4.2structural design for fire conditions by analysis

It is permitted to design structural members, components, and building frames for elevated temperatures in accordance with the requirements of this section.

4.2.1 Design-Basis Fire

A design-basis fire shall be identified to describe the heating and cooling conditions for the structure. These heating and cooling conditions shall relate to the fuel com- modities and compartment characteristics present in the assumed fire area. The fuel

load density based on the occupancy of the space shall be considered when determining the total fuel load. Heating and cooling conditions shall be specified either in terms of a heat flux or temperature of the upper gas layer created by the fire. The variation of the heating and cooling conditions with time shall be determined for the duration of the fire.

The analysis methods in Section 4.2 shall be used in accordance with the provisions for alternative materials, designs, and methods as permitted by the ABC. When the analysis methods in Section 4.2 are used to demonstrate equivalency to hourly ratings based on qualification testing in Section 4.3, the design-basis fire is permitted to be determined in accordance with ASTM E119 or ANSI/UL 263.

4.2.1a Localized Fire

Where the heat release rate from the fire is insufficient to cause flashover, a localized fire exposure shall be assumed. In such cases, the fuel composition, arrangement of the fuel array, and floor area occupied by the fuel shall be used to determine the radiant heat flux from the flame and smoke plume to the structure.

4.2.1b Post-Flashover Compartment Fires

Where the heat release rate from the fire is sufficient to cause flashover, a post-flashover compartment fire shall be assumed. The determination of the temperature versus time profile resulting from the fire shall include fuel load, ventilation characteristics of the space (natural and mechanical), compartment dimensions, and thermal characteristics of the compartment boundary.

The fire duration in a particular area shall be determined from the total combustible mass or fuel load in the space. In the case of either a localized fire or a post-flashover compartment fire, the fire duration shall be determined as the total combustible mass divided by the mass loss rate.

4.2.1c Exterior Fires

The exposure effects of the exterior structure to flames projecting from windows or other wall openings as a result of a post-flashover compartment fire shall be addressed along with the radiation from the interior fire through the opening. The shape and length of the flame projection shall be used along with the distance between the flame and the exterior steelwork to determine the heat flux to the steel. The method identified in Section 4.2.1b shall be used for describing the characteristics of the interior compartment fire.

4.2.1d Active Fire-Protection Systems

The effects of active fire-protection systems shall be addressed when describing the design-basis fire.

Where automatic smoke and heat vents are installed in nonsprinklered spaces, the resulting smoke temperature shall be determined from calculation.

4.2.2 Temperatures in Structural Systems Under Fire Conditions

Temperatures within structural members, components, and frames due to the heating conditions posed by the design-basis fire shall be determined by a heat transfer analysis.

4.2.3 Material Properties at Elevated Temperatures

The effects of elevated temperatures on the physical and mechanical properties of materials shall be considered in the analysis and design of structural members, components, and systems. Any rational method that establishes material properties at elevated temperatures that is based on test data is permitted, including the methods defined in Sections 4.2.3a and 4.2.3b.

4.2.3a Thermal Elongation

The coefficients of thermal expansion shall be taken to be as follows.

• (a) For structural and reinforcing steels: For calculations at temperatures above 150°F (66°C), the coefficient of thermal expansion is 7.8 x 10-6/°F (1.4 x 10-5/°C).
• (b) For normal weight concrete: For calculations at temperatures above 150°F (66°C), the coefficient of thermal expansion is 10 x 10-6/°F (1.8 x10-5/°C).
• (c) For lightweight concrete: For calculations at temperatures above 150°F (66°C), the coefficient of thermal expansion is 4.4 × 10-6/°F (7.9 × 10-6/°C).

4.2.3b Mechanical Properties of Structural Steel, Hot-Rolled Reinforcing Steel, and Concrete at Elevated Temperatures

The uniaxial engineering stress-strain-temperature relationship for structural steel, hot-rolled reinforcing steel, and concrete shall be determined using this section. This applies only to structural and reinforcing steels with a specified minimum yield strength, $F_{y}$, equal to 65 ksi (450 MPa) or less, and to concrete with a specified compressive strength, $f_{c}^{\prime}$, equal to 8 ksi (55 MPa) or less.

(a) Structural and hot-rolled reinforcing steel

Table A-4.2.1 provides retention factors, $k_{E}, k_{p}$, and $k_{y}$, for steel which are expressed as the ratio of the mechanical property at elevated temperature with respect to the property at ambient, assumed to be $68^{\circ} \mathrm{F}\left(20^{\circ} \mathrm{C}\right)$. It is permitted to interpolate between these values. The properties at elevated temperature, $T$, are defined as follows:

$E(T)$ is the modulus of elasticity of steel at elevated temperature, ksi (MPa), which is calculated as the retention factor, $k_{E}$, times the ambient property as specified in Table A-4.2.1.

$G(T)$ is the shear modulus of elasticity of steel at elevated temperature, ksi (MPa), which is calculated as the retention factor, $k_{E}$, times the ambient property as specified in Table A-4.2.1.

$F_{y}(T)$ is the specified minimum yield stress of steel at elevated temperature, ksi (MPa), which is calculated as the retention factor, $k_{y}$, times the ambient property as specified in Table A-4.2.1.

TABLE A-4.2.1 Properties of Steel at Elevated Temperatures

Fp T ( ) is the proportional limit at elevated temperature, which is calculated as the retention factor, kp, times the yield strength as specified in Table A-4.2.1.

$F_{u}(T)$ is the specified minimum tensile strength at elevated temperature, which is equal to $F_{y}(T)$ for temperatures greater than $750^{\circ} \mathrm{F}\left(400^{\circ} \mathrm{C}\right)$. For temperatures less than or equal to $750^{\circ} \mathrm{F}\left(400^{\circ} \mathrm{C}\right), F_{u}$ may be used in place of $F_{u}(T)$.

The engineering stress at elevated temperature, $F(T)$, at each strain range shall be determined as follows:

(1) When in the elastic range $[\varepsilon(T)\leq\varepsilon_{p}(T)]$ $F(T)=E(T)\varepsilon(T)$ (A-4-2) (2) When in the nonlinear range $[\varepsilon_{p}(T)<\varepsilon(T)<\varepsilon_{y}(T)]$ $F(T)=F_{p}(T)-c+\frac{b}{a}\sqrt{a^{2}-[\varepsilon_{y}(T)-\varepsilon(T)]^{2}}$ (A-4-3) (3) When in the plastic range $[\varepsilon_{y}(T)\leq\varepsilon(T)\leq\varepsilon_{u}(T)]$ $F(T)=F_{y}(T)$ (A-4-4)

where

• $\varepsilon(T)=$ engineering strain at elevated temperature, in./in. (mm/mm)
• $\begin{aligned} \epsilon_{p}(T) & =\text { engineering strain at the proportional limit at elevated temperature, } \\ & \text { in./in. (mm/mm) } \\ & =F_{p}(T) / E(T)\end{aligned}$
• $\begin{aligned} \varepsilon_{u}(T) & =\text { ultimate strain at elevated temperature } \\ & =0.15 \text { in./in. (mm/mm) }\end{aligned}$
• $\begin{aligned} \epsilon_{\mathrm{y}}(T) & =\text { engineering yield strain at elevated temperature } \\ & =0.02 \text { in./in. (mm/mm) }\end{aligned}$

$a^{2}\quad=[\varepsilon_{y}(T)-\varepsilon_{p}(T)][\varepsilon_{y}(T)-\varepsilon_{p}(T)+\frac{c}{E(T)}]$ (A-4-5) $b^{2}\quad=E(T)[\varepsilon_{y}(T)-\varepsilon_{p}(T)]c+c^{2}$ (A-4-6) $c\quad=\frac{[F_{y}(T)-F_{p}(T)]^{2}}{E(T)[\varepsilon_{y}(T)-\varepsilon_{p}(T)]-2[F_{y}(T)-F_{p}(T)]}$ (A-4-7)

User Note: The equation for the plastic range conservatively neglects the strain-hardening portion, but strain-hardening may be included. The plateau of the plastic range does not exceed the ultimate strain, $\epsilon_{u}(T)$.

User Note: This section applies to structural steel materials specified in Section A3.1 and to hot-rolled reinforcing steel with a specified minimum yield strength, $F_{y}$, equal to 65 ksi (450 MPa) or less. This includes ASTM A615/A615M Grade 60 (420) and ASTM A706/A706M Grade 60 (420) steel reinforcement.

• (b) Concrete

Table A-4.2.2 provides retention factors, $k_{c}$ and $k_{E c}$, for concrete which are expressed as the ratio of the mechanical property at elevated temperature with respect to the property at ambient, assumed to be $68^{\circ} \mathrm{F}\left(20^{\circ} \mathrm{C}\right)$. It is permitted to interpolate between these values. For lightweight concrete, values of $\varepsilon_{c u}(T)$ shall be obtained from tests. The properties at elevated temperature, $T$, are defined as follows:

• $\begin{aligned} E_{c}(T) & =\text { modulus of elasticity of concrete at elevated temperature, ksi (MPa), } \\ & \text { which is calculated as the retention factor, } k_{E c} \text {, times the ambient property as specified in Table A-4.2.2 }\end{aligned}$
• $\begin{aligned} f_{c}^{\prime}(T) & =\text { specified compressive strength of concrete at elevated temperature, ksi } \\ & \text { (MPa), which is calculated as the retention factor, } k_{c} \text {, times the ambient } \\ & \text { property as specified in Table A-4.2.2 }\end{aligned}$
• $\begin{aligned} \epsilon_{c u}(T) & =\text { concrete strain corresponding to } f_{c}^{\prime}(T) \text { at elevated temperature, in./in. } \\ & \text { (mm/mm), which is specified in Table A-4.2.2 }\end{aligned}$

TABLE A-4.2.2 Properties of Concrete at Elevated Temperatures

The uniaxial stress-strain-temperature relationship for concrete in compression is permitted to be calculated as follows:

$F_c(T)=f_c^{\prime}(T)\left\{\frac{3\left[\frac{\varepsilon_c(T)}{\varepsilon_{cu}(T)}\right]}{2+\left[\frac{\varepsilon_c(T)}{\varepsilon_{cu}(T)}\right]^3}\right\}$ (A-4-8)

where F(T) and & (T) are the concrete compressive stress and strain, respec- tively, at elevated temperature.

User Note: The tensile strength of concrete at elevated temperature can be taken as zero, or not more than 10% of the compressive strength at the corresponding temperature.

• (c) Strengths of bolts at elevated temperatures

Table A-4.2.3 provides the retention factor, $k_{b}$, for high-strength bolts that is expressed as the ratio of the mechanical property at elevated temperature with respect to the property at ambient, which is assumed to be $68^{\circ} \mathrm{F}\left(20^{\circ} \mathrm{C}\right)$. The properties at elevated temperature, $T$, are defined as follows:

TABLE A-4.2.3

Properties of Group 120 and Group 150 High-Strength Bolts at Elevated Temperatures

• Fnt T ( ) = nominal tensile strength of the bolt, ksi (MPa), which is calculated as the retention factor, kb, times the ambient property as specified in Table A-4.2.3
• $F_{n v}(T)=$ nominal shear strength of the bolt, ksi (MPa), which is calculated as the retention factor, $k_{b}$, times the ambient property as specified in Table A-4.2.3

4.2.4 Structural Design Requirements

4.2.4a General Requirements

The structural frame and foundation shall be capable of providing the strength and deformation capacity to withstand, as a system, the structural actions developed during the fire within the prescribed limits of deformation. The structural system shall be designed to sustain local damage with the structural system as a whole remaining stable. Frame stability and required strength shall be determined in accordance with the requirements of Section C1.

Continuous load paths shall be provided to transfer all forces from the exposed region to the final point of resistance.

The size and spacing of vent holes in filled composite members shall be evaluated such that no applicable strength limit states in the steel elements are exceeded due

to the build-up of steam pressure. Any rational method that considers heat transfer through the cross section, water content in concrete, fire protection, and the allowable pressure build up in the member is permitted for calculating the size and spacing of vent holes.

User Note: Section 4.3.2b(a) provides a possible vent hole configuration for filled composite columns.

4.2.4b Strength Requirements and Deformation Limits

Conformance of the structural system to these requirements shall be demonstrated by constructing a mathematical model of the structure based on principles of structural mechanics and evaluating this model for the internal forces and deformations in the members of the structure developed by the temperatures from the design-basis fire.

Individual members shall have the design strength necessary to resist the shears, axial forces, and moments determined in accordance with these provisions.

Structural components shall be designed and detailed to resist the imposed loading and deformation demands during a design-basis fire as required to meet the performance objectives stated in Section 4.1.1. Where the means of providing fire resistance requires the evaluation of deformation criteria, the deformation of the structural system, or members thereof, under the design-basis fire shall not exceed the prescribed limits.

User Note: Typical simple shear connections may need additional design enhancements for ductility and resistance to large compression and tensile forces that may develop during the design-basis fire exposure. A fire exposure will not only affect the magnitude of member end reactions, but may also change the limit state to one different from the controlling mode at ambient temperature.

It is permitted to include membrane action of composite floor slabs for fire resistance if the design provides for the effects of increased connection tensile forces and redistributed gravity load demands on the adjacent framing supports.

4.2.4c Design by Advanced Methods of Analysis

Design by advanced methods of analysis is permitted for the design of all steel building structures for fire conditions. The design-basis fire exposure shall be that determined in Section 4.2.1. The analysis shall include both a thermal response and the mechanical response to the design-basis fire.

The thermal response shall produce a temperature field in each structural element as a result of the design-basis fire and shall incorporate temperature-dependent thermal properties of the structural elements and fire-resistive materials, as per Section 4.2.2.

The mechanical response shall include the forces and deformations in the structural system due to the thermal response calculated from the design-basis fire. The

mechanical response shall take into account explicitly the deterioration in strength and stiffness with increasing temperature, the effects of thermal expansions, inelastic behavior and load redistribution, large deformations, time-dependent effects such as creep, and uncertainties resulting from variability in material properties at elevated temperature. Support and restraint conditions (forces, moments, and boundary condi- tions) shall represent the behavior of the structure during a design-basis fire. Material properties shall be defined as per Section 4.2.3.

The resulting analysis shall address all relevant limit states, such as excessive deflections, connection ruptures, and global and local buckling, and shall demonstrate an adequate level of safety as required by the authority having jurisdiction.

4.2.4d Design by Simple Methods of Analysis

The methods of analysis in this section are permitted to be used for the evaluation of the performance of structural components and frames at elevated temperatures during exposure to a design-basis fire.

When evaluating structural components, the stiffnesses and boundary conditions applicable at ambient temperatures are permitted to be assumed to remain unchanged throughout the fire exposure for the calculation of required strengths.

For evaluating the performance of structural frames during exposure to a design-basis fire, the required strengths are also permitted to be determined through consideration of reduced stiffness at elevated temperatures, boundary conditions, and thermal deformations.

User Note: Determining the required strength assuming ambient temperatures throughout the fire exposure is generally applicable to members in regular gravity frames. Determining the required strength accounting for elevated temperatures may be more appropriate for irregular structural frames.

The design strength shall be determined as in Section B3.1. The nominal strength, $R_{n}$, shall be calculated using material properties, as provided in Section 4.2.3b, at the temperature developed by the design-basis fire and as stipulated in Sections 4.2.4d(a) through (h).

The simple method is only applicable to members with nonslender and/or compact sections.

It is permitted to model the thermal response of steel and composite members using a lumped heat capacity analysis with heat input as determined by the design-basis fire defined in Section 4.2.1, using the temperature equal to the maximum steel temperature. For composite beams, the maximum steel temperature shall be assigned to the bottom flange and a temperature gradient shall be applied to incorporate thermally induced moments as stipulated in Section 4.2.4d(f).

For steel temperatures less than or equal to 400°F (200°C), the member and connection design strengths are permitted to be determined without consideration of temperature effects on the nominal strengths.

User Note: Lumped heat capacity analysis assumes uniform temperature over the section and length of the member, which is generally a reasonable assumption for many structural members exposed to post-flashover fires. Consideration should be given to the use of the uniform temperature assumption as it may not always be applicable or conservative.

The simple methods of analysis are not intended for temperatures below 400°F (200°C). The nominal strengths for temperatures below 400°F (200°C) should be calculated without any consideration of temperature effects on material properties or member behavior.

• (a) Design for tension

The nominal strength for tension shall be determined using the provisions of Chapter D, with steel properties as stipulated in Section 4.2.3b(a) and assuming a uniform temperature over the cross section using the temperature equal to the maximum steel temperature.

• (b) Design for compression

For nonslender-element columns, the nominal strength for flexural buckling of compression members shall be determined using the provisions of Chapter E with steel properties as stipulated in Section 4.2.3b(a). Equation A-4-9 shall be used in lieu of Equations E3-2 and E3-3 to calculate the nominal compressive strength for flexural buckling:

(A-4-9)

where $F_{y}(T)$ is the yield stress at elevated temperature and $F_{e}(T)$ is the critical elastic buckling stress calculated from Equation E3-4 with the elastic modulus, $E(T)$, at elevated temperature. $F_{y}(T)$ and $E(T)$ are obtained using coefficients from Table A-4.2.1.

The strength of gravity-only columns that do not provide resistance to lateral loads is permitted to be increased by the rotational restraints from cooler columns in the stories above and below the story exposed to the fire. This increased strength applies to fires on only one floor and should not be used for multiple story fires. It is permitted to account for the increase in design strength by reducing the column slenderness, $L_{c} / r$, used to calculate $F_{e}(T)$ in Equation A-4-9 to $L_{c}(T) / r$ as follows:

(A-4-10)

(A-4-10M)

where

Lc = effective length of member, in. (mm)

• = KL
• $K=1.0$ for gravity-only columns
• $L=$ laterally unbraced length of the member, in. (mm)
• $T=$ temperature of structural steel, ${ }^{\circ} \mathrm{F}\left({ }^{\circ} \mathrm{C}\right)$

$n=1$ for columns with cooler columns both above and below

• $n=2$ for columns with cooler columns either above or below only
• $r \quad=$ radius of gyration, in. (mm)

User Note: The design equations for compression predict flexural buckling capacities of wide-flange rolled shapes, but do not consider local buckling and torsional buckling. If applicable, these additional limit states must be considered with an alternative method. For most fire conditions, uniform heating and temperatures govern the design for compression. When uniform heating is not a reasonable assumption, alternative methods must be used to account for the effects of nonuniform heating and resulting thermal gradients on the design strength of compression members, as the simple method assumes a uniform temperature distribution.

• (c) Design for compression in filled composite columns

For filled composite columns, the nominal strength for compression shall be determined using the provisions of Section I2.2 with steel and concrete properties as stipulated in Section 4.2.3b. Equation A-4-11 shall be used in lieu of Equations I2-2 and I2-3 to calculate the nominal compressive strength for flexural buckling:

(A-4-11)

where $P_{n o}(T)$ is calculated at elevated temperature using Equations I2-9, I2-10, and I2-11. $P_{e}(T)$ is calculated at elevated temperature using Equation I2-4. $E I_{\text {eff }}(T)$ is calculated at elevated temperature using Equations I2-12 and I2-13. $F_{y}(T), f_{c}^{\prime}(T), E_{s}(T)$, and $E_{c}(T)$ are obtained using coefficients from Tables A-4.2.1 and A-4.2.2.

• (d) Design for compression in filled composite plate shear walls

For filled composite plate shear walls, the nominal strength for compression shall be determined using the provisions of Section I2.3 with steel and concrete properties as stipulated in Section 4.2.3b and Equation A-4-12 used in lieu of Equations I2-2 and I2-3 to calculate the nominal compressive strength for flexural buckling:

(A-4-12)

where $P_{n o}(T)$ is calculated at elevated temperature using Equation I2-15. $P_{e}(T)$ is calculated at elevated temperature using Equation I2-4. $E I_{\text {eff }}(T)$ is calculated at elevated temperatures using Equation II-1. $F_{y}(T), f_{c}^{\prime}(T), E_{s}(T)$, and $E_{c}(T)$ are obtained using coefficients from Tables A-4.2.1 and A-4.2.2.

User Note: For composite members, the steel temperature is determined using heat transfer equations with heat input corresponding to the design-basis fire. The temperature distribution in concrete infill can be calculated using one- or two-dimensional heat transfer equations. The regions of concrete infill will have varying temperatures and mechanical properties. Concrete contribution to axial strength and effective stiffness can therefore be calculated by discretizing the cross section into smaller elements (with each concrete element considered to have a uniform temperature) and summing up the contribution of individual elements.

(e) Design for flexure

For steel beams, the temperature over the depth of the member shall be taken as the temperature calculated for the bottom flange.

The nominal strength for flexure shall be determined using the provisions of Chapter F with steel properties as stipulated in Section 4.2.3b(a). Equations A-4-13 through A-4-19 shall be used in lieu of Equations F2-2 through F2-8 to calculate the nominal flexural strength for lateral-torsional buckling of doubly symmetric compact rolled wide-flange shapes bent about their major axis.

(1) When $L_{b} \leq L_{r}(T)$

(A-4-13)

(2) When $L_{b}>L_{r}(T)$

(A-4-14)

where

(A-4-15)

(A-4-16)

(A-4-17)

(A-4-18)

(A-4-19)

(A-4-19M) and

T = elevated temperature of steel due to unintended fire exposure, °F (°C)

The material properties at elevated temperatures, $E(T)$ and $F_{y}(T)$, and the retention factors, $k_{p}$ and $k_{y}$, are calculated in accordance with Table A-4.2.1, and other terms are as defined in Chapter F.

User Note: $F_{L}(T)$ represents the initial yield stress, which assumes a residual stress of $0.3 F_{y}$. Alternatively, 10 ksi (69 MPa) may be used in place of $0.3 F_{y}$ for calculation of $F_{L}(T)$.

User Note: The equations for lateral-torsional buckling do not consider local buckling. If applicable, the effects of local buckling must be considered with an alternative method.

• (f) Design for flexure in composite beams

For composite beams, the calculated bottom flange temperature shall be taken as constant between the bottom flange and mid-depth of the web and shall decrease linearly by no more than 25% from the mid-depth of the web to the top flange of the beam.

The nominal strength of a composite flexural member shall be determined using the provisions of Chapter I, with reduced yield stresses in the steel as determined from Table A-4.2.1. Steel properties will vary as the temperature along the depth of section changes.

Alternatively, the nominal flexural strength of a composite beam, $M_{n}(T)$, is permitted to be calculated using the bottom flange temperature, $T$, as follows:

(A-4-20)

where

• $M_{n}=$ nominal flexural strength at ambient temperature calculated in accordance with provisions of Chapter I, kip-in. (N-mm)
• $k_{c b}=$ retention factor depending on bottom flange temperature, $T$, as given in Table A-4.2.4
• (g) Design for shear

The nominal strength for shear yielding shall be determined in accordance with the provisions of Chapter G, with steel properties as stipulated in Section 4.2.3b(a) and assuming a uniform temperature over the cross section.

User Note: Shear yielding equations do not consider shear buckling or ten- sion field action. If applicable, these limit states must be considered with an alternative method.

TABLE A-4.2.4 Retention Factor for Flexure in Composite Beams

• (h) Design for combined forces and torsion

The nominal strength for combinations of axial force and flexure about one or both axes, with or without torsion, shall be in accordance with the provisions of Chapter H with the design axial, flexural, and shear strengths as stipulated in Sections 4.2.4d(a), (b), (e), and (g). Nominal strength for torsion shall be determined in accordance with the provisions of Chapter H, with the steel properties as stipulated in Section 4.2.3b(a), assuming uniform temperature over the cross section.

4.2.4e Design by Critical Temperature Method

The critical temperature of a structural member is the temperature at which the demand on the member exceeds its capacity under fire conditions. The temperature of a loaded structural member exposed to the design-basis fire defined in Section 4.2.1 shall not exceed the critical temperature as calculated in this section. The evaluation methods in this section are permitted to be used in lieu of Section 4.2.4d for tension members, continuously braced beams not supporting concrete slabs, or compression members that are assumed to be simply supported and develop a uniform temperature over the cross section throughout the fire exposure.

The use of the critical temperature method shall be limited to steel members with wide-flange rolled shapes that have nonslender elements per Section B4.

• (a) Design for tensile yielding

The critical temperature of a tension member is permitted to be calculated as follows:

(A-4-21)

STRUCTURAL DESIGN FOR FIRE CONDITIONS BY ANALYSIS

Ter = 435-170ln A Ru in °C (A-4-21M) Rn)

where

• $R_{n}=$ nominal yielding strength at ambient temperature determined in accordance with Section D2, kips (N)

$R_{u}=$ required tensile strength at elevated temperature, determined using the load combination in Equation A-4-1 and greater than $0.01 R_{n}$, kips (N)

$T_{c r}=$ critical temperature in ${ }^{\circ} \mathrm{F}\left({ }^{\circ} \mathrm{C}\right)$

User Note: Tensile rupture in the net section is not considered in this critical temperature calculation. It can be considered using an alternative method.

• (b) Design for compression

The critical temperature of a compression member for flexural buckling is permitted to be calculated as follows:

(A-4-22)

(A-4-22M)

where

• $P_{n}=$ nominal compressive strength at ambient temperature determined in accordance with the provisions in Section E3, kips (N)
• $P_{u}=$ required compressive strength at elevated temperature, determined using the load combination in Equation A-4-1, kips (N)
• (c) Design for flexural yielding

The critical temperature of a continuously braced beam not supporting a concrete slab is permitted to be calculated as follows:

(A-4-23)

(A-4-23M)

where

• $\begin{aligned} M_{n} & =\text { nominal flexural strength due to yielding at ambient temperature } \\ & \text { determined in accordance with the provisions in Section F2.1, kip-in. } \\ & \text { (N-mm) }\end{aligned}$
• $\begin{aligned} M_{u} & =\text { required flexural strength at elevated temperature, determined using the } \\ & \text { load combination in Equation A-4-1 and greater than } 0.01 M_{n}, \text { kip-in. } \\ & \text { (N-mm) }\end{aligned}$

$T_{c r}=$ critical temperature in ${ }^{\circ} \mathrm{F}\left({ }^{\circ} \mathrm{C}\right)$

User Note: Lateral-torsional buckling of beams is not considered in this criti- cal temperature calculation. It can be considered using an alternative method.