## Info

4.2.4.9. Development of Bars in Tension

Criteria for development of bars in tension, given in Sections 21.5.4.1 through 21.5.4.4, are as follows:

• For normal weight concrete, the development length £dh for a bar with a standard 90-degree hook shall not be less than the largest of

for bar sizes No. 3 through No. 11. The 90-degree hook shall be located within the confined core of a column or boundary element.

• For lightweight aggregate concrete, the development length £dh for a bar with a standard 90-degree hook shall not be less than the largest of:

for bar sizes No. 3 through No. 11. The 90-degree hook shall be located within the confined core of a column or boundary element.

• For bar sizes No. 3 through No. 11, the development length id for a straight bar shall not be less than:

• 2.5 £dh if the depth of the concrete cast in one lift beneath the bar <12 in.

• 3.5 £dh if the depth of the concrete cast in one lift beneath the bar >12 in.

• Straight bars terminated at a joint shall pass through the confined core of a column or boundary element. Any portion of the straight embedment length not within the confined core shall be increased by a factor of 1.6.

• For epoxy-coated reinforcement, the development lengths in Sections 21.5.4.1— 21.5.4.3 shall be multiplied by

• 1.5 for straight bars with cover less than 3db or clear spacing less than 6db.

• 1.2 for bars terminating in a standard hook.

4.2.5. Shear Walls

4.2.5.1. Minimum Web Reinforcement: Design for Shear

Requirements for minimum web reinforcement and design for shear strength of shear walls are given in Sections 21.7.2.1 through 21.7.4.5. A summary follows:

• The required amounts of vertical and horizontal web reinforcement depend on the magnitude of the design shear force Vu:

Vertical reinf. ratio > 0.0012 for No. 5 bars or smaller,

> 0.0015 for No. 6 bars or larger. Horizontal reinf. ratio > 0.0020 for No. 5 bars or smaller, > 0.0025 for No. 6 bars or larger.

• Reinforcement spacing each way shall not exceed 18 in.

• Reinforcement provided for shear strength shall be continuous and shall be distributed across the shear plane.

For Vu > 2AcvVf, twocurtains of reinforcement must be provided. All continuous reinforcement in structural walls shall be anchored or spliced in accordance with the provisions for reinforcement in tension in Section 21.5.4.

The nominal shear strength Vn of structural walls shall not exceed:

where ac = 3.0 for hw/lw < 1.5 = 2.0 for hw/lw > 2.0. ac varies linearly between 3.0 and 2.0 for hw/lw between 1.5 and 2.0.

The value of hw / lw used for determining Vn for segments of a wall shall be the larger of the ratios for the entire wall and the segment of wall considered. Walls shall have distributed shear reinforcement in two orthogonal directions in the plane of the wall. If hw /lw < 2.0, pv > pn.

Nominal shear strength of all wall piers sharing a common lateral force shall not be assumed to exceed 8A^^f, where Acv is the total cross-sectional area, and the nominal shear strength of any one of the individual wall piers shall not be assumed to exceed 10Acp^fc, where Acp is the cross-sectional area of the pier considered.

Nominal shear strength of horizontal wall segments and coupling beams shall be assumed not to exceed 10A^^lf, where Acp is the cross-sectional area of a horizontal wall segment or coupling beam.

4.2.5.2. Boundary Elements

Boundary element requirements for shear walls given in Sections 21.7.6.2 through 21.7.6.4 are as follows:

• Compression zones of walls or wall piers that are effectively continuous over their entire height and designed to have a single critical section for flexure and axial loads shall be reinforced with special boundary elements where:

• Special boundary element reinforcement shall extend vertically from the critical section a distance not less than the larger of lw or MJ4VU.

• Structural walls not designed by the provisions of Section 21.7.6.2 shall have special boundary elements at boundaries and around openings of structural walls where the maximum extreme fiber compressive stress, corresponding to factored forces including earthquake effects, exceeds 0.2 f'.

• Special boundary elements may be discontinued where the calculated compressive strength is less than 0.15 f'.

• Stresses shall be calculated using a linearly elastic model and gross section properties.

• Where special boundary elements are required by Sections 21.7.6.2 or 21.7.6.3, the following shall be satisfied:

• The boundary element shall extend horizontally from the extreme compression fiber a distance not less than the larger of c - 0.1lw and c/2.

• In flanged sections, the boundary element shall include the effective flange width in compression and shall extend at least 12 in. into the web.

• Special boundary element transverse reinforcement shall satisfy the requirements of Sections 21.4.4.1 through 21.4.4.3, except Eq. (21.3) need not be satisfied.

• Special boundary element transverse reinforcement at the base of the wall shall extend into the support at least the development length of the largest longitudinal bar in the special boundary element. If the special boundary element terminates on a footing or mat, the special boundary element transverse reinforcement shall extend at least 12 in. into the footing or mat.

• Horizontal reinforcement in the web shall be anchored to develop the specified yield strength fy within the confined core of the boundary element.

• Mechanical splices and welded splices of longitudinal reinforcement of boundary elements shall conform to Sections 21.2.6 and 21.2.7, respectively.

Although boundary elements may not be required by calculations, Section 21.6.6.5 stipulates certain requirements as follows:

• Where special boundary elements are not required by Sections 21.7.6.2 or

21.7.6.3, the following shall be satisfied:

• Boundary transverse reinforcement shall satisfy Sections 21.4.4.1(c), 21.4.4.3, and 21.7.6.4(c) if the longitudinal reinforcement ratio at the wall boundary is greater than 400/fy. The maximum longitudinal spacing of transverse reinforcement in the boundary shall not exceed 8 in.

• Horizontal wall reinforcement terminating at the ends of structural walls without boundary elements shall have a standard hook engaging the edge reinforcement or the edge reinforcement shall be enclosed in U-stirrups having the same size and spacing as, and spliced to, the horizontal reinforcement when Vu > AcvJf~'.

4.2.5.3. Coupling Beams

Design requirements for coupling beams given in Sections 21.7.7.1 through 21.7.7.4 are as follows:

• Coupling beams with aspect ratio ln/d > 4 shall satisfy the requirements of Eq. (21.3), except the provisions of Sections 21.3.1.3 and 21.3.1.4(a) shall not be required if it can be shown by analysis that the beam has adequate lateral stability.

• Coupling beams with aspect ratio ln /d < 4 shall be permitted to be reinforced with two intersecting groups of diagonally placed bars symmetrical about the midspan.

• Coupling beams with aspect ratio ln/d < 2 and Vu > 4^f'bwd shall be reinforced with two intersecting groups of diagonally placed bars symmetrical about the midspan, unless it can be shown that loss of stiffness and strength of the coupling beams will not impair the vertical load carrying capacity of the structure, or the egress from the structure, or the integrity of nonstructural components and their connections to the structure.

Coupling beams reinforced with two intersecting groups of diagonally placed bars symmetrical about the midspan shall satisfy the following:

• A minimum of four bars is required in each group of diagonally placed bars. Each diagonal group of bars is assembled in a core having sides measured to the outside of transverse reinforcement greater than or equal to bw /2 perpendicular to the plane of the beam and bw/5 in the plane of the beam and perpendicular to the diagonal bars.

• The nominal shear strength Vn is determined from the following:

• Each group of diagonally reinforced bars shall be enclosed in transverse reinforcement satisfying Sections 21.4.4.1 through 21.4.4.3. The minimum concrete cover required in Section 7.7 shall be assumed on all four sides of each group of diagonally placed reinforcing bars for purposes of computing Ag in Eqs. (10.6) and (21.3).

• The diagonally placed bars shall be developed for tension in the wall.

• The diagonally placed bars shall be considered to contribute to the nominal flexural strength of the coupling beam.

• Reinforcement conforming to Sections 11.8.9 and 11.8.10 shall be provided as a minimum parallel and transverse to the longitudinal axis of the beam.

4.2.6. Frame Members Not Designed to Resist Earthquake Forces

Detailing requirements for frame members not designed to resist earthquake forces are given in Sections 21.11.2 and 21.11.3. Requirements of Section 21.11.2 are for frame members expected to experience only moderate excursions into inelastic range during design earthquake motions. Those given in Section 21.11.3 are for members expected to experience nearly the same magnitude of inelastic deformations as members designed to resist earthquake motions. If Mu < fMn and Vu < fVn, the members are designed according to Section 21.11.2 (case 1). If Mu > fMn and Vu > f2Vn, the detailing requirements are more stringent, i.e., nearly the same as those specified for members proportioned to resist forces induced by earthquake motions (case 2).

• Factored gravity axial force < Af/10

• Satisfy detailing requirements of Section 21.3.2.1.

• Provide stirrups spaced not more than d/2 throughout the length of the member.

• Factored gravity axial force > Agf'10.

• Satisty detailing requirements of Sections 21.4.3, 21.4.4.1(c), 21.4.4.3, and 21.4.5.

• Maximum longitudinal spacing of ties shall be so for the full column height.

• Spacing so shall not be more than the smaller of 6 diameters of the smallest longitudinal bar enclosed or 6 in.

• Factored gravity axial force > 0.35Po.

• Satisfy detailing requirements of Section 21.11.2.2.

• Provide transverse reinforcement > one-half of that required by Section 21.4.4.1.

• Maximum longitudinal spacing of ties shall be so for the full column height.

• Spacing so shall not be more than the smaller of 6 diameters of the smallest longitudinal bar or 6 in.

Case 2: Mu > $ Mn or Vu > $ Vm or induced moments not calculated

• Materials shall satisfy Sections 21.2.4 and 21.2.5. Mechanical and welded splices shall satisfy Sections 21.2.6 and 21.2.7.1, respectively.

• Factored gravity axial force < Af/10.

• Satisfy detailing requirements of Sections 21.3.2.1 and 21.3.4.

• Provide stirrups spaced not more than d/2 throughout the length of the member.

• Factored gravity axial force > Af/10.

• Satisfy detailing requirements of Sections 21.4.4, 21.4.5, and 21.5.2.1.

4.2.7. Diaphragms

4.2.7.1. Minimum Thickness and Reinforcement

Minimum thickness and reinforcement requirements for diaphragms as given in Sections 21.9.4 and 21.9.5.1 through 21.9.5.5 are as follows:

• Concrete slabs and composite topping slabs serving as structural diaphragms to transmit earthquake forces shall not be less than 2 in. thick.

• Topping slabs over precast floor or roof elements, acting as structural diaphragms and not relying on composite action with the precast elements to resist earthquake forces, shall not be less than 2V2 in. thick.

• For structural diaphragms:

• Minimum reinforcement shall be in conformance with Section 7.12.

• Spacing of nonprestressed reinforcement shall not exceed 18 in.

• Where welded wire fabric is utilized to resist shear forces in topping slabs over precast floor and roof elements, the wires parallel to the span of the precast elements shall be spaced not less than 10 in. on center.

• Reinforcement provided for shear strength shall be continuous and shall be distributed uniformly across the shear plane.

• In diaphragm chords or collectors utilizing bonded prestressing tendons as primary reinforcement, the stress due to design seismic forces shall not exceed 60,000 psi.

• Precompression from unbonded tendons shall be permitted to resist diaphragm design forces if a complete load path is provided.

• Structural truss elements, struts, ties, diaphragm chords, and collector elements shall have transverse reinforcement in accordance with Sections 21.4.4.1 through 21.4.4.3 over the length of the element where compressive stresses exceed 0.2f. Special transverse reinforcement may be discontinued where the compressive stress is less than 0.15 f . Stresses shall be calculated for the factored forces using a linearly elastic model and gross section properties.

• All continuous reinforcement in diaphragms, trusses, struts, ties, chords, and collector elements shall be anchored or spliced in accordance with the provisions for reinforcement in tension as specified in Section 21.5.4.

• Type 2 splices are required where mechanical splices are used to transfer forces between the diaphragm and the vertical components of the lateral force-resisting system.

4.2.7.2. Shear Strength

Shear strength requirements for diaphragms given in Section 21.9 are summarized as follows:

• The nominal shear strength Vn of structural diaphragms shall not exceed:

• The nominal shear strength of cast-in-place composite-topping slab diaphragms and cast-in-place noncomposite topping slab diaphragms on a precast floor or roof shall not exceed:

Vn AcvpnJy where Acv is based on the thickness of the topping slab. The required web reinforcement shall be distributed uniformly in both directions.

• Nominal shear strength shall not exceed 8Acv «Jf', where Acv is the gross cross-sectional area of the diaphragm.

4.2.7.3. Boundary Elements

A summary of boundary element requirements for diaphragms given in Sections 21.9.8.1 through 21.9.8.3 are given as follows:

• Boundary elements of structural diaphragms shall be proportioned to resist the sum of the factored axial forces acting in the plane of the diaphragm and the force obtained by dividing the factored moment at the section by the distance between the boundary elements of the diaphragm at that section.

• Splices of tensile reinforcement in chords and collector elements of diaphragms shall develop fy of the reinforcement. Mechanical and welded splices shall conform to Sections 21.2.6 and 21.2.7, respectively.

• Reinforcement for chords and collectors at splices and anchorage zones shall have either

• A minimum spacing of 3 longitudinal bar diameters, but not less than 1V2 in., and a minimum concrete cover of 2V2 longitudinal bar diameters, but not less than 2 in.; or

• Transverse reinforcement per Section 11.5.5.3, except as required in Section 21.9.5.3.

4.2.8. Foundations

4.2.8.1. Footings, Mats, and Piles

Structural requirements for footings, foundation mats, and piles are given in Sections 21.10.2.1 through 21.10.2.5 and in Section 22.10. They are summarized as follows:

• Longitudinal reinforcement of columns and structural walls resisting eartquake-induced forces shall extend into the footing, mat, or pile cap, and shall be fully developed for tension at the interface.

• Columns designed assuming fixed end conditions at the foundation shall comply with Section 21.10.2.1.

• If longitudinal reinforcement of a column requires hooks, the hooks shall have a 90-degree bend and shall be located near the bottom of the foundation with the free end of the bars oriented towards the center of the column.

• Transverse reinforcement in accordance with Section 21.4.4 shall be provided below the top of a footing when columns or boundary elements of special reinforced concrete structural walls have an edge located within one-half the footing depth from an edge of a footing. The transverse reinforcement shall extend into the footing a distance greater than or equal to the smaller of

• Development length in tension of the longitudinal reinforcement.

• Flexural reinforcement shall be provided in the top of a footing, mat, or pile cap supporting columns or boundary elements of special reinforced concrete structural walls subjected to uplift forces from earthquake effects. Flexural reinforcement shall not be less than that required by Section 10.5.

• The use of structural plain concrete in footings and basement walls is prohibited, except for specific cases cited in Section 22.10.

4.2.8.2. Grade Beams and Slabs-on-Grade

Requirements for grade beams and slabs-on-grade given in Sections 21.10.3.1 through

21.10.3.4 are summarized as follows:

• Grade beams acting as horizontal ties between pile caps or footings shall have continuous longitudinal reinforcement that shall be developed within or beyond the supported column. At all discontinuities, the longitudinal reinforcement must be anchored within the pile cap or footing.

• Grade beams acting as horizontal ties between pile caps or footings shall be proportioned such that the smallest cross-section dimension is greater than or equal to the clear spacing between connected columns divided by 20, but need not be greater than 18 in.

• Closed ties shall be provided at a spacing not to exceed the lesser of one-half the smallest orthogonal cross-section dimension or 12 in.

• Grade beams and beams that are part of a mat foundation subjected to flexure from columns that are part of the lateral-force-resisting system shall conform to Section 21.3.

• Slabs on grade that resist seismic forces from columns or walls that are part of the lateral-force-resisting system shall be designed as structural diaphragms per Section 21.9.

• The design drawings shall clearly state that the slab on grade is a structural diaphragm and is part of the lateral-force-resisting system.

4.2.8.3. Piles, Piers, and Caissons

Requirements for piles, piers, and caissons are given in Sections 21.10.4.2 through

21.10.4.7. They may be summarized as follows:

• Piles, piers, or caissons resisting tension loads shall have continuous longitudinal reinforcement over the length resisting the design tension forces. The longitudinal reinforcement shall be detailed to transfer tensile forces between the pile cap and the supported structural members.

• Where tension forces induced by earthquake effects are transferred between a pile cap or mat foundation and a precast pile by reinforcing bars that are grouted or post-installed in the top of the pile, the grouting system shall demonstrate by test that it can develop at least 1.25fy of the bar.

• Piles, piers, or caissons shall have transverse reinforcement in accordance with Section 21.4.4 at the following locations:

• At the top of the member for at least 5 times the member cross-section dimension, but not less than 6 ft below the bottom of the pile cap.

• Along the entire unsupported length plus the length required in Section 21.10.4.4(a) for portions of piles in soil that is not capable of providing lateral support, or in air or water.

• For precast concrete driven piles, the provided length of transverse reinforcement shall be sufficient to account for potential variations in the elevation in pile tips.

• Concrete piles, piers, or caissons in foundations supporting one- and two-story stud bearing wall construction are exempt from the transverse reinforcement requirements of Sections 21.10.4.4 and 21.5.4.5.

• Pile caps incorporating batter piles shall be designed to resist the full com-pressive strength of the batter piles acting as short columns. For portions of piles in soil that is not capable of providing lateral support, or in air or water, the slenderness effects of batter piles shall be considered.

4.2.9. Design Examples*

Several design examples are given in the following sections to explain the provisions of the ACI 318 Building Code. The examples range from ordinary moment-resisting frames, OMRFs (some times referred to as nonseismic frames) to coupled shear walls with diagonal beams, applicable to designs in high seismic zones.

The first eight examples are worked out using the provisions of ACI 318-99, although the reference to design equations and seismic provisions are to ACI 318-02. The last two examples of specially reinforced concrete shear walls (often referred to as California walls) are executed using the provisions of ACI 318-02. Note that the use of ACI 318-99 load factors and f factors is still permitted in ACI 318-02, Appendix C.

An attempt is made to keep the numerical work simple. For example, the tension-controlled flexural reinforcement As is calculated by using the relation

aud with au typically taken at 4.0 or 4.1, for f = 4000 psi and fy = 60,000 psi. Other similar shortcuts are used throughout. The designer is referred to standard reinforced concrete design handbooks for more precise design calculations.

4.2.9.1. Frame Beam Example: Ordinary Reinforced Concrete Moment Frame

Given. Figure 4.32 shows frame beam B3 of an ordinary moment frame of a building located in an area of low seismicity corresponding to UBC 1997 seismic zone 0 or 1. The seismic characteristics of the building site are: Ss = 0.14g and S1 = 0.03g. The

* The author wishes to acknowledge gratitude to Filbert B. Apanay for checking the design examples for numerical accuracy.

(b) Elevation

Figure 4.32. Frame beam and column example; ordinary moment frame: (a) plan; (b) elevation.

(b) Elevation

Figure 4.32. Frame beam and column example; ordinary moment frame: (a) plan; (b) elevation.

building has been analyzed using a commercially avaible three-dimensional analysis program. Cracked section properties have been input for the members; for beams, Ieff = 0.5Ig; for columns, Ieff = 0.7Ig; and for shear walls, Ieff = 0.5Ig. Rigid diaphragms and rigid-end offsets have been assumed, consistent with the assumptions commonly used in practice. The analysis automatically has taken the effects of PA into consideration. The analysis results for beam B3 are as follows:

Dead load D

At supports: M = -150 kip-ft, V = 40 kips At midspan: M = 90 kip-ft, V = 0

Live load L

At supports: M = -20 kip-ft, V = 12 kips At midspan: M = 15 kip-ft, V = 0

Wind W

Required. Design and a schematic reinforcement detail for B3 using the provisions of ACI 318-99. (Note: The design procedure is essentially the same for ACI 318-02 except for the load and f factors)

Solution. The ultimate design load combinations consisting of dead, live, and wind loads are shown in Table 4.4.

Check Limitations on Beam Section Dimensions. According to ACI 318-02 Section 21.2.1.2, the provisions of Chapters 1 through 18 and 22 are adequate to provide a threshold of toughness expected of structures assigned to ordinary categories. These are structures in regions of low seismic risk, corresponding approximately to UBC zones 0 and 1, and assigned to SDC A or B.

No dimensional limitations are specified for frame beams of buildings assigned to SDC A or B. Thus, the given dimensions of 48 in. wide x 18 in. deep for the example

TABLE 4.4 Design Bending Moments and Shear Forces for Frame Beam B3; Ordinary Moment Frame

Load case

Location

Bending moment (kip-ft)

Shear force (kips)

Dead load D Live load L Wind W

Load combinations (ACI 318-99)

Support Midspan Support Midspan Support

Support Midspan Support

Midspan Support

Midspan

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