300 5.00 × 10−5 300 414

[18] E.1.12 BS4360 Gr 50B 400 5.00 × 10−5 284 389

[18] E.1.12 BS4360 Gr 50B 500 5.00 × 10−5 239 300

[18] E.1.12 BS4360 Gr 50B 600 5.00 × 10−5 160 186

[18] E.1.12 BS4360 Gr 50B 700 5.00 × 10−5 83 97

[28] E.1.13 BS15 9J/428/J (dt) 20 5.00 × 10−5 258 259

[28] E.1.13 BS15 9J/428/J (dt) 100 5.00 × 10−5 235 281

[28] E.1.13 BS15 9J/428/J (dt) 150 5.00 × 10−5 250 316

[28] E.1.13 BS15 9J/428/J (dt) 200 5.00 × 10−5 257 323

[28] E.1.13 BS15 9J/428/J (dt) 250 5.00 × 10−5 198 NA

[28] E.1.13 BS15 9J/428/J (dt) 300 5.00 × 10−5 192 288

[28] E.1.13 BS15 9J/428/J (dt) 400 5.00 × 10−5 189 NA

[28] E.1.13 BS15 9J/428/J (dt) 500 5.00 × 10−5 167 215

[28] E.1.13 BS15 9J/428/J (dt) 600 5.00 × 10−5 94 109

[28] E.1.13 BS15 9J/428/J (dt) 700 5.00 × 10−5 48 47

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
75

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[28] E.1.13 BS15 9J/428/J (dt) 800 5.00 × 10−5 29 32

[28] E.1.13 BS15- OJ/055/JFP (ob) 20 5.00 × 10−5 230 274

[28] E.1.13 BS15- OJ/055/JFP (ob) 100 5.00 × 10−5 218 287

[28] E.1.13 BS15- OJ/055/JFP (ob) 150 5.00 × 10−5 221 324

[28] E.1.13 BS15- OJ/055/JFP (ob) 200 5.00 × 10−5 219 335

[28] E.1.13 BS15- OJ/055/JFP (ob) 250 5.00 × 10−5 166 320

[28] E.1.13 BS15- OJ/055/JFP (ob) 300 5.00 × 10−5 159 301

[28] E.1.13 BS15- OJ/055/JFP (ob) 400 5.00 × 10−5 151 270

[28] E.1.13 BS15- OJ/055/JFP (ob) 500 5.00 × 10−5 136 186

[28] E.1.13 BS15- OJ/055/JFP (ob) 600 5.00 × 10−5 78 92

[28] E.1.13 BS15- OJ/055/JFP (ob) 700 5.00 × 10−5 40 43

[28] E.1.13 BS15- OJ/055/JFP (ob) 800 5.00 × 10−5 29 32

[28] E.1.13 BS15 OJ/072/J (ut) 20 5.00 × 10−5 217 314

[28] E.1.13 BS15 OJ/072/J (ut) 100 5.00 × 10−5 201 319

[28] E.1.13 BS15 OJ/072/J (ut) 150 5.00 × 10−5 218 379

[28] E.1.13 BS15 OJ/072/J (ut) 175 5.00 × 10−5 215 377

[28] E.1.13 BS15 OJ/072/J (ut) 200 5.00 × 10−5 211 368

[28] E.1.13 BS15 OJ/072/J (ut) 225 5.00 × 10−5 210 372

[28] E.1.13 BS15 OJ/072/J (ut) 250 5.00 × 10−5 191 354

[28] E.1.13 BS15 OJ/072/J (ut) 300 5.00 × 10−5 175 342

[28] E.1.13 BS15 OJ/072/J (ut) 400 5.00 × 10−5 167 317

[28] E.1.13 BS15 OJ/072/J (ut) 500 5.00 × 10−5 152 230

[28] E.1.13 BS15 OJ/072/J (ut) 600 5.00 × 10−5 94 110

[28] E.1.13 BS15 OJ/072/J (ut) 700 5.00 × 10−5 49 48

[28] E.1.13 BS15 OJ/072/J (ut) 800 5.00 × 10−5 29 32

[28] E.1.13 BS436043A-1 20 5.00 × 10−5 326 326

[28] E.1.13 BS436043A-1 100 5.00 × 10−5 306 309

[28] E.1.13 BS436043A-1 150 5.00 × 10−5 331 351

[28] E.1.13 BS436043A-1 200 5.00 × 10−5 333 416

[28] E.1.13 BS436043A-1 250 5.00 × 10−5 290 348

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
76

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[28] E.1.13 BS436043A-1 300 5.00 × 10−5 247 339

[28] E.1.13 BS436043A-1 400 5.00 × 10−5 223 341

[28] E.1.13 BS436043A-1 500 5.00 × 10−5 209 260

[28] E.1.13 BS436043A-1 600 5.00 × 10−5 110 125

[28] E.1.13 BS436043A-1 700 5.00 × 10−5 48 48

[28] E.1.13 BS436043A-1 800 5.00 × 10−5 29 32

[28] E.1.13 BS436043A-2 20 5.00 × 10−5 284 331

[28] E.1.13 BS436043A-2 100 5.00 × 10−5 278 359

[28] E.1.13 BS436043A-2 150 5.00 × 10−5 283 396

[28] E.1.13 BS436043A-2 200 5.00 × 10−5 284 402

[28] E.1.13 BS436043A-2 250 5.00 × 10−5 267 398

[28] E.1.13 BS436043A-2 300 5.00 × 10−5 220 362

[28] E.1.13 BS436043A-2 400 5.00 × 10−5 213 333

[28] E.1.13 BS436043A-2 500 5.00 × 10−5 198 275

[28] E.1.13 BS436043A-2 600 5.00 × 10−5 140 145

[28] E.1.13 BS436043A-2 700 5.00 × 10−5 53 52

[28] E.1.13 BS436043A-2 800 5.00 × 10−5 29 31

[28] E.1.13 BS436043A-3 20 5.00 × 10−5 278 337

[28] E.1.13 BS436043A-3 100 5.00 × 10−5 272 341

[28] E.1.13 BS436043A-3 150 5.00 × 10−5 272 389

[28] E.1.13 BS436043A-3 200 5.00 × 10−5 270 383

[28] E.1.13 BS436043A-3 250 5.00 × 10−5 244 381

[28] E.1.13 BS436043A-3 300 5.00 × 10−5 212 354

[28] E.1.13 BS436043A-3 400 5.00 × 10−5 205 328

[28] E.1.13 BS436043A-3 500 5.00 × 10−5 187 260

[28] E.1.13 BS436043A-3 600 5.00 × 10−5 127 140

[28] E.1.13 BS436043A-3 700 5.00 × 10−5 57 57

[28] E.1.13 BS436043A-3 800 5.00 × 10−5 37 41

[29] E.1.15 CSA G40.21 350AT 20 1.48 × 10−5 374 NA

[29] E.1.15 CSA G40.21 350AT 100 1.48 × 10−5 346 NA

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
77

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[29] E.1.15 CSA G40.21 350AT 150 1.48 × 10−5 316 NA

[29] E.1.15 CSA G40.21 350AT 200 1.48 × 10−5 280 NA

[29] E.1.15 CSA G40.21 350AT 250 1.48 × 10−5 283 NA

[29] E.1.15 CSA G40.21 350AT 300 1.48 × 10−5 248 NA

[29] E.1.15 CSA G40.21 350AT 20 7.41 × 10−5 377 NA

[29] E.1.15 CSA G40.21 350AT 100 7.41 × 10−5 351 NA

[29] E.1.15 CSA G40.21 350AT 150 7.41 × 10−5 326 NA

[29] E.1.15 CSA G40.21 350AT 200 7.41 × 10−5 308 NA

[29] E.1.15 CSA G40.21 350AT 250 7.41 × 10−5 315 NA

[29] E.1.15 CSA G40.21 350AT 300 7.41 × 10−5 293 NA

[29] E.1.15 CSA G40.21 350AT 20 3.71 × 10−4 380 NA

[29] E.1.15 CSA G40.21 350AT 100 3.71 × 10−4 354 NA

[29] E.1.15 CSA G40.21 350AT 150 3.71 × 10−4 337 NA

[29] E.1.15 CSA G40.21 350AT 200 3.71 × 10−4 307 NA

[29] E.1.15 CSA G40.21 350AT 250 3.71 × 10−4 328 NA

[29] E.1.15 CSA G40.21 350AT 300 3.71 × 10−4 306 NA

[29] E.1.15 CSA G40.21 350AT 20 1.48 × 10−3 389 NA

[29] E.1.15 CSA G40.21 350AT 100 1.48 × 10−3 362 NA

[29] E.1.15 CSA G40.21 350AT 150 1.48 × 10−3 341 NA

[29] E.1.15 CSA G40.21 350AT 200 1.48 × 10−3 316 NA

[29] E.1.15 CSA G40.21 350AT 250 1.48 × 10−3 323 NA

[29] E.1.15 CSA G40.21 350AT 300 1.48 × 10−3 300 NA

[29] E.1.15 CSA G40.21 350WT 20 1.48 × 10−5 218 NA

[29] E.1.15 CSA G40.21 350WT 100 1.48 × 10−5 215 NA

[29] E.1.15 CSA G40.21 350WT 150 1.48 × 10−5 190 NA

[29] E.1.15 CSA G40.21 350WT 200 1.48 × 10−5 203 NA

[29] E.1.15 CSA G40.21 350WT 250 1.48 × 10−5 209 NA

[29] E.1.15 CSA G40.21 350WT 300 1.48 × 10−5 213 NA

[29] E.1.15 CSA G40.21 350WT 350 1.48 × 10−5 190 NA

[29] E.1.15 CSA G40.21 350WT 20 7.41 × 10−5 266 NA

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
78

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[29] E.1.15 CSA G40.21 350WT 100 7.41 × 10−5 243 NA

[29] E.1.15 CSA G40.21 350WT 150 7.41 × 10−5 236 NA

[29] E.1.15 CSA G40.21 350WT 200 7.41 × 10−5 234 NA

[29] E.1.15 CSA G40.21 350WT 250 7.41 × 10−5 237 NA

[29] E.1.15 CSA G40.21 350WT 300 7.41 × 10−5 233 NA

[29] E.1.15 CSA G40.21 350WT 350 7.41 × 10−5 218 NA

[29] E.1.15 CSA G40.21 350WT 20 3.71 × 10−4 269 NA

[29] E.1.15 CSA G40.21 350WT 100 3.71 × 10−4 258 NA

[29] E.1.15 CSA G40.21 350WT 150 3.71 × 10−4 241 NA

[29] E.1.15 CSA G40.21 350WT 200 3.71 × 10−4 232 NA

[29] E.1.15 CSA G40.21 350WT 250 3.71 × 10−4 241 NA

[29] E.1.15 CSA G40.21 350WT 300 3.71 × 10−4 246 NA

[29] E.1.15 CSA G40.21 350WT 350 3.71 × 10−4 237 NA

[29] E.1.15 CSA G40.21 350WT 20 1.48 × 10−3 273 NA

[29] E.1.15 CSA G40.21 350WT 100 1.48 × 10−3 260 NA

[29] E.1.15 CSA G40.21 350WT 150 1.48 × 10−3 242 NA

[29] E.1.15 CSA G40.21 350WT 200 1.48 × 10−3 233 NA

[29] E.1.15 CSA G40.21 350WT 250 1.48 × 10−3 250 NA

[29] E.1.15 CSA G40.21 350WT 300 1.48 × 10−3 239 NA

[29] E.1.15 CSA G40.21 350WT 350 1.48 × 10−3 237 NA

[30] E.1.17 S355 20 5.00 × 10−5 385 397

[30] E.1.17 S355 400 5.00 × 10−5 NA 408

[30] E.1.17 S355 500 5.00 × 10−5 NA 340

[30] E.1.17 S355 600 5.00 × 10−5 NA 212

[30] E.1.17 S355 700 5.00 × 10−5 85 101

[30] E.1.17 S355 750 5.00 × 10−5 54 72

[30] E.1.17 S355 800 5.00 × 10−5 48 62

[30] E.1.17 S355 900 5.00 × 10−5 37 48

[31] E.1.18 AS3679.1 20 3.33 × 10−5 347 374

[31] E.1.18 AS3679.1 20 3.33 × 10−5 350 371

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
79

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[31] E.1.18 AS3679.1 300 3.33 × 10−5 253 376

[31] E.1.18 AS3679.1 300 3.33 × 10−5 271 362

[31] E.1.18 AS3679.1 400 3.33 × 10−5 221 329

[31] E.1.18 AS3679.1 400 3.33 × 10−5 288 365

[31] E.1.18 AS3679.1 500 3.33 × 10−5 214 268

[31] E.1.18 AS3679.1 500 3.33 × 10−5 221 273

[31] E.1.18 AS3679.1 600 3.33 × 10−5 132 136

[31] E.1.18 AS3679.1 600 3.33 × 10−5 132 138

[31] E.1.18 AS3679.1 700 3.33 × 10−5 65 61

[31] E.1.18 AS3679.1 700 3.33 × 10−5 66 59

[31] E.1.18 AS3679.1 800 3.33 × 10−5 39 41

[31] E.1.18 AS3679.1 20 8.00 × 10−4 359 381

[31] E.1.18 AS3679.1 20 8.00 × 10−4 365 353

[31] E.1.18 AS3679.1 400 8.00 × 10−4 253 365

[31] E.1.18 AS3679.1 500 8.00 × 10−4 231 306

[31] E.1.18 AS3679.1 600 8.00 × 10−4 174 188

[31] E.1.18 AS3679.1 700 8.00 × 10−4 98 95

[31] E.1.18 AS3679.1 800 8.00 × 10−4 57 64

[32] E.1.19 SM400A 20 5.00 × 10−5 252 255

[32] E.1.19 SM400A 100 5.00 × 10−5 231 224

[32] E.1.19 SM400A 200 5.00 × 10−5 224 231

[32] E.1.19 SM400A 300 5.00 × 10−5 159 224

[32] E.1.19 SM400A 400 5.00 × 10−5 147 216

[32] E.1.19 SM400A 500 5.00 × 10−5 134 179

[32] E.1.19 SM400A 550 5.00 × 10−5 107 141

[32] E.1.19 SM400A 600 5.00 × 10−5 84 103

[32] E.1.19 SM400A 650 5.00 × 10−5 66 79

[32] E.1.19 SM400A 700 5.00 × 10−5 45 52

[32] E.1.19 SM400A 750 5.00 × 10−5 38 38

[32] E.1.19 SM400A 800 5.00 × 10−5 28 31

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
80

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[33] E.1.20 AS A186:250 27 1.67 × 10−7 232 299

[33] E.1.20 AS A186:250 27 8.33 × 10−7 236 303

[33] E.1.20 AS A186:250 100 8.33 × 10−7 NA NA

[33] E.1.20 AS A186:250 200 8.33 × 10−7 NA NA

[33] E.1.20 AS A186:250 300 8.33 × 10−7 214 354

[33] E.1.20 AS A186:250 350 8.33 × 10−7 197 325

[33] E.1.20 AS A186:250 400 8.33 × 10−7 183 294

[33] E.1.20 AS A186:250 450 8.33 × 10−7 177 265

[33] E.1.20 AS A186:250 500 8.33 × 10−7 119 219

[33] E.1.20 AS A186:250 550 8.33 × 10−7 99 133

[33] E.1.20 AS A186:250 600 8.33 × 10−7 80 76

[33] E.1.20 AS A186:250 650 8.33 × 10−7 45 46

[33] E.1.20 AS A186:250 350 8.33 × 10−6 190 NA

[33] E.1.20 AS A186:250 400 8.33 × 10−6 199 NA

[33] E.1.20 AS A186:250 450 8.33 × 10−6 185 NA

[33] E.1.20 AS A186:250 500 8.33 × 10−6 170 NA

[33] E.1.20 AS A186:250 550 8.33 × 10−6 128 NA

[33] E.1.20 AS A186:250 600 8.33 × 10−6 91 NA

[33] E.1.20 AS A186:250 650 8.33 × 10−6 63 NA

[33] E.1.20 AS A186:250 27 3.33 × 10−5 250 319

[33] E.1.20 AS A186:250 100 3.33 × 10−5 232 327

[33] E.1.20 AS A186:250 200 3.33 × 10−5 214 375

[33] E.1.20 AS A186:250 300 3.33 × 10−5 202 345

[33] E.1.20 AS A186:250 350 3.33 × 10−5 201 339

[33] E.1.20 AS A186:250 400 3.33 × 10−5 202 329

[33] E.1.20 AS A186:250 450 3.33 × 10−5 194 297

[33] E.1.20 AS A186:250 500 3.33 × 10−5 181 254

[33] E.1.20 AS A186:250 550 3.33 × 10−5 145 181

[33] E.1.20 AS A186:250 600 3.33 × 10−5 108 121

[33] E.1.20 AS A186:250 650 3.33 × 10−5 77 82

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
81

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[33] E.1.20 AS A186:250 27 3.33 × 10−4 263 334

[33] E.1.20 AS A186:250 27 3.33 × 10−3 NA 327

[33] E.1.20 AS A186:250 350 3.33 × 10−3 NA 340

[33] E.1.20 AS A186:250 500 3.33 × 10−3 NA 278

[33] E.1.20 AS A186:250 650 3.33 × 10−3 NA 142

[34] E.1.22 Cor-Ten A 10 27 8.33 × 10−5 368 NA

[34] E.1.22 Cor-Ten A 10 93 8.33 × 10−5 346 NA

[34] E.1.22 Cor-Ten A 10 204 8.33 × 10−5 323 NA

[34] E.1.22 Cor-Ten A 10 316 8.33 × 10−5 281 NA

[34] E.1.22 Cor-Ten A 10 427 8.33 × 10−5 258 NA

[34] E.1.22 Cor-Ten A 10 538 8.33 × 10−5 239 NA

[34] E.1.22 Cor-Ten A 10 649 8.33 × 10−5 139 NA

[34] E.1.22 Cor-Ten A 6 27 8.33 × 10−5 354 NA

[34] E.1.22 Cor-Ten A 6 93 8.33 × 10−5 327 NA

[34] E.1.22 Cor-Ten A 6 204 8.33 × 10−5 316 NA

[34] E.1.22 Cor-Ten A 6 316 8.33 × 10−5 277 NA

[34] E.1.22 Cor-Ten A 6 427 8.33 × 10−5 243 NA

[34] E.1.22 Cor-Ten A 6 538 8.33 × 10−5 224 NA

[34] E.1.22 Cor-Ten A 6 649 8.33 × 10−5 135 NA

[34] E.1.22 Cor-Ten A 7 27 8.33 × 10−5 396 NA

[34] E.1.22 Cor-Ten A 7 93 8.33 × 10−5 376 NA

[34] E.1.22 Cor-Ten A 7 204 8.33 × 10−5 352 NA

[34] E.1.22 Cor-Ten A 7 316 8.33 × 10−5 304 NA

[34] E.1.22 Cor-Ten A 7 427 8.33 × 10−5 291 NA

[34] E.1.22 Cor-Ten A 7 538 8.33 × 10−5 262 NA

[34] E.1.22 Cor-Ten A 7 649 8.33 × 10−5 149 NA

[34] E.1.22 Cor-Ten A 8 27 8.33 × 10−5 445 NA

[34] E.1.22 Cor-Ten A 8 93 8.33 × 10−5 414 NA

[34] E.1.22 Cor-Ten A 8 204 8.33 × 10−5 381 NA

[34] E.1.22 Cor-Ten A 8 316 8.33 × 10−5 337 NA

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
82

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[34] E.1.22 Cor-Ten A 8 427 8.33 × 10−5 296 NA

[34] E.1.22 Cor-Ten A 8 538 8.33 × 10−5 241 NA

[34] E.1.22 Cor-Ten A 8 649 8.33 × 10−5 128 NA

[34] E.1.22 Cor-Ten B 12 27 8.33 × 10−5 439 NA

[34] E.1.22 Cor-Ten B 12 93 8.33 × 10−5 416 NA

[34] E.1.22 Cor-Ten B 12 204 8.33 × 10−5 374 NA

[34] E.1.22 Cor-Ten B 12 316 8.33 × 10−5 375 NA

[34] E.1.22 Cor-Ten B 12 427 8.33 × 10−5 364 NA

[34] E.1.22 Cor-Ten B 12 538 8.33 × 10−5 287 NA

[34] E.1.22 Cor-Ten B 12 649 8.33 × 10−5 167 NA

[34] E.1.22 Cor-Ten B 13 27 8.33 × 10−5 399 NA

[34] E.1.22 Cor-Ten B 13 93 8.33 × 10−5 376 NA

[34] E.1.22 Cor-Ten B 13 204 8.33 × 10−5 338 NA

[34] E.1.22 Cor-Ten B 13 316 8.33 × 10−5 332 NA

[34] E.1.22 Cor-Ten B 13 427 8.33 × 10−5 317 NA

[34] E.1.22 Cor-Ten B 13 538 8.33 × 10−5 283 NA

[34] E.1.22 Cor-Ten B 13 649 8.33 × 10−5 189 NA

[34] E.1.22 Cor-Ten B 14 27 8.33 × 10−5 415 NA

[34] E.1.22 Cor-Ten B 14 93 8.33 × 10−5 390 NA

[34] E.1.22 Cor-Ten B 14 204 8.33 × 10−5 355 NA

[34] E.1.22 Cor-Ten B 14 316 8.33 × 10−5 339 NA

[34] E.1.22 Cor-Ten B 14 427 8.33 × 10−5 323 NA

[34] E.1.22 Cor-Ten B 14 538 8.33 × 10−5 253 NA

[34] E.1.22 Cor-Ten B 14 649 8.33 × 10−5 151 NA

[34] E.1.22 Cor-Ten B 15 27 8.33 × 10−5 367 NA

[34] E.1.22 Cor-Ten B 15 93 8.33 × 10−5 350 NA

[34] E.1.22 Cor-Ten B 15 204 8.33 × 10−5 336 NA

[34] E.1.22 Cor-Ten B 15 316 8.33 × 10−5 331 NA

[34] E.1.22 Cor-Ten B 15 427 8.33 × 10−5 306 NA

[34] E.1.22 Cor-Ten B 15 538 8.33 × 10−5 243 NA

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
83

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[34] E.1.22 Cor-Ten B 15 649 8.33 × 10−5 149 NA

[6] E.1.23 AS187:WR350/1 27 1.67 × 10−7 391 394

[6] E.1.23 AS187:WR350/1 350 1.67 × 10−7 292 360

[6] E.1.23 AS187:WR350/1 350 1.67 × 10−7 302 361

[6] E.1.23 AS187:WR350/1 500 1.67 × 10−7 173 183

[6] E.1.23 AS187:WR350/1 500 1.67 × 10−7 177 190

[6] E.1.23 AS187:WR350/1 650 1.67 × 10−7 64 64

[6] E.1.23 AS187:WR350/1 650 1.67 × 10−7 66 61

[6] E.1.23 AS187:WR350/1 27 8.33 × 10−7 392 394

[6] E.1.23 AS187:WR350/1 27 8.33 × 10−7 392 395

[6] E.1.23 AS187:WR350/1 100 8.33 × 10−7 375 389

[6] E.1.23 AS187:WR350/1 200 8.33 × 10−7 359 404

[6] E.1.23 AS187:WR350/1 200 8.33 × 10−7 361 405

[6] E.1.23 AS187:WR350/1 300 8.33 × 10−7 314 378

[6] E.1.23 AS187:WR350/1 350 8.33 × 10−7 304 365

[6] E.1.23 AS187:WR350/1 400 8.33 × 10−7 291 347

[6] E.1.23 AS187:WR350/1 450 8.33 × 10−7 270 317

[6] E.1.23 AS187:WR350/1 475 8.33 × 10−7 248 279

[6] E.1.23 AS187:WR350/1 500 8.33 × 10−7 203 223

[6] E.1.23 AS187:WR350/1 550 8.33 × 10−7 148 159

[6] E.1.23 AS187:WR350/1 600 8.33 × 10−7 111 114

[6] E.1.23 AS187:WR350/1 650 8.33 × 10−7 81 79

[6] E.1.23 AS187:WR350/1 27 8.33 × 10−6 407 405

[6] E.1.23 AS187:WR350/1 350 8.33 × 10−6 308 374

[6] E.1.23 AS187:WR350/1 400 8.33 × 10−6 291 354

[6] E.1.23 AS187:WR350/1 450 8.33 × 10−6 281 336

[6] E.1.23 AS187:WR350/1 500 8.33 × 10−6 246 272

[6] E.1.23 AS187:WR350/1 550 8.33 × 10−6 179 192

[6] E.1.23 AS187:WR350/1 600 8.33 × 10−6 136 143

[6] E.1.23 AS187:WR350/1 650 8.33 × 10−6 NA 102

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
84

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[6] E.1.23 AS187:WR350/1 27 3.33 × 10−5 398 430

[6] E.1.23 AS187:WR350/1 27 3.33 × 10−5 398 401

[6] E.1.23 AS187:WR350/1 100 3.33 × 10−5 379 383

[6] E.1.23 AS187:WR350/1 200 3.33 × 10−5 370 401

[6] E.1.23 AS187:WR350/1 300 3.33 × 10−5 339 401

[6] E.1.23 AS187:WR350/1 350 3.33 × 10−5 309 371

[6] E.1.23 AS187:WR350/1 400 3.33 × 10−5 296 355

[6] E.1.23 AS187:WR350/1 450 3.33 × 10−5 283 336

[6] E.1.23 AS187:WR350/1 450 3.33 × 10−5 283 348

[6] E.1.23 AS187:WR350/1 475 3.33 × 10−5 270 319

[6] E.1.23 AS187:WR350/1 500 3.33 × 10−5 263 294

[6] E.1.23 AS187:WR350/1 550 3.33 × 10−5 204 220

[6] E.1.23 AS187:WR350/1 550 3.33 × 10−5 203 217

[6] E.1.23 AS187:WR350/1 600 3.33 × 10−5 154 159

[6] E.1.23 AS187:WR350/1 650 3.33 × 10−5 112 113

[6] E.1.23 AS187:WR350/1 650 3.33 × 10−5 114 115

[6] E.1.23 AS187:WR350/1 27 3.33 × 10−4 409 408

[6] E.1.23 AS187:WR350/1 350 3.33 × 10−4 300 364

[6] E.1.23 AS187:WR350/1 500 3.33 × 10−4 273 316

[6] E.1.23 AS187:WR350/1 650 3.33 × 10−4 139 144

[6] E.1.23 AS187:WR350/1 27 3.33 × 10−3 NA 416

[6] E.1.23 AS187:WR350/1 350 3.33 × 10−3 323 367

[6] E.1.23 AS187:WR350/1 350 3.33 × 10−3 298 363

[6] E.1.23 AS187:WR350/1 500 3.33 × 10−3 NA NA

[6] E.1.23 AS187:WR350/1 500 3.33 × 10−3 301 350

[6] E.1.23 AS187:WR350/1 500 3.33 × 10−3 290 330

[6] E.1.23 AS187:WR350/1 650 3.33 × 10−3 NA 179

[6] E.1.23 AS187:WR350/1 650 3.33 × 10−3 170 179

[6] E.1.23 AS A186:250 L0 27 8.33 × 10−7 232 308

[6] E.1.23 AS A186:250 L0 350 8.33 × 10−7 192 310

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
85

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[6] E.1.23 AS A186:250 L0 400 8.33 × 10−7 186 289

[6] E.1.23 AS A186:250 L0 450 8.33 × 10−7 196 276

[6] E.1.23 AS A186:250 L0 500 8.33 × 10−7 174 223

[6] E.1.23 AS A186:250 L0 550 8.33 × 10−7 120 136

[6] E.1.23 AS A186:250 L0 600 8.33 × 10−7 72 79

[6] E.1.23 AS A186:250 L0 650 8.33 × 10−7 43 46

[6] E.1.23 AS A186:250 L0 27 3.33 × 10−5 226 303

[6] E.1.23 AS A186:250 L0 350 3.33 × 10−5 221 355

[6] E.1.23 AS A186:250 L0 400 3.33 × 10−5 198 319

[6] E.1.23 AS A186:250 L0 450 3.33 × 10−5 209 311

[6] E.1.23 AS A186:250 L0 500 3.33 × 10−5 176 248

[6] E.1.23 AS A186:250 L0 550 3.33 × 10−5 NA 196

[6] E.1.23 AS A186:250 L0 550 3.33 × 10−5 157 216

[6] E.1.23 AS A186:250 L0 600 3.33 × 10−5 115 133

[6] E.1.23 AS A186:250 L0 650 3.33 × 10−5 80 87

[6] E.1.23 AS A186:400 L15 27 1.67 × 10−7 414 418

[6] E.1.23 AS A186:400 L15 27 8.33 × 10−7 416 414

[6] E.1.23 AS A186:400 L15 300 8.33 × 10−7 286 432

[6] E.1.23 AS A186:400 L15 350 8.33 × 10−7 283 414

[6] E.1.23 AS A186:400 L15 400 8.33 × 10−7 260 368

[6] E.1.23 AS A186:400 L15 450 8.33 × 10−7 236 309

[6] E.1.23 AS A186:400 L15 500 8.33 × 10−7 191 223

[6] E.1.23 AS A186:400 L15 550 8.33 × 10−7 126 135

[6] E.1.23 AS A186:400 L15 600 8.33 × 10−7 77 78

[6] E.1.23 AS A186:400 L15 650 8.33 × 10−7 45 44

[6] E.1.23 AS A186:400 L15 27 3.33 × 10−5 430 430

[6] E.1.23 AS A186:400 L15 100 3.33 × 10−5 400 399

[6] E.1.23 AS A186:400 L15 200 3.33 × 10−5 371 399

[6] E.1.23 AS A186:400 L15 300 3.33 × 10−5 292 462

[6] E.1.23 AS A186:400 L15 350 3.33 × 10−5 292 427

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
86

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[6] E.1.23 AS A186:400 L15 400 3.33 × 10−5 280 423

[6] E.1.23 AS A186:400 L15 450 3.33 × 10−5 254 392

[6] E.1.23 AS A186:400 L15 500 3.33 × 10−5 233 352

[6] E.1.23 AS A186:400 L15 550 3.33 × 10−5 192 291

[6] E.1.23 AS A186:400 L15 600 3.33 × 10−5 137 219

[6] E.1.23 AS A186:400 L15 650 3.33 × 10−5 92 143

[6] E.1.23 AS A186:400 L15 27 3.33 × 10−4 444 93

[6] E.1.23 AS A186:400 L15 27 3.33 × 10−3 450 445

[6] E.1.23 AS A186:400 L15 350 3.33 × 10−3 NA 447

[6] E.1.23 AS A186:400 L15 500 3.33 × 10−3 NA 421

[6] E.1.23 AS A186:400 L15 650 3.33 × 10−3 NA 341

[35] E.1.24 USS A36 27 8.33 × 10−5 248 NA

[35] E.1.24 USS A36 149 8.33 × 10−5 208 NA

[35] E.1.24 USS A36 260 8.33 × 10−5 192 NA

[35] E.1.24 USS A36 371 8.33 × 10−5 175 NA

[35] E.1.24 USS A36 482 8.33 × 10−5 148 NA

[35] E.1.24 USS A36 593 8.33 × 10−5 112 NA

[35] E.1.24 USS A36 704 8.33 × 10−5 53 NA

[35] E.1.24 USS T1 27 8.30 × 10−5 803 NA

[35] E.1.24 USS T1 93 8.30 × 10−5 767 NA

[35] E.1.24 USS T1 204 8.30 × 10−5 703 NA

[35] E.1.24 USS T1 316 8.30 × 10−5 678 NA

[35] E.1.24 USS T1 427 8.30 × 10−5 618 NA

[35] E.1.24 USS T1 538 8.30 × 10−5 519 NA

[35] E.1.24 USS T1 649 8.30 × 10−5 241 NA

[35] E.1.24 USS T1 760 8.30 × 10−5 63 NA

[35] E.1.24 USS T1 871 8.30 × 10−5 46 NA

[35] E.1.24 USS T1 1038 8.30 × 10−5 19 NA

[62] E.1.16 mild steel 20 9.50 × 10−7 190 236

[62] E.1.16 mild steel 200 3.40 × 10−5 177 276

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
87

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[62] E.1.16 mild steel 600 3.40 × 10−5 53 75

[62] E.1.16 mild steel 20 8.50 × 10−4 214 250

[62] E.1.16 mild steel 200 8.50 × 10−4 181 307

[62] E.1.16 mild steel 400 8.50 × 10−4 211 274

[62] E.1.16 mild steel 200 2.00 × 10−2 188 314

[62] E.1.16 mild steel 600 2.00 × 10−2 112 162

[62] E.1.16 mild steel 20 5.00 × 10−1 259 290

[62] E.1.16 mild steel 200 5.00 × 10−1 228 276

[62] E.1.16 mild steel 400 5.00 × 10−1 233 284

[62] E.1.16 mild steel 20 1.00 × 102 452 NA

[62] E.1.16 mild steel 400 1.87 × 102 274 329

[62] E.1.16 mild steel 200 2.00 × 102 392 416

[62] E.1.16 mild steel 600 2.00 × 102 303 349

[62] E.1.16 mild steel 20 3.02 × 102 506 508

[62] E.1.16 mild steel 400 6.00 × 102 281 339

[40] E.1.10 A992 20 1.67 × 10−4 429 425

[40] E.1.10 A992 100 1.67 × 10−4 409 408

[40] E.1.10 A992 200 1.67 × 10−4 406 425

[40] E.1.10 A992 300 1.67 × 10−4 315 418

[40] E.1.10 A992 400 1.67 × 10−4 298 395

[40] E.1.10 A992 500 1.67 × 10−4 254 316

[40] E.1.10 A992 600 1.67 × 10−4 171 193

[40] E.1.10 A992 700 1.67 × 10−4 88 89

[40] E.1.10 A992 800 1.67 × 10−4 37 39

[40] E.1.10 A992 900 1.67 × 10−4 27 30

[40] E.1.10 A992 20 1.67 × 10−3 436 438

[40] E.1.10 A992 100 1.67 × 10−3 406 406

[40] E.1.10 A992 200 1.67 × 10−3 401 419

[40] E.1.10 A992 300 1.67 × 10−3 332 431

[40] E.1.10 A992 400 1.67 × 10−3 297 383

NA: not available; data not calculated

S

002

y = Sy(0.002 offset) : 0.2 % offset yield strength

S

02

y = Sy(0.02 elong) : stress measured at 2 % total strain

continued on next page
88

Table 10: Data for structural steels from literature sources.

Continued from the previous page

Reference Section Steel T  S  ̇

002

y S

02

y

◦C 1/s MPa MPa

[40] E.1.10 A992 500 1.67 × 10−3 255 322

[40] E.1.10 A992 600 1.67 × 10−3 191 216

[40] E.1.10 A992 700 1.67 × 10−3 112 116

[40] E.1.10 A992 800 1.67 × 10−3 54 64

[40] E.1.10 A992 900 1.67 × 10−3 45 48

NA: not available

Sy(0.002 offset) : 0.2 % offset yield strength

Sy(0.02 elong) : stress measured at 2 % total strain

E.3 Retained strength

Figure 2 overlays all the data on a single plot. Figure 30 replots the Figure 2 data,

identified by source [6,12,18,23–35] . Within each panel, different symbols denote

individual steels from the same literature source.

E.4 Elastic Modulus

E.4.1 Recommended value

The NIST World Trade Center collapse investigation [12] (Chapter 2) determined

the elastic modulus for three plate steels using a thermo-mechanical analyzer operating in three-point bending at 1 hz. Specimens were nominally (50×10×1) mm.

The temperature range was (−140 < T < 600)

◦C. Table 11 summarizes the information on the steels. Figure 31 plots the data for the five determinations of the

modulus.

The data were fit with a four-term polynomial:

E = E0 + e1T + e2T

2 + e3T3

(17)

where

E0 = 206 GPa is the elastic modulus at T = 0 ◦C.

e1 = −4.326 × 10−2 GPa/◦C

−1

e2 = −3.502 × 10−5 GPa/◦C

−2

e3 = −6.592 × 10−8 GPa/◦C

−3

The intercept, E0, was not fit, but instead set to the average value of the T = 0 ◦C

elastic modulus of the individual determinations. Figure 31 also overplots the fit

of Eq. (6) to the data for each steel. In all cases the maximum deviation of the

measured modulus and the fit is less than 4 GPa.
89

T /°C

R

0.0

0.4

0.8

1.2

0 200 600 1000

 Ref. 12 Ref. 18

0 200 600 1000

 Ref. 23

 Ref. 24 Ref. 25

0.0

0.4

0.8

1.2

 Ref. 26

0.0

0.4

0.8

1.2

 Ref. 27 Ref. 28 Ref. 29

 Ref. 30 Ref. 31

0.0

0.4

0.8

1.2

 Ref. 32

0.0

0.4

0.8

1.2

 Ref. 33 Ref. 34 Ref. 35

0.0

0.4

0.8

1.2

 Ref. 6

Figure 30: Normalized, retained yield strength, R, as a function of temperature,

from Figure 2. Strips in each panel identify the source from the reference list.

Sources: [6, 12, 18, 23–35] .

Table 11: Data for the three steels

Designation No. of runs Fy

ksi

C68-C3T1-EP-2 2 50

N9-C2B-FR-1 1 55

S9-C3T-FL-1 2 50
90

T /°C

E /GPa

160

180

200

0 200 400 600

50ksi 50mm plate 55ksi plate N9

160

180

200

55ksi plate S9 C68-C351-EP2 Run 1

C68-C351-EP2 Run 2

N9-C2B-FR1 Run 1

S9-C3T-FL-1 Run 1

S9-C3T-FL-1 Run 2

Figure 31: Temperature dependence of the elastic modulus of structural steel determined from the NIST WTC collapse investigation. Dashed line is the fit of Eq.(6).

E.4.2 Other determinations and representations of elastic modulus

Investigators have determined the temperature dependence of the elastic modulus

of structural steel many times in the past century, using a variety of techniques.

Lie [15] summarizes some historical measurements of elastic modulus; two of

these [66,67] date back into the early 20th century and are not included in the plots

of this section. Figure 32 plots the change in elastic modulus with temperature for

various structural steels and pure iron determined by various techniques. Figure 33

breaks out the data of Figure 32 into individual plots by reference number. Table 12
91

T /°C

E /GPa

100

150

200

0 500 1000

Reference/Steel

58 all structural

68 [C]<0.3%

68 [C]>0.3%

69 SAE1015

70 [C]=0.12 %

71 SAE1015

72 Timken Co.

73 Austenite

73 Ferrite

74 AS A151 ASTM GS 5

74 AS A151 ASTM GS 8-9

75 mild steel

76 not reported

76 structural

8 Arbed 

8 Euronorm 25-1972

Figure 32: Literature determinations of the temperature dependence of the elastic

modulus of structural steel.

summarizes the literature sources for data used in Figure 32; Section E.4.3 describes the steels and determinations in greater detail. Finally, Table 13 at the end

of this section tabulates the values of the modulus used in the individual figures.

The modulus data naturally fall into two groups determined by the method

used to measure the modulus. Figure 34 replots the data of Figure 32 but breaks it

into three measurement method groups: dynamic, static, and not reported. Values

measured by various dynamic methods [69, 70, 72, 73, 75], generally at around

400 hz, are the largest, and drop off slowest with increasing temperature. Values

measured in tensile tests are labelled “static.” The types labeled “not reported”
92

T /°C

E /GPa

0

50

100

150

200

0 500 1000

 Ref. 58 Ref. 68

0 500 1000

 Ref. 69 Ref. 70

 Ref. 71 Ref. 72 Ref. 73

0

50

100

150

200

 Ref. 74

0

50

100

150

200

 Ref. 75

0 500 1000

 Ref. 76 Ref. 8 Method

not reported

dynamic

static

Figure 33: Literature determinations of the temperature dependence of the elastic

modulus of structural steel. Colors and symbols denote the measurement method,

and the strip in each plot notes the reference number.

[8, 58, 76] are also probably derived from quasi-static tests tensile tests, where the

modulus is determined from the stress-strain curve. However, the sources do not

identify the method. The static tests can contain significant anelastic, or timedependent elastic effects, for example in the data of Ritter [74].

E.4.3 Notes on literature reports of recommended values for elastic modulus

Figure 35 plots the recommended modulus from four organizations concerned with

the performance of steel in fire: Eq. (6) used in the WTC investigation [12], the rec-
93

Table 12: Summary of literature determinations of elastic modulus of structural

steel.

Ref. Pg. Author Steel Year T range Method

◦C

[68] 93 ASME [C]<0.3% NA −198 < T < 593 not reported

[68] 93 ASME [C]>0.3% NA −198 < T < 649 not reported

[58] 96 USS all structural 1968 93 < T < 538 not reported

[69] 97 Clark SAE1015 1953 23 < T < 650 ultrasonic pulse

technique

[8] 97 Cooke Arbed 1986 91 < T < 1135 not reported

[8] 97 Cooke Euronorm

25-1972

1980 0 < T < 793 various

including static

and dynamic

[70] 97 Date [C]=0.12 % 1969 20 < T < 600 sonic resonance

at 400 hz

[71] 97 Garafolo SAE1015 1952 24 < T < 482 static beam

bending

[72] 97 Garafolo Timken Co. 1948 22 < T < 760 NA

[73] 97 Koester Austenite 1948 905 < T < 985 not reported

[73] 97 Koester Ferrite 1948 20 < T < 720 not reported

[74] 97 Ritter AS A151

ASTM GS 5

1970 20 < T < 572 tensile test

[74] 97 Ritter AS A151

ASTM GS 8-9

1970 20 < T < 550 tensile test

[75] 97 Roberts mild steel 1947 20 < T < 600 sonic resonance

at 400 hz

[76] 98 Uddin not reported NA 93 < T < 649 not reported

[76] 98 Uddin structural 1961 93 < T < 649 not reported

ommended value of the Eurocode 3 [1], the recommended value of the American

Society of Civil Engineers (ASCE) [77], and the recommended value of the European Convention on Constructional Steelwork (ECCS) [9]. References 58, 68. The

experimental data of Figure 32 are plotted as symbols. None of the original references, summarized below, document the rationale for choosing the specific form

of the behavior.
94

T /°C

E /GPa

0

50

100

150

200

0 500 1000

Method

not reported

dynamic

static

Figure 34: Temperature dependence of the elastic modulus of structural steel identified by the measurement method.

ASME The American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code [68] provides typical values for many physical properties, including elastic modulus. The Code describes the data as tending “to be closer to average

values,” but does not describe the source or the measurement technique. The data

are segregated in to steels with carbon content above and below 0.3 % by weight

in the temperature range (−198 < T < 593)

◦C. However, the difference between

the two is 1.4 GPa at all temperatures.
95

T /°C

E /GPa

0

50

100

150

200

0 500 1000

Recommended

Eurocode 3

ASCE

ECCS

ASME

Figure 35: Values of the recommended elastic modulus from various organizations:

Eurocode 3 [1], ASCE [77], and ECCS [9].

ASCE The American Society of Civil Engineers (ASCE) Structural Fire Protection Manual [77], Appendix, page 225 and Figure 2.7, see also Kodur [78],

recommends an an expression

E =







E0





1 +

T

e1 loge(

T

e2

)





T ≤ 600 ◦C

E0



e3 − e4T

T − e5



T > 600 ◦C

(18)
96

where e1 = 2000 ◦C, e2 = 1100 ◦C, e3 = 690, e4 = 0.69 ◦C

−1

, e5 = 53.5

◦C.

The value of the function goes to zero at 1000 ◦C, but then continues, unphysically,

into negative modulus for higher temperatures. The appendix of the manual does

not discuss either the origin or limitations of this expression. The text contains a

reference number, but that number does not appear in the corresponding reference

list. The values predicted by Eq. (18) are drop off more quickly than the smoothed

curve that Lie, the editor of the Structural Fire Protection Manual, presented in his

1974 paper [15].

Eurocode 3 Section F explains the functional dependence of the elastic modulus

of the Eurocode 3 model [1]. The origins of the parameters are not documented.

ECCS The European Convention for Constructional Steelwork, ECCS, published

a stress-strain model in 1983 [9] that includes an elastic term.

EECCS = E0



1 + e1T + e2T

2 + e3T3 + e4T4



(19)

where

e1 = +15.9 × 10−5 ◦C

−1

e2 = −34.5 × 10−7 ◦C

−2

e3 = +11.8 × 10−9 ◦C

−3

e4 = −17.2 × 10−12 ◦C

−4

E0 is the elastic modulus at T = 0 ◦C.

Figure r-3 in the ECCS report [9] shows that E0 = 210 GPa. The function is

explicitly undefined for T > 600 ◦C. The origin of the data used to model the

material behavior is undocumented, other than that it was “based on data obtained

in the Netherlands and elsewhere.” Appendix G summarizes the stress-strain behavior the ECCS model.

E.4.4 Notes on literature reports of elastic modulus measurements

The following paragraphs summarize the methods and limitations of the data for

the steels that appear in Figure 32.

United States Steel (USS) The United States Steel Corp. “Steel Design Manual” [58] recommends a value of E = 200 GPa (E = 29 × 106 psi) for the

room-temperature elastic modulus for all steels (p. 8). Figure 1.7 in the Steel

Design Manual graphically represents the behavior of the elastic modulus up to

T = 538 ◦C. It does not state how the modulus was measured. Because Garofalo [71, 72] (see below) worked for United States Steel, it is possible that the

values in the Steel Design Manual are the values he reported earlier, and that any

differences represent digitization errors from the graphical plots.
97

Clark Clark [69] reprinted elastic modulus data for SAE 1015 steel measured

using an ultrasonic pulse technique, from Frederick’s [79] thesis and conference

report in the temperature range (23 < T < 650)

◦C.

Cooke Cooke [8] presented a smooth curve of the variation of elastic modulus in

the temperature range (0 < T < 793)

◦C from an unpublished 1980 survey made

by Stirland of British Steel Corp. using “many dynamically and some statically

derived data for different grades (FE310, 360, 430, and 510 of Euronorm 25-1972

structural steel.)” He also reported a smoothed curve from unpublished work from

Schleich of Arbed steel, of an unknown structural steel in the temperature range

(91 < T < 1135)

◦C.

Date Date [70], from the British Steel Corporation, measured the elastic modulus of low-carbon steel (C=0.12, Mn=0.47, Si=0.16) at 400 hz using a resonance

technique in the range (20 < T < 600)

◦C. Although the data of Date [70] and

Cooke [8] both originated from the British Steel Corporation, they diverge significantly for T > 300 ◦C.

Garofalo Garofalo [71, 72] reported elastic modulus data measured in his laboratory obtained using simultaneous quasi-static bending and torsion of SAE 1015

steel at stresses less than 28 MPa in the range (22 < T < 482)

◦C. Both papers

also contain data for SAE 1015 steel that he describes as coming from unpublished

investigations by the Steel and Tube division of the Timken Roller Bearing Co,

during 1948–1950. He describes the measurements as “dynamic,” but provides no

other information.

Koster  ̈ Koster [73] measured the elastic modulus of pure metals including iron  ̈

in the temperature range (−150 < T < 1000)

◦C using a dynamic technique. His

measurements are unique in that they extend into the austenite field of the iron

phase diagram.

Ritter As part of a study of stress-relaxation of welds, Ritter et al. [74] measured

the temperature dependence of the stress-strain and elastic modulus of an Australian niobium-strengthened structural steel AS A151 in the temperature range

(20 < T < 572)

◦C. An interesting aspect of the study was that they tested both an

as-normalized plate and a plate heat-treated to produce a larger grain size. The temperature dependence of the modulus of the two steels was significantly different,

and demonstrates that anelastic effects can be significant and that grade and chemistry may not predict behavior. See Figure 33, for Reference 74. They attributed

this difference to grain-boundary relaxation effects.

Roberts Roberts and Nortcliffe [75] measured the elastic modulus of 18 steels,

including a “mild steel” in the temperature range (20 < T < 600)

◦C using a

resonance technique at approximately 400 hz.
98

Uddin Uddin and Culver [76] reported values for elastic modulus measured using unknown techniques on steels of unknown origin by Tall (1961) and by Stanzak

(date and steel unknown) in the temperature range (93 < T < 649)

◦C. The data

of Tall come from an unavailable report. The data of Stanzak are mis-cited, and

cannot be located.

Table 13: Data for elastic modulus of steels from literature sources.

Reference Page Author Steel T E

◦C GPa

[68] 93 ASME [C]<0.3% -198 216

[68] 93 ASME [C]<0.3% -129 212

[68] 93 ASME [C]<0.3% -73 209

[68] 93 ASME [C]<0.3% 21 203

[68] 93 ASME [C]<0.3% 93 199

[68] 93 ASME [C]<0.3% 149 195

[68] 93 ASME [C]<0.3% 204 192

[68] 93 ASME [C]<0.3% 260 188

[68] 93 ASME [C]<0.3% 316 183

[68] 93 ASME [C]<0.3% 371 176

[68] 93 ASME [C]<0.3% 427 167

[68] 93 ASME [C]<0.3% 482 155

[68] 93 ASME [C]<0.3% 538 141

[68] 93 ASME [C]<0.3% 593 124

[68] 93 ASME [C]>0.3% -198 215

[68] 93 ASME [C]>0.3% -129 211

[68] 93 ASME [C]>0.3% -73 208

[68] 93 ASME [C]>0.3% 21 201

[68] 93 ASME [C]>0.3% 93 197

[68] 93 ASME [C]>0.3% 149 194

[68] 93 ASME [C]>0.3% 204 191

[68] 93 ASME [C]>0.3% 260 187

[68] 93 ASME [C]>0.3% 316 182

[68] 93 ASME [C]>0.3% 371 174

[68] 93 ASME [C]>0.3% 427 166

[68] 93 ASME [C]>0.3% 482 154

[68] 93 ASME [C]>0.3% 538 139

[68] 93 ASME [C]>0.3% 593 123

continued on next page
99

Table 13: Data for elastic modulus of steels from literature sources.

Continued from the previous page

Reference Page Author Steel T E

◦C GPa

[68] 93 ASME [C]>0.3% 649 106

[58] 96 USS all structural 93 194

[58] 96 USS all structural 204 188

[58] 96 USS all structural 316 179

[58] 96 USS all structural 371 175

[58] 96 USS all structural 427 167

[58] 96 USS all structural 482 158

[58] 96 USS all structural 538 140

[69] 97 Clark SAE1015 23 212

[69] 97 Clark SAE1015 95 209

[69] 97 Clark SAE1015 205 202

[69] 97 Clark SAE1015 425 184

[69] 97 Clark SAE1015 595 166

[69] 97 Clark SAE1015 650 157

[8] 97 Cooke Arbed 91 212

[8] 97 Cooke Arbed 186 209

[8] 97 Cooke Arbed 247 204

[8] 97 Cooke Arbed 298 197

[8] 97 Cooke Arbed 355 188

[8] 97 Cooke Arbed 406 178

[8] 97 Cooke Arbed 448 166

[8] 97 Cooke Arbed 497 152

[8] 97 Cooke Arbed 541 135

[8] 97 Cooke Arbed 598 113

[8] 97 Cooke Arbed 645 94

[8] 97 Cooke Arbed 713 72

[8] 97 Cooke Arbed 772 55

[8] 97 Cooke Arbed 862 34

[8] 97 Cooke Arbed 928 21

[8] 97 Cooke Arbed 1023 9

[8] 97 Cooke Arbed 1135 2

[8] 97 Cooke Euronorm 25-1972 0 212

[8] 97 Cooke Euronorm 25-1972 94 213

continued on next page
100

Table 13: Data for elastic modulus of steels from literature sources.

Continued from the previous page

Reference Page Author Steel T E

◦C GPa

[8] 97 Cooke Euronorm 25-1972 135 203

[8] 97 Cooke Euronorm 25-1972 230 192

[8] 97 Cooke Euronorm 25-1972 287 184

[8] 97 Cooke Euronorm 25-1972 358 169

[8] 97 Cooke Euronorm 25-1972 415 156

[8] 97 Cooke Euronorm 25-1972 473 140

[8] 97 Cooke Euronorm 25-1972 530 122

[8] 97 Cooke Euronorm 25-1972 584 104

[8] 97 Cooke Euronorm 25-1972 621 89

[8] 97 Cooke Euronorm 25-1972 667 68

[8] 97 Cooke Euronorm 25-1972 728 48

[8] 97 Cooke Euronorm 25-1972 778 34

[8] 97 Cooke Euronorm 25-1972 793 31

[70] 97 Date [C]=0.12 % 20 210

[70] 97 Date [C]=0.12 % 100 204

[70] 97 Date [C]=0.12 % 200 198

[70] 97 Date [C]=0.12 % 300 190

[70] 97 Date [C]=0.12 % 400 182

[70] 97 Date [C]=0.12 % 500 172

[70] 97 Date [C]=0.12 % 600 161

[71] 97 Garafolo SAE1015 24 202

[71] 97 Garafolo SAE1015 149 193

[71] 97 Garafolo SAE1015 260 184

[71] 97 Garafolo SAE1015 371 177

[71] 97 Garafolo SAE1015 482 154

[72] 97 Garafolo Timken Co. 22 212

[72] 97 Garafolo Timken Co. 93 208

[72] 97 Garafolo Timken Co. 149 205

[72] 97 Garafolo Timken Co. 204 201

[72] 97 Garafolo Timken Co. 260 196

[72] 97 Garafolo Timken Co. 316 192

[72] 97 Garafolo Timken Co. 371 188

[72] 97 Garafolo Timken Co. 427 183

continued on next page
101

Table 13: Data for elastic modulus of steels from literature sources.

Continued from the previous page

Reference Page Author Steel T E

◦C GPa

[72] 97 Garafolo Timken Co. 482 179

[72] 97 Garafolo Timken Co. 538 174

[72] 97 Garafolo Timken Co. 593 170

[72] 97 Garafolo Timken Co. 649 161

[72] 97 Garafolo Timken Co. 704 151

[72] 97 Garafolo Timken Co. 760 141

[73] 97 Koester Austenite 905 120

[73] 97 Koester Austenite 912 120

[73] 97 Koester Austenite 930 118

[73] 97 Koester Austenite 935 117

[73] 97 Koester Austenite 965 114

[73] 97 Koester Austenite 985 112

[73] 97 Koester Ferrite 20 211

[73] 97 Koester Ferrite 105 206

[73] 97 Koester Ferrite 245 196

[73] 97 Koester Ferrite 390 186

[73] 97 Koester Ferrite 498 176

[73] 97 Koester Ferrite 600 167

[73] 97 Koester Ferrite 680 157

[73] 97 Koester Ferrite 715 147

[73] 97 Koester Ferrite 720 145

[74] 97 Ritter AS A151 ASTM GS 5 20 210

[74] 97 Ritter AS A151 ASTM GS 5 98 205

[74] 97 Ritter AS A151 ASTM GS 5 147 204

[74] 97 Ritter AS A151 ASTM GS 5 254 195

[74] 97 Ritter AS A151 ASTM GS 5 300 191

[74] 97 Ritter AS A151 ASTM GS 5 348 182

[74] 97 Ritter AS A151 ASTM GS 5 356 178

[74] 97 Ritter AS A151 ASTM GS 5 424 175

[74] 97 Ritter AS A151 ASTM GS 5 499 165

[74] 97 Ritter AS A151 ASTM GS 5 548 162

[74] 97 Ritter AS A151 ASTM GS 5 571 160

[74] 97 Ritter AS A151 ASTM GS 5 572 157

continued on next page
102

Table 13: Data for elastic modulus of steels from literature sources.

Continued from the previous page

Reference Page Author Steel T E

◦C GPa

[74] 97 Ritter AS A151 ASTM GS 8-9 20 210

[74] 97 Ritter AS A151 ASTM GS 8-9 147 200

[74] 97 Ritter AS A151 ASTM GS 8-9 149 202

[74] 97 Ritter AS A151 ASTM GS 8-9 199 196

[74] 97 Ritter AS A151 ASTM GS 8-9 298 173

[74] 97 Ritter AS A151 ASTM GS 8-9 299 178

[74] 97 Ritter AS A151 ASTM GS 8-9 299 175

[74] 97 Ritter AS A151 ASTM GS 8-9 350 157

[74] 97 Ritter AS A151 ASTM GS 8-9 350 152

[74] 97 Ritter AS A151 ASTM GS 8-9 350 151

[74] 97 Ritter AS A151 ASTM GS 8-9 350 147

[74] 97 Ritter AS A151 ASTM GS 8-9 400 152

[74] 97 Ritter AS A151 ASTM GS 8-9 400 147

[74] 97 Ritter AS A151 ASTM GS 8-9 401 142

[74] 97 Ritter AS A151 ASTM GS 8-9 448 148

[74] 97 Ritter AS A151 ASTM GS 8-9 448 148

[74] 97 Ritter AS A151 ASTM GS 8-9 449 144

[74] 97 Ritter AS A151 ASTM GS 8-9 498 144

[74] 97 Ritter AS A151 ASTM GS 8-9 499 143

[74] 97 Ritter AS A151 ASTM GS 8-9 499 146

[74] 97 Ritter AS A151 ASTM GS 8-9 500 137

[74] 97 Ritter AS A151 ASTM GS 8-9 550 139

[74] 97 Ritter AS A151 ASTM GS 8-9 550 143

[74] 97 Ritter AS A151 ASTM GS 8-9 550 140

[75] 97 Roberts mild steel 20 208

[75] 97 Roberts mild steel 200 196

[75] 97 Roberts mild steel 400 182

[75] 97 Roberts mild steel 600 161

[76] 98 Uddin not reported 93 200

[76] 98 Uddin not reported 204 184

[76] 98 Uddin not reported 260 170

[76] 98 Uddin not reported 316 152

[76] 98 Uddin not reported 371 132

continued on next page
103

Table 13: Data for elastic modulus of steels from literature sources.

Continued from the previous page

Reference Page Author Steel T E

◦C GPa

[76] 98 Uddin not reported 427 114

[76] 98 Uddin not reported 482 99

[76] 98 Uddin not reported 538 86

[76] 98 Uddin not reported 649 66

[76] 98 Uddin structural 93 200

[76] 98 Uddin structural 204 193

[76] 98 Uddin structural 260 186

[76] 98 Uddin structural 316 182

[76] 98 Uddin structural 371 175

[76] 98 Uddin structural 427 167

[76] 98 Uddin structural 482 159

[76] 98 Uddin structural 538 146

[76] 98 Uddin structural 649 121

E.5 Strain rate sensitivity of literature steels

Figure 5 combines data from several of the literature sources. [6, 25, 29, 31, 33,

40, 62] Where possible, the strain rate sensitivity, m, for each of the steels in

these sources was calculated from the reported strain rates and 0.2 % offset yield

strengths, Sy(0.002 offset), summarized in Table 10. At each temperature, a linear

regression of that yield strength, loge(Sy), on the natural logarithm of the strain

rate, loge( ̇) produced an estimate of the strain rate sensitivity, m. If the data

contained more than two points at that temperature, the regression also yields an

estimate of the uncertainty of the strain rate sensitivity, u(m). Table 8, at the end

of this section, compiles the computed strain rate sensitivities for each steel.

Figure 36 shows the data used to calculate the strain rate sensitivity, m, for the

steels listed in Table 15, grouped by temperature range.

E.5.1 A model for m(T) for structural steel

Figure 5 plots a fit of Eq. (9) to the entire data set including the steels of this report

and the literature steels that the previous section describes. Table 3 summarizes the

parameters. Like other non-linear least-squares fits to data in this report, the fit was

constrained:

m0 not fit,

1 ≤ m1 ≤ 10,
104

log10(ε

⋅

) / 1/s

S

y /MPa

100

200

300

400

500

-6 -4 -2 0 2

A992 Ref. 40 AS187:WR350/1 Ref. 6

-6 -4 -2 0 2

AS3679.1 Ref. 31

AS A186:250 L0 Ref. 6 AS A186:250 Ref. 33

100

200

300

400

500

AS A186:400 L15 Ref. 6

100

200

300

400

500

ASME-SA516 Ref. 25 CSA G40.21 350AT Ref. 29 CSA G40.21 350WT Ref. 29

100

200

300

400

500

mild steel Ref. 62

T range

(0,200] °C

(200,350] °C

(350,500] °C

(500,600] °C

(600,650] °C

(650,950] °C

Figure 36: 0.2 % offset yield strength, Sy(0.2 % offset), as a function of strain rate,

 ̇ for literature data. Data are grouped by temperature range.

(100 ≤ m2 ≤ 3000)

◦C,

0.01 ≤ m3 ≤ 0.25,

T ≥ 390 ◦C,

data from Ref. 62 omitted.

The strain rate sensitivity at room temperature, m0, was not fit. Instead it was set to

the mean value of the room-temperature data. None of the values of the parameters

in Table 14 are near the constraints.
105

Table 14: Output of the regression for m(T).

Parameter Estimate Standard Error t

m1 7.30844 1.54486 4.73082

m2 613.10509 21.78958 28.13754

m3 0.12602 0.01321 9.54318

RSD: 0.03259 on 68 degrees of freedom

m0 0.01079 0.00261

uncertainty of m0 calculated from the standard deviation of

23 measurements of m0.

Table 15: Literature values of strain rate sensitivity m used in Figure 5.

Reference Section Steel T m u(m)

◦C

[25] E.1.16 ASME-SA516 25 0.01512 0.00548

[25] E.1.16 ASME-SA516 315 0.02204 0.00305

[25] E.1.16 ASME-SA516 427 0.00989 0.00319

[25] E.1.16 ASME-SA516 537 0.02574 0.00281

[25] E.1.16 ASME-SA516 649 0.06432 0.0017

[25] E.1.16 ASME-SA516 760 0.10941 0.0072

[25] E.1.16 ASME-SA516 815 NA NA

[25] E.1.16 ASME-SA516 871 0.0878 0.00542

[25] E.1.16 ASME-SA516 927 NA NA

[62] E.1.16 mild steel 20 0.05047 0.01083

[62] E.1.16 mild steel 200 0.05142 0.01211

[62] E.1.16 mild steel 400 0.02178 0.00204

[62] E.1.16 mild steel 600 0.11158 0.00256

[31] E.1.16 AS3679.1 20 0.01195 0.00294

[31] E.1.16 AS3679.1 300 NA NA

[31] E.1.16 AS3679.1 400 0.00089 0.07214

[31] E.1.16 AS3679.1 500 0.01898 0.00877

[31] E.1.16 AS3679.1 600 0.0869 0.0

[31] E.1.16 AS3679.1 700 0.12675 0.00416

[31] E.1.16 AS3679.1 800 0.11937 NA

NA: not available

continued on next page
106

Table 15: Literature values of strain rate sensitivity m used in Figure 5.

Continued from the previous page

Reference Steel Steel T m u(m)

◦C

[33] E.1.16 AS A186:250 27 0.01645 0.00133

[33] E.1.16 AS A186:250 100 NA NA

[33] E.1.16 AS A186:250 200 NA NA

[33] E.1.16 AS A186:250 300 -0.01565 NA

[33] E.1.16 AS A186:250 350 0.0033 0.01495

[33] E.1.16 AS A186:250 400 0.02776 0.00679

[33] E.1.16 AS A186:250 450 0.02429 0.004

[33] E.1.16 AS A186:250 500 0.11788 0.0291

[33] E.1.16 AS A186:250 550 0.10429 0.00573

[33] E.1.16 AS A186:250 600 0.07879 0.01795

[33] E.1.16 AS A186:250 650 0.14569 0.00035

[6] E.1.16 AS187:WR350/1 27 0.00562 0.00177

[6] E.1.16 AS187:WR350/1 100 0.00288 NA

[6] E.1.16 AS187:WR350/1 200 0.00743 0.0013

[6] E.1.16 AS187:WR350/1 300 0.02077 NA

[6] E.1.16 AS187:WR350/1 350 0.00335 0.00267

[6] E.1.16 AS187:WR350/1 400 0.00415 0.00326

[6] E.1.16 AS187:WR350/1 450 0.01261 0.00215

[6] E.1.16 AS187:WR350/1 475 0.02304 NA

[6] E.1.16 AS187:WR350/1 500 0.05179 0.00583

[6] E.1.16 AS187:WR350/1 550 0.08645 0.00193

[6] E.1.16 AS187:WR350/1 600 0.08872 0.00039

[6] E.1.16 AS187:WR350/1 650 0.09698 0.00316

[6] E.1.16 AS A186:250 L0 27 -0.0071 NA

[6] E.1.16 AS A186:250 L0 350 0.03814 NA

[6] E.1.16 AS A186:250 L0 400 0.01695 NA

[6] E.1.16 AS A186:250 L0 450 0.01741 NA

[6] E.1.16 AS A186:250 L0 500 0.0031 NA

[6] E.1.16 AS A186:250 L0 550 0.07287 NA

[6] E.1.16 AS A186:250 L0 600 0.12696 NA

[6] E.1.16 AS A186:250 L0 650 0.16832 NA

[6] E.1.16 AS A186:400 L15 27 0.00905 0.00075

NA: not available

continued on next page
107

Table 15: Literature values of strain rate sensitivity m used in Figure 5.

Continued from the previous page

Reference Steel Steel T m u(m)

◦C

[6] E.1.16 AS A186:400 L15 100 NA NA

[6] E.1.16 AS A186:400 L15 200 NA NA

[6] E.1.16 AS A186:400 L15 300 0.00563 NA

[6] E.1.16 AS A186:400 L15 350 0.00849 NA

[6] E.1.16 AS A186:400 L15 400 0.02009 NA

[6] E.1.16 AS A186:400 L15 450 0.01993 NA

[6] E.1.16 AS A186:400 L15 500 0.05389 NA

[6] E.1.16 AS A186:400 L15 550 0.1142 NA

[6] E.1.16 AS A186:400 L15 600 0.15622 NA

[6] E.1.16 AS A186:400 L15 650 0.19389 NA

[40] E.1.16 A992 20 0.00703 NA

[40] E.1.16 A992 100 -0.0032 NA

[40] E.1.16 A992 200 -0.00538 NA

[40] E.1.16 A992 300 0.02283 NA

[40] E.1.16 A992 400 -0.00146 NA

[40] E.1.16 A992 500 0.00171 NA

[40] E.1.16 A992 600 0.04804 NA

[40] E.1.16 A992 700 0.10474 NA

[40] E.1.16 A992 800 0.16419 NA

[40] E.1.16 A992 900 0.22185 NA

[29] E.1.16 CSA G40.21 350AT 20 0.00806 0.00194

[29] E.1.16 CSA G40.21 350AT 100 0.00927 0.00144

[29] E.1.16 CSA G40.21 350AT 150 0.01705 0.00182

[29] E.1.16 CSA G40.21 350AT 200 0.02347 0.00883

[29] E.1.16 CSA G40.21 350AT 250 0.02887 0.01191

[29] E.1.16 CSA G40.21 350AT 300 0.04061 0.01845

[29] E.1.16 CSA G40.21 350WT 20 0.04512 0.02008

[29] E.1.16 CSA G40.21 350WT 100 0.04133 0.01083

[29] E.1.16 CSA G40.21 350WT 150 0.04919 0.02241

[29] E.1.16 CSA G40.21 350WT 200 0.02672 0.01558

[29] E.1.16 CSA G40.21 350WT 250 0.03618 0.0104

[29] E.1.16 CSA G40.21 350WT 300 0.02649 0.0117

NA: not available

continued on next page
108

Table 15: Literature values of strain rate sensitivity m used in Figure 5.

Continued from the previous page

Reference Steel Steel T m u(m)

◦C

[29] E.1.16 CSA G40.21 350WT 350 0.04902 0.01298

NA: not available

F Eurocode stress-strain model

No publicly available document explains the basis for the choices of the form of the

Eurocode 3 [1] stress-strain model or the values of the parameters in it. This section

summarizes the Eurocode 3 stress-strain model and compares its predictions to the

data of this report.

F.1 Shape of the stress-strain curve

The shape of the engineering stress-strain, S − e, curve in the Eurocode 3 formulation comprises four regions:

1. a linear elastic region,

2. a plastic region described by an ellipse that connects the end of the linearelastic region to e = 0.02,

3. a plastic region of constant maximum stress with increasing strain, possibly

with a short region of strain hardening for T < 400 ◦C, and

4. a plastic region where the stress decreases from the maximum to zero.

Figure 37 shows the shape of the engineering stress-strain curve in the Eurocode 3

model in regions I, II, and III. The temperature dependence of the engineering

stress-strain behavior in the first three regions is captured in four parameters:

1. a temperature-dependent Young’s modulus, E ̄

a,θ,

2. a temperature-dependent proportional limit, fap,θ,

3. a temperature-dependent maximum stress, famax,θ, and

4. a temperature-dependent tensile strength with strain hardening, fau,θ
109

Figure 37: The shape of the Eurocode 3 stress-strain curve. Dashed line shows the

shape of the curve for temperatures, T ≤ 400 ◦C.

Three separate equations describe the change in engineering stress, S, in the first

three regions of engineering strain, e:

S =







E ̄

a,θ e for 0 ≤ e ≤

fap,θ

E ̄

a,θ

, (Reg. 1)

b

a

p

a

2 + (0.02 − e)2 + fap,θ − c for

fap,θ

E ̄

a,θ

≤ e ≤ 0.02, (Reg. 2)

famax,θ for e ≥ 0.02 and T > 400 ◦C, (Reg. 3)

(20)

For temperatures below 400 ◦C, Region III is modified to express strain hardening.

For these conditions

S =









fau,θ − famax,θ

0.02 

e − fau,θ + 2famax,θ for 0.02 < e < 0.04

fau,θ for e ≥ 0.04

(21)
110

The parameters, a, b, and c that describe the ellipse that connects the elastic region

(I) to the constant plastic region (III) are

a =

s

(0.02 −

fap,θ

E ̄

a,θ

)(0.02 −

fap,θ

E ̄

a,θ

+

c

E ̄

a,θ

) (22)

b =

s

E ̄

a,θ(0.02 −

fap,θ

E ̄

a,θ

)c + c

2 (23)

c =

(famax,θ − fap,θ)

2

E ̄

a,θ(0.02 −

fap,θ

E ̄

a,θ

) − 2(famax,θ − fap,θ)

(24)

The temperature dependence of the three terms that describe the change in

shape of the stress-strain curve, Figure 37, are expressed as discrete points connected by linear segments rather than by smooth functions. In addition, they are

expressed as values normalized to either the room-temperature elastic modulus, in

the case of E ̄

a,θ, or the room-temperature yield strength, Sy(0.2 % offset) in the

case of fap,θ, famax,θ, and fau,θ:

kE,θ =

E ̄

a,θ

E ̄

T =20 ◦C

Modulus (25)

kp,θ =

fap,θ

Sy

Proportional limit (26)

kmax,θ =

famax,θ

Sy

Maximum stress (27)

ku,θ =

fau,θ

Sy

Tensile strength (28)

where Sy = Sy(0.2 % offset), the room-temperature 0.2 % offset yield strength. It

is important to recognize that neither the proportional limit, fap,θ, nor the maximum

stress, famax,θ, in the Eurocode 3 formulation corresponds to points usually calculated in room- or elevated-temperature stress-strain curves. Figure 38 and Table 16

show the temperature dependence of the four parameters. Symbols in Figure 38

indicate the fixed points.

Figure 39 shows the evolution of the engineering stress-strain curve with temperature. Note that the individual curves for (20 ≤ T ≤ 300) ◦C lie on top of each

other for e > 0.02. Only the shape of the curve for e < 0.02 changes for those

temperatures, as the knee at T = 20 ◦C transforms into a shallower ellipse.
111

T /°C

Parameter value

0.0

0.5

1.0

0 200 400 600 800 1000 1200

Tensile strength

Maximum stress

Modulus

Proportional limit

Figure 38: Temperature dependence of the four strength parameters in the Eurocode 3 stress-strain equation: tensile strength fau,θ, maximum stress famax,θ, elastic modulus E ̄

a,θ, and proportional limit fap,θ. Equations (25), (26), (27), and (28)

define the parameters.

F.2 Computing the yield strength

The Eurocode 3 stress-strain model does not contain an explicit expression for the

traditional e = 0.002 offset yield strength, Sy(0.002 offset), that typically appears

in literature reports. It is possible, however to compute it for by solving numerically

for the intersection of the offset elastic modulus line and the stress-strain curve.
112

Engineering strain

Normalized Engineering stress

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.000 0.005 0.010 0.015 0.020 0.025 0.030

(a) small strain

Engineering strain

Normalized Engineering stress

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.05 0.10 0.15

T /°C

20

200

300

350

400

500

600

700

800

900

(b) large strain

Figure 39: Temperature dependence of the Eurocode 3 engineering stress-strain

curve. (a) small strain, and (b) large strain

.
113

Table 16: Eurocode 3 non-dimensional reduction factors used in Eq. (25), Eq. (26),

Eq. (27), and Eq. (28).

T kE,θ kp,θ kmax,θ ku,θ

◦C

20 1.0000 1.0000 1.0000 1.2500

100 1.0000 1.0000 1.0000 1.2500

200 0.9000 0.8070 1.0000 1.2500

300 0.8000 0.6130 1.0000 1.2500

400 0.7000 0.4200 1.0000 1.0000

500 0.6000 0.3600 0.7800 0.7800

600 0.3100 0.1800 0.4700 0.4700

700 0.1300 0.0750 0.2300 0.2300

800 0.0900 0.0500 0.1100 0.1100

900 0.0675 0.0375 0.0600 0.0600

1000 0.0450 0.0250 0.0400 0.0400

1100 0.0225 0.0125 0.0200 0.0200

1200 0.0000 0.0000 0.0000 0.0000

The strain at the intersection, e

0

, occurs at the minimum of the function

f =

q

(S(e) − E ̄

a,θ(e − 0.002))2 (29)

The stress, S(e), is defined in Eq. (20) and Eq. (21), and the linear elastic portion,

E ̄

a,θ, is defined in Eq. (25) The yield strength is can be calculated from Sy(e

0

). This

line is plotted in Figure 2, using Sy(0.2 % offset)=250 MPa (approximately 36 ksi)

and room-temperature Young’s modulus E ̄

a,20 ◦C = 210 GPa. The absolute value

of the retained strength, R, is a very weak function of the yield strength chosen.

F.3 Comparison to Eurocode prediction

Figure 40, which complements the relative deviation plot, Fig. 8, plots the absolute

deviations of the stress-strain curves between the Eurocode prediction, Eq. (20) and

the data of this study. Note that the Eurocode prediction for the five lowest-strength

steels is consistently lower than the actual data. Figures 41 through 49 compare

the prediction of the NIST global model, Eq. (10) and Table 3, to the prediction

of the Eurocode 3 stress-strain model, Eq. (20) and (21). In the following figures,

the prediction of the Eurocode 3 engineering stress-strain, S − e, model has been
114

transformed to true stress-strain σ −  behavior by

σ = S(1 + e) (30)

 = loge(1 + e) (31)

For the NIST models of the individual steels, the only input is the measured roomtemperature yield strength.

True Strain

Absolute deviation /MP

a

-200

-100

0

100

200

0.00 0.10 0.20

 226 MPa C65_FL

0.00 0.10 0.20

 233 MPa C80_FL_L

0.00 0.10 0.20

 234 MPa C128

-200

-100

0

100

200

 362 MPa HH_FL_1 386 MPa C53BA 406 MPa C132

-200

-100

0

100

200

 436 MPa C40_C2M_IW 473 MPa N8_C1B1A T /°C

20

300

400

431

500

539

600

647

650

701

Figure 40: Absolute deviation, Da between true stress predicted by the Eurocode 3

stress-strain model, Eq. (20), and the observed behavior.
115

True strain

True stress /MPa

0

200

400

600

0.00 0.05 0.10 0.15

This report

0.00 0.05 0.10 0.15

data

0.00 0.05 0.10 0.15

Eurocode 3

C65_FL

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 41: Comparison of predicted true stress, Eq. (10), to prediction of Eurocode 3 model for specimen C65 FL. Sy(0.2 % offset) = 226 MPa. Left plot:

this report; center plot: original data; right plot: Eurocode 3 prediction.
116

True strain

True stress /MPa

0

200

400

600

0.00 0.05 0.10 0.15

This report

0.00 0.05 0.10 0.15

data

0.00 0.05 0.10 0.15

Eurocode 3

C80_FL_L

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 42: Comparison of predicted true stress, Eq. (10), to prediction of Eurocode 3 model for specimen C80 FL L. Sy(0.2 % offset) = 233 MPa. Left plot:

this report; center plot: original data; right plot: Eurocode 3 prediction.
117

True strain

True stress /MPa

0

100

200

300

400

500

600

0.00 0.05 0.10 0.15

This report

0.00 0.05 0.10 0.15

data

0.00 0.05 0.10 0.15

Eurocode 3

C128

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 43: Comparison of predicted true stress, Eq. (10), to prediction of Eurocode 3 model for specimen C128. Sy(0.2 % offset) = 234 MPa. Left plot:

this report; center plot: original data; right plot: Eurocode 3 prediction.
118

True strain

True stress /MPa

0

200

400

600

0.00 0.05 0.10 0.15

This report

0.00 0.05 0.10 0.15

data

0.00 0.05 0.10 0.15

Eurocode 3

HH_FL_1

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 44: Comparison of predicted true stress, Eq. (10), to prediction of Eurocode 3 model for specimen HH FL 1. Sy(0.2 % offset) = 362.1 MPa. Left

plot: this report; center plot: original data; right plot: Eurocode 3 prediction.
119

True strain

True stress /MPa

0

200

400

600

0.00 0.05 0.10 0.15

This report

0.00 0.05 0.10 0.15

data

0.00 0.05 0.10 0.15

Eurocode 3

C53BA

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 45: Comparison of predicted true stress, Eq. (10), to prediction of Eurocode 3 model for specimen C53BA. Sy(0.2 % offset) = 386 MPa. Left plot:

this report; center plot: original data; right plot: Eurocode 3 prediction.
120

True strain

True stress /MPa

0

200

400

600

0.00 0.05 0.10 0.15

This report

0.00 0.05 0.10 0.15

data

0.00 0.05 0.10 0.15

Eurocode 3

C132

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 46: Comparison of predicted true stress, Eq. (10), to prediction of Eurocode 3 model for specimen C132. Sy(0.2 % offset) = 406 MPa. Left plot:

this report; center plot: original data; right plot: Eurocode 3 prediction.
121

True strain

True stress /MPa

0

200

400

600

0.00 0.05 0.10 0.15

This report

0.00 0.05 0.10 0.15

data

0.00 0.05 0.10 0.15

Eurocode 3

C40_C2M_IW

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 47: Comparison of predicted true stress, Eq. (10), to prediction of Eurocode 3 model for specimen C40 C2M IW. Sy(0.2 % offset) = 436 MPa. Left

plot: this report; center plot: original data; right plot: Eurocode 3 prediction.
122

True strain

True stress /MPa

0

200

400

600

800

0.00 0.05 0.10 0.15

This report

0.00 0.05 0.10 0.15

data

0.00 0.05 0.10 0.15

Eurocode 3

N8_C1B1A

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 48: Comparison of predicted true stress, Eq. (10), to prediction of Eurocode 3 model for specimen N8 C1B1A. Sy(0.2 % offset) = 473.4 MPa. Left

plot: this report; center plot: original data; right plot: Eurocode 3 prediction.
123

True strain

True stress /MPa

0

200

400

600

800

1000

0.00 0.05 0.10 0.15

This report

0.00 0.05 0.10 0.15

data

0.00 0.05 0.10 0.15

Eurocode 3

C10_C1M_FL

T /°C

20

300

400

431

500

539

593

600

647

650

701

Figure 49: Comparison of predicted true stress, Eq. (10), to prediction of Eurocode 3 model for specimen C10 C1M FL. Sy(0.2 % offset) = 760 MPa. Left

plot: this report; center plot: original data; right plot: Eurocode 3 prediction.
124

G ECCS stress-strain model

The European Convention for Constructional Steelwork (ECCS) Technical Committee 3 published a recommended stress-strain model [9] for structural steel in

1983. Aside from a citations by some of the report’s authors [39], the stress-strain

model has not been frequently used. The model itself was “based on data obtained

in the Netherlands and elsewhere.” Unlike other models of the era, it includes

the effects of time-dependent deformation through an effective yield strength that

degrades with temperature faster than the measured yield strength. The report,

however, does not explain the technical basis for the calculation of effective yield

strength or support the model with any data. The reduction, R, in effective yield

strength is

R = 1 +

T

te1 loge

T

te2

0

◦C ≤ T ≤ 600 ◦C (32)

R =

te3(1 −

T

te4

)

T − te5

600 ◦C ≤ T ≤ 1000 ◦C

where

te1 = 767 ◦C,

te2 = 1750 ◦C,

te3 = 108,

te4 = 1000 ◦C, and

te5 = 440 ◦C.

Figure 50 compares the retained strength from Eq. (32) to the other retained strength

models, including the Eurocode 3 [1], section F.2 and the four-parameter function

of this report, Eq. (1). The ECCS model predicts the lowest retained strength,

which is consistent with its assertion that it incorporates time-dependent deformation. The retained strength line lies well below all the other models for T = 400 ◦C,

where creep is not significant, however.

The ECCS report does not describe the stress-strain behavior analytically, but

instead displays stress-strain curves for discrete temperatures graphically as Fig.

r-1. Figure 51 compares the the Eurocode 3 [1] and the ECCS stress-strain models

digitized from the report in the range 0 < e < 0.04, for a steel with specified yield

strength, Fy = 235 MPa. The stress-strain curves strain harden briefly after yield

to the effective yield strain, which typically occurs e < 0.005, and then become

perfectly plastic. The individual points on the stress-strain curves are not calculated
125

T /°C

R

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 200 400 600 800 1000

R= 0.5

538 °C

Literature

This study

full fit

WTC fit

Eurocode 3

ECCS

(a) full temperature range

T /°C

R

0.0

0.2

0.4

0.6

0.8

1.0

450 500 550 600 650 700

538 °C

Literature

This study

full fit

WTC fit

Eurocode 3

ECCS

(b) expanded temperature range

Figure 50: ECCS recommended effective retained yield strength compared to other

retained strength models. (a) full temperature range. (b) temperature range where

strength drop is largest.
126

Engineering Strain

Engineering Stress /MP

a

0

50

100

150

200

250

300

0.00 0.02 0.04

T=20°C T=200°C

0.00 0.02 0.04

T=250°C T=275°C

T=300°C T=350°C T=400°C

0

50

100

150

200

250

300

T=450°C

0

50

100

150

200

250

300

T=500°C

0.00 0.02 0.04

T=550°C T=600°C

Eurocode 3

ECCS

Figure 51: ECCS stress-strain model compared to the Eurocode 3 stress-strain

model.

from an analytical function, but are instead tabulated as individual points at specified temperatures for different grades of steel. Consistent with the retained strength

behavior, the ECCS model predicts lower strength for all strains and temperatures.
127

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