Adopts With Amendments:

ACI 318 2019

Part 1: General

Part 2: Loads & Analysis

Part 3: Members

Part 4: Joints/Connections/Anchors

Part 5: Earthquake Resistance

Part 6: Materials & Durability

Part 7: Strength & Serviceability

Part 8: Reinforcement

Part 9: Construction

Part 10: Evaluation

REFERENCES & Appendices

Heads up: There are no amended sections in this chapter.
This chapter shall apply to the design of structural concrete members, or regions of members, where load or geometric discontinuities cause a nonlinear distribution of longitudinal strains within the cross section.
Any structural concrete member, or discontinuity region in a member, shall be permitted to be designed by modeling the member or region as an idealized truss in accordance with this chapter.
Strut-and-tie models shall consist of struts and ties connected at nodes to form an idealized truss in two or three dimensions.
Geometry of the idealized truss shall be consistent with the dimensions of the struts, ties, nodal zones, bearing areas, and supports.
Strut-and-tie models shall be capable of transferring all factored loads to supports or adjacent B-regions.
The internal forces in strut-and-tie models shall be in equilibrium with the applied loads and reactions.
Ties shall be permitted to cross struts and other ties.
Struts shall intersect or overlap only at nodes.
The angle between the axes of any strut and any tie entering a single node shall be at least 25 degrees.
The effects of prestressing shall be included in the strut-and-tie model as external loads with load factors in accordance with 5.3.13. For pretensioned members, it shall be permitted to assume that the prestress force is applied at the end of the strand transfer length.
Deep beams designed using the strut-and-tie method shall satisfy 9.9.2.1, 9.9.3.1, and 9.9.4.
Brackets and corbels with shear span-to-depth ratio av/d < 2.0 designed using the strut-and-tie method shall satisfy 16.5.2, 16.5.6, and Eq. (23.2.10).
Asc ≥ 0.04(fc'/fy)(bwd) (23.2.10)
The shear friction requirements of 22.9 shall apply where it is appropriate to consider shear transfer across any given plane, such as an existing or potential crack, an interface between dissimilar materials, or an interface between two concretes cast at different times.
Members designed using strut-and-tie models that are part of seismic-force-resisting system shall meet the additional requirements of 23.11, if applicable.
For each applicable factored load combination, design strength of each strut, tie, and nodal zone in a strut-and-tie model shall satisfy ϕSnU, including (a) through (c):
(a) Struts: ϕFnsFus
(b) Ties: ϕFntFut
(c) Nodal zones: ϕFnnFun
ϕ shall be in accordance with 21.2.
The nominal compressive strength of a strut, Fns, shall be calculated by (a) or (b):
(a) Strut without longitudinal reinforcement
Fns = fce Acs (23.4.1a)
(b) Strut with longitudinal reinforcement
Fns = fce Acs + As'fs' (23.4.1b)
where Fns shall be evaluated at each end of the strut and taken as the lesser value; Acs is the cross-sectional area at the end of the strut under consideration; fce is given in 23.4.3; As' is the area of compression reinforcement along the length of the strut; and fs' is the stress in the compression reinforcement at the nominal axial strength of the strut. It shall be permitted to take fs' equal to fy for Grade 40 or 60 reinforcement.
Effective compressive strength of concrete in a strut, fce, shall be calculated in accordance with 23.4.3.
Effective compressive strength of concrete in a strut, fce, shall be calculated by:
fce = 0.85 βcβsfc' (23.4.3)
where βs is in accordance with Table 23.4.3(a) and βc is in accordance with Table 23.4.3(b).
Table 23.4.3(a)—Strut coefficient βs
Strut location Strut type Criteria βs
Tension members or tension zones of members Any All cases 0.4 (a)
All other cases Boundary struts All cases 1.0 (b)
Interior struts Reinforcement satisfying (a) or (b) of Table 23.5.1 0.75 (c)
Located in regions satisfying 23.4.4 0.75 (d)
Beam-column joints 0.75 (e)
All other cases 0.4 (f)
Table 23.4.3(b)—Strut and node confinement modification factor βc
Location βc
• End of a strut connected to a node that includes a bearing surface
Node that includes a bearing surface
Lesser of , where A1 is defined by the bearing surface (a)
2.0 (b)
Other cases 1.0 (c)
If use of βs of 0.75 is based on line (d) of Table 23.4.3(a), member dimensions shall be selected to satisfy Eq. (23.4.4), where λs is defined in 23.4.4.1.
(23.4.4)
The size effect modification factor, λs, shall be determined by (a) or (b), as applicable:
(a) If distributed reinforcement is provided in accordance with 23.5, λs shall be taken as 1.0.
(b) If distributed reinforcement is not provided in accordance with 23.5, λs shall be taken in accordance with Eq. (23.4.4.1).
(23.4.4.1)
In D-regions designed using the strut-and-tie method, minimum distributed reinforcement shall be provided across the axes of interior struts in accordance with Table 23.5.1.
Table 23.5.1—Minimum distributed reinforcement
Lateral restraint of strut Reinforcement configuration Minimum distributed reinforcement ratio
Not restrained Orthogonal grid 0.0025 in each direction (a)
Reinforcement in one direction crossing strut at angle α1 (b)
Restrained Distributed reinforcement not required (c)
Distributed reinforcement required by 23.5.1 shall satisfy (a) and (b):
(a) Spacing shall not exceed 12 in.
(b) Angle α1 shall not be less than 40 degrees.
Struts are considered laterally restrained if they are restrained perpendicular to the plane of the strut-and-tie model in accordance with (a), (b), or (c):
(a) The discontinuity region is continuous perpendicular to the plane of the strut-and-tie model.
(b) The concrete restraining the strut extends beyond each side face of the strut a distance not less than half the width of the strut.
(c) The strut is in a joint that is restrained in accordance with 15.2.8.
Reinforcement required in 23.5.1 shall be developed beyond the extent of the strut in accordance with 25.4.
Compression reinforcement in struts shall be parallel to the axis of the strut and enclosed along the length of the strut by closed ties in accordance with 23.6.3 or by spirals in accordance with 23.6.4.
Compression reinforcement in struts shall be anchored to develop fs' at the face of the nodal zone, where fs' is calculated in accordance with 23.4.1.
Closed ties enclosing compression reinforcement in struts shall satisfy 25.7.2 and this section.
Spacing of closed ties, s, along the length of the strut shall not exceed the smallest of (a) through (c):
(a) Smallest dimension of cross section of strut
(b) 48db of bar or wire used for closed tie reinforcement
(c) 16db of compression reinforcement
The first closed tie shall be located not more than 0.5s from the face of the nodal zone at each end of a strut.
Closed ties shall be arranged such that every corner and alternate longitudinal bar shall have lateral support provided by crossties or the corner of a tie with an included angle of not more than 135 degrees and no longitudinal bar shall be farther than 6 in. clear on each side along the tie from such a laterally supported bar.
Spirals enclosing compression reinforcement in struts shall satisfy 25.7.3.
Tie reinforcement shall be nonprestressed or prestressed.
The nominal tensile strength of a tie, Fnt, shall be calculated by:
Fnt = Atsfy + AtpΔfp (23.7.2)
where Atp is zero for nonprestressed members.
In Eq. (23.7.2), it shall be permitted to take Δfp equal to 60,000 psi for bonded prestressed reinforcement and 10,000 psi for unbonded prestressed reinforcement. Higher values of Δfp shall be permitted if justified by analysis, but Δfp shall not be taken greater than (fpyfse).
The centroidal axis of the tie reinforcement shall coincide with the axis of the tie assumed in the strut-and-tie model.
Tie reinforcement shall be anchored by mechanical devices, post-tensioning anchorage devices, standard hooks, or straight bar development in accordance with 23.8.3, except for ties extending from curved-bar nodes designed in accordance with 23.10.
Tie force shall be developed in each direction at the point where the centroid of the reinforcement in the tie leaves the extended nodal zone.
The nominal compressive strength of a nodal zone, Fnn, shall be calculated by:
Fnn = fceAnz (23.9.1)
where fce is defined in 23.9.2 or 23.9.3 and Anz is given in 23.9.4 or 23.9.5.
The effective compressive strength of concrete at a face of a nodal zone, fce, shall be calculated by:
fce = 0.85βcβnfc' (23.9.2)
where βn shall be in accordance with Table 23.9.2 and βc is in accordance with Table 23.4.3(b).
Table 23.9.2—Nodal zone coefficient βn
Configuration of nodal zone βn
Nodal zone bounded by struts, bearing areas, or both 1.0 (a)
Nodal zone anchoring one tie 0.80 (b)
Nodal zone anchoring two or more ties 0.60 (c)
If confining reinforcement is provided within the nodal zone and its effect is documented by tests and analyses, it shall be permitted to use an increased value of fce when calculating Fnn.
The area of each face of a nodal zone, Anz, shall be taken as the smaller of (a) and (b):
(a) Area of the face of the nodal zone perpendicular to the line of action of Fus
(b) Area of a section through the nodal zone perpendicular to the line of action of the resultant force on the section
In a three-dimensional strut-and-tie model, the area of each face of a nodal zone shall be at least that given in 23.9.4, and the shape of each face of the nodal zone shall be similar to the shape of the projection of the end of the strut onto the corresponding face of the nodal zone.
Curved-bar nodes shall be designed and detailed in accordance with this section.
If specified clear cover normal to plane of bend is 2db or greater, the bend radius rb shall be in accordance with (a) or (b), but shall not be less than half the minimum bend diameter specified in 25.3.
(a) Curved bar nodes with bends less than 180 degrees:
(23.10.2a)
(b) Ties anchored by 180-degree bends:
(23.10.2b)
If specified clear cover normal to plane of bend is less than 2db, rb required by 23.10.2 shall be multiplied by the ratio 2db/cc, where cc is the specified clear cover to the side face.
If curved-bar nodes are formed by more than one layer of reinforcement, Ats shall be taken as the total area of tie reinforcement, and rb shall be taken as the bend radius of the innermost layer.
At frame corners, the joint and reinforcement shall be proportioned such that the center of bar curvature is located within the joint.
cb shall be sufficient to develop any difference in force between the straight legs of the bars extending from the bend region.
Regions of a seismic-force-resisting system assigned to Seismic Design Category (SDC) D, E, or F and designed with the strut-and-tie method shall be in accordance with (a) and (b):
(b) 23.11.2 through 23.11.5 unless design earthquake-induced force, E, in the strut-and-tie element is multiplied by an overstrength factor, Ωo, not less than 2.5 unless a smaller value of Ωo can be justified by a detailed analysis.
Effective compressive strength determined in accordance with 23.4 shall be multiplied by 0.8.
Struts shall have reinforcement satisfying the detailing requirements of 23.11.3.2 or 23.11.3.3.
Struts shall be reinforced with a minimum of four longitudinal bars with a bar in each corner of the transverse reinforcement. Transverse reinforcement shall be placed perpendicular to the direction of the strut and satisfy (a) through (d):
(a) Detailed in accordance with 18.7.5.2(a) through (e)
(b) Ash/sbc determined in accordance with Table 23.11.3.2(a)
(c) Spacing satisfying 18.7.5.3(d) and not exceeding the values specified in Table 23.11.3.2(b)
(d) Continued through the nodal zone
Table 23.11.3.2(a)—Transverse reinforcement for struts[1][2]
Transverse reinforcement Applicable expressions
Ash/sbc for rectilinear hoops Greater of (a)
(b)
[1]Ach is measured to the outside edges of the transverse reinforcement for the strut.
[2]It shall be permitted to configure hoops using two pieces of reinforcement as specified in 18.6.4.3.
Table 23.11.3.2(b)—Transverse reinforcement spacing limitation
Reinforcement Maximum transverse bar spacing
Grade 60 Lesser of 6db
6 in.
Grade 80 Lesser of 5db
6 in.
Grade 100 Lesser of 4db
6 in.
Table 23.11.3.3—Transverse reinforcement for the entire member cross section
Transverse reinforcement Applicable expressions
Ash/sbc for rectilinear hoops Greater of (a)
(b)
Transverse reinforcement shall be provided in each orthogonal direction and through the thickness of the entire member cross section or for the region of the member containing struts and shall satisfy (a) through (d).
(a) Detailed in accordance with 18.7.5.2(a) through (e)
(b) Ash/sbc determined in accordance with Table 23.11.3.3.
(c) Spacing measured along the longitudinal axis of the member not exceeding the values specified in Table 23.11.3.2(b).
(d) Spacing of crossties or legs of hoops both vertically and horizontally in the plane of the member cross section shall not exceed 8 in. Each crosstie and each hoop leg shall engage a longitudinal bar of equal or greater diameter.
For tie reinforcement, development length shall be 1.25 times the length determined in accordance with 25.4.
The nominal compressive strength of a nodal zone calculated in accordance with 23.9 shall be multiplied by 0.8.
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