Critical steel temperature - Revision history

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

2026-11-02T15:42:05Z

Add 3 watermarked SVG illustrations from the Advanced visual plan

← Older revision		Revision as of 16:42, 2 November 2026
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	The distinction also affects the meaning of [[Fire resistance\|fire resistance]]. A temperature is a thermal state, whereas a resistance duration describes performance during a specified exposure. Reaching a selected temperature after one heating history does not establish the same elapsed time under another. The exposure, heat transfer and structural response form separate parts of the assessment.<ref name="M-209" /><ref name="M-222" />		The distinction also affects the meaning of [[Fire resistance\|fire resistance]]. A temperature is a thermal state, whereas a resistance duration describes performance during a specified exposure. Reaching a selected temperature after one heating history does not establish the same elapsed time under another. The exposure, heat transfer and structural response form separate parts of the assessment.<ref name="M-209" /><ref name="M-222" />
			[[File:fse-critical-steel-temperature-v1.svg\|thumb\|upright=1.5\|alt=Separate structural and thermal calculation paths meet in a steel performance comparison.\|The structural limit and the temperature history come from different parts of the assessment. Based on Milke (2002), pp. 4-209 and 4-222.]]

	== Material properties and failure mechanisms ==		== Material properties and failure mechanisms ==
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	For a slender column, instability can govern before the material reaches the stress associated with yielding throughout its section. Elastic buckling resistance depends on modulus of elasticity, effective length and section geometry. Heating reduces stiffness and can therefore reduce the load at which buckling becomes possible. Stockier columns require a different treatment when their response enters the inelastic range.<ref name="M-231-232" />		For a slender column, instability can govern before the material reaches the stress associated with yielding throughout its section. Elastic buckling resistance depends on modulus of elasticity, effective length and section geometry. Heating reduces stiffness and can therefore reduce the load at which buckling becomes possible. Stockier columns require a different treatment when their response enters the inelastic range.<ref name="M-231-232" />
			[[File:fse-critical-steel-temperature-v3.svg\|thumb\|upright=1.5\|alt=Sketches of bending, column instability and restraint during steel heating.\|Different mechanical conditions enter a critical-temperature assessment. Based on Milke (2002), pp. 4-230–4-232, and Australian Building Codes Board (2020), p. 43.]]

	Thermal expansion introduces another part of the problem. A restrained member cannot necessarily expand as a freely heated specimen would. The surrounding framing and connections influence restraint, and therefore the stresses and deformations that develop. The ABCB 2020 guidance identifies these thermally induced effects and interactions as matters for the structural stage of a fire assessment.<ref name="M-210">Milke (2002), p. 4-210.</ref><ref name="AB-43">Australian Building Codes Board (2020), p. 43.</ref>		Thermal expansion introduces another part of the problem. A restrained member cannot necessarily expand as a freely heated specimen would. The surrounding framing and connections influence restraint, and therefore the stresses and deformations that develop. The ABCB 2020 guidance identifies these thermally induced effects and interactions as matters for the structural stage of a fire assessment.<ref name="M-210">Milke (2002), p. 4-210.</ref><ref name="AB-43">Australian Building Codes Board (2020), p. 43.</ref>
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	Increasing the load parameter from 0.40 to 0.60 is a calculated increase of 50%. Within this row, the associated limiting temperature decreases from 540 °C to 430 °C. The difference is 110 °C. The calculation demonstrates that greater demand relative to the stated reference resistance leaves less capacity to accommodate temperature-related deterioration.<ref name="M-table10" />		Increasing the load parameter from 0.40 to 0.60 is a calculated increase of 50%. Within this row, the associated limiting temperature decreases from 540 °C to 430 °C. The difference is 110 °C. The calculation demonstrates that greater demand relative to the stated reference resistance leaves less capacity to accommodate temperature-related deterioration.<ref name="M-table10" />
			[[File:fse-critical-steel-temperature-v2.svg\|thumb\|upright=1.5\|alt=Published critical beam temperatures decrease from 585 °C to 360 °C as the specified load parameter increases from 0.3 to 0.7.\|Critical temperatures vary with the specified load parameter in the cited plastic-design method. Based on Milke (2002), p. 4-232.]]

	The table also contains different values for elastic design and for different structural arrangements. Changing rows changes the underlying assumptions, rather than refining the precision of the same answer. A temperature taken from the plastic row cannot therefore be transferred unexamined to a column or a restrained beam assessed by another method. The example is a comparison within the published method's own terms.<ref name="M-231-232" />		The table also contains different values for elastic design and for different structural arrangements. Changing rows changes the underlying assumptions, rather than refining the precision of the same answer. A temperature taken from the plastic row cannot therefore be transferred unexamined to a column or a restrained beam assessed by another method. The example is a comparison within the published method's own terms.<ref name="M-231-232" />

Peter: New FSE wiki article: Critical steel temperature (written by GPT-6)

2026-11-01T22:26:58Z

New FSE wiki article: Critical steel temperature (written by GPT-6)

New page

'''Critical steel temperature''' is the temperature at which a steel member can no longer sustain a specified load or satisfy its structural limit. The value depends on the member, its loading and the assumed failure condition. It is therefore a result of a structural assessment or a specified test criterion, rather than one universal temperature for steel.<ref name="M-230">Milke (2002), p. 4-230.</ref>

Heating changes the properties governing [[Steel in fire|steel in fire]], including yield strength and stiffness. A member may become unable to resist its applied load, develop instability or exceed an accepted deformation limit. The temperature associated with that condition depends on how the member is supported and restrained as well as on its material properties.<ref name="M-229-232">Milke (2002), pp. 4-229–4-232.</ref>

Critical temperature and the time taken to reach it answer different questions. Structural analysis establishes the limiting condition, while heat-transfer analysis predicts the member's temperature history during a stated exposure. Protection, exposed perimeter and thermal properties affect the latter. Combining the two analyses can estimate the duration for which the selected structural criterion remains satisfied.<ref name="M-209">Milke (2002), p. 4-209.</ref><ref name="M-222">Milke (2002), p. 4-222.</ref>

== A limit tied to a structural condition ==

The word critical identifies the condition used to judge the member's performance. Milke defines critical temperature through the reduction in material properties that prevents carrying a specified load or stress. His discussion includes excessive stress, impending buckling and excessive deflection. These alternatives explain why a temperature quoted without a loading and failure description is incomplete.<ref name="M-230" />

A calculation can instead ask for the critical load at a specified temperature. This is the minimum applied load that produces the selected failure condition for the heated member. The two questions use the same temperature-dependent mechanical information but hold different quantities fixed. Neither can be answered solely from the gas temperature surrounding the steel.<ref name="M-231">Milke (2002), p. 4-231.</ref>

Deflection provides another way to express performance. A heated beam can deform through elastic strain, plastic strain, thermal expansion and creep. Creep is the accumulation of deformation with time under sustained stress. Milke describes assessing both total deflection and its rate against chosen limits, showing that a structural criterion can involve the deformation history rather than a single strength value.<ref name="M-230" />

The distinction also affects the meaning of [[Fire resistance|fire resistance]]. A temperature is a thermal state, whereas a resistance duration describes performance during a specified exposure. Reaching a selected temperature after one heating history does not establish the same elapsed time under another. The exposure, heat transfer and structural response form separate parts of the assessment.<ref name="M-209" /><ref name="M-222" />

== Material properties and failure mechanisms ==

The [[Strength reduction at elevated temperatures|strength reduction at elevated temperatures]] describes one part of the changing mechanical response. Yield strength concerns the stress associated with the adopted yielding definition, while stiffness describes resistance to deformation. Milke identifies both strength and modulus of elasticity as relevant to critical-temperature calculations. Their different roles mean that a strength-only comparison is not sufficient for every member.<ref name="M-230" /><ref name="M-231" />

For a beam assessed through bending resistance, the relationship between applied moment and available section resistance matters. The applicable expression depends on whether the design uses elastic or plastic behaviour. These approaches represent different distributions of stress within the cross-section. Milke's comparison also includes the reserve available through the geometry and through redistribution of moments in a connected structure.<ref name="M-231-232">Milke (2002), pp. 4-231–4-232.</ref>

For a slender column, instability can govern before the material reaches the stress associated with yielding throughout its section. Elastic buckling resistance depends on modulus of elasticity, effective length and section geometry. Heating reduces stiffness and can therefore reduce the load at which buckling becomes possible. Stockier columns require a different treatment when their response enters the inelastic range.<ref name="M-231-232" />

Thermal expansion introduces another part of the problem. A restrained member cannot necessarily expand as a freely heated specimen would. The surrounding framing and connections influence restraint, and therefore the stresses and deformations that develop. The ABCB 2020 guidance identifies these thermally induced effects and interactions as matters for the structural stage of a fire assessment.<ref name="M-210">Milke (2002), p. 4-210.</ref><ref name="AB-43">Australian Building Codes Board (2020), p. 43.</ref>

Consequently, the selected material-property relationships must match the structural calculation. A yield-strength curve cannot replace a stiffness curve in a buckling equation. Likewise, a member model based on one support arrangement does not automatically describe another arrangement with different restraint. The critical temperature expresses the combined assumptions of the calculation, rather than the material data in isolation.<ref name="M-231-232" />

== Temperature criteria in resistance tests ==

Standard resistance tests can use prescribed temperature endpoints as practical performance criteria. Milke describes their relationship to allowable reductions in load-bearing capacity and the loading assumptions of structural standards. He also distinguishes tests conducted with load from those performed without it. The selected endpoint belongs to the named test arrangement and cannot automatically be treated as an observed collapse temperature.<ref name="M-210" />

The historical ASTM E119 discussion in the handbook includes structural integrity and temperature criteria among the possible endpoints. The complete test may also consider flame passage and other requirements appropriate to the assembly. Temperature therefore represents one part of a test's performance definition. Describing a member as reaching a temperature limit does not establish which other test conditions were satisfied.<ref name="M-210" />

Milke notes that experimental steel members have sometimes exceeded temperatures used as conventional limits without collapsing. This observation does not establish a higher universal limit. It demonstrates that actual loading, restraint and structural behaviour can differ from the assumptions underlying a simplified temperature criterion. The governing comparison must retain the basis of the selected limit.<ref name="M-230" />

The same distinction matters when applying a test-derived empirical correlation. Such a correlation reflects the exposure, loading and span represented by its underlying experiments. Milke explicitly limits these correlations to the conditions for which they were developed. Where those conditions change materially, the analysis needs a method able to represent the changed exposure and structural system.<ref name="M-209" />

== Equations for two different structural checks ==

Milke presents a simple plastic-design relationship between the required residual yield strength and the factor of safety. The equation states the fraction of the room-temperature yield strength that remains available at the selected limiting state. Its factor belongs to that particular design formulation. It is not a universal substitute for load combinations or partial factors in other structural methods.<ref name="M-table9">Milke (2002), p. 4-231, Table 4-9.9.</ref>

<div class="fse-equation">σy,T/σy,0 = 1/Fp</div>

For elastic column buckling, the corresponding stress relationship uses stiffness and slenderness. Effective length represents the support conditions, and the radius of gyration represents how the cross-sectional area is distributed. The equation applies only where buckling remains elastic. Milke warns that columns outside that regime require a more appropriate structural treatment.<ref name="M-euler">Milke (2002), pp. 4-231–4-232, Equation 6.</ref>

<div class="fse-equation">σcr = π²ET/λ²; λ = KL/r</div>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| σy,T || Critical yield stress at elevated temperature || MPa
|-
| σy,0 || Yield stress at room temperature || MPa
|-
| Fp || Factor of safety in the cited plastic-design relationship || Dimensionless
|-
| σcr || Euler elastic buckling stress || MPa
|-
| ET || Modulus of elasticity at the steel temperature || MPa
|-
| λ || Slenderness ratio || Dimensionless
|-
| KL || Effective column length || m
|-
| r || Radius of gyration || m
|}

For a selected Fp of 2.0, the first equation gives a residual yield-strength ratio of 0.50. Converting that ratio to a temperature still requires the appropriate temperature-dependent material curve. The equation alone therefore does not return a temperature in degrees. It expresses the mechanical requirement that the chosen material relationship must subsequently satisfy.<ref name="M-table9" /><ref name="M-230" />

The buckling equation illustrates a different dependence. A change in effective length changes the slenderness ratio, while a change in temperature changes the modulus of elasticity. Both affect the stress at instability. Therefore two columns made from the same steel can have different limiting temperatures when their lengths, supports or applied stresses differ.<ref name="M-euler" />

Milke describes the elastic equation as generally applicable to sufficiently slender columns, while stockier members can buckle in the plastic range. He also identifies an intermediate range in which the failure mode is difficult to predict reliably. Residual stresses from fabrication introduce another limitation when simpler estimates are used. These observations restrict the equation to its stated mechanical assumptions; they do not support applying one elastic formula to every steel column.<ref name="M-euler" />

== A worked comparison using published beam values ==

Milke reproduces beam critical temperatures for several design assumptions and load parameters. The plastic-design row uses the parameter kq*/qp, where q* is applied load, k is a load multiplier and qp is ultimate plastic load. The values below preserve that particular parameter and design basis. They are historical method values, rather than a generic temperature table for all steel beams.<ref name="M-table10">Milke (2002), p. 4-232, Table 4-9.10.</ref>

{| class="wikitable"
! Load parameter kq*/qp !! Critical temperature in the plastic-design row
|-
| 0.30 || 585 °C
|-
| 0.40 || 540 °C
|-
| 0.50 || 490 °C
|-
| 0.60 || 430 °C
|-
| 0.70 || 360 °C
|}

Increasing the load parameter from 0.40 to 0.60 is a calculated increase of 50%. Within this row, the associated limiting temperature decreases from 540 °C to 430 °C. The difference is 110 °C. The calculation demonstrates that greater demand relative to the stated reference resistance leaves less capacity to accommodate temperature-related deterioration.<ref name="M-table10" />

The table also contains different values for elastic design and for different structural arrangements. Changing rows changes the underlying assumptions, rather than refining the precision of the same answer. A temperature taken from the plastic row cannot therefore be transferred unexamined to a column or a restrained beam assessed by another method. The example is a comparison within the published method's own terms.<ref name="M-231-232" />

The load multiplier in this table also prevents interpreting its horizontal parameter as an unqualified fraction of everyday building load. The numerator and denominator must follow the cited formulation. Using a different definition of load utilisation can produce a numerically similar ratio with a different meaning. The parameter definition is consequently part of the evidence supporting each tabulated temperature.<ref name="M-table10" />

== Heating rate, section geometry and protection ==

Once the limiting temperature is established, thermal analysis determines whether the member reaches it during the selected exposure. Milke describes calculations ranging from lumped heat-capacity approximations to numerical heat-transfer models. These methods require a description of the steel, any insulation and the surrounding heating conditions. They predict thermal response rather than directly determining the structural load capacity.<ref name="M-222" /><ref name="M-229">Milke (2002), p. 4-229.</ref>

The [[Section factor|section factor]] relates the heated boundary to the amount of steel being heated. Milke expresses related geometry through heated perimeter, cross-sectional area and mass per unit length. A larger steel mass requires more energy for the same temperature rise, while a larger heated perimeter offers more area for heat transfer. This affects the time history used in the critical-temperature comparison.<ref name="M-216-217">Milke (2002), pp. 4-216–4-217.</ref>

Protective boards, spray-applied products and concrete encasement alter heat transfer to the steel. Milke lists [[Intumescent material|intumescent material]] among the protective coating types considered. Protection performance depends on the properties and arrangement represented by the method. It does not turn the underlying steel into a material with an exposure-independent resistance time.<ref name="M-213-214">Milke (2002), pp. 4-213–4-214.</ref><ref name="M-209" />

Installation condition can change the predicted result. Milke describes calculations in which missing protection significantly reduced the resistance of protected columns. The ABCB guidance similarly calls for material and installation variability to be considered in thermal assessment. A nominal protection thickness therefore needs the accompanying assumptions about coverage, attachment and material behaviour.<ref name="M-229" /><ref name="AB-42">Australian Building Codes Board (2020), p. 42.</ref>

The thermal properties of protective materials can change during heating. Milke describes representing evaporation of free water in a cementitious coating through an increased specific heat over a narrow temperature interval. Such treatment changes the predicted temperature history because energy is associated with the material transformation. A constant room-temperature insulation property may therefore miss a process that affects when the steel approaches its selected limiting temperature.<ref name="M-229" />

== Limits of a single-temperature assessment ==

A uniform member temperature can be a useful approximation, but it is not appropriate for every heated section. Milke discusses beams with temperature differences caused by their relationship to a concrete slab. Where the gradient matters, a different thermal or structural treatment is needed. An average temperature can conceal a distribution relevant to local material resistance and deformation.<ref name="M-224">Milke (2002), p. 4-224.</ref>

The surrounding structure can also affect the result through restraint and interaction between members. The ABCB guidance recognises cases requiring analysis of the whole structure or substantial parts of it. Isolating one member can omit those interactions. The adequacy of a critical-temperature approach therefore depends on whether the chosen limit and thermal model represent the intended structural behaviour.<ref name="AB-43" />

Numerical heat-transfer calculations have additional resolution requirements. Milke notes that models using explicit time integration require suitable time steps and spatial meshes to obtain stable solutions. A numerically unstable temperature curve cannot establish a meaningful crossing time for the critical-temperature limit. The computational method therefore needs verification alongside the physical description of the member and its exposure.<ref name="M-229" />

The ABCB guidance allows direct use of experimental evidence when the heating and loading conditions represent the proposed assessment. Where they differ, their influence requires an engineering basis. This keeps the limiting condition connected to the evidence used to establish it.<ref name="AB-43" />

Uncertainty enters through fire exposure, material properties, installation condition and the structural boundary conditions. Increasing the complexity of a numerical model does not eliminate those inputs. Milke identifies both material data and end conditions as limitations of structural calculations. Reporting the governing assumptions makes the calculated temperature traceable to the structural condition it is intended to represent. The resulting time remains conditional on the fire exposure and the structural criterion selected for that assessment.<ref name="M-209" /><ref name="M-210" /><ref name="AB-42" />

== See also ==
* [[Eurocodes]]

== Notes ==
<references />

== References ==
* Australian Building Codes Board. (2020). ''Fire safety verification method data sheets: Handbook annex'' (Version 1.1).
* 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.

[[Category:Structural Fire Engineering]]