This chapter shall apply to the design of nonprestressed and prestressed beams, including:
(a) Composite beams of concrete elements constructed in separate placements but connected so that all elements resist loads as a unit
(b) One-way joist systems in accordance with 9.8
For torsional design according to 22.7, the overhanging flange width used to calculate Acp, Ag, and pcp shall be in accordance with (a) and (b):
(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.
For nonprestressed beams not supporting or attached to partitions or other construction likely to be damaged by large deflections, overall beam depth h shall satisfy the limits in Table 126.96.36.199, unless the calculated deflection limits of 9.3.2 are satisfied.
Table 188.8.131.52—Minimum depth of nonprestressed beams
|Support condition||Minimum h|
|One end continuous||ℓ/18.5|
|Both ends continuous||ℓ/21|
For fy other than 60,000 psi, the expressions in Table 184.108.40.206 shall be multiplied by (0.4 + fy/100,000).
For beams built integrally with supports, Vu at the support shall be permitted to be calculated at the face of support.
Sections between the face of support and a critical section located d from the face of support for nonprestressed beams and h/2 from the face of support for prestressed beams shall be permitted to be designed for Vu at that critical section if (a) through (c) are satisfied:
(a) Support reaction, in direction of applied shear, introduces compression into the end region of the beam
(c) No concentrated load occurs between the face of support and critical section
Unless determined by a more detailed analysis, it shall be permitted to take the torsional loading from a slab as uniformly distributed along the beam.
For beams built integrally with supports, Tu at the support shall be permitted to be calculated at the face of support.
Sections between the face of support and a critical section located d from the face of support for nonprestressed beams or h/2 from the face of support for prestressed beams shall be permitted to be designed for Tu 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.
Longitudinal and transverse reinforcement required for torsion shall be added to that required for the Vu, Mu, and Pu that act in combination with the torsion.
It shall be permitted to reduce the area of longitudinal torsional reinforcement in the flexural compression zone by an amount equal to Mu/(0.9dfy), where Mu occurs simultaneously with Tu at that section, except that the longitudinal reinforcement area shall not be less than the minimum required in 9.6.4.
For solid sections with an aspect ratio h/bt ≥ 3, 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 220.127.116.11 apply.
For solid precast sections with an aspect ratio h/bt ≥ 4.5, 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 18.104.22.168 need not be satisfied.
A minimum area of shear reinforcement, Av,min, shall be provided in all regions where Vu > 0.5ϕVc except for the cases in Table 22.214.171.124. For these cases, at least Av,min shall be provided where Vu > ϕVc.
Table 126.96.36.199—Cases where Av,min is not required if 0.5ϕVc < Vu ≤ ϕVc
|Shallow depth||h ≤ 10 in.|
|Integral with slab||h ≤ greater of 2.5tf or 0.5bw
h ≤ 24 in.
|Constructed with steel fiber-reinforced normalweight concrete conforming to 188.8.131.52.1(a), 184.108.40.206(d), and 220.127.116.11(a) and with f'c ≤ 6000 psi||h ≤ 24 in.
|One-way joist system||In accordance with 9.8|
If shown by testing that the required Mn and Vn can be developed, 18.104.22.168 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.
If shear reinforcement is required and torsional effects can be neglected according to 22.214.171.124, Av,min shall be in accordance with Table 126.96.36.199.
Table 188.8.131.52—Required Av,min
|Nonprestressed and prestressed with Apsfse< 0.4(Apsfpu + Asfy)||Greater of:||(a)|
|Prestressed with Apsfse≥ 0.4(Apsfpu+ Asfy)||Lesser of:||Greater of:||(c)|
For nonprestressed and Class C prestressed beams with h exceeding 36 in., longitudinal skin reinforcement shall be uniformly distributed on both side faces of the beam for a distance h/2 from the tension face. Spacing of skin reinforcement shall not exceed s given in 24.3.2, where cc 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.
Reinforcement shall extend beyond the point at which it is no longer required to resist flexure for a distance equal to the greater of d and 12db, except at supports of simply-supported spans and at free ends of cantilevers.
Flexural tension reinforcement shall not be terminated in a tension zone unless (a), (b), or (c) is satisfied:
(a) Vu ≤ (2/3)ϕVn 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 Vu ≤ (3/4)ϕVn
At simple supports and points of inflection, db for positive moment tension reinforcement shall be limited such that ℓd 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.
(a) ℓd ≤ (1.3Mn/Vu + ℓa) if end of reinforcement is confined by a compressive reaction
(b) ℓd ≤ (Mn/Vu + ℓa) if end of reinforcement is not confined by a compressive reaction
Mn is calculated assuming all reinforcement at the section is stressed to fy, and Vu is calculated at the section. At a support, ℓa is the embedment length beyond the center of the support. At a point of inflection, ℓa is the embedment length beyond the point of inflection limited to the greater of d and 12db.
If torsional reinforcement is required, longitudinal torsional reinforcement shall be distributed around the perimeter of closed stirrups that satisfy 184.108.40.206 or hoops with a spacing not greater than 12 in. The longitudinal reinforcement shall be inside the stirrup or hoop, and at least one longitudinal bar or tendon shall be placed in each corner.
Longitudinal torsional reinforcement shall extend for a distance of at least (bt + d) beyond the point required by analysis.
Transverse reinforcement shall be in accordance with this section. The most restrictive requirements shall apply.
Transverse torsional reinforcement shall extend a distance of at least (bt + d) beyond the point required by analysis.
Longitudinal compression reinforcement shall be arranged such that every corner and alternate compression bar shall be enclosed by the corner of the transverse reinforcement with an included angle of not more than 135 degrees, and no bar shall be farther than 6 in. clear on each side along the transverse reinforcement from such an enclosed bar.
For beams along the perimeter of the structure, structural integrity reinforcement shall be in accordance with (a) through (c):
(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
For other than perimeter beams, structural integrity reinforcement shall be in accordance with (a) or (b):
(a) At least one-quarter of the maximum positive moment reinforcement, but not less than two bars or strands, shall be continuous.
Splices shall be full mechanical, full welded, or Class B tension lap splices.
Nonprestressed one-way joist construction consists of a monolithic combination of regularly spaced ribs and a top slab designed to span in one direction.
Width of ribs shall be at least 4 in. at any location along the depth.
Overall depth of ribs shall not exceed 3.5 times the minimum width.
Vc shall be permitted to be taken as 1.1 times the value calculated in 22.5.
For structural integrity, at least one bottom bar in each joist shall be continuous and shall be anchored to develop fy at the face of supports.
Slab thickness over fillers shall be at least the greater of one-twelfth the clear distance between ribs and 1.5 in.
For calculation of shear and negative moment strength, it shall be permitted to include the vertical shells of fillers in contact with the ribs. Other portions of fillers shall not be included in strength calculations.
Deep beams are members that are loaded on one face and supported on the opposite face such that strut-like compression elements can develop between the loads and supports and that satisfy (a) or (b):
(a) Clear span does not exceed four times the overall member depth h
(b) Concentrated loads exist within a distance 2h from the face of the support
Distributed reinforcement along the side faces of deep beams shall be at least that required in (a) and (b):
(a) The area of distributed reinforcement perpendicular to the longitudinal axis of the beam, Av, shall be at least 0.0025bws, where s is the spacing of the distributed transverse reinforcement.