**,**

*A*_{cp}**, and**

*A*_{g}**shall be in accordance with (a) and (b):**

*p*_{cp}(a) The overhanging flange width shall include that portion of slab on each side of the beam extending a distance equal to the projection of the beam above or below the slab, whichever is greater, but not greater than four times the slab thickness.

(b) The overhanging flanges shall be neglected in cases where the parameter ** A_{cp}^{2}/p_{cp}** for solid sections or

**/**

*A*_{g}^{2}**for hollow sections calculated for a beam with flanges is less than that calculated for the same beam ignoring the flanges.**

*p*_{cp}**shall satisfy the limits in Table 9.3.1.1, unless the calculated deflection limits of 9.3.2 are satisfied.**

*h***Table 9.3.1.1â€”Minimum depth of nonprestressed beams**

Support condition | Minimum h^{[1]} |
---|---|

Simply supported | â„“/16 |

One end continuous | â„“/18.5 |

Both ends continuous | â„“/21 |

Cantilever | â„“/8 |

^{[1]}Expressions applicable for normalweight concrete and *f _{y}* = 60,000 psi. For other cases, minimum

*h*shall be modified in accordance with 9.3.1.1.1 through 9.3.1.1.3, as appropriate.

**other than 60,000 psi, the expressions in Table 9.3.1.1 shall be multiplied by**

*f*_{y}**(0.4 +**.

*f*/100,000)_{y}**in the range of 90 to 115 lb/ft**

*w*_{c}^{3}, the expressions in Table 9.3.1.1 shall be multiplied by the greater of (a) and (b):

(a) **1.65 â€” 0.005 w_{c}**

(b) **1.09**

**at the support shall be permitted to be calculated at the face of support.**

*M*_{u}**at the support shall be permitted to be calculated at the face of support.**

*V*_{u}**from the face of support for nonprestressed beams and**

*d***from the face of support for prestressed beams shall be permitted to be designed for**

*h*/2**at that critical section if (a) through (c) are satisfied:**

*V*_{u}(a) Support reaction, in direction of applied shear, introduces compression into the end region of the beam

(b) Loads are applied at or near the top surface of the beam

(c) No concentrated load occurs between the face of support and critical section

**at the support shall be permitted to be calculated at the face of support.**

*T*_{u}**from the face of support for nonprestressed beams or**

*d***from the face of support for prestressed beams shall be permitted to be designed for**

*h*/2**at that critical section unless a concentrated torsional moment occurs within this distance. In that case, the critical section shall be taken at the face of the support.**

*T*_{u}**in accordance with 22.7.3.**

*T*_{u}**Ï•**including (a) through (d). Interaction between load effects shall be considered.

*S*â‰¥_{n}*U*(a) **Ï• M_{n} â‰¥ M_{u}**

(b) **Ï• V_{n} â‰¥ V_{u}**

(c) **Ï• T_{n} â‰¥ T_{u}**

(d) **Ï• P_{n} â‰¥ P_{u}**

*V*shall be calculated in accordance with 22.5.

_{n}**, where**

*T*< Ï•_{u}*T*_{th}**is given in 22.7, it shall be permitted to neglect torsional effects. The minimum reinforcement requirements of 9.6.4 and the detailing requirements of 9.7.5 and 9.7.6.3 need not be satisfied.**

*T*_{th}*T*shall be calculated in accordance with 22.7.

_{n}**,**

*V*_{u}**, and**

*M*_{u}**that act in combination with the torsion.**

*P*_{u}**and**

*A*_{s}**, at each section shall be designed to resist**

*A*_{ps}**at that section, plus an additional concentric longitudinal tensile force equal to**

*M*_{u}**, based on**

*A*_{â„“}f_{y}**at that section.**

*T*_{u}**, where**

*M*/(0.9_{u}*df*)_{y}**occurs simultaneously with**

*M*_{u}**at that section, except that the longitudinal reinforcement area shall not be less than the minimum required in 9.6.4.**

*T*_{u}**, it shall be permitted to use an alternative design procedure, provided the adequacy of the procedure has been shown by analysis and substantial agreement with results of comprehensive tests. The minimum reinforcement requirements of 9.6.4 need not be satisfied, but the detailing requirements of 9.7.5 and 9.7.6.3 apply.**

*h*/*b*â‰¥ 3_{t}**, it shall be permitted to use an alternative design procedure and open web reinforcement, provided the adequacy of the procedure and reinforcement have been shown by analysis and substantial agreement with results of comprehensive tests. The minimum reinforcement requirements of 9.6.4 and detailing requirements of 9.7.5 and 9.7.6.3 need not be satisfied.**

*h*/*b*â‰¥ 4.5_{t}**, shall be provided at every section where tension reinforcement is required by analysis.**

*A*_{s,min}**and**

*A*_{s}**shall be adequate to develop a factored load at least 1.2 times the cracking load calculated on the basis of**

*A*_{ps}**defined in 19.2.3.**

*f*_{r}**shall be:**

*A*_{s,min}A = 0.004_{s,min}A_{ct} | (9.6.2.3) |

where ** A_{ct}** is the area of that part of the cross section between the flexural tension face and the centroid of the gross section.

**, shall be provided in all regions where**

*A*_{v,min}**except for the cases in Table 9.6.3.1. For these cases, at least**

*V*> 0.5Ï•_{u}*V*_{c}**shall be provided where**

*A*_{v,min}**.**

*V*> Ï•_{u}*V*_{c}**Table 9.6.3.1â€”Cases where A_{v,mi}_{n} is not required if 0.5Ï•V_{c} < V_{u} â‰¤ Ï•V_{c}**

Beam type | Conditions |
---|---|

Shallow depth | h â‰¤ 10 in. |

Integral with slab | h â‰¤ greater of 2.5t or 0.5_{f}b_{w}and h â‰¤ 24 in. |

Constructed with steel fiber-reinforced normalweight concrete conforming to 26.4.1.5.1(a), 26.4.2.2(d), and 26.12.5.1(a) and with f' â‰¤ 6000 psi_{c} |
h â‰¤ 24 in.and |

One-way joist system | In accordance with 9.8 |

*and*

**M**_{n}**can be developed, 9.6.3.1 need not be satisfied. Such tests shall simulate effects of differential settlement, creep, shrinkage, and temperature change, based on a realistic assessment of these effects occurring in service.**

*V*_{n}**shall be in accordance with Table 9.6.3.3.**

*A*_{v,min}**Table 9.6.3.3â€”Required A_{v,min}**

Beam type | A/_{v,min}s | |||
---|---|---|---|---|

Nonprestressed and prestressed with A< 0.4(_{ps}f_{se}A + _{ps}f_{pu}A)_{s}f_{y} | Greater of: | (a) | ||

(b) | ||||

Prestressed with Aâ‰¥ 0.4(_{ps}f_{se}A+ _{ps}f_{pu}A)_{s}f_{y} | Lesser of: | Greater of: | (c) | |

(d) | ||||

(e) |

**in accordance with 22.7.**

*T*â‰¥ Ï•_{u}*T*_{th}**(**shall be the greater of (a) and (b):

*A*+ 2_{v}*A*)_{t}_{min}/*s*(a)

(b)

**shall be the lesser of (a) and (b):**

*Aâ„“,min*(a)

(b)

**given in 24.3.**

*s***exceeding 36 in., longitudinal skin reinforcement shall be uniformly distributed on both side faces of the beam for a distance**

*h***from the tension face. Spacing of skin reinforcement shall not exceed**

*h*/2**given in 24.3.2, where**

*s***is the clear cover from the skin reinforcement to the side face. It shall be permitted to include skin reinforcement in strength calculations if a strain compatibility analysis is made.**

*c*_{c}**and**

*d***12**, except at supports of simply-supported spans and at free ends of cantilevers.

*d*_{b}**beyond the point where bent or terminated tension reinforcement is no longer required to resist flexure.**

*â„“*_{d}(a) ** V_{u} â‰¤ (2/3)Ï•V_{n}** at the cutoff point

(b) For No. 11 bars and smaller, continuing reinforcement provides double the area required for flexure at the cutoff point and *V _{u}* â‰¤ (3/4)Ï•

*V*

_{n}(c) Stirrup or hoop area in excess of that required for shear and torsion is provided along each terminated bar or wire over a distance **3/4 d** from the termination point. Excess stirrup or hoop area shall be at least

**60**. Spacing

*b*/_{w}s*f*_{yt}*s*shall not exceed

*d*/(8Î²_{b})**at the face of the support.**

*f*_{y}**for positive moment tension reinforcement shall be limited such that**

*d*_{b}**for that reinforcement satisfies (a) or (b). If reinforcement terminates beyond the centerline of supports by a standard hook or a mechanical anchorage at least equivalent to a standard hook, (a) or (b) need not be satisfied.**

*â„“*_{d}(a) ** â„“_{d} â‰¤ (1.3M_{n}/V_{u} + â„“_{a})** if end of reinforcement is confined by a compressive reaction

(b) ** â„“_{d} â‰¤ (M_{n}/V_{u} + â„“_{a})** if end of reinforcement is not confined by a compressive reaction

** M_{n}** is calculated assuming all reinforcement at the section is stressed to

**, and**

*f*_{y}**is calculated at the section. At a support,**

*V*_{u}**is the embedment length beyond the center of the support. At a point of inflection,**

*â„“*_{a}**is the embedment length beyond the point of inflection limited to the greater of**

*â„“*_{a}**and**

*d***12**.

*d*_{b}**,**

*d***12**, and

*d*_{b}**.**

*â„“*/16_{n}(a) At least ** â„“_{n}/3** in positive moment areas and be centered in those areas

(b) At least ** â„“_{n}/6** on each side of the face of support in negative moment areas

^{3}/

_{8}in.

**(**beyond the point required by analysis.

*b*+_{t}*d*)**Table 9.7.6.2.2â€”Maximum spacing of shear reinforcement**

V_{s} | Maximum s, in. | ||
---|---|---|---|

Nonprestressed beam | Prestressed beam | ||

Lesser of: | d/2 | 3h/4 | |

24 | |||

Lesser of: | d/4 | 3h/8 | |

12 |

**toward the reaction from mid-depth of member to longitudinal tension reinforcement, shall be crossed by at least one line of shear reinforcement.**

*d*/2**beyond mid-depth of member.**

*d*/2**(**beyond the point required by analysis.

*b*+_{t}*d*)**0.5**.

*A*/_{oh}*p*_{h}(a) No. 3 for longitudinal bars No. 10 and smaller

(b) No. 4 for longitudinal bars No. 11 and larger and for longitudinal bundled bars

(a) **16 d_{b}** of longitudinal reinforcement

(b) **48 d_{b}** of transverse reinforcement

(c) Least dimension of beam

(a) At least one-quarter of the maximum positive moment reinforcement, but not less than two bars or strands, shall be continuous

(b) At least one-sixth of the negative moment reinforcement at the support, but not less than two bars or strands, shall be continuous

(c) Longitudinal structural integrity reinforcement shall be enclosed by closed stirrups in accordance with 25.7.1.6 or hoops along the clear span of the beam

(a) At least one-quarter of the maximum positive moment reinforcement, but not less than two bars or strands, shall be continuous.

(b) Longitudinal reinforcement shall be enclosed by closed stirrups in accordance with 25.7.1.6 or hoops along the clear span of the beam.

**at the face of the support.**

*f*_{y}(a) Positive moment reinforcement shall be spliced at or near the support

(b) Negative moment reinforcement shall be spliced at or near midspan

*V*shall be permitted to be taken as 1.1 times the value calculated in 22.5.

_{c}**at the face of supports.**

*f*_{y}(a) Clear span does not exceed four times the overall member depth *h*

(b) Concentrated loads exist within a distance **2 h** from the face of the support

(9.9.2.1) |

(a) The area of distributed reinforcement perpendicular to the longitudinal axis of the beam, ** A_{v}**, shall be at least

**0.0025**, where

*b*_{w}s**is the spacing of the distributed transverse reinforcement.**

*s*(b) The area of distributed reinforcement parallel to the longitudinal axis of the beam, ** A_{vh}**, shall be at least

**0.0025**, where

*b*_{w}s_{2}**is the spacing of the distributed longitudinal reinforcement.**

*s*_{2}**, shall be determined in accordance with 9.6.1.**

*A*_{s,min}**and 12 in.**

*d*/5**at the face of the support. If a deep beam is designed using Chapter 23, the positive moment tension reinforcement shall be anchored in accordance with 23.8.2 and 23.8.3.**

*f*_{y}(a) Negative moment tension reinforcement shall be continuous with that of the adjacent spans.

(b) Positive moment tension reinforcement shall be continuous or spliced with that of the adjacent spans.