New FSE wiki article: Concrete in fire (written by Kimi Code CLI) |
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'''Concrete in fire''' describes the | '''Concrete in fire''' describes the heating, material changes and structural response of concrete members exposed to fire. Concrete is noncombustible and can delay the heating of embedded reinforcement through its relatively low thermal conductivity, and its cooler interior can continue carrying load while the exposed surface becomes hot. These advantages do not prevent all forms of thermal damage or structural failure.<ref name="FB_4-239">Fleischmann and Buchanan (2002), p. 4-239.</ref> | ||
The response depends on the complete member, rather than compressive strength alone. Aggregate, moisture, cover depth, geometry, applied load and support conditions affect different stages of the assessment. Surface material can also break away during heating, changing the protection available to the reinforcement. A calculation that considers only intact concrete may then miss an influential change in the section.<ref name="KH_1-156">Kodur and Harmathy (2002), p. 1-156.</ref><ref name="KH_1-163_1-164">Kodur and Harmathy (2002), pp. 1-163–1-164.</ref><ref name="FB_4-239" /> | |||
Assessment | Assessment normally connects a defined fire exposure to an internal temperature distribution and then to structural performance. Separating elements also have a heat-transmission function. Each calculation therefore needs a stated endpoint and material data suitable for the relevant temperature range.<ref name="FB_4-239_4-242">Fleischmann and Buchanan (2002), pp. 4-239–4-242.</ref> | ||
== | == Material structure and fire exposure == | ||
Concrete combines aggregates with a cement paste containing pores and moisture, and these constituents respond differently when heated, so concrete cannot be represented as one chemically uniform solid. Aggregate type, density, porosity and moisture influence its thermal behaviour. The properties needed for a fire calculation consequently extend beyond its specified compressive strength at ordinary temperature.<ref name="KH_1-155_1-156">Kodur and Harmathy (2002), pp. 1-155–1-156.</ref> | |||
Concrete | The material can perform both a structural and an insulating role. Concrete around steel reinforcement absorbs and conducts heat before the reinforcement reaches a high temperature. Meanwhile, cooler parts of a concrete section can continue to carry load. These functions are related, but they require different calculations and different material properties.<ref name="KH_1-157">Kodur and Harmathy (2002), p. 1-157.</ref><ref name="FB_4-239" /> | ||
Fire exposure is the boundary condition for those calculations. A prescribed furnace temperature history differs from a natural compartment fire, whose development depends on fuel, ventilation and enclosure properties. A temperature curve also differs from a heat release rate curve: one describes temperature, while the other describes thermal power. Confusing them would change the physical problem being assessed.<ref name="VR_8.6">Van Rossum (2027), §8.6.</ref> | |||
The exposed faces matter as much as the nominal temperature history. A slab or separating wall may receive fire exposure predominantly on one side. A beam can be heated on several sides, while a column can be exposed around its perimeter. Fleischmann and Buchanan describe these arrangements separately because they produce different internal temperature distributions.<ref name="FB_4-242">Fleischmann and Buchanan (2002), p. 4-242.</ref> | |||
== | == Heat penetration and material properties == | ||
[[ | Heat entering the exposed surface moves through solid concrete mainly by conduction. [[Thermal conductivity]] describes how readily a temperature difference drives that transfer. Density and specific heat describe the energy stored as the material warms. Together, these quantities determine how rapidly a temperature disturbance spreads into the section.<ref name="FB_4-242" /><ref name="VR_5.2">Van Rossum (2027), §5.2.</ref> | ||
The exposed surface and the interior therefore need not reach the same temperature. During early heating, a substantial temperature gradient can exist through a thick section. The cooler interior is one reason a concrete member may continue functioning while its surface becomes very hot. A single furnace temperature does not represent the temperature of every reinforcement bar.<ref name="FB_4-239" /><ref name="FB_4-242" /><ref name="VR_5.2" /> | |||
Moisture changes the energy balance because evaporation consumes heat. Heating also changes the material itself, including its microstructure and relevant thermal properties. Van Rossum consequently treats calculations with constant properties as approximations. The diffusivity used at one stage of heating need not describe the entire fire exposure.<ref name="VR_5.2" /><ref name="KH_1-157" /> | |||
A steady calculation assumes that the temperature profile through the whole construction has already developed. That assumption can be unsuitable during the initial heating of a thick wall. A transient calculation instead follows the changing temperatures as energy enters and spreads through the material. This distinction affects both reinforcement temperature and heat transfer to the unexposed side.<ref name="VR_5.2" /><ref name="FB_4-239" /> | |||
== A worked heat-penetration example == | |||
Thermal diffusivity divides conductivity by the volumetric heat capacity, which is density multiplied by specific heat. For a sudden surface-temperature change, the square root of diffusivity multiplied by time gives a characteristic penetration depth. This depth describes a scale of temperature change, rather than a sharp front separating hot and cold concrete.<ref name="VR_5.2" /> | |||
<math display="block">\alpha=\frac{\lambda}{\rho c_p},\qquad d\approx\sqrt{\alpha t}</math> | |||
{| class="wikitable" | |||
! Symbol !! Description !! Unit | |||
|- | |||
| <math>\alpha</math> || Thermal diffusivity || m²/s | |||
|- | |||
| <math>\lambda</math> || Thermal conductivity || W/(m·K) | |||
|- | |||
| <math>\rho</math> || Density || kg/m³ | |||
|- | |||
| <math>c_p</math> || Specific heat || J/(kg·K) | |||
|- | |||
| <math>t</math> || Heating duration || s | |||
|- | |||
| <math>d</math> || Characteristic penetration depth || m | |||
|} | |||
Van Rossum's comparison of thick concrete and timber walls uses rounded concrete properties of 1.7 W/(m·K), 2,300 kg/m³ and 900 J/(kg·K). With these inputs, the calculated diffusivity is 8.21 × 10⁻⁷ m²/s. After 3,600 s, the characteristic depth is approximately 0.054 m, or 54 mm. The calculation reproduces the source example using unrounded intermediate values.<ref name="VR_5.2" /> | |||
That result does not mean that concrete outside a 54 mm layer remains exactly at its initial temperature. Nor does it identify a spalling depth, a damaged zone or the position of a failure boundary. The model has no mechanical failure criterion and uses fixed thermal properties. Its purpose is to explain the scale of transient heating in a thick material.<ref name="VR_5.2" /> | |||
A separate example in the same section considers a 200 mm concrete wall over the first 900 s. It uses a different stated diffusivity, 9.88 × 10⁻⁷ m²/s. The source's approximate boundary between thermally thick and thin behaviour, twice the penetration depth, is then 60 mm. The 200 mm wall is thermally thick for that example, but this observation does not assign it a fire-resistance rating.<ref name="VR_5.2" /> | |||
== Spalling and loss of cover == | |||
[[Spalling]] is the breaking away of concrete from the heated surface. Kodur and Harmathy distinguish early explosive loss from later loss associated with weakened material. The process matters because the section can lose both material and thermal protection. Reinforcement formerly enclosed by concrete may then receive more direct heating.<ref name="KH_1-163_1-164" /> | |||
One proposed mechanism involves moisture movement and pressure within the pores. Heating drives moisture towards cooler regions, where a relatively saturated zone can impede further transport. Pressure can rise if vapour cannot escape readily. The handbook also discusses explanations based on thermal stresses and fracture, so pore pressure is not the sole mechanism considered.<ref name="KH_1-163">Kodur and Harmathy (2002), p. 1-163.</ref> | |||
[[ | [[File:fse-concrete-in-fire-v1.svg|thumb|upright=1.5|alt=Heat drives moisture into a low-permeability concrete clog, raising pressure and cracking the surface.|Moisture clog and pressure can contribute to spalling. Based on Kodur and Harmathy (2002), p. 1-163.]] | ||
The source illustrates the pressure mechanism using approximately 8 MPa vapour pressure at 300 °C and approximately 5 MPa tensile strength for high-strength concrete. This comparison demonstrates how internal pressure can exceed a resisting tensile stress; it is an explanatory example, not a universal pressure-temperature failure rule. Actual spalling also depends on permeability, moisture, loading and the heating conditions.<ref name="KH_1-163_1-164" /> | |||
[[ | [[File:fse-concrete-in-fire-v3.svg|thumb|upright=1.5|alt=Example vapour pressure 8 MPa versus tensile strength 5 MPa at 300 °C.|Example of internal pressure exceeding concrete tensile strength. Based on Kodur and Harmathy (2002), p. 1-163.]] | ||
High compressive strength at room temperature does not by itself prevent spalling. Dense, low-permeability concrete can restrict moisture escape during rapid heating. Once surface material is lost, deeper concrete and reinforcement heat more rapidly. A model that retains the original section throughout the exposure cannot automatically represent that change.<ref name="KH_1-163_1-164" /> | |||
Thermal stress offers a different way for cracking to develop. The heated surface tends to expand while cooler material restricts that movement. Kodur and Harmathy discuss fracture-based explanations in which these stresses contribute to surface loss. An analysis based only on vapour pressure therefore addresses one proposed contribution, rather than demonstrating that other mechanisms are absent.<ref name="KH_1-163" /> | |||
The distinction between tensile and compressive behaviour is also relevant. The pressure example compares internal pressure with tensile resistance, whereas the familiar concrete grade describes compressive strength; these are different material quantities. Increasing the specified compressive strength cannot by itself resolve a cracking mechanism involving internal pressure, restrained expansion and tensile fracture.<ref name="KH_1-163_1-164" /> | |||
== | == Reinforcement and load-carrying capacity == | ||
[[Strength reduction at elevated temperatures]] affects both the concrete and the embedded steel. Fleischmann and Buchanan distinguish hot-rolled reinforcement from cold-drawn prestressing steel and high-strength alloy steel, and their strength-temperature relationships differ, reflecting the materials and mechanical properties considered. A single generic steel curve cannot represent every reinforced or prestressed member.<ref name="FB_4-239_4-240">Fleischmann and Buchanan (2002), pp. 4-239–4-240.</ref> | |||
Concrete strength also depends on aggregate and on the conditions of the material test. The handbook compares specimens heated under load with specimens heated before being loaded to failure, and these procedures can produce different measured strengths at the same temperature. Material data therefore need an accompanying description of the loading and heating history.<ref name="FB_4-240_4-241">Fleischmann and Buchanan (2002), pp. 4-240–4-241.</ref> | |||
The modulus of elasticity describes stiffness, or resistance to elastic deformation, and it can decrease substantially during heating even when part of the compressive strength remains. Consequently, a strength calculation and a deformation calculation address different effects. Thermal expansion adds another source of deformation and can alter the forces arising in restrained construction.<ref name="FB_4-240_4-241" /> | |||
[[File:fse-concrete-in-fire-v2.svg|thumb|upright=1.5|alt=Concrete section with cover, reinforcement and spalled region reducing protection and stiffness.|Concrete and reinforcement respond together to heat and section loss. Based on Fleischmann and Buchanan (2002), pp. 4-241–4-242 and Kodur and Harmathy (2002), p. 1-164.]] | |||
In a simplified thermal analysis, the reinforcement temperature may be approximated by the concrete temperature at the bar centre. This connects the heat-transfer calculation to the subsequent structural calculation. The cover depth, exposed faces and heating duration then affect the steel properties used in that analysis. The approximation belongs to the stated modelling approach, rather than every possible member configuration.<ref name="FB_4-242" /> | |||
The load present during heating affects how a property curve is established. In the concrete results discussed by Fleischmann and Buchanan, some specimens carried 40% of their compressive strength while being heated. They were then loaded to failure at the temperature of interest. That procedure describes strength while hot, rather than a measurement of residual strength after cooling.<ref name="FB_4-240">Fleischmann and Buchanan (2002), p. 4-240.</ref> | |||
A temperature-dependent property curve consequently carries more information than its axes alone, and its concrete type, initial condition and testing sequence affect what the result represents. A curve measured for one aggregate and load history cannot be assumed to describe another without supporting evidence. This is separate from uncertainty in the furnace temperature or the calculated temperature within the member.<ref name="FB_4-240_4-241" /> | |||
== Beams, slabs and structural continuity == | |||
A simply supported slab provides a useful starting model: its ends permit expansion and rotation under the idealised support conditions described by Fleischmann and Buchanan. As reinforcement heats and weakens, the section's resistance to bending decreases. Structural failure is assessed by comparing that remaining resistance with the bending demand from the applied load.<ref name="FB_4-245">Fleischmann and Buchanan (2002), p. 4-245.</ref> | |||
Concrete near the compression face may remain cooler than reinforcement near the fire-exposed underside. The structural calculation therefore uses the temperature distribution, rather than applying one reduction to the entire section. If part of the compression zone becomes sufficiently hot, the source method reduces its contribution. That step depends on the chosen material model and calculation procedure.<ref name="FB_4-245" /> | |||
A continuous member behaves differently because it can redistribute bending moments between the span and its supports. Redistribution can extend endurance, but the remaining sections must still resist the transferred demand. Fleischmann and Buchanan describe failure through the formation of a mechanism involving several yielding regions. Continuity is therefore a structural condition, not an automatic allowance added to a rating.<ref name="FB_4-246">Fleischmann and Buchanan (2002), p. 4-246.</ref> | |||
[[Structural fire engineering]] combines this structural response with the preceding fire and thermal calculations. The assessment depends on loads, geometry, reinforcement and support conditions as well as temperature. More specialised structural behaviour is addressed in the related topic [[Tensile membrane action]]. The heat-penetration example above does not calculate any redistribution or membrane resistance.<ref name="FB_4-239" /><ref name="FB_4-245_4-246">Fleischmann and Buchanan (2002), pp. 4-245–4-246.</ref> | |||
== Testing and fire-resistance assessment == | |||
[[Fire resistance]] is evaluated against specified functions under a defined exposure. A separating concrete floor may need to support loads and limit heat transfer to the space above. A column has a different structural role and exposure arrangement. The required endpoints follow the assembly and assessment method, rather than the material name alone.<ref name="FB_4-239" /><ref name="FB_4-242" /> | |||
For standard exposure, empirical methods can relate dimensions and other parameters to results from furnace tests. Nonstandard exposure generally requires a more explicit thermal analysis followed by structural evaluation. Fleischmann and Buchanan describe both approaches and their different information requirements. A correlation derived from a standard test does not independently establish performance for an arbitrary natural fire.<ref name="FB_4-239" /> | |||
New Zealand's C/VM2, second edition of 2025, defines a fire resistance rating using three durations, and their order is structural adequacy, integrity and insulation. The definition permits standard testing or a specified calculation method verified against standard fire-resistance tests. This is the terminology of that New Zealand document, rather than a universal notation for every jurisdiction.<ref name="CVM_64">Ministry of Business, Innovation and Employment (2025), p. 64.</ref> | |||
== Limits of simplified predictions == | |||
A | A numerical model can follow changing temperatures with more detail than a penetration-depth estimate. The concrete chapter describes models that include temperature-dependent properties and changing boundary conditions, but it also notes that the cited implementations did not explicitly model moisture migration. Representing evaporation through adjusted thermal properties does not itself calculate pore-pressure-driven spalling.<ref name="FB_4-243">Fleischmann and Buchanan (2002), p. 4-243.</ref><ref name="KH_1-163" /> | ||
The same distinction applies to a good match with measured temperatures. Such a match supports the thermal calculation for the tested conditions, but it does not independently demonstrate the correct structural restraint, reinforcement strength or response to section loss. Those questions require evidence relevant to the mechanical model and the construction being assessed.<ref name="FB_4-239" /><ref name="FB_4-243" /><ref name="KH_1-164">Kodur and Harmathy (2002), p. 1-164.</ref> | |||
A source value also carries limits associated with its concrete and test history. Aggregate type, moisture and applied load can affect the measured response, while rapid heating can introduce additional damage mechanisms. These dependencies explain why the handbook presents several material relationships and calculation approaches. Selecting one requires identifying the physical conditions it represents.<ref name="FB_4-240_4-241" /><ref name="KH_1-163_1-164" /> | |||
== See also == | == See also == | ||
* [[ | * [[Conduction]] | ||
* [[ | * [[Steel in fire]] | ||
* [[ | * [[Restrained thermal expansion]] | ||
== Notes == | == Notes == | ||
| Line 125: | Line 125: | ||
== References == | == References == | ||
* Fleischmann, C., & Buchanan, A. (2002). Analytical methods for determining fire resistance of concrete members. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 4-239–4-256). National Fire Protection Association. | |||
* 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., pp. 1-155–1-181). National Fire Protection Association. | |||
* Fleischmann, C., & Buchanan, A. (2002). Analytical methods for determining fire resistance of concrete members. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed.). National Fire Protection Association. | * Ministry of Business, Innovation and Employment. (2025). ''C protection from fire: Verification method C/VM2'' (2nd ed.). | ||
* 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. | * Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy. | ||
* Ministry of Business, Innovation and Employment. (2025). ''C protection from fire: Verification method C/VM2'' (2nd ed.) | |||
* | |||
[[Category:Structural Fire Engineering]] | [[Category:Structural Fire Engineering]] | ||
Latest revision as of 19:41, 2 November 2026
Concrete in fire describes the heating, material changes and structural response of concrete members exposed to fire. Concrete is noncombustible and can delay the heating of embedded reinforcement through its relatively low thermal conductivity, and its cooler interior can continue carrying load while the exposed surface becomes hot. These advantages do not prevent all forms of thermal damage or structural failure.[1]
The response depends on the complete member, rather than compressive strength alone. Aggregate, moisture, cover depth, geometry, applied load and support conditions affect different stages of the assessment. Surface material can also break away during heating, changing the protection available to the reinforcement. A calculation that considers only intact concrete may then miss an influential change in the section.[2][3][1]
Assessment normally connects a defined fire exposure to an internal temperature distribution and then to structural performance. Separating elements also have a heat-transmission function. Each calculation therefore needs a stated endpoint and material data suitable for the relevant temperature range.[4]
Material structure and fire exposure
Concrete combines aggregates with a cement paste containing pores and moisture, and these constituents respond differently when heated, so concrete cannot be represented as one chemically uniform solid. Aggregate type, density, porosity and moisture influence its thermal behaviour. The properties needed for a fire calculation consequently extend beyond its specified compressive strength at ordinary temperature.[5]
The material can perform both a structural and an insulating role. Concrete around steel reinforcement absorbs and conducts heat before the reinforcement reaches a high temperature. Meanwhile, cooler parts of a concrete section can continue to carry load. These functions are related, but they require different calculations and different material properties.[6][1]
Fire exposure is the boundary condition for those calculations. A prescribed furnace temperature history differs from a natural compartment fire, whose development depends on fuel, ventilation and enclosure properties. A temperature curve also differs from a heat release rate curve: one describes temperature, while the other describes thermal power. Confusing them would change the physical problem being assessed.[7]
The exposed faces matter as much as the nominal temperature history. A slab or separating wall may receive fire exposure predominantly on one side. A beam can be heated on several sides, while a column can be exposed around its perimeter. Fleischmann and Buchanan describe these arrangements separately because they produce different internal temperature distributions.[8]
Heat penetration and material properties
Heat entering the exposed surface moves through solid concrete mainly by conduction. Thermal conductivity describes how readily a temperature difference drives that transfer. Density and specific heat describe the energy stored as the material warms. Together, these quantities determine how rapidly a temperature disturbance spreads into the section.[8][9]
The exposed surface and the interior therefore need not reach the same temperature. During early heating, a substantial temperature gradient can exist through a thick section. The cooler interior is one reason a concrete member may continue functioning while its surface becomes very hot. A single furnace temperature does not represent the temperature of every reinforcement bar.[1][8][9]
Moisture changes the energy balance because evaporation consumes heat. Heating also changes the material itself, including its microstructure and relevant thermal properties. Van Rossum consequently treats calculations with constant properties as approximations. The diffusivity used at one stage of heating need not describe the entire fire exposure.[9][6]
A steady calculation assumes that the temperature profile through the whole construction has already developed. That assumption can be unsuitable during the initial heating of a thick wall. A transient calculation instead follows the changing temperatures as energy enters and spreads through the material. This distinction affects both reinforcement temperature and heat transfer to the unexposed side.[9][1]
A worked heat-penetration example
Thermal diffusivity divides conductivity by the volumetric heat capacity, which is density multiplied by specific heat. For a sudden surface-temperature change, the square root of diffusivity multiplied by time gives a characteristic penetration depth. This depth describes a scale of temperature change, rather than a sharp front separating hot and cold concrete.[9]
| Symbol | Description | Unit |
|---|---|---|
| Thermal diffusivity | m²/s | |
| Thermal conductivity | W/(m·K) | |
| Density | kg/m³ | |
| Specific heat | J/(kg·K) | |
| Heating duration | s | |
| Characteristic penetration depth | m |
Van Rossum's comparison of thick concrete and timber walls uses rounded concrete properties of 1.7 W/(m·K), 2,300 kg/m³ and 900 J/(kg·K). With these inputs, the calculated diffusivity is 8.21 × 10⁻⁷ m²/s. After 3,600 s, the characteristic depth is approximately 0.054 m, or 54 mm. The calculation reproduces the source example using unrounded intermediate values.[9]
That result does not mean that concrete outside a 54 mm layer remains exactly at its initial temperature. Nor does it identify a spalling depth, a damaged zone or the position of a failure boundary. The model has no mechanical failure criterion and uses fixed thermal properties. Its purpose is to explain the scale of transient heating in a thick material.[9]
A separate example in the same section considers a 200 mm concrete wall over the first 900 s. It uses a different stated diffusivity, 9.88 × 10⁻⁷ m²/s. The source's approximate boundary between thermally thick and thin behaviour, twice the penetration depth, is then 60 mm. The 200 mm wall is thermally thick for that example, but this observation does not assign it a fire-resistance rating.[9]
Spalling and loss of cover
Spalling is the breaking away of concrete from the heated surface. Kodur and Harmathy distinguish early explosive loss from later loss associated with weakened material. The process matters because the section can lose both material and thermal protection. Reinforcement formerly enclosed by concrete may then receive more direct heating.[3]
One proposed mechanism involves moisture movement and pressure within the pores. Heating drives moisture towards cooler regions, where a relatively saturated zone can impede further transport. Pressure can rise if vapour cannot escape readily. The handbook also discusses explanations based on thermal stresses and fracture, so pore pressure is not the sole mechanism considered.[10]
The source illustrates the pressure mechanism using approximately 8 MPa vapour pressure at 300 °C and approximately 5 MPa tensile strength for high-strength concrete. This comparison demonstrates how internal pressure can exceed a resisting tensile stress; it is an explanatory example, not a universal pressure-temperature failure rule. Actual spalling also depends on permeability, moisture, loading and the heating conditions.[3]
High compressive strength at room temperature does not by itself prevent spalling. Dense, low-permeability concrete can restrict moisture escape during rapid heating. Once surface material is lost, deeper concrete and reinforcement heat more rapidly. A model that retains the original section throughout the exposure cannot automatically represent that change.[3]
Thermal stress offers a different way for cracking to develop. The heated surface tends to expand while cooler material restricts that movement. Kodur and Harmathy discuss fracture-based explanations in which these stresses contribute to surface loss. An analysis based only on vapour pressure therefore addresses one proposed contribution, rather than demonstrating that other mechanisms are absent.[10]
The distinction between tensile and compressive behaviour is also relevant. The pressure example compares internal pressure with tensile resistance, whereas the familiar concrete grade describes compressive strength; these are different material quantities. Increasing the specified compressive strength cannot by itself resolve a cracking mechanism involving internal pressure, restrained expansion and tensile fracture.[3]
Reinforcement and load-carrying capacity
Strength reduction at elevated temperatures affects both the concrete and the embedded steel. Fleischmann and Buchanan distinguish hot-rolled reinforcement from cold-drawn prestressing steel and high-strength alloy steel, and their strength-temperature relationships differ, reflecting the materials and mechanical properties considered. A single generic steel curve cannot represent every reinforced or prestressed member.[11]
Concrete strength also depends on aggregate and on the conditions of the material test. The handbook compares specimens heated under load with specimens heated before being loaded to failure, and these procedures can produce different measured strengths at the same temperature. Material data therefore need an accompanying description of the loading and heating history.[12]
The modulus of elasticity describes stiffness, or resistance to elastic deformation, and it can decrease substantially during heating even when part of the compressive strength remains. Consequently, a strength calculation and a deformation calculation address different effects. Thermal expansion adds another source of deformation and can alter the forces arising in restrained construction.[12]
In a simplified thermal analysis, the reinforcement temperature may be approximated by the concrete temperature at the bar centre. This connects the heat-transfer calculation to the subsequent structural calculation. The cover depth, exposed faces and heating duration then affect the steel properties used in that analysis. The approximation belongs to the stated modelling approach, rather than every possible member configuration.[8]
The load present during heating affects how a property curve is established. In the concrete results discussed by Fleischmann and Buchanan, some specimens carried 40% of their compressive strength while being heated. They were then loaded to failure at the temperature of interest. That procedure describes strength while hot, rather than a measurement of residual strength after cooling.[13]
A temperature-dependent property curve consequently carries more information than its axes alone, and its concrete type, initial condition and testing sequence affect what the result represents. A curve measured for one aggregate and load history cannot be assumed to describe another without supporting evidence. This is separate from uncertainty in the furnace temperature or the calculated temperature within the member.[12]
Beams, slabs and structural continuity
A simply supported slab provides a useful starting model: its ends permit expansion and rotation under the idealised support conditions described by Fleischmann and Buchanan. As reinforcement heats and weakens, the section's resistance to bending decreases. Structural failure is assessed by comparing that remaining resistance with the bending demand from the applied load.[14]
Concrete near the compression face may remain cooler than reinforcement near the fire-exposed underside. The structural calculation therefore uses the temperature distribution, rather than applying one reduction to the entire section. If part of the compression zone becomes sufficiently hot, the source method reduces its contribution. That step depends on the chosen material model and calculation procedure.[14]
A continuous member behaves differently because it can redistribute bending moments between the span and its supports. Redistribution can extend endurance, but the remaining sections must still resist the transferred demand. Fleischmann and Buchanan describe failure through the formation of a mechanism involving several yielding regions. Continuity is therefore a structural condition, not an automatic allowance added to a rating.[15]
Structural fire engineering combines this structural response with the preceding fire and thermal calculations. The assessment depends on loads, geometry, reinforcement and support conditions as well as temperature. More specialised structural behaviour is addressed in the related topic Tensile membrane action. The heat-penetration example above does not calculate any redistribution or membrane resistance.[1][16]
Testing and fire-resistance assessment
Fire resistance is evaluated against specified functions under a defined exposure. A separating concrete floor may need to support loads and limit heat transfer to the space above. A column has a different structural role and exposure arrangement. The required endpoints follow the assembly and assessment method, rather than the material name alone.[1][8]
For standard exposure, empirical methods can relate dimensions and other parameters to results from furnace tests. Nonstandard exposure generally requires a more explicit thermal analysis followed by structural evaluation. Fleischmann and Buchanan describe both approaches and their different information requirements. A correlation derived from a standard test does not independently establish performance for an arbitrary natural fire.[1]
New Zealand's C/VM2, second edition of 2025, defines a fire resistance rating using three durations, and their order is structural adequacy, integrity and insulation. The definition permits standard testing or a specified calculation method verified against standard fire-resistance tests. This is the terminology of that New Zealand document, rather than a universal notation for every jurisdiction.[17]
Limits of simplified predictions
A numerical model can follow changing temperatures with more detail than a penetration-depth estimate. The concrete chapter describes models that include temperature-dependent properties and changing boundary conditions, but it also notes that the cited implementations did not explicitly model moisture migration. Representing evaporation through adjusted thermal properties does not itself calculate pore-pressure-driven spalling.[18][10]
The same distinction applies to a good match with measured temperatures. Such a match supports the thermal calculation for the tested conditions, but it does not independently demonstrate the correct structural restraint, reinforcement strength or response to section loss. Those questions require evidence relevant to the mechanical model and the construction being assessed.[1][18][19]
A source value also carries limits associated with its concrete and test history. Aggregate type, moisture and applied load can affect the measured response, while rapid heating can introduce additional damage mechanisms. These dependencies explain why the handbook presents several material relationships and calculation approaches. Selecting one requires identifying the physical conditions it represents.[12][3]
See also
Notes
- ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Fleischmann and Buchanan (2002), p. 4-239.
- ↑ Kodur and Harmathy (2002), p. 1-156.
- ↑ 3.0 3.1 3.2 3.3 3.4 3.5 Kodur and Harmathy (2002), pp. 1-163–1-164.
- ↑ Fleischmann and Buchanan (2002), pp. 4-239–4-242.
- ↑ Kodur and Harmathy (2002), pp. 1-155–1-156.
- ↑ 6.0 6.1 Kodur and Harmathy (2002), p. 1-157.
- ↑ Van Rossum (2027), §8.6.
- ↑ 8.0 8.1 8.2 8.3 8.4 Fleischmann and Buchanan (2002), p. 4-242.
- ↑ 9.0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 Van Rossum (2027), §5.2.
- ↑ 10.0 10.1 10.2 Kodur and Harmathy (2002), p. 1-163.
- ↑ Fleischmann and Buchanan (2002), pp. 4-239–4-240.
- ↑ 12.0 12.1 12.2 12.3 Fleischmann and Buchanan (2002), pp. 4-240–4-241.
- ↑ Fleischmann and Buchanan (2002), p. 4-240.
- ↑ 14.0 14.1 Fleischmann and Buchanan (2002), p. 4-245.
- ↑ Fleischmann and Buchanan (2002), p. 4-246.
- ↑ Fleischmann and Buchanan (2002), pp. 4-245–4-246.
- ↑ Ministry of Business, Innovation and Employment (2025), p. 64.
- ↑ 18.0 18.1 Fleischmann and Buchanan (2002), p. 4-243.
- ↑ Kodur and Harmathy (2002), p. 1-164.
References
- Fleischmann, C., & Buchanan, A. (2002). Analytical methods for determining fire resistance of concrete members. In P. J. DiNenno (Ed.), SFPE handbook of fire protection engineering (3rd ed., pp. 4-239–4-256). National Fire Protection Association.
- 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., pp. 1-155–1-181). National Fire Protection Association.
- Ministry of Business, Innovation and Employment. (2025). C protection from fire: Verification method C/VM2 (2nd ed.).
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