## Yfu

The designer is referred to ACI 318-02, Section 9.2, for load combinations that include loads due to:

1. H = weight and pressure of soil, water in soil, or other materials.

2. F = weight and pressures of fluids.

3. T = temperature, creep, shrinkage, differential settlement.

ACI 318-02 permits a reduction of 50% on the load factor for L, except for garages, areas occupied as places of public assembly, and all areas where the live load L is greater than 100 lb/ft2.

The load factor of 1.6 for wind is based on the premise that the designers will be using wind loads determined by the provisions of ASCE 7-02 which includes a factor for directionality that is equal to 0.85 for buildings. Therefore, the corresponding load factor for wind is increased accordingly in the ACI 318-02 (1.3/0.85 = 1.53 rounded up to 1.6). Use of a previous wind load factor of 1.3 is permitted when wind load is obtained from other sources that do not include the directionality factor.

A reduced load factor of 1.0 for earthquake forces is used because model building codes such as ASCE 7-02 have converted earthquake forces to strength level.

ASCE 7-02 and IBC-03 require the same combinations except the effect of seismic load E is defined as follows:

where

E = the effect of horizontal and vertical earthquake-induced forces SDS = the design spectral response acceleration at short periods D = the effect of dead load p = the reliability or the penalty factor for buildings in which the lateral resistance is limited to only few members in the structure. The maximum value of p is limited to 1.5. Qe = the effect of horizontal seismic forces

The factor 0.2SDS placed on the dead load in the above equations is to account for the effects of vertical acceleration.

For situations where failure of an isolated, individual, brittle element can result in the loss of a complete lateral force-resisting system or in instability and collapse, ASCE 7-02 has a specific requirement to determine the seismic design forces. These elements are referred to as collector elements. Columns supporting discontinuous lateral load-resisting elements such as walls also fall under this category. Seismic loads for such elements are as follows:

where Qo is the system overstrength factor, defined as the ratio of the ultimate lateral force the structure is capable of resisting to the design strength. The value of Qo varies between 2 to 3 depending on the type of lateral force-resisting system (See Table 4.3).

In concrete buildings, the capacity of a structural element is calculated by applying a strength reduction factor, f, to the nominal strength of the element. The factor f is intended to take account of variations in material strength and uncertainties in the estimation of the nominal member strength, the nature of the expected failure mode, and the importance of a member to the overall safety of the structure. The values of the strength reduction factor f are f = 0.90 for tension-controlled sections (no change from the previous edition) f = 0.70 for spirally reinforced compression members f = 0.65 for other reinforced members f = 0.75 for shear and torsion f = 0.65 for bearing on concrete (except for post-tensioned anchorage zones and strut-and-tie models)

f = 0.85 for post-tensioned anchorage zones

However, an exception to the value of f = 0.75 in shear is specified for structures designed in high seismic zones. For shear capacity calculations of structural members other than joints, a value f = 0.60 is used when the nominal shear strength of a member is less than the shear corresponding to the development of the nominal flexural strength of the member. For shear in joints and diagonally reinforced coupling beams, f is equal to 0.85. The above exception applies mainly to brittle members such as low-rise walls, portions of walls between openings, or diaphragms that are impractical to reinforce to raise their nominal shear strength above nominal flexural strength for the pertinent loading conditions.

Reference is made in the remainder of this chapter to various equations and sections given in ACI 318. Unless specifically stated otherwise, it is understood, that these refer to ACI 318-02.

### 4.2.2. Integrity Reinforcement

The goal of structural integrity is: If a structure or part of a structure is subjected to an abnormal loading condition, or if a primary element sustains damage from an unanticipated event, tying the members together should result in confining the resulting damage to a relatively small area. Requirements for structural integrity included in Sections 7.13 and 13.3.8.5, focus on the structural detailing of cast-in-place concrete. Basically, prescribed amounts of longitudinal reinforcement must be continuous over the support or reinforcing bars that terminate at discontinuous ends of a member and must be anchored with hooks.

Since accidents and misuse are normally unforeseeable events, they cannot be defined precisely. Similarly, providing general structural integrity to a structure is a requirement that cannot be stated in simple terms. The Code's performance provision—"a structure shall be effectively tied together to improve integrity of the overall structure"—requires considerable judgment on the part of the design engineer. Opinions among engineers differ on the effectiveness of a general structural integrity solution for a particular framing system. However, the Code does set forth specific examples of certain reinforcing details for cast-in-place joists, beams, and two-way slab construction.

With damage to a support, top reinforcement that is continuous over the support will tend to tear out of the concrete. It will not provide the catenary action needed to bridge the damaged support unless it is confined by stirrups. By making a portion of the bottom reinforcement in beams continuous over supports, some catenary action can be provided. By providing some continuous top and bottom reinforcement in edge or perimeter beams, an entire structure can be tied together. Also, continuous ties provided to perimeter beams of a structure will toughen the exterior portion of a structure, should an exterior column be severely damaged.

Provisions for integrity reinforcement, first introduced in ACI 318-89, require continuous reinforcement in beams around the perimeter of the structure. The required amount is at minimum one-sixth of the tension reinforcement for negative moment at the support and one-fourth of the tension reinforcement for positive moment at the midspan. In either case a minimum of two bars is required. Continuity in rebars is achieved by providing class A tension lap splicers, mechanical or welded splices in cast-in-place joists and beams.

Two-way slabs. In a two-way slab construction, all bottom bars within the column strip in each direction must be lap-spliced with class A tension laps. Figure 13.3.8 given in the ACI 318-02 (Fig. 4.16 of this text) shows the locations where the lap splices are permitted. At least two of the bottom bars in the column strip must pass within the core of the columns and be anchored at exterior supports.

Joists. At least one reinforcing bar in the bottom of a rib is to be continuous over supports or the bar must be spliced with a class A tension lap splice to a bar in the adjacent span. At discontinuous ends of joists, anchorage of at least one bottom bar must be provided with a standard hook (Fig. 4.17).

Beams. Beams are categorized as either perimeter or nonperimeter beams. A spandrel beam would be a perimeter beam. The detailing of top and bottom bars and of stirrups in perimeter beams is impacted by the structural integrity provisions. At least one-sixth of the -As required for negative-factored moment at the face of supports and one-quarter of the + As required for positive-factored moment at midspan are to be made continuous around the perimeter of the structure. Closed stirrups are also required in perimeter beams. It is not necessary to place closed stirrups within the joints. It is permissible to provide continuity of the top and bottom bars by splicing the top bars at midspan and the bottom bars at or near the supports. Lap-splicing with class A tension lap splices is required (Fig. 4.18).

For nonperimeter beams, the engineer has two choices to satisfy the structural integrity requirements: 1) provide closed stirrups; or 2) make at least one-quarter of the + As

required for positive-factored moment at midspan continuous. Splicing the prescribed number of bottom bars over the supports with class A tension lap spices is acceptable. At discontinuous ends of nonperimeter beams, the bottom bars must be anchored with standard hooks (Fig. 4.19). In all cases, mechanical or welded splices may be used instead of class A tension lap splices.

4.2.3. Intermediate Moment-Resisting Frames

4.2.3.1. General Requirements: Frame Beams

General requirements for frame beams of intermediate moment frames given in ACI 318-02 Sections 21.12.2 and 21.12.3 are as follows:

Class A tension splice, mech. or

• Reinforcement details in a frame member shall satisfy Section 21.12.4 if the factored compressive axial load < Ag f/10.

• If the factored compressive axial load > Af/10, frame reinforcement details shall satisfy Section 21.12.5, unless the member has spiral reinforcement in accordance with Eq. (10-5).

• If a two-way slab system without beams is treated as part of the lateral force-resisting system, reinforcement details in any span-resisting moments caused by lateral forces shall satisfy Section 21.12.6.

• Design shear strength of beams, columns, and two-way slabs resisting earthquake effects shall not be less than either

• The sum of the shear forces associated with development of nominal moment strengths of the member at each restrained end of the clear span and the shear force calculated for factored gravity loads; or

• The maximum shear force obtained from design load combinations that include earthquake effects, with the shear force from earthquake effects assumed to be twice that prescribed by the governing code for earthquake-resistant design.

4.2.3.2. Flexural and Transverse Reinforcement: Frame Beams

Flexural and transverse reinforcement requirements for frame beams given in Sections 21.12.4.1, 21.12.4.2, and 21.12.4.3 are as follows:

• Positive moment strength at joint face > one-third negative moment strength provided at that face of the joint.

• Neither the negative nor the positive moment strength at any section along the member length shall be less than one-fifth the maximum moment strength provided at the face of either joint.

• Stirrups shall be provided at both ends of a member over a length equal to 2h from the face of the supporting member toward midspan.

• The first stirrup shall be located no more than 2 in. from the face of the supporting member.

• Maximum stirrup spacing shall not exceed

• 8 x diameter of smallest longitudinal bar.

• Stirrups shall be spaced at no more than d/2 throughout the length of the member.

Refer to Figs. 4.20 and 4.21 for schematic flexural and transverse reinforcement details for frame beams.

4.2.3.3. Transverse Reinforcement: Frame Columns

Transverse reinforcement requirements for frame columns given in Sections 20.12.5.1 through 20.12.5.4 are as follows:

• Maximum tie spacing shall not exceed so over a length £0 measured from each joint face. Spacing so shall not exceed the smallest of:

Figure 4.20. Intermediate moment-resisting frame (IMRF); flexural reinforcement requirements for frame beams.

Figure 4.20. Intermediate moment-resisting frame (IMRF); flexural reinforcement requirements for frame beams.

• 8 x diameter of smallest longitudinal bar.

• Minimum member dimension/2.

• The length £0 shall not be less than the largest of

• Maximum cross-sectional dimension of member.

• The first tie shall be located no farther than s0/2 from the joint face.

• Joint reinforcement shall conform to Section 11.11.2.

• Tie spacing outside of the length £0 shall not exceed 2s0.

Figure 4.22 provides a schematic interpretation of these requirements.

ffl si d/4

6 x smallest long, bar diameter 24 x stirrup bar diameter 12"

Stirrups

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