I3Flexure

This section applies to three types of composite members subjected to flexure: composite beams with steel anchors consisting of steel headed stud anchors or steel channel anchors, encased members, and filled members.

I3.1 General

I3.1a Effective Width

The effective width of the concrete slab shall be the sum of the effective widths for each side of the beam centerline, each of which shall not exceed

• (a) one-eighth of the beam span, center-to-center of supports;
• (b) one-half the distance to the centerline of the adjacent beam; or
• (c) the distance to the edge of the slab.

I3.1b Strength During Construction

When temporary shores are not used during construction, the structural steel section alone shall have sufficient strength to support all loads applied prior to the concrete attaining 75% of its specified strength, $f_{c}^{\prime}$. The available flexural strength of the steel section shall be determined in accordance with Chapter F.

I3.2 Composite Beams with Steel Headed Stud or Steel Channel Anchors

I3.2a Positive Flexural Strength

The design positive flexural strength, $\phi_{b} M_{n}$, and allowable positive flexural strength, $M_{n} / \Omega_{b}$, shall be determined for the limit state of yielding as follows:

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

(a) When $h / t_{w} \leq 3.76 \sqrt{E / F_{y}}$

$M_{n}$ shall be determined from the plastic stress distribution on the composite section for the limit state of yielding (plastic moment).

User Note: All current ASTM A6/A6M W, S, and HP shapes satisfy the limit given in Section I3.2a(a) for $F_{y} \leq 70 \mathrm{ksi}(485 \mathrm{MPa})$.

(b) When $h / t_{w}>3.76 \sqrt{E / F_{y}}$

$M_{n}$ shall be determined from the superposition of elastic stresses, considering the effects of shoring, for the limit state of yielding (yield moment).

I3.2b Negative Flexural Strength

The available negative flexural strength shall be determined for the structural steel section alone, in accordance with the requirements of Chapter F.

Alternatively, the available negative flexural strength shall be determined from the plastic stress distribution for the composite section, for the limit state of yielding (plastic moment), with

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

provided that the following limitations are met:

• (a) The steel beam is compact and is braced in accordance with Chapter F.
• (b) Steel headed stud or steel channel anchors connect the slab to the steel beam in the negative moment region.
• (c) The slab longitudinal reinforcement parallel to the steel beam, within the effective width of the slab, meets the development length requirements.

User Note: To check compactness of a composite beam in negative flexure, Case 10 in Table B4.1b is appropriate to use for flanges, and Case 15 of Table B4.1b is appropriate to use for webs.

I3.2c Composite Beams with Formed Steel Deck

I3.2c.1 General

The available flexural strength of composite construction consisting of concrete slabs on formed steel deck connected to steel beams shall be determined

by the applicable portions of Sections I3.2a and I3.2b, with the following requirements:

• (a) The nominal rib height shall not be greater than 3 in. (75 mm). The average width of concrete rib or haunch, $w_{r}$, shall not be less than 2 in. (50 mm), but shall not be taken in calculations as more than the minimum clear width near the top of the steel deck.
• (b) The concrete slab shall be connected to the steel beam with steel headed stud anchors welded either through the deck or directly to the steel cross section. Steel headed stud anchors, after installation, shall extend not less than 1½ in. (38 mm) above the top of the steel deck and there shall be at least ½ in. (13 mm) of specified concrete cover above the top of the steel headed stud anchors.
• (c) The slab thickness above the steel deck shall be not less than 2 in. (50 mm).
• (d) Steel deck shall be anchored to all supporting members at a spacing not to exceed 18 in. (450 mm). Such anchorage shall be provided by steel headed stud anchors, a combination of steel headed stud anchors and arc spot (puddle) welds, or other devices specified by the design documents and specifications issued for construction.

I3.2c.2 Deck Ribs Oriented Perpendicular to Steel Beam

Concrete below the top of the steel deck shall be neglected in determining composite section properties and in calculating $A_{c}$ for deck ribs oriented perpendicular to the steel beams.

I3.2c.3 Deck Ribs Oriented Parallel to Steel Beam

Concrete below the top of the steel deck is permitted to be included in determining composite section properties and in calculating $A_{c}$.

Formed steel deck ribs over supporting beams are permitted to be split longitudinally and separated to form a concrete haunch.

When the nominal depth of steel deck is 1½ in. (38 mm) or greater, the average width, $w_{r}$, of the supported haunch or rib shall be not less than 2 in. (50 mm) for the first steel headed stud anchor in the transverse row plus four stud diameters for each additional steel headed stud anchor.

I3.2d Load Transfer Between Steel Beam and Concrete Slab

I3.2d.1 Load Transfer for Positive Flexural Strength

The entire horizontal shear at the interface between the steel beam and the concrete slab shall be assumed to be transferred by steel headed stud or steel channel anchors, except for concrete-encased beams as defined in Section I3.3. For composite action with concrete subjected to flexural compression, the nominal shear force between the steel beam and the concrete slab transferred by steel anchors, $V^{\prime}$, between the point of maximum positive moment and the point of zero moment shall be determined as the lowest value in accordance with the limit states of concrete crushing, tensile yielding of the steel section, or the shear strength of the steel anchors:

where

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

$\begin{aligned} A_{s} & =\text { cross-sectional area of structural steel section, in. }^{2}\left(\mathrm{~mm}^{2}\right)\end{aligned}$

$\begin{aligned} \Sigma Q_{n} & =\text { sum of nominal shear strengths of steel headed stud or steel channel } \\ & \text { anchors between the point of maximum positive moment and the point } \\ & \text { of zero moment, kips (N) }\end{aligned}$

The effect of ductility (slip capacity) of the shear connection at the interface of the concrete slab and the steel beam shall be considered.

I3.2d.2 Load Transfer for Negative Flexural Strength

• In continuous composite beams where longitudinal reinforcing steel in the negative moment regions is considered to act compositely with the steel beam, the total horizontal shear between the point of maximum negative moment and the point of zero moment shall be determined as the lower value in accordance with the following limit states:
• (a) For the limit state of tensile yielding of the slab longitudinal reinforcement

$V^{\prime}=F_{y s r} A_{s r}$ (13-2a)

where

$A_{s r}=$ area of developed longitudinal reinforcing steel within the effective width of the concrete slab, in. ${ }^{2}\left(\mathrm{~mm}^{2}\right)$

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

(b) For the limit state of shear strength of steel headed stud or steel channel anchors

(I3-2b)

I3.3 Encased Composite Members

I3.3a Limitations

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

• (a) The available flexural strength of concrete-encased members shall be determined as follows:

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

The nominal flexural strength, $M_{n}$, shall be determined using one of the following methods:

• (1) The superposition of elastic stresses on the composite section, considering the effects of shoring for the limit state of yielding (yield moment).

• (2) The plastic stress distribution on the steel section alone, for the limit state of yielding (plastic moment) on the steel section.

• (3) The plastic stress distribution on the composite section or the strain-compatibility method, for the limit state of yielding (plastic moment) on the composite section. For concrete-encased members, steel anchors shall be provided.

• (b) The total cross-sectional area of the steel core shall comprise at least 1% of the total composite cross section.

• (c) Concrete encasement of the steel core shall be reinforced with continuous longitudinal bars and transverse reinforcement (stirrups, ties, hoops, or spirals).

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

Transverse reinforcement that consists of stirrups, ties, or hoops shall be 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) 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. ${ }^{2}\left(\mathrm{~mm}^{2}\right)$

$A_{s r}=$ area of continuous longitudinal reinforcing bars, in. ${ }^{2}\left(\mathrm{~mm}^{2}\right)$

• (e) Composite beam members with $P_{u}<0.10 P_{n}$ shall be tension controlled as defined in ACI 318. The determination of $P_{n}$ shall include the area of both the structural steel section and the longitudinal reinforcement.

User Note: The effect of this limitation is to restrict the reinforcement ratio to provide ductile behavior in case of an overload. Refer to ACI 318 for additional longitudinal and transverse steel provisions. Refer to Section I4 for shear requirements.

I3.3b Detailing Requirements

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

I3.4 Filled Composite Members

I3.4a Limitations

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

• (a) Filled composite sections shall be classified for local buckling according to Section II.4.

• (b) The total cross-sectional area of the structural steel section shall comprise at least 1% of the total composite cross section.

• (c) Longitudinal reinforcement is not required.

Where longitudinal reinforcement is provided, the minimum reinforcement ratio for continuous longitudinal reinforcement, $\rho_{s r}$, shall be 0.0004 , where $\rho_{s r}$ is given by

(I3-4)

If longitudinal reinforcement is provided, internal transverse reinforcement is not required for strength; however, minimum internal transverse reinforcement shall be provided. The minimum transverse reinforcement shall be hoops and ties or hoops alone consisting 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) Composite beam members with $P_{u}<0.10 P_{n}$ shall be tension controlled as defined in ACI 318. The determination of $P_{n}$ shall include the area of both the structural steel section and the longitudinal reinforcement.

User Note: The effect of this limitation is to restrict the longitudinal reinforcement ratio to provide ductile behavior in case of an overload. Refer to ACI 318 for additional provisions for the longitudinal and transverse steel reinforcement. Refer to Section I4 for shear requirements. The limitations and requirements of Section I3.4a are not applicable to composite plate shear walls.

I3.4b Flexural Strength

The available flexural strength of filled composite members shall be determined as follows:

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

The nominal flexural strength, $M_{n}$, shall be determined as follows:

(a) For compact composite sections

(13-5a)

where

$M_{p}=$ moment corresponding to plastic stress distribution over the composite cross section, kip-in. (N-mm)

• (b) For noncompact composite sections

(I3-5b)

where

$\lambda, \lambda_{p}$, and $\lambda_{r}$ are width-to-thickness ratios determined from Table II.1b.

$M_{y}=$ yield moment corresponding to yielding of the tension flange and first yield of the compression flange, kip-in. (N-mm). The capacity at first yield shall be calculated assuming a linear elastic stress distribution with the maximum concrete compressive stress limited to $0.7 f_{c}^{\prime}$ and the maximum steel stress limited to $F_{y}$.

(c) For slender-element composite sections, $M_{n}$ shall be determined as the first yield moment. The compression flange stress shall be limited to the critical buckling stress, $F_{n}$, determined using Equation I2-10 or I2-11. The concrete stress distribution shall be linear elastic with the maximum compressive stress limited to $0.70 f_{c}^{\prime}$.

I3.4c Detailing Requirements

Clear spacing between the inside of the 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).

I3.5 Composite Plate Shear Walls

The available flexural strength of composite plate shear walls shall be determined in accordance with Section II.2, where

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