Strength reduction at elevated temperatures - Revision history

Emma: Add 3 watermarked SVG illustrations from the Advanced visual plan

2026-11-02T15:46:11Z

Add 3 watermarked SVG illustrations from the Advanced visual plan

← Older revision		Revision as of 16:46, 2 November 2026
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	The reference property must be identified before a reduction factor can be interpreted. A common expression divides strength at the elevated temperature by the same type of strength at room temperature. Both values must use compatible definitions and units. A factor below unity then indicates a reduction relative to that reference condition.<ref name="KH-158" />		The reference property must be identified before a reduction factor can be interpreted. A common expression divides strength at the elevated temperature by the same type of strength at room temperature. Both values must use compatible definitions and units. A factor below unity then indicates a reduction relative to that reference condition.<ref name="KH-158" />
			[[File:fse-strength-reduction-at-elevated-temperatures-v1.svg\|thumb\|upright=1.5\|alt=A flow diagram connects material data with a structural calculation that also requires geometry and loading.\|Material strength reduction is one input to structural resistance. Based on Kodur and Harmathy (2002), pp. 1-155 and 1-158; Milke (2002), pp. 4-229–4-231.]]

	<div class="fse-equation">k<sub>f,T</sub> = f<sub>T</sub> / f<sub>ref</sub>;   f<sub>T</sub> = k<sub>f,T</sub> f<sub>ref</sub></div>		<div class="fse-equation">k<sub>f,T</sub> = f<sub>T</sub> / f<sub>ref</sub>;   f<sub>T</sub> = k<sub>f,T</sub> f<sub>ref</sub></div>
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	For an illustrative reference yield strength of 250 MPa, the calculated factors are approximately 0.612 at 500 °C and 0.462 at 600 °C. Multiplication gives approximately 153 MPa and 115 MPa respectively. The reference strength is an assumed example input; the factors come from the published expression. They are calculated values, rather than additional test observations. Using the same reference strength at both temperatures isolates the temperature dependence of the selected relationship. Changing that reference would scale both calculated strengths proportionally.<ref name="L-134" /><ref name="L-136" />		For an illustrative reference yield strength of 250 MPa, the calculated factors are approximately 0.612 at 500 °C and 0.462 at 600 °C. Multiplication gives approximately 153 MPa and 115 MPa respectively. The reference strength is an assumed example input; the factors come from the published expression. They are calculated values, rather than additional test observations. Using the same reference strength at both temperatures isolates the temperature dependence of the selected relationship. Changing that reference would scale both calculated strengths proportionally.<ref name="L-134" /><ref name="L-136" />
			[[File:fse-strength-reduction-at-elevated-temperatures-v2.svg\|thumb\|upright=1.5\|alt=Two bars show factors of about 0.612 at 500 °C and 0.462 at 600 °C.\|Illustrative outputs from the NIST empirical steel relationship. Based on Luecke et al. (2005), Equation 6–1 and Table 6–2, pp. 134 and 136.]]

	The calculation describes neither the time needed to reach these temperatures nor the capacity of a complete steel member. It also does not remove the discrepancy between the empirical curve and measurements discussed in the report. Selecting a relationship for an actual analysis requires compatibility with the material, test definition and structural model. Reproducing an equation correctly is only one part of that selection.<ref name="L-134-137" /><ref name="M-229-231">Milke (2002), pp. 4-229–4-231.</ref>		The calculation describes neither the time needed to reach these temperatures nor the capacity of a complete steel member. It also does not remove the discrepancy between the empirical curve and measurements discussed in the report. Selecting a relationship for an actual analysis requires compatibility with the material, test definition and structural model. Reproducing an equation correctly is only one part of that selection.<ref name="L-134-137" /><ref name="M-229-231">Milke (2002), pp. 4-229–4-231.</ref>
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	One important distinction is whether a specimen carries load while it is heated. The handbook presents concrete datasets for specimens heated without load and others heated under a sustained compressive load. It also presents residual-strength results obtained after heating, cooling and subsequent conditioning. These procedures examine different material histories even when the maximum temperature is the same.<ref name="KH-169">Kodur and Harmathy (2002), p. 1-169.</ref>		One important distinction is whether a specimen carries load while it is heated. The handbook presents concrete datasets for specimens heated without load and others heated under a sustained compressive load. It also presents residual-strength results obtained after heating, cooling and subsequent conditioning. These procedures examine different material histories even when the maximum temperature is the same.<ref name="KH-169">Kodur and Harmathy (2002), p. 1-169.</ref>
			[[File:fse-strength-reduction-at-elevated-temperatures-v3.svg\|thumb\|upright=1.5\|alt=Three timelines distinguish loaded and unloaded hot tests from a test conducted after cooling.\|Concrete strength curves depend on the testing sequence. Based on Kodur and Harmathy (2002), p. 1-169.]]

	A residual-strength curve therefore cannot silently replace a hot-strength curve in a calculation during fire. The former includes the effects of cooling and the stated post-heating treatment. The latter concerns strength while the specimen remains hot. Recording the testing sequence is necessary to identify which structural question the reported property can answer.<ref name="KH-169" />		A residual-strength curve therefore cannot silently replace a hot-strength curve in a calculation during fire. The former includes the effects of cooling and the stated post-heating treatment. The latter concerns strength while the specimen remains hot. Recording the testing sequence is necessary to identify which structural question the reported property can answer.<ref name="KH-169" />

Peter: New FSE wiki article: Strength reduction at elevated temperatures (written by GPT-6)

2026-11-01T22:39:21Z

New FSE wiki article: Strength reduction at elevated temperatures (written by GPT-6)

New page

'''Strength reduction at elevated temperatures''' is the change in a material's tensile, compressive or yield strength as its temperature increases. It is commonly expressed as a fraction of the corresponding strength at a reference temperature. Kodur and Harmathy distinguish this strength change from changes in elastic modulus and creep, which also influence structural behaviour during fire.<ref name="KH-158">Kodur and Harmathy (2002), p. 1-158.</ref>

The reduction depends on the material, the property being measured and the conditions of the test. A factor for structural steel cannot automatically describe prestressing steel, concrete or timber. Even within one material family, heating history, moisture, strain rate and the definition of strength can affect the result. These distinctions become important when laboratory data are converted into inputs for a structural calculation.<ref name="KH-165-169">Kodur and Harmathy (2002), pp. 1-165–1-169.</ref><ref name="L-134-137">Luecke et al. (2005), pp. 134–137.</ref>

A strength reduction factor describes a material response; it does not by itself give the fire resistance of a member. The calculation must also represent temperatures within the section, loading, geometry and the relevant failure mechanism. Loss of material through charring or spalling requires additional treatment because it changes the section as well as its properties.<ref name="KH-155">Kodur and Harmathy (2002), p. 1-155.</ref><ref name="I-9-10">Australian Building Codes Board et al. (2005), pp. 2.6-9–2.6-10.</ref>

== Meaning of a reduction factor ==

The reference property must be identified before a reduction factor can be interpreted. A common expression divides strength at the elevated temperature by the same type of strength at room temperature. Both values must use compatible definitions and units. A factor below unity then indicates a reduction relative to that reference condition.<ref name="KH-158" />

<div class="fse-equation">kf,T = fT / fref;   fT = kf,T fref</div>

{| class="wikitable"
! Symbol !! Meaning !! Unit
|-
| kf,T || Strength at temperature T divided by reference strength || Dimensionless
|-
| fT || Specified tensile, compressive or yield strength at temperature T || MPa
|-
| fref || Corresponding strength at the stated reference temperature || MPa
|-
| T || Material temperature || °C, where required by the chosen relationship
|}

The word strength needs a precise qualification in this expression. Concrete assessment commonly concerns compressive strength, whereas tensile and compressive behaviour are both relevant to steel. A tensile ultimate strength is also different from a yield strength. Substituting one for another can change the apparent temperature dependence before any structural calculation has begun.<ref name="KH-158" />

Stiffness requires a separate property, usually an elastic modulus or an appropriate slope of the stress–strain relationship. Its reduction need not follow the same curve as strength. The distinction matters because a member can become more deformable while retaining substantial strength. Creep adds deformation that depends on sustained stress and time, further extending the information required beyond a single reduction factor.<ref name="KH-158" /><ref name="KH-165-167">Kodur and Harmathy (2002), pp. 1-165–1-167.</ref>

A plotted curve can represent mean test observations, an empirical model or a deliberately conservative design relationship. These interpretations are not interchangeable. Kodur and Harmathy illustrate the distinction with cold-formed steel curves based on different strain levels and statistical interpretations. The source and intended use of a curve therefore belong alongside its numerical values.<ref name="KH-167">Kodur and Harmathy (2002), p. 1-167.</ref>

== Steel strength and its definition ==

The behaviour of [[Steel in fire|steel in fire]] depends partly on how the steel was manufactured and strengthened. The handbook distinguishes hot-rolled structural and reinforcing steels from cold-drawn prestressing wires and strands. These materials have different microstructures and mechanical responses. Their room-temperature strength alone does not establish that they share the same elevated-temperature reduction curve.<ref name="KH-165-167" />

A second distinction concerns the point selected on the stress–strain curve. At elevated temperatures the response becomes increasingly nonlinear, so a sharply defined yield point may not provide a convenient description. A reported strength can instead correspond to an offset definition or to a stated total strain. Comparing values without preserving that definition can give a misleading impression of agreement or disagreement.<ref name="KH-167" /><ref name="L-136">Luecke et al. (2005), p. 136.</ref>

Luecke and colleagues demonstrate this issue when comparing their steel measurements with the [[Eurocodes|Eurocodes]] discussed in the 2005 investigation. Their reported offset yield strength differs from both the proportional limit and the maximum flow stress at two per cent strain in the cited model. The different quantities occupy different positions on the stress–strain relationship. One cannot be substituted merely because each is described informally as steel strength.<ref name="L-136" />

The same investigation identifies strain rate as a source of disagreement between datasets. Its elevated-temperature measurements were often below a curve representing earlier literature data. The authors associated much of that difference with the slower testing rates used in their investigation. The example shows why a temperature and a steel grade do not fully describe a mechanical test result.<ref name="L-134-137" />

Some steel data also show an intermediate-temperature increase in flow stress associated with dynamic strain ageing. Luecke and colleagues did not attempt to predict that effect with their simplified model. A smooth decreasing curve is consequently an engineering representation of selected evidence, rather than a statement that every measured stress decreases monotonically under every testing condition.<ref name="L-134-137" />

== Worked example using a published steel relationship ==

The NIST investigation provides an empirical relationship for normalised yield strength. Its parameters were selected to represent the main trend of literature observations, particularly in the steeply declining temperature range. The authors expressly state that the parameters have no physical significance. The following example reproduces that relationship to illustrate calculation and interpretation, rather than to prescribe properties for a particular design.<ref name="L-134">Luecke et al. (2005), p. 134.</ref>

<div class="fse-equation">ky,T = (1 − A2) exp{−½[(T / s1)m1 + (T / s2)m2]} + A2</div>

{| class="wikitable"
! Quantity !! Meaning or value !! Unit
|-
| ky,T || Modelled yield strength divided by the reference yield strength at 23 °C || Dimensionless
|-
| T || Steel temperature entered in the empirical expression || °C
|-
| A2 || 0.074692 || Dimensionless
|-
| m1, m2 || 8.325929 and 1.000000 || Dimensionless
|-
| s1, s2 || 638.384277 and 523.523132 || °C
|}

These parameters are the yield-strength column of Table 6–2 in the report. The adjacent tensile-strength column contains different parameters and must not be combined with them. Temperature is entered in degrees Celsius because that is how this empirical relationship was defined. Converting the input to kelvin without changing the model would produce a different and unsupported result.<ref name="L-134" /><ref name="L-136" />

For an illustrative reference yield strength of 250 MPa, the calculated factors are approximately 0.612 at 500 °C and 0.462 at 600 °C. Multiplication gives approximately 153 MPa and 115 MPa respectively. The reference strength is an assumed example input; the factors come from the published expression. They are calculated values, rather than additional test observations. Using the same reference strength at both temperatures isolates the temperature dependence of the selected relationship. Changing that reference would scale both calculated strengths proportionally.<ref name="L-134" /><ref name="L-136" />

The calculation describes neither the time needed to reach these temperatures nor the capacity of a complete steel member. It also does not remove the discrepancy between the empirical curve and measurements discussed in the report. Selecting a relationship for an actual analysis requires compatibility with the material, test definition and structural model. Reproducing an equation correctly is only one part of that selection.<ref name="L-134-137" /><ref name="M-229-231">Milke (2002), pp. 4-229–4-231.</ref>

== Concrete and the conditions of testing ==

The treatment of [[Concrete in fire|concrete in fire]] requires particular attention to composition and experimental history. The handbook distinguishes aggregate types, normal-strength and high-strength concretes, and fibre-reinforced mixtures. Their elevated-temperature properties do not follow one universal relationship. The temperature dependence of compressive strength must therefore be associated with the concrete and testing conditions from which it was obtained.<ref name="KH-168-172">Kodur and Harmathy (2002), pp. 1-168–1-172.</ref>

One important distinction is whether a specimen carries load while it is heated. The handbook presents concrete datasets for specimens heated without load and others heated under a sustained compressive load. It also presents residual-strength results obtained after heating, cooling and subsequent conditioning. These procedures examine different material histories even when the maximum temperature is the same.<ref name="KH-169">Kodur and Harmathy (2002), p. 1-169.</ref>

A residual-strength curve therefore cannot silently replace a hot-strength curve in a calculation during fire. The former includes the effects of cooling and the stated post-heating treatment. The latter concerns strength while the specimen remains hot. Recording the testing sequence is necessary to identify which structural question the reported property can answer.<ref name="KH-169" />

Higher compressive strength at room temperature does not automatically imply better resistance to heating. The handbook describes different reduction trends for high-strength and normal-strength concrete, with moisture, porosity and mixture composition among the influential variables. Its discussion also identifies explosive spalling as a potential concern for high-strength concrete. A single ambient strength value cannot capture these mechanisms.<ref name="KH-172">Kodur and Harmathy (2002), p. 1-172.</ref>

Spalling creates an additional problem beyond changing the strength of the remaining concrete. It removes section material and can expose reinforcement to greater heating than assumed. The IFEG discussion therefore connects spalling with both sectional resistance and the temperature of embedded steel. Applying a concrete reduction factor to the original, intact section would leave those changes unrepresented.<ref name="I-9">Australian Building Codes Board et al. (2005), p. 2.6-9.</ref>

== Timber, grain direction and loss of section ==

The assessment of [[Timber in fire|timber in fire]] combines changing material properties with loss of cross-section. Wood is orthotropic: its mechanical properties differ with direction relative to the grain. Temperature and moisture also influence strength and stiffness. A reduction relationship derived for clear wood in one direction cannot be treated as a complete description of every timber member.<ref name="KH-174">Kodur and Harmathy (2002), p. 1-174.</ref>

The material remaining behind a char boundary is not necessarily at room temperature. The handbook shows reductions in the strength and stiffness of heated, uncharred wood. Thus, removing the visibly charred region and assigning unaffected properties to everything remaining can overlook a mechanically weakened zone. The structural method must account for that zone in a consistent way.<ref name="KH-174" /><ref name="W-265-267">White (2002), pp. 4-265–4-267.</ref>

White describes approaches that reduce the properties of the residual section and approaches that remove an additional effective layer. These are alternative representations within their respective calculation methods. Combining allowances from different methods without checking their basis can count the same weakening twice. The char depth, effective section and adopted strength must be compatible parts of one assessment.<ref name="W-265-267" />

The geometry change also has a structural effect independent of a local material factor. Section loss changes the area available for axial force and the geometry relevant to bending or instability. The IFEG discussion links charring directly to decreasing effective section dimensions and load-bearing ability. A property curve alone therefore cannot describe the changing resistance of a burning timber member.<ref name="I-9-10" />

== Temperature history and time-dependent deformation ==

A strength measurement taken during a short mechanical test does not describe every effect of sustained heating. Kodur and Harmathy define creep as time-dependent plastic deformation under stress. Its importance increases with temperature and applied stress, and it depends on the duration of exposure. Two specimens reaching the same peak temperature can therefore undergo different deformation histories.<ref name="KH-159">Kodur and Harmathy (2002), p. 1-159.</ref>

A conventional creep experiment maintains the specimen at a specified temperature and approximately constant load while recording deformation over time. The initial elastic deformation is followed by changing creep rates. The handbook distinguishes primary, secondary and tertiary stages, with accelerating deformation preceding rupture in the final stage. Those observations explain why an instantaneous strength ratio cannot by itself represent the time evolution of a loaded material.<ref name="KH-159" />

The issue also affects comparisons between stress–strain tests. At room temperature, curves for similar metals can be relatively insensitive to the rate of testing. At sufficiently high temperatures, deformation develops even while stress is held constant. Changing the duration of the mechanical test can consequently change the measured curve. The testing rate is part of the evidence, rather than an incidental laboratory detail.<ref name="KH-159" /><ref name="L-134-137" />

Thermal property data have a separate role in establishing the temperature history to which the mechanical model responds. Conductivity and heat storage govern how heat moves into and through a member. Thermal expansion or shrinkage contributes additional deformation as the material heats. These properties must accompany strength information when the analysis calculates temperature gradients and restrained structural response.<ref name="KH-160">Kodur and Harmathy (2002), p. 1-160.</ref><ref name="M-229-231" />

The handbook cautions that many building materials undergo physical or chemical changes in the temperature range relevant to fire. Those transformations can alter their microstructure and properties. Data obtained during heating may also differ from data obtained during cooling because some changes are irreversible. A model based solely on the current temperature can miss history effects unless its adopted relationships already represent them appropriately.<ref name="KH-157-160">Kodur and Harmathy (2002), pp. 1-157–1-160.</ref>

There is also a distinction between independently measured properties and values adjusted to reproduce a particular assembly test. Kodur and Harmathy warn that such adjustment can produce apparent agreement without establishing general validity. A successful calculation for one specimen does not automatically justify the same property assumptions for another exposure or construction. The underlying evidence must support the intended transfer between applications.<ref name="KH-157">Kodur and Harmathy (2002), p. 1-157.</ref>

== From material properties to structural resistance ==

A thermal analysis supplies the material temperatures to which reduction relationships are applied. Those temperatures may vary across a section and along a member. A structural analysis then combines the temperature-dependent properties with loading, restraint and geometry. Milke separates these stages because knowing the gas temperature or a material strength factor does not directly establish structural failure.<ref name="M-229-231" />

The [[Critical steel temperature|critical steel temperature]] is one possible outcome or simplifying criterion within that structural assessment. It depends on the resistance required under the specified loading and failure mechanism. A steel member governed by buckling also depends on stiffness and effective length. A factor based only on yield strength cannot represent all those influences.<ref name="M-229-231" />

An assessment must preserve the meaning of its input evidence. Material family, property definition, reference temperature and hot or residual test condition determine what a reduction factor represents. Heating history and rate effects may add further qualifications. Keeping these conditions explicit allows the strength data to be used alongside compatible thermal and structural models.<ref name="KH-165-169" /><ref name="L-134-137" />

== See also ==
* [[Spalling]]
* [[Reduced cross-section method]]

== Notes ==
<references />

== References ==
* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing. (2005). ''International fire engineering guidelines''.
* Kodur, V. K. R., & Harmathy, T. Z. (2002). Properties of building materials. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., Chapter 1-10, pp. 1-155–1-181). National Fire Protection Association.
* Luecke, W. E., McColskey, J. D., McCowan, C. N., Banovic, S. W., Fields, R. J., Foecke, T., Siewert, T. A., & Gayle, F. W. (2005). ''Mechanical properties of structural steels'' (NIST NCSTAR 1-3D). National Institute of Standards and Technology.
* Milke, J. A. (2002). Analytical methods for determining fire resistance of steel members. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., Chapter 4-9). National Fire Protection Association.
* White, R. H. (2002). Analytical methods for determining fire resistance of timber members. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., Chapter 4-11). National Fire Protection Association.

[[Category:Structural Fire Engineering]]