Transverse reinforcement detailing is applied automatically in accordance with ACI 9.7.
Transverse reinforcement detailing is applied according to ACI Chapter 18 in earthquake resistant structure beams.
Ag = gross area of concrete section, in2
bw = web width or diameter of circular section, in.
bt = width of that part of cross section containing the closed stirrups resisting torsion, in.
d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.
db = nominal diameter of bar, wire, or prestressing strand, in
fc' = specified compressive strength of concrete, psi
√fc‘ = square root of specified compressive strength of concrete, psi
fy = specified yield strength of nonprestressed reinforcement, psi
fyt = specified yield strength of transverse reinforcement, psi
h = overall thickness, height, or depth of member, in.
ph = perimeter of centerline of outermost closed transverse torsional reinforcement, in.
s = center-to-center spacing of items, such as longitudinal reinforcement, transverse reinforcement, tendons, or anchors, in.
Ve = design shear force for load combinations including earthquake effects, lb
Vn = nominal shear strength, lb
Vs = nominal shear strength provided by shear reinforcement, lb
Vu = factored shear force at section, lb
ϕ = strength reduction factor
Details of transverse reinforcement are applied in accordance with Transverse Reinforcement title.
Hoops consist of a closed tie or continuously wound tie, which can consist of several reinforcement elements each having seismic hooks at both ends (Transverse Reinforcement).
Shear reinforcement is provided using stirrups, hoops, or longitudinal bent bars. Also, additional shear reinforcement called hanger reinforcement (ACI Fig R22.214.171.124.1), should be placed to transfer shear from the end of the supported beam. According to ACI R126.96.36.199.1 hanger reinforcement is not requred if the bottom of supported beam is at or above middepth of the supporting beam or if the factored shear transferred from the supported beam is less than 3√fc‘bwd.
According to ACI 188.8.131.52.2. maximum shear reinforcement leg spacing along the length of the beam and across the width of the beam should be in accordance with given ACI Table 184.108.40.206.2. below.
Shear strength provided by bent-up longitudinal reinforcement is neglected.
According to ACI 220.127.116.11.2, transverse torsional reinforcement should extend it beyond the point required by the analysis by at least (bt + d) distance.
According to ACI 18.104.22.168.3, maximum spacing of transverse torsional shoul be the lesser of ph/8 and 12 in.
Lateral support of compression reinforcement
Transverse reinforcement is provided throughout the distance where longitudinal copression reinforcement is required. Closed stirrups or hoops provide lateral support of longitudinal compression reinforcement.
According to ACI 22.214.171.124.2; transverse reinforcement size should be at least one of the two conditions below,
No. 3 for longitudinal bars No.10 and smaller
No. 4 for longitudinal bars No.11 and larger
According to ACI 126.96.36.199.3; maximum spacing of transverse reinforcement should not exceed the least of three conditions below,
16db of longitudinal reinforcement
48db of transverse reinforcement
Least dimension of beam
According to ACI 188.8.131.52.4, Longitudinal compression reinforcement in each corner and alternative copression bar shall be arranged to be surrounded by transverse reinforcement around the corner with an included angle of not more than 135 degrees. Also no bar shall be farther than 6 in. clear on each side along the transverse reinforcement from such an enclosed bar.
Reinfocement Limits for Beams of Earthquake Reistant Structures
Ordinary moment frames
All the conditions described above are valid for beams of ordinary moment frames.
Intermediate moment frames
All the conditions described above are valid for beams of intermediate moment frames.
According to ACI 184.108.40.206, hoop should be provided over a minimum length 2h measured from the face of the supporting member toward midspan, at both ends of the beam. The first hoop should be located a length of at least 2 in. from the face of the supporting member. Spacing og hoop should not exceed the smallest of values given below,
Eight times the diameter of the smallest longitudinal bar enclosed
24 times the diameter of the hoop bar
According to ACI 220.127.116.11, spacing of transverse reinforcement should not exceed d/2 throughout the length of the beam.
According to ACI 18.104.22.168, if factored axial compressive force of beams exceed 0.10fc’Ag , transverse reinforcement required by ACI 22.214.171.124 shall conform to ACI 126.96.36.199 and either ACI 188.8.131.52 or ACI 184.108.40.206.
Special moment frames
All the conditions described above are valid for beams of special moment frames.
According to ACI 220.127.116.11, Hoops should be provide in the beam regions given below,
Over a length equal to twice the beam depth measured from the face of the supporting column toward midspan, at both ends of the beam
Over lengths equal to twice the beam depth on both sides of a section where flexural yielding is likely to occur as a result of lateral displacements beyond the elastic range of behavior.
According to ACI 18.104.22.168, where hoops are required, primary longitudinal reinforcing bars should have lateral support in accordance with Transverse Reinforcement title. The maximum spacing og transversely supported flexural reinforcing bars are 14 in.
According to ACI 22.214.171.124, hoops in beams can consis of two pieces of reinforcement. These pieces are a stirrup havin seismic hooks at both ends and closed by a crosstie. If the longitudinal reinforcing bars secured by the crossties are confined by a slab on only one side of the beam, the 90-degree hooks of the crossties shall be placed on that side.
According to ACI 126.96.36.199, The first hoop should be located a length of at least 2 in. from the face of a supporting column. The maximum spacing of the hoops should be the smallest of the values given below.
For Grade 60 or S420, 6db of the smallest primary flexural reinforcing bar excluding longitudinal skin reinforcement required by ACI 188.8.131.52
For Grade 80, 5db of the smallest primary flexural reinforcing bar excluding longitudinal skin reinforcement required by ACI 184.108.40.206
According to ACI 220.127.116.11, Hoops should be designed to resist the design shear force, Ve, in accordance with ACI 18.6.5.
According to ACI 18.104.22.168, where hoops are not required, stirrups with seismic hooks at both ends should be spaced at a distance not more than d/2 along the length of the beam.
According to ACI 22.214.171.124, if Pu≥ 0.10fc’Ag , hoops satisfying columns of special moment frames transverse reinforcement detailing should be provided along the lengths given in ACI 126.96.36.199. Along the remaining length, maximum hoop spacing s should be the smallest of the values given below,
6db of the smallest Grade 60 or S420 enclosed longitudinal beam bar
5db of the smallest Grade 80 enclosed longitudinal beam bar
If concrete cover over transverse reinforcement exceeds 4 in., additional transverse reinforcement having cover not exceeding 4 in. and spacing not exceeding 12 in. should be provided.