Transverse Reinforcement (CRD)

Notation

A_g = gross area of concrete section, in.² For a hollow section, A_g is the area of the concrete only and does not include the area of the void(s)
A_b = area of an individual bar or wire, in.²
b_w = width of compression face of member, in.
d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.
d_b = nominal diameter of bar, wire, or prestressing strand, in
f_c^' = specified compressive strength of concrete, psi
f_y = specified yield strength of nonprestressed reinforcement, psi
h = overall thickness, height, or depth of member, in.
h_x = maximum center-to-center spacing of longitudinal bars laterally supported by corners of crossties or hoop legs around the perimeter of a column or wall boundary element, in.
l_d = development length in tension of deformed bar, deformed wire, plain and deformed welded wire reinforcement, or pretensioned strand, in.
l_o = length, measured from joint face along axis of member, over which special transverse reinforcement must be provided, in.
l_u = unsupported length of column or wall, in.
P_u = factored axial force; to be taken as positive for compression and negative for tension, lb
s = center-to-center spacing of items, such as longitudinal reinforcement, transverse reinforcement, tendons, or anchors, in.

s_o = center-to-center spacing of transverse reinforcement within the length l_o, in.

The spacing of transverse reinforcement is is determined automatically to meet the most restrictive requirements. Detail of transverse reinforcemen are in accordance with Transverse Reinforcement title. The conditions given in heading Transverse Reinforcement for column gies are given below.

Column Ties

Ties, applies closed loop of deformed bar, satisfies the rules:

• Center-to-center spacing does not exceed the least of 16d_b of longitudinal bar.

Minimum diameter of tie bar is controlled automatically according to ACI 25.7.2.2. Diameter of tie bar is at least:

• No. 3 enclosing No.10 or smaller longitudinal bars

• No. 4 enclosing No.11 or larger longitudinal bars or bundled longitudinal bars

Rectilinear ties are arranged to satisfy conditions given below:

• Every corner and alternate longitudinal bar have lateral support provided by the corner of a tie with an included angle of not more than 135 degrees

• No unsupported bar is farther than 6 in. clear on each side along the tie from a laterally supported bar

Lateral support of longitudinal bars using ties, hoops and spirals

In any story, the bottom tie or hoop above the top of footing or slab can be located at most half the distance of the tie or hoop spacing. Similarly, in any story, the top tie or hoop below the lowest horizontal reinforcement int he slab, drop panel or shear cap can be located at most half the distance of tie or hoop spacing. (ACI 10.7.6.2)

In any story, the bottom of the spiral should be located at the top of footing or slab. The top of the spiral should be located in accordance with ACI Table 10.7.6.3.2.

In cases where longitudinal bars are offset, horizontal support should be provided by ties, hoops, spirals or parts of the floor construction should also be designed to resist 1.5 times the horizontal component of the calculated force in the inclined portion of the offset bar (ACI 10.7.6.4).

According to ACI 10.7.6.4.2, Transverse reinforcement should be placed not more than 6in. from points of bend.

Maximum spacing of shear reinforcement for nonprestressed column is given ACI Table 10.7.6.5.2.

Columns of Earthquake Reistant Structures

Ordinary moment frames

All the transverse reinforment detailing conditions described above are applied to columns of ordinary moment frames.

Columns of Earthquake Reistant Structures

Intermediate moment frames

All the transverse reinforment detailing conditions described above are applied to columns of intermediate moment frames.

According to ACI 18.4.3.3, at the top and bottom ends of the column, hoops should be provided at spacing s_o along a length l_o measured from the joint face.

Spacing s_o should not be greater than all of the tree conditions given below.

• For Grade 60 or S420, the smaller of 8d_b of the smallest longitudinal bar enclosed and 8 in.

• For Grade 80, the smaller of 6d_b of the smallest longitudinal bar enclosed and 6 in.

• One-half of the smallest cross-sectional dimension of the column.

Length l_o should be greater than the maximum of conditions given below.

• One-sixth of the clear span of the column

• Maximum cross-sectional dimension of the column

• 18 in.

According to ACI 18.4.3.4, the maximum distance between first hoop and the joint face is s_o/2.

ACI 18.4.3.6 states that, Columns supporting reactions from discontinuous stiff members, such as walls, should be provided with transverse reinforcement at the spacing s_o in accordance with ACI 18.4.3.3 over the full height beneath the level at which the discontinuity occurs if the portion of factored axial compressive force in these members related to earthquake effects exceeds A_gf_c′/10. If design forces have been magnified to account for the overstrength of the vertical elements of the seismic-force-resisting system, the limit of A_gf_c′/10 should be increased to A_gf_c′/4. Transverse reinforcement shall extend above and below the column in accordance with ACI 18.7.5.6(b).

Columns of Earthquake Reistant Structures

Special moment frames

All the transverse reinforment detailing conditions described above are applied to columns of special moment frames.

According to ACI 18.7.5.1, Length l_o should be greater than the maximum of conditions given below.

• The depth of the column at the joint face or at the section where flexural yielding is likely to occur

• One-sixth of the clear span of the column

• 18 in.

The transverse reinforcement should be satisfied all the conditions given below along the length l_o from each joint face and on both sides of any section where flexural yielding is likely to occur as a result of lateral displacements beyond the elastic range of behavior. According to ACI 18.7.5.2, transverse reinforcement should be in accordance with following,

• Transverse reinforcement should consist of single or overlapping spirals, circular hoops, or single or overlapping rectilinear hoops with or without crossties.

• Bends of rectilinear hoops and crossties should engage peripheral longitudinal reinforcing bars.

• Provided that ACI 25.7.2.2 limits are met, the size of the crossover may be equal to or smaller than the stirrup bar size. Consecutive crossties should be alternated end for end along the longitudinal reinforcement and around the perimeter of the cross section.

• Where rectilinear hoops or crossties are used, they shall provide lateral support to longitudinal reinforcement in accordance with ACI 25.7.2.2 and ACI 25.7.2.3.

• While arranging the reinforcement, spacing of longitudinal bars laterally supported by the corner of a crosstie or hoop leg, h_x, will not exceed 14 in. around the perimeter of the column.

• Where P_u>0.3A_gf_c' or f_c'>10,000 in colums with rectilinear hoops, every longitudinal bar or bundle of bars around the perimeter of the column core should have lateral support provided by the corner of a hoop or by a seismic hook, and h_x smaller than 8 in.
  

According to ACI 18.7.5.3, maximum spacing of transverse reinforcement should be the least of conditions give below;

• One-fourth of the minimum column dimension

• For Grade 60 or S420, 6d_b of the smallest longitudinal bar

• For Grade 80, 5d_b of the smallest longitudinal bar

• s_o, as calculated by using ACI Eq. (18.7.5.3); (The value of s_o shall not exceed 6 in. and need not be taken less than 4 in.)

According to ACI 18.7.5.5, beyond the length l_o, conditions given below should be satisfed;

• The column should contain spiral reinforcement the column shall contain spiral reinforcement in accordance with ACI 25.7.3 or hoop and crosstie reinforfcement should satisfy ACI 25.7.2 and ACI 25.7.4, with spacing s no more than 6 in.

• For Grade 60 or S420, 6d_b of the smallest longitudinal bar

• For Grade 80, 5d_b of the smallest longitudinal bar

According to ACI 18.7.5.6, columns supporting reaction from discontinued stiff memebers, such as walls, should satisfy two conditions below;

• If the factored axial compressive force, P_u, of these colums is greater than A_gf_c′/10, transverse reinforcement required by ACI 18.7.5.2, 18.7.5.3 and 18.7.5.4 should be provided over the full height at all levels beneath the discontinutiy. The limit of A_gf_c′/10 shall be increased to A_gf_c′/4, if design forces have been magnified to account for the overstrength of the vertical element of the earthquake resistance structure.

• Where l_d is in accordance with ACI 18.8.5., transverse reinforcement shall extend into the discontinued member at least l_d of the largest longitudinal column bar. Where the lower end of the column terminates on a wall, the required transverse reinforcement should extend into the wall at least l_d of the largest longitudinal column bar at the point of termination. If the column terminates on a footing or mat, the required transverse reinforcement will extend at least 12 inches into the footing or mat.

According to ACI 18.7.5.7. if the concrete cover outside the confining transverse reinforcement greater than 4 in., additional transverse reinforcement additional transverse reinforcement having cover not exceeding 4 in. and spacing not exceeding 12 in. should be provided.

According to ACI 18.7.6.2.1, if both two conditions given below occur, transverse reinforcement over the lenghts l_o should be designed to resist shear assuming V_c=0.

• The earthquake-induced shear force, calculated in accordance with ACI 18.7.6.1, is at least one-half of the maximum required shear strength within l_o.

• The factored axial compressive force P_u including earthquake effects is less than A_gf_c′/10.