I2Axial force

This section applies to encased composite members, filled composite members, and composite plate shear walls subjected to axial force.

I2.1 Encased Composite Members

I2.1a Limitations

For encased composite members, the following limitations shall be met:

• (a) The cross-sectional area of the steel core shall comprise at least 1% of the total composite cross section.
• (b) Concrete encasement of the steel core shall be reinforced with continuous longitudinal bars and transverse reinforcement consisting of ties, hoops, and/or spirals.

Detailing and placement of longitudinal reinforcement, including bar spacing and concrete cover requirements, shall conform to ACI 318.

Transverse reinforcement where specified as ties or hoops shall consist of a minimum of either a No. 3 (10 mm) bar spaced at a maximum of 12 in. (300 mm) on center, or a No. 4 (13 mm) bar or larger spaced at a maximum of 16 in.

(400 mm) on center. Deformed wire or welded wire reinforcement of equivalent area is permitted.

Maximum spacing of ties or hoops shall not exceed 0.5 times the smaller column dimension.

• (c) The minimum reinforcement ratio for continuous longitudinal reinforcement, $\rho_{s r}$, shall be 0.004 , where $\rho_{s r}$ is given by

where

$A_{g}=$ gross area of composite member, in. ${ }^{2}\left(\mathrm{~mm}^{2}\right)$

Asr = area of continuous longitudinal reinforcing bars, in.2 (mm2)

• (d) The maximum reinforcement ratio for continuous longitudinal reinforcement, $\rho_{s r}$, shall meet ACI 318 with the gross area of concrete, $A_{g}$, assumed in the cal- culations.

User Note: Refer to ACI 318 for additional longitudinal and transverse steel provisions. Refer to Section I4 for shear requirements.

I2.1b Compressive Strength

The design compressive strength, $\phi_{c} P_{n}$, and allowable compressive strength, $P_{n} / \Omega_{c}$, of doubly symmetric axially loaded encased composite members shall be determined for the limit state of flexural buckling based on member slenderness as follows:

$\phi_{c}=0.75$ (LRFD) $\quad \Omega_{c}=2.00$ (ASD)

• (a) When $\frac{P_{n o}}{P_{e}} \leq 2.25$

(I2-2)

• (b) When $\frac{P_{n o}}{P_{e}}>2.25$

(I2-3)

where

• $\begin{aligned} P_{e} & =\text { elastic critical buckling load determined in accordance with Chapter C } \\ & \text { or Appendix } 7, \text { kips (N) } \\ & =\pi^{2}\left(E I\right)_{e f f} / L_{c}^{2} \end{aligned}$
• $\begin{aligned} (E I)_{e f f} & =\text { effective stiffness of composite section, kip-in. }^{2}(\mathrm{~N}-\mathrm{mm}^{2}) \\ & =E_{s} I_{s}+E_{s} I_{s r}+C_{1} E_{c} I_{c} \end{aligned}$
• C₁ = coefficient for calculation of effective rigidity of an encased composite compression member

(I2-6)

• $\begin{aligned} E_{c} & =\text { modulus of elasticity of concrete } \\ & =w_{c}^{1.5} \sqrt{f_{c}^{\prime}}, \mathrm{ksi}\left(0.043 w_{c}^{1.5} \sqrt{f_{c}^{\prime}}, \mathrm{MPa}\right)\end{aligned}$

• $f_{c}^{\prime} \quad=$ specified compressive strength of concrete, ksi (MPa)

• wc = weight of concrete per unit volume (90 ≤ wc ≤ 155 lb/ft3 or 1 500 ≤ wc ≤ 2 500 kg/m3)

• $E_{s} \quad=$ modulus of elasticity of steel

• = 29,000 ksi (200 000 MPa)

• $\begin{aligned} I_{c} & =\text { moment of inertia of the concrete section about the elastic neutral axis of } \\ & \text { the composite section, in. }{ }^{4}\left(\mathrm{~mm}^{4}\right)\end{aligned}$

• $\begin{aligned} I_{s} & =\text { moment of inertia of steel shape about the elastic neutral axis of the com-posite section, in. }^{4}\left(\mathrm{~mm}^{4}\right)\end{aligned}$

• $I_{s r}$ = moment of inertia of reinforcing bars about the elastic neutral axis of the composite section, in. ${ }^{4}\left(\mathrm{~mm}^{4}\right)$

• $L_{c}$ = effective length of the member, in. (mm)

• = KL

• $K \quad=$ effective length factor

• $L \quad$ = laterally unbraced length of the member, in. (mm)

• $\begin{aligned} P_{n o} & =\text { nominal axial compressive strength without consideration of length effects, } \\ & \text { kips (N) }\end{aligned}$

• $= F_{y} A_{s}+F_{y s r} A_{s r}+0.85 f_{c}^{\prime} A_{c}$

• $A_{c} \quad=$ area of concrete, in. ${ }^{2}\left(\mathrm{~mm}^{2}\right)$

• $A_{s} \quad$ = cross-sectional area of structural steel section, in. ${ }^{2}\left(\mathrm{~mm}^{2}\right)$

• $F_{y} \quad=$ specified minimum yield stress of structural steel section, ksi (MPa)

• $F_{y s r}=$ specified minimum yield stress of reinforcing steel, ksi (MPa)

The available compressive strength need not be less than that determined for the bare steel member in accordance with Chapter E.

I2.1c Tensile Strength

The available tensile strength of axially loaded encased composite members shall be determined for the limit state of yielding as

(12-8)

$\phi_{t}=0.90$ (LRFD) $\quad \Omega_{t}=1.67$ (ASD)

I2.1d Load Transfer

Load transfer requirements for encased composite members shall be determined in accordance with Section I6.

I2.1e Detailing Requirements

For encased composite members, the following detailing requirements shall be met:

• (a) Clear spacing between the steel core and longitudinal reinforcing bars shall be a minimum of 1.5 longitudinal reinforcing bar diameters, but not less than 1.5 in. (38 mm).
• (b) If the composite cross section is built up from two or more encased steel shapes, the shapes shall be interconnected with lacing, tie plates, or comparable components to prevent buckling of individual shapes due to loads applied prior to hardening of the concrete.

User Note: Refer to ACI 318 for additional longitudinal and transverse reinforc- ing steel requirements. Refer to Section I4 for requirements for members subjected to shear. The requirements of Section I2.1.1e are not applicable to composite plate shear walls.

I2.2 Filled Composite Members

I2.2a Limitations

For filled composite members, the following limitations shall be met:

• (a) The cross-sectional area of the structural steel section shall comprise at least 1% of the total composite cross section.
• (b) Filled composite members shall be classified for local buckling according to Section II.4.
• (c) Minimum longitudinal reinforcement is not required. If longitudinal reinforcement is provided, internal transverse reinforcement is not required for strength; however, minimum internal transverse reinforcement shall be provided. Transverse reinforcement where specified as ties or hoops shall consist of a minimum of either a No. 3 (10 mm) bar spaced at a maximum of 12 in. (300 mm) on center, or a No. 4 (13 mm) bar or larger spaced at a maximum of 16 in. (400 mm) on center. Deformed wire or welded wire reinforcement of equivalent area is permitted.
• (d) If longitudinal reinforcing steel is provided for strength, the maximum reinforce- ment ratio shall be based on ACI 318 requirements for the gross area of concrete.

User Note: Refer to ACI 318 for additional longitudinal and transverse steel provisions. Refer to Section I4 and Section I4 Commentary for shear in filled composite members.

I2.2b Compressive Strength

The available compressive strength of axially loaded doubly symmetric filled composite members shall be determined for the limit state of flexural buckling in accordance with Section I2.1b with the following modifications:

(a) For compact composite sections

(I2-9a)

where

(b) For noncompact composite sections

Specification for Structural Steel Buildings, August 1, 2022 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

where

$\lambda_{p}$ and $\lambda_{r}$ are width-to-thickness ratios determined from Table II.1a. $P_{p}$ is determined from Equation I2-9b.

(12-9d)

(c) For slender composite sections

where

the critical buckling stress for the structural steel section of filled composite members, $F_{n}$, is determined as follows:

(1) For rectangular filled sections

(2) For round filled sections

(12-11)

See Section II.4 for definitions of maximum width-to-thickness ratio, $\lambda$; width, $D$; and thickness, $t$, for rectangular and round HSS and box sections of uniform thickness.

The effective stiffness of the composite section, $(E I)_{e f f}$, for all sections shall be

where

C3 = coefficient for calculation of effective rigidity of a filled composite compression member

The available compressive strength need not be less than that determined for the bare steel member in accordance with Chapter E.

I2.2c Tensile Strength

The available tensile strength of axially loaded filled composite members shall be determined for the limit state of yielding as

(I2-14)

$\phi_{t}=0.90$ (LRFD) $\quad \Omega_{t}=1.67$ (ASD)

I2.2d Load Transfer

Load transfer requirements for filled composite members shall be determined in accordance with Section I6.

I2.2e Detailing Requirements

Clear spacing between the inside of the structural steel section and longitudinal reinforcing steel, where provided, shall be a minimum of 1.5 reinforcing bar diameters, but not less than 1.5 in. (38 mm).

I2.3 Composite Plate Shear Walls

I2.3a Compressive Strength

The available compressive strength of axially loaded composite plate shear walls shall be determined for the limit state of flexural buckling in accordance with Section I2.1b. The value of flexural stiffness from Section II.5 shall be used along with $P_{n o}$ determined as follows:

(12-15)

$\phi_{c}=0.90$ (LRFD) $\quad \Omega_{c}=1.67$ (ASD)

I2.3b Tensile Strength

The available tensile strength of axially loaded composite plate shear walls shall be determined for the limit state of yielding as

(12-16)

$\phi_{t}=0.90$ (LRFD) $\quad \Omega_{t}=1.67$ (ASD)