ACI_314R_16_Guide_to_Simplified_Design_for_Reinforced_Concrete_Buildings | Simplified_Design_for_Reinforced_Concrete_Buildings

Document Content and Description Below

Guide to Simplified Design for Reinforced Concrete Buildings (For Buildings of Limited Size and Height, based on ACI 318-14 and ACI IPS-1, “Essential Requirements for Reinforced Concrete Build... ings”) Reported by ACI Committee 314 ACI 314R-16First Printing June 2016 ISBN: 978-1-942727-93-4 Guide to Simplified Design for Reinforced Concrete Buildings Copyright by the American Concrete Institute, Farmington Hills, MI. All rights reserved. This material may not be reproduced or copied, in whole or part, in any printed, mechanical, electronic, film, or other distribution and storage media, without the written consent of ACI. The technical committees responsible for ACI committee reports and standards strive to avoid ambiguities, omissions, and errors in these documents. In spite of these efforts, the users of ACI documents occasionally find information or requirements that may be subject to more than one interpretation or may be incomplete or incorrect. Users who have suggestions for the improvement of ACI documents are requested to contact ACI via the errata website at http://concrete.org/Publications/ DocumentErrata.aspx. Proper use of this document includes periodically checking for errata for the most up-to-date revisions. ACI committee documents are intended for the use of individuals who are competent to evaluate the significance and limitations of its content and recommendations and who will accept responsibility for the application of the material it contains. Individuals who use this publication in any way assume all risk and accept total responsibility for the application and use of this information. All information in this publication is provided “as is” without warranty of any kind, either express or implied, including but not limited to, the implied warranties of merchantability, fitness for a particular purpose or non-infringement. ACI and its members disclaim liability for damages of any kind, including any special, indirect, incidental, or consequential damages, including without limitation, lost revenues or lost profits, which may result from the use of this publication. It is the responsibility of the user of this document to establish health and safety practices appropriate to the specific circumstances involved with its use. ACI does not make any representations with regard to health and safety issues and the use of this document. The user must determine the applicability of all regulatory limitations before applying the document and must comply with all applicable laws and regulations, including but not limited to, United States Occupational Safety and Health Administration (OSHA) health and safety standards. Participation by governmental representatives in the work of the American Concrete Institute and in the development of Institute standards does not constitute governmental endorsement of ACI or the standards that it develops. Order information: ACI documents are available in print, by download, on CD-ROM, through electronic subscription, or reprint and may be obtained by contacting ACI. Most ACI standards and committee reports are gathered together in the annually revised ACI Manual of Concrete Practice (MCP). American Concrete Institute 38800 Country Club Drive Farmington Hills, MI 48331 Phone: +1.248.848.3700 Fax: +1.248.848.3701 www.concrete.orgACI Committee Reports, Guides, and Commentaries are intended for guidance in planning, designing, executing, and inspecting construction. This document is intended for the use of individuals who are competent to evaluate the significance and limitations of its content and recommendations and who will accept responsibility for the application of the material it contains. The American Concrete Institute disclaims any and all responsibility for the stated principles. The Institute shall not be liable for any loss or damage arising therefrom. Reference to this document shall not be made in contract documents. If items found in this document are desired by the Architect/Engineer to be a part of the contract documents, they shall be restated in mandatory language for incorporation by the Architect/Engineer. ACI 314R-16 supersedes ACI 314R-11 and became effective June 2016. Copyright © 2016, American Concrete Institute. All rights reserved including rights of reproduction and use in any form or by any means, including the making of copies by any photo process, or by electronic or mechanical device, printed, written, or oral, or recording for sound or visual reproduction or for use in any knowledge or retrieval system or device, unless permission in writing is obtained from the copyright proprietors. 1 ACI 314R-16 Guide to Simplified Design for Reinforced Concrete Buildings (For Buildings of Limited Size and Height, based on ACI 318-14 and ACI IPS-1, “Essential Requirements for Reinforced Concrete Buildings”) Reported by ACI Committee 314 Michael C. Mota, Chair Esteban Anzola, Secretary John Aidoo Iyad M. Alsamsam JoAnn P. Browning James R. Cagley Omar D. Cardona Julian Carrillo W. Gene Corley Om P. Dixit David A. Fanella Yosef Farbiarz Luis E. García Jose M. Izquierdo-Encarnación Mahmoud E. Kamara Jason J. Krohn James S. Lai Lionel A. Lemay Andres Lepage Adolfo B. Matamoros Mustafa Mahamid Lila Gabriela Mendez Florez Javeed Munshi T. George Muste Ronald L. O’Kane Guney Ozcebe Viral B. Patel Santiago Pujol William E. Rushing Jr. Guillermo Santana Jorge I. Segura Larbi M. Sennour Dorian P. Tung Jairo Uribe This guide presents simplified methods and design techniques that facilitate and speed the engineering of low-rise buildings within certain limitations. Material is presented in an order that follows typical design process with procedures introduced as the designer will need them in the course of a building design. Much of the information presented in this guide is derived from ACI 318, ASCE 7, and the 2015 International Building Code (IBC) (International Code Council 2015). The quality and testing of materials used in construction are covered by references to the appropriate ASTM standard specifications. Whereas many of the tables, charts, and values included in this guide originated from the aforementioned reference documents, they have been modified or reorganized to be more conservative, to match design process flow, or better support the holistic and simplified design approach presented. Although this guide is not written in mandatory language, the information is presented in such a manner that a structure designed following this guide will, in principle, comply with the codes and standards on which it was based. Although this guide is written in nonmandatory language, it is meant to be applied as a whole, because the simplified provisions are interdependent, and it would be unsafe to employ only a portion of this guide and disregard the remainder. This guide is not a code and is not deemed to satisfy ACI 318, ASCE 7, and the International Building Code (International Code Council 2015). This guide is expected to be especially useful in the education and training of engineers in reinforced concrete design of low-rise structures of small to medium floor areas. There are many options within these standards that are not considered in this guide, such as the use of supplementary cementitious materials in concrete mixtures. As this guide will be used as a design aid, it is the licensed design professional’s responsibility to ensure that the structure design satisfies the requirements of ACI 318, ASCE 7, the International Building Code (International Code Council 2015), and the legal requirements of the local jurisdiction. The original draft of the guide, published as ACI IPS-1 (2002), was produced by a Joint Committee of Instituto Colombiano de Normas Técnicas y Certificación (Colombian Institute for Technical Standards and Certification) (ICONTEC) and Asociación Colombiana de Ingeniería Sísmica (Colombian Association for Earthquake Engineering) (AIS). The initial drafting of ACI IPS-1 (2002) was motivated by frequent worldwide discussions that reinforced concrete codes might be unnecessarily sophisticated for some applications, such as small low-rise buildings. Current knowledge of reinforced concrete behavior obtained through experimentation and experiSpecial acknowledgment to J. P. Browning, L. E. García, J. M. Izquierdo-Encarnación, J. S. Lai, M. C. Mota, S. Pujol, and J. I. Segura for their contributions to this guide. This document is dedicated to the memory of late subcommittee member W. Gene Corley.American Concrete Institute – Copyrighted © Material – www.concrete.org 2 GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) ence, and its status and dissemination as a structural material used worldwide, made developing a simplified design and construction guide feasible. This guide used ACI IPS-1 (2002) as a basis, with information derived from ACI 318, ASCE 7, and the International Building Code (International Code Council 2015). This guide presents simplified approaches to assist engineers in designing low-rise buildings within certain limitations, in addition to the following: (a) Information on the order needed in the course of a design (b) Explanatory material at appropriate places (c) Computations only requiring a hand calculator (d) Graphs and graphical explanations (e) Design information based on simplified strength models (f) Other limit states accounted for by minimum dimensions (g) Conservative loads and simplified analysis guidelines (h) Simplified geotechnical information to help define soilbearing capacity (i) Shear walls as the seismic-force-resisting system (j) Material and construction guidelines based on commonly available steel grades and medium-strength concrete that can be site mixed. Keywords: concrete quality; foundation design; frame analysis; inspection; low-rise building construction; low-rise structure; mixing; placing; section analysis; seismic design; simplified design; specifications; structure design; structure layout. CONTENTS CHAPTER 1—GENERAL, p. 3 1.1—Scope, p. 3 1.2—Purpose, p. 3 1.3—Limitations, p. 3 1.4—Supporting codes and standards, p. 4 1.5—Design and construction procedure, p. 5 1.6—Limit states, p. 6 1.7—Strength design, p. 6 1.8—Serviceability design, p. 7 CHAPTER 2—NOTATION AND DEFINITIONS, p. 7 2.1—Notation, p. 7 2.2—Definitions, p. 10 CHAPTER 3—STRUCTURAL SYSTEM LAYOUT, p. 14 3.1—Description of structural components, p. 14 3.2—General, p. 15 3.3—Structural layout, p. 15 3.4—Feasibility of guide usage, p. 16 CHAPTER 4—LOADS, p. 16 4.1—General, p. 16 4.2—Load factors and load combinations, p. 16 4.3—Mass and weight, p. 17 4.4—Weight of materials, p. 17 4.5—Dead loads, p. 17 4.6—Live loads, p. 21 4.8—Rain load, p. 22 4.9—Snow load, p. 22 4.10—Wind loads, p. 22 4.12—Soil weight and lateral pressure, p. 26 4.13—Lateral loads, p. 26 4.14—Lateral-force-resisting system, p. 27 4.15—Minimum amount of reinforced concrete structural walls, p. 29 CHAPTER 5—GENERAL REINFORCED CONCRETE INFORMATION, p. 31 5.1—Scope, p. 31 5.2—Materials for reinforced concrete, p. 31 5.3—Minimum and maximum reinforcing bar diameter, p. 31 5.5—Minimum reinforcement bend diameter, p. 32 5.8—Development length, lap splicing, and anchorage of reinforcement, p. 34 5.9—Longitudinal reinforcement, p. 34 5.10—Transverse reinforcement, p. 35 5.11—Flexure, p. 35 5.12—Axial loads with or without flexure, p. 36 5.13—Shear, p. 37 5.14—Bearing, p. 39 CHAPTER 6—FLOOR SYSTEMS, p. 39 6.1—Types of floor systems, p. 39 6.2—Selection of floor system, p. 42 6.3—Structural integrity, p. 42 6.4—One-way and two-way load paths, p. 42 6.5—Minimum depth for floor system members, p. 42 6.6—Trial dimensions for floor system, p. 44 6.7—Floor finish, p. 44 6.8—Ducts, shafts, openings, and embedded piping, p. 44 CHAPTER 7—SOLID SLABS SUPPORTED ON GIRDERS, BEAMS, JOISTS, OR REINFORCED CONCRETE WALLS, p. 45 7.1—General, p. 45 7.2—Loads, p. 45 7.3—Reinforcement details, p. 45 7.4—Shear strength, p. 47 7.5—Slab between joists, p. 47 7.6—Cantilevers of slabs supported on girders, beams, or walls, p. 48 7.7—One-way, single-span solid slabs spanning between girders, beams, or reinforced concrete walls, p. 49 7.8—One-way solid slabs supported on girders, beams, or walls with two or more spans, p. 50 7.9—Two-way solid slabs spanning between girders, beams, or reinforced concrete walls, p. 51 CHAPTER 8—GIRDERS, BEAMS, AND JOISTS, p. 59 8.1—General, p. 59 8.2—Loads, p. 59 8.3—Reinforcement types, p. 59 8.4—Longitudinal reinforcement, p. 60 8.5—Transverse reinforcement, p. 64 8.6—Joists and beams supported by girders, p. 66 8.7—Girders that are part of a frame, p. 70American Concrete Institute – Copyrighted © Material – www.concrete.org GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) 3 CHAPTER 9—SLAB-COLUMN SYSTEMS, p. 72 9.1—General, p. 72 9.2—Loads, p. 72 9.3—Dimensional limits, p. 73 9.4—Reinforcement details, p. 74 9.5—Shear strength, p. 76 9.6—Minimum slab thickness as required by punching shear, p. 77 9.7—Minimum slab thickness as required by beam action, p. 77 9.8—Flexure, p. 78 9.9—Calculation of support reactions, p. 80 CHAPTER 10—COLUMNS, p. 80 10.1—General, p. 80 10.2—Loads, p. 80 10.3—Dimensional limits, p. 81 10.4—Reinforcement details, p. 82 10.5—Flexure, p. 86 10.6—Shear, p. 86 10.7—Calculation of foundation reaction, p. 87 CHAPTER 11—SEISMIC RESISTANCE, p. 87 11.1—Special reinforcement details for seismic zones, p. 87 11.2—Interaction with nonstructural elements, p. 93 CHAPTER 12—REINFORCED CONCRETE WALLS, p. 94 12.1—General, p. 94 12.2—Loads, p. 94 12.3—Dimensional limits, p. 95 12.4—Reinforcement details, p. 95 12.5—Flexure, p. 97 12.6—Shear, p. 97 12.7—Calculation of reactions at the foundation, p. 97 12.8—Core walls, p. 98 CHAPTER 13—OTHER STRUCTURAL MEMBERS, p. 98 13.1—Stairways and ramps, p. 98 13.2—Small water tanks (for potable water storage), p. 100 CHAPTER 14—FOUNDATIONS, p. 101 14.1—Soil investigation, p. 101 14.2—Allowable soil-bearing capacity, p. 101 14.3—Settlement criteria, p. 102 14.4—Dimensioning foundation members, p. 102 14.5—Spread footings, p. 102 14.6—Wall footings, p. 106 14.7—Combined footings, p. 107 14.8—Piles and caissons, p. 108 14.9—Footings on piles, p. 108 14.10—Foundation mats, p. 108 14.11—Retaining walls, p. 110 14.12—Grade beams (foundation beams), p. 114 14.13—Slabs-on-ground, p. 115 CHAPTER 15—DRAWINGS AND SPECIFICATIONS, p. 115 15.1—General, p. 115 15.2—Structural drawings, p. 116 15.3—Project specifications, p. 117 CHAPTER 16—CONSTRUCTION, p. 117 16.1—Introduction, p. 117 16.2—Concrete mixture proportioning, p. 118 16.4—Concrete mixing and transportation, p. 120 16.5—Concrete strength evaluation, p. 122 16.6—Concrete curing, p. 123 16.7—Form removal, p. 123 CHAPTER 17—REFERENCES, p. 124 APPENDIX A—COMPARISON OF ACI 314R-16 TO ACI 318-14, INTERNATIONAL BUILDING CODE (2015), AND ASCE 7-10, p. 125 CHAPTER 1—GENERAL 1.1—Scope This guide is intended for the planning, design, and construction of reinforced concrete structures in new lowrise buildings of restricted occupancy, number of stories, and area. Although the information presented was developed to produce, when properly used, a reinforced concrete structure with an appropriate margin of safety, this guide is not a replacement for a licensed design professional’s experience and working knowledge. For the structure designed by this guide to attain the intended margin of safety, the guide should be used as a whole, and alternative procedures should be used only when explicitly permitted herein. The minimum dimensioning prescribed in the guide replace, in most cases, more detailed procedures prescribed in ACI 318, ASCE 7, and the International Building Code (International Code Council 2015). 1.2—Purpose This guide provides a licensed design professional with sufficient information to design structural reinforced concrete members that comprise the structural framing of a low-rise building with the limits set in 1.3. Design rules set forth in this guide are simplifications that, when used together, comply with the more detailed requirements of ACI 318, ASCE 7, and the International Building Code (International Code Council 2015). 1.3—Limitations This guide is only meant for buildings meeting all the limitations set forth in 1.3.1 to 1.3.10. These limits maintain the guide scope in close adherence to the collective experience of the original drafting committee (ICONTEC-AIS). Buildings within this scope are expected to have a normal rectangular footprint with simple standard geometries and member dimensions in both plan and vertical directions. Such buildings also depend primarily on reinforced concreteAmerican Concrete Institute – Copyrighted © Material – www.concrete.org 4 GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) structural walls for lateral load resistance. Observing these limits justifies the simplified analysis and design methods herein without the need for special analyses, including slenderness and second-order effects. Buildings with offsets, reentrant corners, and vertical or horizontal irregularities are outside the scope of this guide. 1.3.1 Use and occupancy 1.3.1.1 Permitted uses and occupancies—Table 1.3.1.1 lists building occupancy groups and subgroups, indicating for each whether the use of this guide is permitted. 1.3.1.2 Mixed occupancy—Recommendations described in this guide apply to cases involving only combinations for which the use of this guide is permitted, as identified in Table 1.3.1.1. 1.3.2 Maximum number of stories—Recommendations described in this guide apply to buildings with five or fewer stories above ground and no more than one basement level. 1.3.3 Maximum area per floor—The area per floor should not exceed 10,000 ft2 (1000 m2). 1.3.4 Maximum story height—Story height, measured from floor finish to floor finish, should not exceed 13 ft (4 m). 1.3.5 Maximum span length—The span length for girders, beams, and slab-column systems, measured center-to-center of the supports, should not exceed 30 ft (10 m). 1.3.6 Maximum difference in span length—Spans should be approximately equal, and the shorter of two adjacent spans should be at least 80 percent of the larger span, except in elevator and stair cores. Refer to 7.9.1 for cores. 1.3.7 Minimum number of spans—There should be at least two spans in each of the two principal directions of the building in plan. Single spans may be permitted in one- and two-story buildings if the span length does not exceed 15 ft (5 m). 1.3.8 Maximum overhang—For girders, beams, and slabs with overhangs, the length of the overhang should not exceed one-third of the length of the first interior span of the member. 1.3.9 Maximum slope for slabs, girders, beams, and joists—When sloping slabs, girders, beams, or joists are used, the slope of the member should not exceed 15 degrees. 1.3.10 Maximum slope of the terrain—The slope of the terrain surrounding the building should not exceed 30 degrees (Fig. 1.3.10) or the ratio of the height of the first story to the smaller dimension of the building in plan. 1.4—Supporting codes and standards For cases within the limits described in 1.3, this guide is intended to be a simplification complying with the following supporting codes and standards: a) ACI 318 Table 1.3.1.1—Permitted uses and occupancies Occupancy group Occupancy subgroup Permitted Group A—Assembly A-1 Fixed-seating theaters, television, and radio studios NO A-2 A-3 Building having an assembly room with capacity less than 100 persons and not having a stage YES A-4 Arenas, skating rinks, swimming pools, and tennis courts NO A-5 Amusement parks, bleachers, grandstands, and stadiums NO Group B—Business B Building for use as offices, or professional services containing eating and drinking establishments with less than 50 occupants YES Group E—Educational E Educational purposes with less than 500 students and staff YES Group F—Factory F-1 Light industries not using heavy machinery YES F-2 Heavy industries using heavy machinery NO Group H—Hazardous H Manufacturing, processing, generation, or storage of materials that constitute a physical or health hazard NO Group I—Institutional I-1 Residential board and care facilities YES I-2 Hospitals NO I-3 Prisons, jails, reformatories, and detention centers YES I-4 Daycare facilities YES Group M—Mercantile M Display and sale of merchandise YES Group R—Residential R-1 Hotels having an assembly room with capacity less than 100 persons and not having a stage YES R-2 Apartment buildings and dormitories YES R-3 Houses YES R-4 Residential care and assisted-living facilities YES Group S—Storage S-1 Storage of heavy or hazardous materials NO S-2 Storage of light materials YES Group U—Utility and miscellaneous U Utilities, water supply systems, and power-generating plants NO U Garages for vehicles with carrying capacity up to 4000 lb (1800 kg) YES U Garages for trucks of more than 4000 lb (1800 kg) carrying capacity NOAmerican Concrete Institute – Copyrighted © Material – www.concrete.org GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) 5 b) ASCE 7 c) International Building Code (International Code Council 2015) Other cases are not covered by this guide. Please refer to Table A.1 in Appendix A for a guide by section to corresponding topics in the supporting codes and standards. 1.5—Design and construction procedure 1.5.1 Procedure—The design procedure comprises the steps listed in Table 1.5.1. Refer also to Fig. 1.5.1a and 1.5.1b. Note that by conforming to the dimensional limits and cover of this guide, a 1-hour fire rating is achieved. This rating is usually sufficient for the permitted occupancies in this guide. Other fire ratings are beyond the scope of this guide, and such designs should be performed using ACI 318, ASCE 7, and the International Building Code (International Code Council 2015). 1.5.2 Design documentation—The design steps should be recorded as follows. 1.5.2.1 Calculation record—The licensed design professional should document all design steps in a calculation record. This record should contain, at a minimum, the following: (a) General structural program, as defined in Chapter 3 (b) Description of the structural system (c) Loads (d) Characteristics, strength, and fabrication standards for all structural materials Fig. 1.3.10—General structural layout in elevation. Table 1.5.1—Design and construction procedure steps Step Description Related chapter(s) A Verification that the limitations for using the guide are met. Definition of the layout in plan and height of the structure. 1 and 3 B Calculation of all gravity loads that act on the structure, excluding the self-weight of the structural members. 4 C Definition of an appropriate floor system, depending on the span lengths and the magnitude of the gravity loads. 6 D Selection of trial dimensions for the slab of the floor system. Calculation of the self-weight of the system and design of the members that comprise it, correcting the dimension if needed by the strength and serviceability limit states, complying with the limits for slab systems with beams, or slab-column systems. 6, 7, and 9 E Trial dimensions for the beams and girders (if needed). Calculation of the self-weight of girders, beams, and joists. Flexural and shear design of the beams and girders, correcting the dimensions if needed by the strength and serviceability limit states. 6 and 8 F Trial dimensions for the columns. Verification of column slenderness through the use of minimum dimensions. Calculation of the self-weight of the columns. Design of the columns for combination of axial load, moment, and shear. Correcting the dimensions if needed by the strength and serviceability limit states. 10 G If lateral load, such as earthquake, wind, or lateral earth pressure, is beyond nominal, magnitude and application point are to be established; otherwise the designer may proceed to Step I. 4 H Preliminary location and trial dimensions for reinforced concrete walls capable of resisting lateral loads. For earthquake loads, the influence of wall self-weight is evaluated. Flexure and shear design of the reinforced concrete walls. 11 and 12 I Design of the stairways, ramps, small potable water tanks, and retaining walls. 13 J Loads at the foundation level are determined. Definition of the foundation system is performed. Design of the structural members of the foundation. 14 K Production of the structural drawings and specifications. 15 L The structure is built complying with the construction and inspection requirements. 16American Concrete Institute – Copyrighted © Material – www.concrete.org 6 GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) (e) Justification of all design calculation (f) Sketches of the reinforcement layout for all structural members 1.5.2.2 Geotechnical report—The geotechnical report should record, at a minimum, the soil investigation performed, selected allowable bearing capacity of the soil, soil profile type, lateral soil pressures anticipated for design of any soil-retaining structures, and all other information indicated in Chapters 4 and 14. 1.5.2.3 Structural drawings—Structural drawings should include, at a minimum, all the plans indicated by Chapter 15 for construction of the building. 1.5.2.4 Project specifications—Project specifications should include, at a minimum, all the construction specifications described in Chapter 15. 1.5.3 Precast concrete components—Precast concrete components may be used, including prestressed concrete manufactured in offsite facilities. Such components should be designed by a licensed design professional in accordance with ACI 318, ASCE 7, and the International Building Code (International Code Council 2015). Calculations should be reviewed by the licensed design professional of record (1.2) and included in the calculation record (1.5.2.1). Detailing and placing drawings conforming to 15.2.2 should be furnished and included as part of the structural drawings (1.5.2.3). Manufacture of precast components should be done in a facility with demonstrated capability of producing quality products. 1.6—Limit states The design approach of this guide is based on limit states, where a limit state is a condition beyond which a structure or member becomes unfit for service and is judged to be unsafe or no longer useful for its intended function. The designer should verify that the strength and serviceability limit states are accounted for in the resulting structure.The following are considered implicitly in the design procedure: (a) Structural integrity (b) Lateral load story drift (c) Durability (d) Fire resistance 1.7—Strength design 1.7.1 General—In strength design, the structure and the structural members are dimensioned to have design strengths Fig. 1.5.1a—Design and construction procedure. Fig. 1.5.1b—Design and construction procedure for earthquake regions.American Concrete Institute – Copyrighted © Material – www.concrete.org GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) 7 at all sections at least equal to the demands calculated for the combinations of factored loads described in Chapter 4. The basic expression for the strength limit state is resistances ≥ load effects (1.7.1a) Because resistances may be less than computed and the load effects could be larger than computed, strength reduction factors ϕ less than 1, and load factors γ generally greater than 1, are used ϕRn ≥ γ1S1 + γ2S2 + … (1.7.1b) where Rn is nominal strength, and S is load effects based on the loads described in Chapter 4. Therefore, the strength design requires that design strength ≥ required strength (1.7.1c) ϕ (nominal strength) ≥ U (1.7.1d) where the required strength is U = γ1S1 + γ2S2 + … 1.7.2 Required strength—The required strength U should be computed for the combinations of factored loads listed in 4.2. 1.7.3 Design strength—The design strength provided by a member, its connections to other members, and its cross sections in terms of flexure, axial load, and shear, is the nominal strength multiplied by a strength reduction factor ϕ. Nominal strength should be calculated for each particular force effect in each of the member types at the defined critical sections. The following strength reduction factors ϕ should be used: a) Flexure, without axial load: ϕ = 0.90 b) Axial tension and axial tension with flexure: ϕ = 0.90 c) Axial compression and axial compression with flexure: i. Columns with ties and reinforced concrete walls: ϕ = 0.65 ii. Columns with spiral reinforcement: ϕ = 0.75 d) Shear and torsion: ϕ = 0.75 e) Bearing of concrete: ϕ = 0.65 1.8—Serviceability design To ensure adequate response during service, follow the recommendations in this guide for limiting dimensions, cover, detailing, and construction. These serviceability conditions include effects such as: (a) Long-term environmental effects, including exposure to aggressive environment or corrosion of the reinforcement (b) Dimensional changes due to variations in temperature, relative humidity, and other effects (c) Excessive cracking of the concrete (d) Excessive vertical deflections (e) Excessive vibration CHAPTER 2—NOTATION AND DEFINITIONS 2.1—Notation A a = effective seismic peak ground horizontal acceleration in rock for short periods of vibration, expressed as a fraction of gravity g Ab = area of an individual reinforcing bar or wire, in.2 (mm2) Acb = bearing area of concrete, in.2 (mm2) A cs = area of core of spirally reinforced compression member measured to outside diameter of spiral, in.2 (mm2) Af = contact area of footing with soil, ft2 (m2) A g = gross area of section, or area of concrete only excluding area of voids, in.2 (mm2) Ai = area of additional hanger reinforcement where beams are supported by girders or other beams, in.2 (mm2) A j = effective cross-sectional shear area within a joint, in.2 (mm2) A p = component, or cladding, wind-exposed surface area, ft2 (m2) A s = area of longitudinal tension reinforcement, in.2 (mm2) A s′ = area of longitudinal compression reinforcement, in.2 (mm2) A se = steel area at the extreme face of column or reinforced concrete wall, in.2 (mm2) As,min= minimum area of longitudinal tension reinforcement, in.2 (mm2) A ss = steel area at the side face of column or reinforced concrete wall, in.2 (mm2) Ast = total area of longitudinal reinforcement, in.2 (mm2) A su = wind-exposed surface area, ft2 (m2) A v = area of shear reinforcement, in.2 (mm2) a = depth of equivalent rectangular compressive stress block, in. (mm) aw = distance from edge of wall footing to the resultant of soil reaction in wall footing, in. (mm) Bf = short horizontal dimension of footing, in. (mm) b = width of compression flange of member, or width of member, in. (mm) bc = width of column section, and for punching shear evaluation, the smallest plan dimension of pedestal, column capital, or drop panel, or thickness change in stepped footings, in. (mm) bf = width of compression face of member, in. (mm) bo = perimeter of critical section for two-way shear (punching shear) in slabs, in. (mm) bw = web width of section, or wall width, in. (mm) Cp = component, or cladding, wind surface pressure coefficient Csu = wind surface pressure coefficient Cvx = coefficient defined in 4.11.4 for design of seismic loads cc = least distance from surface of reinforcement to the side face, in. (mm) D = dead loads or related internal moments and loads d = effective depth of section, taken as distance from extreme compression fiber to centroid of tension reinforcement, in. (mm) d′ = distance from extreme compression fiber to centroid of compression reinforcement, in. (mm) db = nominal diameter of reinforcing bar or wire, in. (mm) dc = distance from extreme tension fiber to centroid of tension reinforcement, in. (mm) ds = outside diameter of spiral reinforcement, in. (mm) E = seismic loads or related internal moments and loadsAmerican Concrete Institute – Copyrighted © Material – www.concrete.org 8 GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) Ec = modulus of elasticity of concrete, psi (MPa) eB = eccentricity of resultant applied to footing in direction parallel to Bf, in. (mm) eH = eccentricity of resultant applied to footing in direction parallel to Hf, in. (mm) ex = eccentricity, measured in x-direction, between story center of lateral stiffness and application point of story lateral loads acting in y-direction, in. (mm) e y = eccentricity, measured in y-direction, between story center of lateral stiffness and application point of story lateral loads acting in x-direction, in. (mm) F = loads due to weight and pressure of fluids with well-defined densities and controllable maximum heights or related internal moments and loads Fa = seismic site coefficient for short periods of vibration F ac = total lateral active soil force, lb (kN) Fi, Fx= wind or seismic force applied at level i or x, respectively, lb (kN) Fo = total lateral at-rest soil force, lb (kN) F pw = equivalent static wind force for components and cladding acting normal to wind-exposed surface, lb (kN) F su = equivalent static wind force acting normal to windexposed surface, lb (kN) Fui, Fux = factored lateral force applied to wall at level i or x, respectively, lb (kN) fc′ = specified compressive strength of concrete, psi (MPa) √fc′ = square root of specified compressive strength of concrete; the result has units of psi (MPa) fcr′ = required average compressive strength of concrete used as the basis for selection of concrete proportions, psi (MPa) fcu = extreme fiber compressive stress due to factored loads at edges of structural walls, psi (MPa) fy = specified yield strength of reinforcement, psi (MPa) fypr = probable specified maximum strength of reinforcement, psi (MPa) (fypr = 1.25fy) fyt = specified yield strength of transverse or spiral reinforcement, psi (MPa) g = acceleration due to gravity, 386 in./s2 (9.8 m/s2 ≈ 10 m/s2) H = loads due to weight and pressure of soil, water in soil, or other materials, or related internal moments and loads Hf = long horizontal dimension of footing, in. (mm) h = overall depth or thickness of member, or height of section of member, or outside diameter of circular section, in. or ft (mm or m) hb = vertical distance measured from bottom of supporting girder to bottom of supported beam, ft (m) hc = depth of column, or dimension of column in direction parallel to girder span; and for punching shear evaluation, the largest plan dimension of capital, drop panel, pedestal, or thickness change in stepped footings, in. (mm) hf = flange thickness, in. (mm) h g = total depth of supporting girder, in. (mm) hi, hx= height above base to level i or x, respectively, ft (m) hn = clear vertical distance between lateral supports of columns and walls, in. (mm) h pi = story height of floor i measured from floor finish of story to floor finish of story immediately below, ft (m) hr = mean roof height for wind design, measured over terrain, ft (m) hs = depth of soil against retaining wall, in. (mm) hw = height of wall from base to top, in. (mm) Ic = moment of inertia of column section, in.4 (mm4) Ka = active soil pressure coefficient Ko = at-rest soil pressure coefficient Kp = passive soil pressure coefficient kr = story total rotational stiffness kx , ky = wall lateral stiffness in direction x or y, respectively, lb/in. (N/mm) (Eq. (4.14.5a(a)) and Eq. (4.14.5a(b)) L = live loads or related internal moments and loads L r = roof live load or related internal moments and loads ℓ0 = column confinement length, in. (mm) ℓ1 = length of span in direction of moments, measured center-to-center of supports, in. (mm) ℓ2 = length of span transverse to ℓ1, measured center-tocenter of supports, in. (mm) ℓa = length of clear span in short direction of two-way slabs or in direction of moments, measured face-toface of beams or other supports, in. (mm) ℓc = length of clear span in long direction of two-way slabs or systems, measured face-to-face of beams or other supports, in. (mm) ℓd = development length, in. (mm) ℓn = length of clear span, in long direction for two-way systems, measured face-to-face of beams or other supports, in. (mm) ℓ ps = factor to calculate punching shear strength (9.5.4.3) ℓs = center-to-center span length; shortest distance between adjacent parallel column centerlines, in. (mm) ℓw = horizontal length of wall, in. (mm) Ma = factored moment in short direction in two-way slabs, lb·in. (N∙m) per unit slab width M+ a or b = factored positive moment at section, lb·in. (N∙m) per unit slab width M– a or b = factored negative moment at section, lb·in. (N∙m) per unit slab width Mb = factored moment in long direction in two-way slabs, lb·in. (N·m) per unit slab width Mbn = nominal moment strength at section at balanced conditions, lb·in. (N∙m) Mi, Mx = unfactored overturning moment due to lateral loads for story i or x, respectively, lb·in. (kN∙m) Miu, Mxu = factored story moment due to lateral loads at story i or x, respectively, lb·in. (kN∙m) Mn = nominal moment strength at section, lb·in. (N∙m) Mo = total factored moment at section, lb·in. (kN∙m) Mot = unfactored overturning moment due to lateral loads at base of structure, lb·in. (kN∙m) Motu = factored overturning moment due to lateral loads at base of structure, lb·in. (kN∙m) M pr = probable flexural strength of member at joint face, computed using fypr and ϕ of 1.0, lb·in. (N∙m)American Concrete Institute – Copyrighted © Material – www.concrete.org GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) 9 Mu = factored moment at section, lb·in. (N∙m) Mu + = actored positive moment at section, lb·in. (N∙m) Mu – = factored negative moment at section, lb·in. (N∙m) M ux = factored moment at section in x direction, lb·in. (N∙m) M uy = factored moment at section in y direction, lb·in. (N∙m) M xu = factored overturning moment due to lateral loads for story x, lb·in. (kN∙m) N = number of blows in standard penetration test (SPT) N = average soil SPT resistance, measured in number of blows per ft (0.305 m) of penetration, averaged over upper 100 ft (30 m) of soil profile nc = number of interior columns in story in direction under consideration, for the entire structure ne = number of edge columns in story in direction under consideration, for the entire structure ns = number of stories in the building above the base Pbn = nominal compression axial compression strength at section at balanced conditions, lb (N) P cu = factored compression load on wall boundary element, including seismic effects, lb (N) Pd = unfactored dead load axial force at section, lb (kN) Pℓ = unfactored live load axial force at section, lb (kN) P n = nominal axial compression strength at given eccentricity, lb (N) Pn(max)= maximum compression nominal axial compression strength at section, lb (N) P on = nominal compression, without flexure, or axial compression strength at section, lb (N) P ov = maximum vertical load applied to footing including wind or seismic overturning effects, lb (N) Ptn = nominal tension, without flexure, or axial tension strength at section, lb (N) Ptu = factored tension force on wall boundary element, including seismic effects, lb (N) P u = factored axial or concentrated load, or factored axial load at given eccentricity, lb (N or kN) Pub = factored axial load at base of column, lb (N) P v = maximum vertical load applied to footing not including wind or seismic, lb (N) PI = soil plasticity index, equal to difference in percentage of moisture content at liquid limit and at plastic limit p = unfactored pressure for braced retaining walls, psi or lb/ft2 (kPa or kN/m2) pa = unfactored active pressure, psi or lb/ft2 (kPa or kN/m2) pd = unfactored concentrated dead load applied directly to member, lb (kN) pℓ = unfactored concentrated live load applied directly to member, lb (kN) po = unfactored pressure at rest, psi or lb/ft2 (kPa or kN/m2) pp = unfactored passive pressure, lb/ft2 (kPa or kN/m2) pt = unfactored vertical surcharge pressure on top of retaining wall backfill, lb/ft2 (kPa or kN/m2) pu = factored concentrated load applied directly to member, lb (kN) putw = factored design horizontal pressure for retaining walls caused by surcharge pressure on top of retaining wall backfill, lb/ft2 (kPa or kN/m2) puw = factored design horizontal pressure for retaining walls, lb/ft2 (kPa or kN/m2) pz = at-rest, or active, lateral soil pressure at depth x, lb/ ft2 (kPa or kN/m2) qa = unfactored allowable bearing capacity of soil, lb/ft2 (kPa or kN/m2) qc = standard cone penetration resistance in cone penetration test, lb/ft2 (kPa or kN/m2) qd = unfactored dead load per unit area, lb/ft2 (kN/m2) qh = wind velocity pressure at height h over terrain, lb/ ft2 (kN/m2) qℓ = unfactored live load per unit area, lb/ft2 (kN/m2) qo = overburden pressure, or unfactored gravity loads applied directly to slab in mat foundations, lb/ft2 (kN/m2) qu = factored load per unit area, lb/ft2 (kN/m2) quc = unconfined compression strength of soil, lb/ft2 (kPa or kN/m2) qun = factored net soil reaction pressure on footing, lb/ft2 (kN/m2) R = rain load or related internal moments and loads R n = nominal strength in terms of flexure, axial load, shear or bearing strength R pi = reaction from lateral soil pressure at story i, lb (kN) R s = response modification factor related to energy dissipation capacity in inelastic range of seismicresistant structural system R u = factored reaction from supported structural member, lb (kN) r u = factored uniformly distributed reaction from slab on supporting girder, beam, or reinforced concrete wall, lb/ft (kN/m) S = snow load or related internal moments and loads Sa = value of elastic acceleration design response spectrum, for damping ratio of 5 percent of critical, expressed as fraction of acceleration of gravity SDS = value of design earthquake spectral acceleration parameter at short period Si = nominal load effect based on load i s = spacing of transverse reinforcement, stirrups, or wall reinforcement measured along axis of member, in. (mm) sj = center-to-center spacing between parallel joists, in. (mm) ss = sample standard deviation, psi (MPa) ssk = spacing of skin reinforcement, in. (mm) su = shear strength of undrained cohesive soil, lb/ft2 (kPa or kN/m2) T = cumulative effect of temperature, creep, shrinkage, differential settlement, and shrinkage-compensating concrete Ti, Tx = unfactored story torsional moment due to lateral loads at story i or x, respectively, lb·in. (kN∙m) To = unfactored story torsional moment due to lateral loads at base of structure, lb·in. (kN∙m) T ou = factored story torsional moment due to lateral loads at base of structure, lb·in. (kN∙m) Tu = factored torsional moment at section, lb·in. (N∙mm)American Concrete Institute – Copyrighted © Material – www.concrete.org 10 GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) T xu, Tiu =factored story torsional moment due to lateral loads at story i or x, respectively, lb·in. (kN∙m) tx , ty = structural vertical member cross-sectional dimension in direction x or y, respectively, in. (mm) U = required strength to resist factored loads or related internal moments and loads V = basic wind speed, mph (m/s), corresponding to 3-second gust speed at 33 ft (10 m) above ground Vbs = seismic design base shear, lb (kN) Vc = nominal shear strength provided by concrete, lb (N) Vi, Vx= unfactored story shear due to lateral loads at story i or x, respectively, lb (kN) Viu, Vxu =factored story shear due to lateral loads at story i or x, respectively, lb (kN) Vn = nominal shear strength at section, lb (N) Vo = unfactored story shear due to lateral loads at base of structure, lb (kN) Vou = factored story shear due to lateral loads at base of structure, lb (kN) Vs = nominal shear strength at section provided by transverse reinforcement, lb (kN) Vsw = contribution of the horizontal wall reinforcement to the nominal shear strength at section, lb (kN) Vu = factored shear, lb (N) Vw = wind design base shear, lb (kN) W = wind loads or related internal moments and loads Ws = total building weight for seismic design, lb (kN) Wu = total factored uniformly distributed design load per unit member length, lb/in. (kN/m) Wuf = total factored uniformly distributed design load per unit member length, lb/ft (kN/m) w = moisture content of the soil, percentage wd = unfactored dead load per unit member length applied directly to the member, lb/in. (kN/m) wdf = unfactored dead load per unit member length applied directly to the member, lb/ft (kN/m) wi, wx = part of Ws corresponding to story i or x, respectively, lb (kN) wℓ = unfactored live load per unit member length applied directly to the member, lb/in. (kN/m) wu = factored load per unit member length applied directly to the member, lb/ft (kN/m) x y , = story lateral stiffness center coordinates in directions x and y, respectively, in. (mm) z = depth of soil, ft (m) αa = fraction of load acting in short direction in two-way slabs-on-girders αb = fraction of load acting in long direction in two-way slabs-on-girders αc = coefficient defining the concrete strength contribution to wall shear strength αf = parameter of Eq. (5.11.4.2) αsh = factor affecting equivalent shear force due to unbalanced moment at column-slab connection in Eq. (9.5.4.4) αw = horizontal angle between normal to wind exposed surface and wind direction, degrees β = ratio of clear spans in long to short direction of two-way slabs βf = ratio of long side to short side of footing βw = vertical angle between normal to wind exposed surface and horizontal line, degrees ∆M u= factored unbalanced moment at column-girder joint or wall-girder joint, lb·in. (N∙mm) ∆Mu-ad = additional factored unbalanced moment at columnslab connection, lb·in. (N∙mm) ∆Ve = factored design shear force from development of probable flexural capacity of member at faces of joints, lb (N) ∆Vu = factored shear force due to unbalanced moment at column-slab connection, lb (N) ∆Vut = increase in wall factored shear due to torsional effects, lb (kN) ϕ = strength reduction factor ϕs = angle of internal friction of soil γ = unit weight of material or soil, lb/ft3 (kN/m3) γi = load factor for load effect i ρ = ratio of longitudinal tension reinforcement As/(bd) ρ′ = ratio of longitudinal compression reinforcement A s′/(bd) ρℓ = ratio of total longitudinal reinforcement area to gross concrete section area Ast/(bh) ρmax = maximum ratio of longitudinal flexural tension reinforcement ρmin = minimum ratio of longitudinal flexural tension reinforcement ρs = ratio of volume of spiral reinforcement to core volume confined by spiral reinforcement (measured out-to-out) ρt = ratio of horizontal shear reinforcement area to gross concrete area of vertical section ρvw = ratio of vertical reinforcement in reinforced concrete walls ∑Mc= sum of nominal flexural strengths (Mn) of columns framing into joint, lb·in. (N∙m) ∑Mg= sum of nominal flexural strengths (Mn) of girders framing into joint, lb·in. (N∙m) ∑Pu = sum of factored concentrated loads within span, lb (kN) ∑Ru = sum of factored reactions from supported structural members at same story, lb (kN) 2.2—Definitions ACI provides a comprehensive list of definitions through an online resource, “ACI Concrete Terminology,” https:// www.concrete.org/store/productdetail.aspx?ItemID=CT13. Definitions provided herein complement that resource. admixture—material other than water, aggregate, or hydraulic cement, used as an ingredient of concrete and added to concrete before or during its mixing to modify its properties. aggregate—granular material, such as sand, gravel, crushed stone, and iron blast-furnace slag, used with a cementing medium to form a hydraulic cement concrete or mortar.American Concrete Institute – Copyrighted © Material – www.concrete.org GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) 11 allowable bearing capacity—maximum pressure to which a soil or other material should be subjected to guard against shear failure or excessive settlement. anchorage—device embedded in concrete for the purpose of providing a connection to another member or structure. base of structure—level at which the horizontal earthquake ground motions are assumed to be imparted to a building; this level does not necessarily coincide with the ground level. beam—structural member subjected to axial load and flexure but primarily to flexure. See also girder. bending moment—bending effect at any section of a structural element; it is equal to the algebraic sum of the moments of the internal compression and tension forces acting at the section, with respect to the centroidal axis of a member, on a free body of the member. boulders—coarse materials more than 8 in. (200 mm) in diameter. boundary element—portion along wall edges strengthened by longitudinal and transverse reinforcement. Boundary elements do not necessarily require an increase in thickness of the wall. cement—any of a number of materials that are capable of binding aggregate particles together. clay—natural mineral material having plastic properties and composed of very fine particles; the clay mineral fraction of a soil is usually considered to be the portion consisting of particles finer than 8 × 10–5 in. (2 μm); clay minerals are essentially hydrous aluminum silicates or occasionally hydrous magnesium silicates. coarse-grained soil—soil in which the larger grain sizes, such as sand and gravel, predominate. column—member with a ratio of height-to-least lateral dimension exceeding 3 used primarily to support axial compressive load. collector element—element that acts in axial tension or compression to transmit earthquake-induced loads between a structural diaphragm and a vertical element of the seismicforce-resisting system. combined footing—structural unit or assembly of units supporting more than one column. compression flange—the widened portion of an I, T, or similar cross section that is shortened or compressed by bending under normal loads, such as the horizontal portion of the cross section of a simple span T-beam. compression reinforcement—reinforcement designed to carry compressive stresses. concrete—mixture of portland cement and any other hydraulic cement, fine aggregate, coarse aggregate, and water, with or without admixtures. concrete cover—least distance between the surface of embedded reinforcement and the closest outer surface of the concrete. concrete mixture proportioning—proportions of ingredients that make the most economical use of available materials to produce mortar or concrete of the required properties. confinement stirrup or tie—see also hoop. construction documents—written, graphic, electronic, and pictorial documents describing the design, locations, and physical characteristics of the project required to verify compliance with the standard. contraction joint—formed, sawed, or tooled groove in a concrete structure to create a weakened plane and regulate the location of cracking resulting from the dimensional change of different parts of the structure. corrosion—destruction of metal by a chemical, electrochemical, or electrolytic reaction within its environment. crosstie—continuous reinforcing bar having a seismic hook at one end and a hook not less than 90 degrees with at least a six-diameter extension at the other end; the hooks shall engage peripheral longitudinal bars; the 90-degree hooks of two successive crossties engaging the same longitudinal bars shall be alternated end for end. curing—action taken to maintain moisture and temperature conditions in a freshly placed cementitious mixture to allow hydraulic cement hydration and (if applicable) pozzolanic reactions to occur so that the potential properties of the mixture may develop. curtain wall—walls that are part of the façade or enclosure of the building that do not form part of the gravity- or lateral-load-resisting system. deformed reinforcement—metal bars, wire, or fabric with a manufactured pattern of surface ridges that provide a locking anchorage with surrounding concrete (deformed reinforcement includes deformed reinforcing bars, welded plain wire fabric, and welded deformed wire fabric conforming to the appropriate ASTM standards). depth of member, h—distance in a flexural member, measured from extreme compression fiber to the extreme tension fiber. design strength—nominal strength multiplied by a strength reduction factor ϕ. development length—length of embedded reinforcement required to develop the design strength of reinforcement at a critical section. development length for a bar with a standard hook— shortest distance between the critical section (where the strength of the bar is to be developed) and a tangent to the outer edge of the 90- or 180-degree hook. diaphragm—structural member, such as a floor or roof slab, that transmits loads acting in the plane of the member to the vertical elements of the seismic-force-resisting system. differential settlement—lowering in elevation of various parts of a foundation by different amounts. effective depth of section, d—distance measured from extreme compression fiber to centroid of tension reinforcement. embedment length—length of embedded reinforcement provided beyond a critical section. factored load—load, multiplied by appropriate load factors, used to proportion members by the strength design method of this guide. fine-grained soil—soil in which the smaller grain sizes predominate, such as fine sand, silt, and clay.American Concrete Institute – Copyrighted © Material – www.concrete.org 12 GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) fire resistance—property of a material or assembly to withstand fire or give protection from it; as applied to elements of buildings, it is characterized by the ability to confine a fire or, when exposed to fire, to continue to perform a given structural function, or both. flexural reinforcement—reinforcement provided to resist the tension and compression stresses induced by flexural moments acting on the member section. floor system—structural members that comprise the floor of a story in a building, including girders, beams, joists, and the slab that spans between them, or the slab only where it is directly supported on columns, as in slab-column systems. footing—structural element of a foundation that transmits loads directly to the soil. formwork—total system of support for freshly placed concrete, including the mold or sheathing in contact with the concrete as well as supporting members, hardware, and necessary bracing. foundation—system of structural elements that transmit loads from the structure above to the earth. foundation beam (grade beam)—reinforced concrete beam, usually at ground level, that strengthens or stiffens the foundation or supports overlying construction. girder—large beam, usually horizontal, that serves as a main structural member often supporting reactions from other beams or girders. See also beam. gravel— 1. Granular material predominantly retained on the No. 4 (4.75 mm) sieve and resulting either from natural disintegration and abrasion of rock or processing of weakly bound conglomerate; and 2. That portion of an aggregate retained on the No. 4 (4.75 mm) sieve resulting either from natural disintegration and abrasion of rock or processing of weakly bound conglomerate. gravity loads—loads that act downward and are caused by the acceleration of gravity acting on the mass of the elements and content that cause the dead and live loads. hook—bend in the end of a reinforcing bar. hoop—closed tie or continuously wound tie; a closed tie can be made up of several reinforcement elements each having seismic hooks at both ends, and a continuously wound tie shall have a seismic hook at both ends. isolation joint—separation between adjoining parts of a concrete structure, usually a vertical plane, at a designed location such as to interfere least with performance of the structure, yet such as to allow relative movement in three directions and avoid formation of cracks elsewhere in the concrete and through which all or part of the bonded reinforcement is interrupted. joist—comparatively narrow beam used in closely spaced parallel arrangements to support floor or roof slabs. lap splice—connection of reinforcing steel made by lapping the ends of bars. lateral-force-resisting system—portion of the structure composed of members proportioned to resist loads related to lateral loads. lateral seismic load—lateral load corresponding to the appropriate distribution of the base shear force for seismicresistant design. licensed design professional—individual who is licensed to practice structural design as defined by the statutory requirements of the professional licensing laws of the state or jurisdiction in which the project is to be constructed and who is in responsible charge of the structural design. lightweight aggregate—aggregate meeting the requirements of ASTM C330/C330M and having a loose bulk density of 70 lb/ft3 (1120 kg/m3) or less, determined in accordance with ASTM C29/C29M (concrete manufactured using lightweight aggregate is not covered by this guide). lightweight concrete—concrete containing lightweight aggregate and an equilibrium density, as determined by ASTM C567/C567M, between 90 and 115 lb/ft3 (1440 to 1840 kg/m3) (this type of concrete is not covered by this guide). limit state—condition beyond which a structure or member becomes unfit for service and is judged either to be no longer useful for its intended function (serviceability limit state) or to be unsafe (strength limit state). live load—live load specified by general building code (without load factor). load—loads or other actions that result from the weight of all building materials, occupants and other variable or permanent contents, environmental effects, differential movement, and restrained dimensional changes. Permanent loads are those loads in which variations over time are rare or of small magnitude. All other loads are variable loads. load combinations—combinations of factored loads and loads. load effects—loads and deformations produced in structural members by the applied loads. load factor—factor by which a service load is multiplied to determine a factored load used in the strength design method. longitudinal reinforcement—reinforcement parallel to the length of a concrete member. mat foundation—continuous footing supporting an array of columns in several rows in each direction, having a slablike shape with or without depressions or openings. modulus of elasticity—ratio of normal stress to corresponding strain for tensile or compressive stresses below proportional limit of material. negative moment—condition of flexure in which top fibers of a horizontally placed member, or external fibers of a vertically placed exterior member, are subjected to tensile stresses. negative reinforcement—steel reinforcement for negative moment. nominal bar diameter—value computed using the nominal bar area. nominal strength—strength of a member or cross section calculated in accordance with provisions and assumptions of the strength design method of this guide before application of any strength reduction factors.American Concrete Institute – Copyrighted © Material – www.concrete.org GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) 13 nonstructural elements—architectural, mechanical, and electrical components and systems permanently attached to the building. occupancy—purpose for which a building or other structure, or part thereof, is used or intended to be used. partitions—nonstructural interior wall that spans horizontally or vertically from support to support; supports may be the basic building frame, subsidiary structural members, or other portions of the partition system. pedestal—upright compression member with a ratio of unsupported height to average least lateral dimension not exceeding 3. permanent load—load in which variations over time are rare or of small magnitude. pile—structural element that is driven, jetted, or otherwise embedded on end in the ground to resist loads or compact the soil. pile cap—concrete element that transfers load from a column or pedestal to the top of one or more supporting piles. plain concrete—structural concrete with no reinforcement or with less reinforcement than the minimum amount specified for reinforced concrete (plain concrete is not covered by this guide). plain reinforcement—reinforcement without surface deformations, or having deformations that do not conform to the applicable requirements. positive moment—condition of flexure in which, for a horizontal simply supported member, the deflected shape is normally considered to be concave downward and the top fibers subjected to compression stresses; for other members and other conditions, consider positive and negative as relative terms. positive reinforcement—steel reinforcement to resist positive bending moment. precast concrete—structural concrete element cast elsewhere than its final position in the structure (precast concrete is not covered by the guide, except as described in 1.5.3). prestressed concrete—structural concrete in which internal stresses have been introduced to reduce potential tensile stresses in concrete resulting from loads (prestressed concrete is not covered by the guide, except as described in 1.5.3). project drawings—drawings that, along with the project specifications, complete the descriptive information for constructing the work required in the construction documents. project specifications—written documents that specify requirements for a project in accordance with the service parameters and other specific criteria established by the owner. reinforced concrete—structural concrete reinforced with no less than the minimum amounts of reinforcement. reinforced concrete wall—structural concrete wall reinforced with no less than the minimum amount of prestressing steel or nonprestressed reinforcement as specified in the applicable building code; a shear wall is a reinforced concrete wall. reinforcement—deformed steel bars, wire, or wire mesh, embedded in concrete in such a manner that it and the concrete act together in resisting loads. reshores—shores placed snugly under a concrete slab or other structural member after the original forms and shores have been removed to allow the new slab or structural member to deflect and support its own weight. required strength—strength of a member or cross section required to resist factored loads or related internal moments and loads in specified load combinations. retaining wall—wall built to hold back earth. sand— 1. Granular material passing the 3/8 in. (9.5 mm) sieve and almost entirely passing the No. 4 (4.75 mm) sieve and predominantly retained on the No. 200 (75 μm) sieve, and resulting either from natural disintegration and abrasion of rock or processing of completely friable sandstone; and 2. That portion of an aggregate passing the No. 4 (4.75 mm) sieve and predominantly retained on the No. 200 (75 μm) sieve, and resulting either from natural disintegration and abrasion of rock or processing of completely friable sandstone. seismic hook—hook on a stirrup, or crosstie having a bend not less than 135 degrees, except that circular hoops shall have a bend not less than 90 degrees; hooks shall have a 6db (but not less than 3 in. [75 mm]) extension that engages the longitudinal reinforcement and projects into the interior of the stirrup or hoop. self-weight—weight of the structural member, caused by the material that composes the member. service load—all loads, static or transitory, imposed on a structure, or element thereof, during operation of a facility (without load factors). settlement—downward movement of the supporting soil. shear—internal force tangential to the plane on which it acts. shear reinforcement—reinforcement designed to resist shear or diagonal tension stresses. shore—vertical or inclined support member designed to carry the weight of the formwork, concrete, and construction loads above. shrinkage and temperature reinforcement—reinforcement provided to resist shrinkage and temperature stresses in concrete. silt—granular material resulting from the disintegration of rock, with grains largely passing a No. 200 (75 μm) sieve; alternatively, such particles in the range from 8 × 10–5 to 0.002 in. (2 to 50 μm) diameter. slab—molded layer of reinforced concrete, flat, horizontal (or nearly so), usually of uniform but sometimes of variable thickness, either on the ground or supported by beams, columns, walls, or other framework. slab-on-ground—shallow foundation consisting of a continuous concrete slab, placed over native soil or engineered subgrade, where loads are locally distributed and transmitted to the ground. soil—generic term for unconsolidated natural surface material above bedrock.American Concrete Institute – Copyrighted © Material – www.concrete.org 14 GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) soil-bearing capacity—maximum stress under a foundation that provides adequate safety against soil failure and against excessive soil settlement. solid slab—slab of uniform thickness. span length—horizontal distance between supports of a horizontal structural member such as a slab, joist, beam, or girder, measured center to center of support. specifications—written document describing in detail the scope of work, materials to be used, method of installation, and quality of workmanship. specified compressive strength of concrete—compressive cylinder strength of concrete at 28 days used in design and evaluated in accordance with the appropriate ASTM standards, expressed in psi (MPa); whenever the quantity fc′ is under a radical sign (√fc′), square root of numerical value only is intended, and the result maintains the units as psi (MPa). spread footing—generally rectangular prism of concrete, larger in lateral dimensions than the column or wall it supports, to distribute the load of a column or wall to the subgrade. spiral reinforcement—continuously wound reinforcement in the form of a cylindrical helix. stirrup—reinforcement used to resist shear and torsion stresses in a structural member; typically bars, wires, or welded wire fabric (plain or deformed) either single leg or bent into L, U, or rectangular shapes and located perpendicular to or at an angle to longitudinal reinforcement; usually applied to lateral reinforcement in beams and girders, ties usually refers to those in columns. story height—vertical distance from the floor finish of a story to the floor finish of the story below. strength design method—method of member proportioning based on ensuring that the design strength obtained by reducing the nominal strength is larger than the required strength obtained by applying load factors to service loads. strength reduction factor ϕ—capacity reduction factor in structural design; a number less than 1.0 by which the nominal strength of a structural member or element in terms of load, moment, shear, or stress is required to be multiplied to determine design strength or capacity. stress—intensity of force per unit area. structural concrete—all concrete used for structural purposes, including prestressed and reinforced concrete, and, under special circumstances, plain concrete. structural integrity—design concept that after an overload event or after damage occurs to a major supporting member, the structure has sufficient toughness to confine the damage to a local area and sufficient overall stability to prevent immediate collapse. tank—container for the storage of water or other fluids (this guide only covers tanks used for storage of potable water in locations where the water supply system is unreliable). tension reinforcement—reinforcement designed to carry tensile stresses such as those in the bottom of a simple beam. tie—loop of reinforcing bar or wire enclosing longitudinal reinforcement; a continuously wound bar or wire in the form of a circle, rectangle, or other polygon shape without reentrant corners is acceptable. tie elements—elements that serve to transmit inertia loads and prevent separation of building components such as footings and walls. transverse reinforcement—reinforcement located perpendicular to the longitudinal axis of the member, comprising stirrups, ties, and spiral reinforcement. wall—member, usually vertical, used to enclose or separate spaces. See also reinforced concrete wall. web—thin vertical portion of an I-shaped section that connects the flanges. wind load—nominal pressure of wind to be used in design. wire—reinforcing bar of small diameter. wire mesh—welded wire reinforcement. work—entire construction, or separately identifiable parts thereof, that are required to be furnished under the construction documents. working stress—maximum permissible design stress using working-stress design methods. yield strength fy—specified minimum yield strength or yield point of reinforcement; yield strength or yield point should be determined in tension according to applicable ASTM standards. CHAPTER 3—STRUCTURAL SYSTEM LAYOUT 3.1—Description of structural components The building structure should be divided into components as described by 3.1.1 through 3.1.5. 3.1.1 Floor system—The floor system consists of structural members that comprise the floor of a story in a building. Chapter 6 describes different types of floor systems. The floor system can include girders, beams, joists, and the slab that spans between them or the slab only, where it is directly supported by columns, as in slab-column systems. 3.1.2 Vertical supporting members—Support the floor system at each story and carry accumulated gravity loads down to the foundation of the structure. Vertical supporting members should be either columns or reinforced concrete walls. 3.1.3 Foundation—Comprises structural elements through which the load of a structure is transmitted to the earth. It includes members such as spread footings, combined footings, foundation mats, basement and retaining walls, and grade beams. Foundation members are described in Chapter 14. Deep foundations, such as piles, caissons, pile footings, and caps, are beyond the scope of the guide. 3.1.4 Lateral-force-resisting system—Comprises the structural members that, acting jointly, resist and transmit to the ground the lateral loads arising from seismic motions, wind, and lateral earth pressure. The floor system acts as a diaphragm that carries in its plane the lateral force from the application point to the vertical members of the lateralforce-resisting system. Vertical members of the lateralforce-resisting system, in turn, collect the loads arising from all floors and transmit them down to the foundation and through the foundation to the underlying soil. For areas with moderate or high seismic risk, the main vertical membersAmerican Concrete Institute – Copyrighted © Material – www.concrete.org GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) 15 of the lateral-force-resisting system should be reinforced concrete walls. 3.1.5 Other structural members—Other parts of the building structure that are covered in this guide are stairways, ramps, small potable water tanks, and slabs-on-ground. 3.2—General 3.2.1 Architectural program—A general architectural program of the building should be coordinated with the licensed design professional before the structural design begins. The general architectural program should include the following items as a minimum: a) Plan geometry and dimensions of all building floors b) Building elevation and the terrain, including the basement, if any c) Type of roof, its shape and slopes, the type of waterproofing, the means to facilitate the runoff of water from rain and melting snow or hail, and the location of drainage gutters d) Use of internal spaces of the building, its subdivision, and means of separation, in all stories e) Minimum architectural clear height in all floors f) Location and dimensions of stairways, ramps, and elevators g) Type of building enclosure, internal partitions, and architectural and nonstructural elements h) Locations of ducts and shafts for utilities such as power supply, lighting, thermal control, ventilation, water supply, and wastewater, including enough information to detect interference with the structural members i) Architectural features that may reduce effective concrete cover of reinforcement 3.2.2 Structural program—Based on the general architectural program information, the licensed design professional should define the general structural program for the building being designed. The general structural program includes the following items as a minimum: a) Intended use of the building b) Nominal loads related to the use of the building c) Special loads defined by the owner d) Design seismic loads, if the building is located in a seismic zone e) Wind loads appropriate for the site f) Loads from snow, hail, or rain g) Fire rating h) Type of roof and associated loads when not built of reinforced concrete i) Site information related to slopes and site drainage j) Allowable soil-bearing capacity and recommended foundation system derived from the geotechnical investigation and additional restrictions related to expected settlement k) Environmental conditions derived from local seasonal and daily temperature variations, humidity, presence of deleterious chemicals, and salts l) Availability, type, and quality of materials such as reinforcing bars, cement, and aggregates m) Availability of formwork materials n) Availability of a testing lab for concrete mixture proportioning and quality control during construction o) Availability of qualified work force p) General and local sustainable construction practices 3.3—Structural layout 3.3.1 General structural layout—The licensed design professional should define a general structural layout in plan, including all information common to all structure levels of the structure (Fig. 3.3.1). The general structural layout in plan should include: a) A dimensioned axis grid, or centerlines, in both principal directions in plan, located at the intersection of the vertical supporting members (columns and reinforced concrete walls) b) Location in plan of all vertical supporting members, columns, and reinforced concrete walls. These vertical supporting members should be aligned vertically and be continuous to the foundation. Reinforced concrete walls are permitted if they are continuous to the foundation and have no openings for windows or doors. c) Location of all ducts, shafts, elevators, and stairways that are continuous from floor to floor d) Horizontal distance between centerlines, ℓs, which corresponds to the center-to-center span lengths of the floor system e) Location and distribution of all reinforced concrete walls 3.3.2 Floor layout—For each floor, the licensed design professional should develop a structural floor layout (Fig. 3.3.2). The structural floor layout includes: a) Location of the floor perimeter on the general axis grid b) Girder and beam locations, or column and middle strips for slab-column systems c) All substantial architectural openings in the floor d) An approximate load path from all floor areas to the supporting beams and girders 3.3.3 Vertical layout—The licensed design professional should define a general structural layout in elevation. (Fig. 1.3.10). The general structural layout in elevation includes: a) Number of stories Fig. 3.3.1—General structural layout in plan.American Concrete Institute – Copyrighted © Material – www.concrete.org 16 GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) b) Story height for each floor, defined as the vertical distance from floor finish to floor finish c) Slope and shape of the roof d) Architectural clearance from floor finish to ceiling for each floor e) Space necessary to accommodate power distribution, water supply and drainage, and heating, ventilation, and air conditioning f) Slope of the terrain and its relationship to the ground floor or basement g) Supporting soil stratum depth and water-table depth 3.4—Feasibility of guide usage If any of the conditions stated in Chapter 3 are not met, the structural design should be performed using ACI 318, ASCE 7, and the International Building Code (International Code Council 2015). CHAPTER 4—LOADS 4.1—General The load information in this chapter is based on the requirements of the model code (International Building Code [International Code Council 2015]) and the reference standard (ASCE 7). In jurisdictions where the local governing authority has adopted other standards, they should be used rather than the load information in this chapter. 4.2—Load factors and load combinations The largest required factored strength U, as defined in 1.7.1, for the structural member should be determined by using load factors and load combinations of this section. The following apply: a) Each relevant strength limit state should be investigated, including effects of one or more loads not acting simultaneously. b) In load combinations where the symbol “±” is used in factoring alternating loads that act in one direction or the opposite, it should be interpreted as the sign that leads to the maximum (positive) or minimum (negative) value of U. c) The most unfavorable effects from both wind and seismic loads should be investigated, but they need not be considered to act simultaneously. 4.2.1 Dead and live load—Required factored strength U to resist dead load D and live load L should be the greater of U = 1.4D (4.2.1a) U = 1.2D + 1.6L (4.2.1b) 4.2.2 Rain load, snow load, and sloping roof live load— Required factored strength U to resist rain load R, snow load S, or sloping roof live load Lr should be evaluated based on the following load combinations U = 1.2D + 1.6L + 0.5(R or S or Lr) (4.2.2a) U = 1.2D + 1.0L + 1.6(R or S or Lr) (4.2.2b) 4.2.3 Wind loads—Required factored strength U to resist wind loads W should be evaluated based on the following load combinations U = 1.2D + 1.0L ± 1.0W + 0.5(R or S or Lr) (4.2.3a) U = 1.2D ± 0.5W + 1.6(R or S or Lr) (4.2.3b) U = 0.9D ± 1.0W (4.2.3c) Note: In ASCE 7-10, wind forces are defined at strength level. In previous versions of ASCE 7, wind forces w -- - - - -- - - - - - - - - - - - - - - - - - - - - - -- A note on employment of inch-pound units: Computed moments generally are in units of lb·ft because they are determined from concentrated loads in lb, distributed loads in lb/ft, and spans in ft. They should be converted to lb·in (12 lb·in. = 1·lb·ft), for use with fy in psi, d and b in inches, and As in in.2 A note on employment of SI units: The computed moments generally are in units of kN·m because they are determined from concentrated loads in kN, distributed loads in kN/m, and spans in m. They should be converted to N·mm (1 kN·m = 106 × N·mm), for use with fy in MPa (1 MPa = 1 N/mm2), d and b in mm, and As in mm2. 8.4.9 Compression reinforcement in girders, beams, and joists 8.4.9.1 Tension reinforcement less than maximum—For moment strength calculations, compression reinforcement is not necessary when the tension reinforcement ratio ρ is less than ρmax. 8.4.9.2 Shallow doubly reinforced sections—For moment strength calculations, compression reinforcement is not necessary when the value of ratio d/d′ is less than the values given in Table 8.4.9.2. 8.4.9.3 Design moment strength with compression reinforcement—For moment strength calculations with compression reinforcement, use Eq. (8.4.9.3) (Fig. 8.4.9.3) ϕMn = ϕ[0.85(As – As′)fyd + As′fy(d – d′)] (8.4.9.3) where ϕ = 0.90. Equation (8.4.9.3) assumes the compression reinforcement yields, which should be verified. 8.4.9.4 Flexural tension and compression reinforcement area—The area of flexural tension reinforcement, As, and compression reinforcement, As′, should be computed using Mu as follows ( ) ( ) 0.85 2 u max s y M bd A f d d d d ρ ′ = − φ − − ′ ′ (8.4.9.4a) A s + As′ + ρmaxbd (8.4.9.4b) The ratio ρmax should be determined from 8.4.6 when the minimum d/d′ is met. After reinforcing bars are selected, ρmax, as given in Eq. (8.4.6b), should be checked. 8.4.9.5 Transverse reinforcement where flexural compression reinforcement is present—Longitudinal flexural compression reinforcement should be enclosed by ties or stirrups satisfying the size and spacing limitations of column ties in 10.4.3.2. Such ties or stirrups should be provided throughout the distance where compression reinforcement is needed. 8.4.10 T-beam effect—Where a beam is monolithic with a slab and a moment induces compression in the slab, the slab may be assumed to act as a beam flange, and the design should comply with 8.4.10.1 to 8.4.10.5. 8.4.10.1 Effective flange width for beams with slab on both sides—The effective flange width b should not exceed the least of (a), (b), and (c) (Fig. 8.4.10.1): (a) One-fourth the beam span length (b) Sixteen times the slab thickness hf plus the web thickness bw (c) The clear distance between webs plus the web thickness bw 8.4.10.2 Effective flange width for beams with slab on one side only—The effective flange width b should not exceed the least of (a), (b), and (c) (Fig. 8.4.10.2): (a) One-twelfth the beam span length plus the web thickness bw Fig. 8.4.6—Section with tension and compression reinforcement. Table 8.4.9.2—Minimum values of d/d′ for compression reinforcement to be effective fy, psi (MPa) 40,000 (280) 60,000 (420) d/d′ ≥ 4 7 Fig. 8.4.8.2—Design dimensions for moment strength: tension reinforcement only. Fig. 8.4.9.3—Design dimensions for moment strength: sections with compression reinforcement.American Concrete Institute – Copyrighted © Material – www.concrete.org GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) 63 (b) Six times the flange thickness hf plus the web thickness bw (c) One-half the clear distance to the next web plus the web thickness bw 8.4.10.3 Isolated T-beams—Flange thickness hf in isolated T-beams should be at least one-half of the web thickness bw, and the effective flange width b should not exceed the smaller of 4bw and bf (Fig. 8.4.10.3). 8.4.10.4 Design moment strength of T-beams—The design moment strength should be calculated using 8.4.8 for sections where the flange is in compression (Fig. 8.4.10.4), and the depth of the equivalent uniform stress block a lies within the flange thickness hf, as computed by Eq. (8.4.10.4). and 0.85 s y f c A f h a a f b ≥ = ′ (8.4.10.4) 8.4.10.5 Flexural tension reinforcement ratio—When the value ρ given by Eq. (8.4.10.5) is not exceeded, the flexural tension reinforcement ratio, ρ = As/(bd) for T-beams, should be computed using As from Eq. (8.4.8.2). 0.85 c f y f h f d ′ ρ ≤ (8.4.10.5) Where the value of ρ is smaller than ρmin from 8.4.5, As should be increased. Where the value of ρ is greater than ρmax from 8.4.6, member dimensions should be increased, correcting the self-weight. 8.4.11 Reinforcement in T-beam flanges—The minimum T-beam flange reinforcement of 8.4.11.1 and 8.4.11.2 should apply to girders and beams but not to joist construction. Flange reinforcement should not be less than needed by the slab system. 8.4.11.1 Distribution of negative moment reinforcement— Where T-beam flanges are in tension, negative moment beam reinforcement should be distributed over a width equal to the smaller of the effective flange width as defined in 8.4.10, or 1/10 of the beam span. The portion of the effective flange width that exceeds 1/10 of the beam span should have a minimum of shrinkage and temperature reinforcement (7.3.3) in the beam direction. Refer to Fig. 8.4.11.1. The restrictions of 8.4.3 should not apply to this item. 8.4.11.2 Transverse flange reinforcement—In the slab, reinforcement perpendicular to the beam should resist a factored negative moment computed assuming the flange width acts as a cantilever supported by the beam (Fig. 8.4.11.1) and, for isolated T-beams, the full width of the overhanging flange. This reinforcement should also comply with 7.3.6. 8.4.12 Skin reinforcement—Where the height h of a girder, beam, or joist exceeds 36 in. (900 mm), longitudinal skin reinforcement should be provided along both side faces of the member for a vertical distance equal to h/2 nearest the flexural tension reinforcement. Vertical spacing ssk between bars should not exceed the least value of Eq. (8.4.12), d/6, and 12 in. (300 mm) (Fig. 8.4.12). 900,000 720,000 2.5 159,600 126,000 2.5 (SI) sk c y y sk c y y s c f f s c f f = − ≤     = − ≤     (8.4.12) 8.4.13 Value of dc and d to use in girders, beams, and joists—Calculation of dc, the distance from extreme tension fiber to centroid of tension reinforcement, should consider concrete cover from 5.4, bar diameters, and reinforcement layers. The following values of dc can be used to compute d as d = h – dc for cases where only one reinforcement layer is used. For girders and beams, dc = 2.4 in. (60 mm) for interior Fig. 8.4.10.1—Effective flange width for T-beams with slab on both sides. Fig. 8.4.10.2—Effective flange width for T-beams with slab on one side only. Fig. 8.4.10.3—Effective flange width for isolated T-beams. Fig. 8.4.10.4—Effective cross section for moment strength calculation of T-beams.American Concrete Institute – Copyrighted © Material – www.concrete.org 64 GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) exposure, and dc = 2.8 in. (70 mm) for exterior exposure. For joists, dc = 2 in. (50 mm) for interior exposure, and dc = 2.4 in. (60 mm) for exterior exposure. 8.4.14 Positive moment reinforcement 8.4.14.1 Description—Positive moment reinforcement should be provided in the girder, beam, or joist section, as indicated in Chapter 8, and should comply with 8.4 and the particular limitations for each member type in 8.6 or 8.7. 8.4.14.2 Location—Positive moment reinforcement should be placed longitudinally in the girder, beam, or joist. Positive moment reinforcement should be located as close to the bottom surface of the girder, beams, or joist as practicable following the concrete cover of 5.4. Where girders, beams, or joists support other girders, beams, or joists, the positive moment reinforcement of the supported member should be placed above the positive moment reinforcement of the supporting member. 8.4.14.3 Cutoff amount—No more than one-half the positive moment reinforcement at midspan may be cut off at the locations indicated in 8.6.5 or 8.7.5. 8.4.14.4 Reinforcement splicing—The remaining positive moment reinforcement from 8.4.14.3 may be lap spliced between the cutoff point and the opposite face of the support. 8.4.14.5 Embedment at interior supports—Positive moment reinforcement terminated at an interior support should be continued to the opposite face of the support plus the lap-splice distance of 5.8.2. 8.4.14.6 End anchorage of reinforcement—At the end of the girder, beam, or joist, the positive moment reinforcement should extend to the edge and end in a standard hook. 8.4.15 Negative moment reinforcement 8.4.15.1 Description—Negative moment reinforcement should be provided in the girder, beam, or joist section and at edges and supports as indicated in Chapter 8, and should comply with 8.4 and the particular provisions of 8.6 or 8.7. 8.4.15.2 Location—Negative moment reinforcement should be provided at all supports and located as close to the upper surface of the girder, beam, or joist as practicable following concrete cover of 5.4. At supports where girders or beams intersect, the negative moment reinforcement of the member with the longer span should be located on top. 8.4.15.3 Cutoff amount—Negative moment reinforcement at the locations indicated in 8.6.5 or 8.7.5 may be cut off, except cantilever negative moment reinforcement is not allowed to be cut off. Where adjacent spans are unequal, negative moment reinforcement cutoff points should be based on the longer span. 8.4.15.4 Reinforcement splicing—Negative moment reinforcement between cutoff point and the support should not be lap spliced. 8.4.15.5 End anchorage—Negative moment reinforcement at the end of a girder, beam, or joist should end in a standard hook at the far edge of the supporting girder, beam, column, or reinforced concrete wall, complying with anchorage distance described by 5.8.3. At the external edge of cantilevers, negative moment reinforcement should end in a standard hook. 8.4.15.6 Stirrup support—In areas where no negative reinforcement is needed, top bars should be provided for attachment and anchorage of stirrups. The diameter of these top bars should be equal to or greater than the stirrup bar diameter. Minimum lap length of these top bars should be 6 in. (150 mm). 8.5—Transverse reinforcement 8.5.1 Description—Transverse reinforcement for girders, beams, and joists should consist of stirrups that enclose the longitudinal reinforcement and are placed perpendicular to the longitudinal axis of the member at varying intervals. The main functions for transverse reinforcement in girders, beams, and joists are: (a) Contribute to member shear strength (b) Provide lateral support for longitudinal reinforcement subjected to compression stresses (c) Act as hanger reinforcement in girders, supporting beams and joists (d) Contribute to member torsion strength (e) Provide confinement to the concrete in seismic zones at selected locations within the member 8.5.2 Stirrup shape—A stirrup should consist of single or multiple vertical legs. Each vertical leg should engage Fig. 8.4.11.1—Reinforcement in T-beam flanges. Fig. 8.4.12—Skin reinforcement for girders, beams, and joists with h > 36 in. (900 mm).American Concrete Institute – Copyrighted © Material – www.concrete.org GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) 65 a longitudinal bar either by bending around it when the stirrup continues or by using a standard stirrup hook (5.6) to surround the longitudinal bar at the stirrup end (Fig. 8.5.2a and 8.5.2b). 8.5.2.1 Permitted stirrup shape for girders and beams— All stirrups in girders and beams should be closed stirrups with 135-degree hooks, as shown in Fig. 8.5.2a(a). The other stirrup shapes are in common use but are shown to clarify that they are not to be used with this guide. In seismic areas, the stirrup shape is further limited. 8.5.2.2 Permitted stirrup shape for joists—All stirrup types shown in Fig. 8.5.2a and 8.5.2b may be used in joists. 8.5.2.3 Minimum clear spacing between stirrups legs—In girders, beams, and joists, the minimum clear space between stirrups or parallel legs in a stirrup should be 1 in. (25 mm). 8.5.2.4 Stirrup support—Stirrups should be attached to longitudinal bars so that stirrups do not displace during concrete placement (8.4.15.6). 8.5.2.5 Stirrup leg splicing—Stirrup bars should not be lap spliced. 8.5.3 Location of transverse reinforcement—Stirrup spacing intervals s should comply with 8.5.4.5 (Fig. 8.5.3). 8.5.4 Contribution of transverse reinforcement to shear strength 8.5.4.1 General—Beam-action shear accompanies flexural moments and occurs in girders, beams, and joists along their length, and is of greater magnitude in the vicinity of supports and concentrated loads. 8.5.4.2 Design shear strength—Design shear strength ϕVn of a girder, beam, or joist section should be computed following the procedure in 5.13.4 for beam-action shear as ϕVn = ϕ(Vc + Vs) (8.5.4.2) where ϕVc is the concrete contribution to the design shear strength; ϕVs is the shear reinforcement contribution to the design shear strength; and ϕ = 0.75. 8.5.4.3 Contribution of concrete to shear strength—At each location to be investigated (Fig. 8.5.4.3), the concrete contribution of the web of the girder, beam, or joist should be taken into account (Fig. 8.5.3) and should be computed using Eq. (8.5.4.3), with ϕ = 0.75. 2 0.17 (SI) c c w c c w V f b d V f b d φ = φ ′     φ = φ ′ (8.5.4.3) 8.5.4.4 Contribution of transverse reinforcement to shear strength—For reinforcement perpendicular to the member axis, its contribution to design shear strength should be v yt s A f d V s φ = φ (8.5.4.4a) where Av is the area of shear reinforcement perpendicular to the member axis (the stirrup bar area Ab multiplied by the number of vertical stirrup legs) within a distance s; fyt is the yield strength of the shear reinforcement steel; and ϕ = 0.75. Reinforcement contribution to the design shear strength should not be taken greater than 8 4 0.66 4 (SI) s c w c s c w c V f b d V V f b d V φ ≤ φ = φ ′     φ ≤ φ = φ ′ (8.5.4.4b) 8.5.4.5 Design of shear reinforcement—Shear reinforcement in girders, beams, and joists should be provided using stirrups perpendicular to the member axis with a maximum spacing s, measured along member axis: (a) Where the factored shear Vu is less than ϕVc/2, the use of shear reinforcement may be waived. (b) Where Vu exceeds ϕVc/2 and is less than ϕVc, a minimum area of shear reinforcement should be provided as specified by Eq. (8.5.4.5). The spacing s along the member axis should not exceed the smaller of d/2 and 24 in. (600 mm) (Fig. 8.5.4.5). 0.75 0.062 (SI) w v c yt w v c yt b s A f f b s A f f = ′     = ′     (8.5.4.5) where Av is Ab multiplied by the number of stirrup legs. (c) Where Vu exceeds ϕVc, the difference (Vu – ϕVc) should be provided for by shear reinforcement, using Eq. (8.5.4.3) and Eq. (8.5.4.4a), and the limitations (i) through (iv) should apply (Table 8.5.4.5): Fig. 8.5.2a—Typical stirrup shapes for girders and beams. Fig. 8.5.2b—Typical stirrup shape for joists, in addition to Fig. 8.5.2a.American Concrete Institute – Copyrighted © Material – www.concrete.org 66 GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) i. Minimum shear reinforcement area should not be less than that determined using Eq. (8.5.4.5). ii. Where the value of ϕVs, calculated using Eq. (8.5.4.4a), is less than 2ϕVc, the spacing limits of (b) should be used. iii. Where the value of ϕVs, calculated using Eq. (8.5.4.4a), is greater than 2ϕVc, spacing limits should be half the values specified in (b). iv. The value of ϕVs, calculated using Eq. (8.5.4.4a), should not be taken greater than 4ϕVc. 8.5.4.6 Shear diagram—The value of Vu at the support face should be determined in conformance with 8.6 or 8.7. A diagram showing the shear variation within the span should be constructed, with the value of Vu at the left support face taken as positive. The shear from this point proceeding to the right should be decreased at a rate equal to ( ) ( ) u u u left supp. right supp. n     V V P + − ∑  (8.5.4.6) where ∑Pu corresponds to the sum of all factored concentrated loads on the span. At the point where a concentrated load is applied, the value of Pu should be subtracted from the value of shear at the left of the load point. For beams with point loads, proceeding to the right, at the face of the right support, the negative value of Vu is reached (Fig. 8.5.4.6). At all sections within the span, the value of ϕVn, as determined from Eq. (8.5.4.2), should be equal to or greater than the absolute value of Vu(x) as shown in Fig. 8.5.4.6. Limits for ϕVn, as defined in Table 8.5.4.5, should be marked in the shear diagram, and stirrup spacing s should be defined for different regions within the shear diagram. The first stirrup should be placed not further than s/2 from the face of the supporting member, with s being the stirrup spacing at the support. The minimum stirrup spacing should comply with 8.5.2.3. If the computed s is less than 2 in. (50 mm), using stirrups with more vertical legs or a larger bar diameter should be investigated. 8.5.5 Hanger stirrups—Where a beam is supported by a girder of similar depth, hanger reinforcement should be provided in the joint. The reaction from the supported beam tends to push down the bottom of the supporting girder. This reaction should be resisted by hanger reinforcement in the form of closed stirrups placed in both members. Hanger stirrups are in addition to stirrups needed for shear (Fig. 8.5.5) and should comply with 8.5.5.1 and 8.5.5.2. 8.5.5.1 Hanger stirrup area (a) Provide hanger stirrups where Vu from the supported beam at the interface is equal to or greater than φ3 f b d c w ′ [ 0.25 (SI)] φ f b d c w ′ , where ϕ = 0.75. (b) Provide hanger stirrups where hb is equal to or less than one-half the total depth of the supporting girder, where hb is the vertical dimension from the bottom of the supporting girder to the bottom of the supported beam (Fig. 8.5.5). (c) The area of hanger reinforcement, Ai, should be determined from Eq. (8.5.5.1). 1 ( / ) b g u i yt h h V A f     − ≥ φ (8.5.5.1) where Vu is the beam factored shear at the support face; Ai is the total area of hanger stirrups; hg is the girder height; fyt is the stirrup specified yield strength; and ϕ = 0.75. 8.5.5.2 Hanger stirrup placement—At least two-thirds of Ai should be evenly distributed within the supported beam width bw, plus hb at each side. The remaining area of hanger stirrups, not more than one-third of Ai, should be evenly distributed within d/4 from the supporting girder face, where d is the supported beam effective depth. Beam bottom longitudinal bars should be placed above the girder bottom longitudinal bars. 8.6—Joists and beams supported by girders 8.6.1 General—Section 8.6 applies to joists and beams, monolithic with and supported by girders. Two-way joist systems or waffle-on-beams systems, as described in 6.1.3.3, should also comply with 8.6. Waffle-slab systems without beams spanning between columns as described in 6.1.4.5 should be designed using Chapter 9 for slab-column systems. Fig. 8.5.3—Typical stirrup spacing along the girder, beam, or joist. Fig. 8.5.4.3—Contribution of concrete to beam-action shear strength in girders, beams, and joists.American Concrete Institute – Copyrighted © Material – www.concrete.org GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) 67 8.6.2 Dimensional limits 8.6.2.1 Joists—In addition to Chapter 8, joists should comply with the dimensional limits of 1.3 and the restrictions of 6.1.3.1. Ducts, shafts, and openings should comply with 6.8. Minimum depth should comply with 6.5.3 for one-way joists and 6.5.4 for two-way joists. 8.6.2.2 Beams—In addition to Chapter 8, beams supported by girders should comply with the dimensional limits of 1.3 and the restrictions of 6.1.2. Ducts, shafts, and openings should comply with 6.8. Minimum depth should comply with 6.5.3. Beam web width bw should not be less than 8 in. (200 mm). Maximum spacing between lateral supports of isolated beams should be 50 times the least width b of the compression flange. 8.6.2.3 Cantilevers—All cantilevers of joists or beams should be continuous with at least one interior span. A double cantilever without an interior span is not permitted. 8.6.3 Required moment strength 8.6.3.1 Cantilevers—The factored negative moment Mu (required moment strength) for beam and joist cantilevers supported by girders, beams, or reinforced concrete walls should be calculated using Eq. (8.6.3.1), assuming: (a) One-half of the distributed factored load Wu acts as a concentrated load at the cantilever tip along with all concentrated loads that act on the cantilever span ∑Pu. (b) One-half Wu acts as uniformly distributed load over the full span. 3 2 4 u n u n u W M P − = +   ∑ (8.6.3.1) The cantilever-required negative moment strength at the support should equal or exceed the maximum negative factored moment at the first interior support and one-third the positive factored moment of the first interior span. 8.6.3.2 Single-span joists and beams supported by beams, girders, or reinforced concrete walls—Factored positive and negative moment Mu (required moment strength) for Table 8.5.4.5—Shear reinforcement in girders, beams, and joists, maximum spacing s Value of factored required shear strength Vu Limiting value of ϕVs Minimum area of shear reinforcement Av within a distance s Maximum spacing s 2 c u V φ > V — Not needed — 2 c c u V V V φ φ > ≥ — 0.75 0.062 (SI) w v c yt w v c yt b s A f f b s A f f = ′     = ′     2 min. of 24 in. (600 mm) d s  ≤   Vu ≥ ϕVc 2ϕVc > ϕVs ( ) u c v yt V V s A f d − φ = φ /2 min. of 24 in. (600 mm) v yt w v yt /(50 ) [ /(0.35 ) (SI)] w d s A f b A f b  ≤   4ϕVc > ϕVs ≥ 2ϕVc ( ) u c v yt V V s A f d − φ = φ /4 min. of 12 in. (300 mm) A f b A f b v yt w v yt /(50 ) [ /(0.35 ) (SI)] w  ≤   ϕVs ≥ 4ϕVc Not permitted — Fig. 8.5.4.5—Minimum shear reinforcement in girders, beams, and joists when (ϕVc/2 ≤ Vu < ϕVc). Fig. 8.5.4.6—Calculation of the shear diagram of a girder, beam, or joist.American Concrete Institute – Copyrighted © Material – www.concrete.org 68 GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) single-span beams and single-span one-way joists should be calculated using Table 8.6.3.2, where ∑Pu is the sum of all factored concentrated loads that act on the span. 8.6.3.3 Multi-span joists and beams supported by beams, girders, or walls—Factored positive and negative moment Mu (required moment strength) for beams and one-way joists, with two or more spans, supported by beams, girders, or reinforced concrete walls, should be calculated using Table 8.6.3.3, where ∑Pu is the sum of all factored concentrated loads that act on the span. 8.6.3.4 Use of frame analysis—Frame analysis, which meets 8.1.2, may be used to determine factored moments and shears as a substitute for values in 8.6.3.1 to 8.6.3.3. 8.6.3.5 Two-way joists supported by beams, girders, or walls—Required moment strength for two-way joists supported by beams, girders, or structural walls may be obtained using 7.9.1 and 7.9.2, ignoring the minimum depth of the supporting beams or girders as given by 7.9.1(c) and 6.1.3.3. 8.6.4 Required shear strength 8.6.4.1 Cantilevers of joists and beams supported by beams, girders, or walls—Factored shear Vu at the cantilever support should be calculated using Eq. (8.6.4.1). Vu = Wuℓn + ∑Pu (8.6.4.1) where ∑Pu is the sum of all factored concentrated loads that act on the span. 8.6.4.2 Single-span joists and beams supported by beams, girders, or walls—Factored shear Vu for single-span beams and single-span one-way joists should be calculated using Eq. (8.6.4.2). 0.8 2 u n u u W V P = +  ∑ (8.6.4.2) where ∑Pu is the sum of all factored concentrated loads that act on the span. 8.6.4.3 Joists and beams supported by beams, girders, or walls, with two or more spans—Factored shear Vu for beams and one-way joists with two or more spans supported by beams, girders, or structural walls should be calculated using equations given in Table 8.6.4.3, where ∑Pu corresponds to the sum of all factored concentrated loads on the span. Table 8.6.3.3—Factored moment for beams and one-way joists with two or more spans Positive moment at end spans: 2 11 9 u n n u u W M P + = +   ∑ Interior spans: 2 16 5 u n n u u W M P + = +   ∑ (8.6.3.3a) (8.6.3.3b) Negative moment at interior face of external support: 2 24 16 u n n u u W M P − = +   ∑ Exterior face of first internal support, only two spans: 2 9 6 u n n u u W M P − = +   ∑ Faces of internal supports, more than two spans: 2 10 7 u n n u u W M P − = +   ∑ Faces of all supports for joists with spans not exceeding 10 ft (3 m): 2 12 8 u n n u u W M P − = +   ∑ (8.6.3.3c) (8.6.3.3d) (8.6.3.3e) (8.6.3.3f) Table 8.6.4.3—Factored shear for beams and one-way joists with two or more spans Exterior face of first interior support: 1.15 0.8 2 u n u u W V P = +  ∑ Faces of all other supports: 0.75 2 u n u u W V P = +  ∑ (8.6.4.3a) (8.6.4.3b) Table 8.6.3.2—Factored moment for single-span beams and joists Positive moment: 2 8 4 u n n u u W M P + = +   ∑ (8.6.3.2a) Negative moment at supports: 2 24 16 u n n u u W M P − = +   ∑ (8.6.3.2b) Fig. 8.5.5—Hanger reinforcement.American Concrete Institute – Copyrighted © Material – www.concrete.org GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) 69 8.6.4.4 Use of frame analysis—Frame analysis, meeting 8.1.2, may be used to determine factored shear as a substitute for the values determined from 8.6.4.1 to 8.6.4.3. 8.6.4.5 Two-way joists supported by beams, girders, or walls—Factored shear for two-way joists supported by beams, girders, or structural walls may be determined using 7.9.1 and 7.9.4, ignoring the minimum depth of the supporting beams or girders indicated in 7.9.1(c) and 6.1.3.3. 8.6.5 Reinforcement 8.6.5.1 Positive moment reinforcement—The positive moment reinforcement area should be determined for the calculated value of Mu+. When a slab is present in the upper part of the section or when the beam or joist is T-shaped, the T-beam effect may be used. Positive moment reinforcement should comply with 8.4.14. At internal supports, at a distance equal to ℓn/8 measured from the face of the supports into the span, up to one-half the positive moment reinforcement may be cut off if there are no concentrated loads within that distance (Fig. 8.6.5.1). For single-span beams and joists, positive moment reinforcement should not be cut off. 8.6.5.2 Negative moment reinforcement—The negative moment reinforcement area should be determined for the larger value of Mu– calculated for both sides of the support. This reinforcement should comply with 8.4.15. When a slab is present in the upper part of the section or when the beam or joist is T-shaped, negative moment reinforcement should comply with 8.4.11.1. At a distance equal to ℓn/4 for external supports and ℓn/3 for internal supports, measured from the internal face of the support into the span, all negative moment reinforcement may be cut off (Fig. 8.6.5.1). Negative moment reinforcement should not be cut off in cantilevers. 8.6.5.3 Transverse reinforcement—Values of Vu at the right and left support faces should be determined by the appropriate equation from 8.6.4. The transverse reinforcement should comply with 8.5. 8.6.6 Reactions on beams and girders 8.6.6.1 One-way joists—Factored reaction on the joist system support may be considered as uniformly distributed. Factored reaction on the supports, ru, per unit length, should be the value determined from Eq. (8.6.6.1) plus the uniformly distributed reaction from any cantilever spanning from that support. u s u j n V r s =   (8.6.6.1) where Vu is the factored shear from 8.6.4; ℓs is the center-tocenter span of the joist; ℓn is the clear span of the joist; and sj is the center-to-center spacing between parallel joists. 8.6.6.2 Two-way joists supported by beams, girders, or walls—Factored reactions for two-way joists supported by beams, girders, or structural walls may be calculated using 7.9.1 and 7.9.5, ignoring minimum depth of the supporting beams or girders given in 7.9.1(c) and 6.1.3.3. 8.6.6.3 Beams—Factored reactions on the supports, Ru, should be the values determined from Eq. (8.6.6.3) plus the factored reaction from any cantilever spanning from that support. u s u n V R =   (8.6.6.3) where Vu is the factored shear from 8.6.4; ℓs is the center-tocenter span; and ℓn is the clear span of the beam. Fig. 8.6.5.1—Reinforcement for beams and joists supported by beams or girders. Fig. 8.7.2.2—Limits on girder depth and width.American Concrete Institute – Copyrighted © Material – www.concrete.org 70 GUIDE TO SIMPLIFIED DESIGN FOR REINFORCED CONCRETE BUILDINGS (ACI 314R-16) 8.7—Girders that are part of a frame 8.7.1 General—Section 8.7 applies to girders that are part of a moment-resisting frame where the girders are monolithic and are directly supported by columns or reinforced concrete walls. 8.7.2 Dimensional limits 8.7.2.1 General—In addition to Chapter 8, girders that are part of a frame should comply with the dimensional limits set forth in 1.3. Embedded conduits and pipes should comply with 6.8. 8.7.2.2 Girder depth and width—The girder should be prismatic without haunches, brackets, or corbels. The height h should comply with the minimum depth of 6.5.3. Clear span of the member should not be less than four times its height h. The width-to-height ratio bwh should not be less than 0.3. The width bw should not be less than 8 in. (200 mm), nor exceed the corresponding width of the supporting column plus 3/4h on each side of the supporting column (Fig. 8.7.2.2). 8.7.2.3 Girders supported by reinforced concrete walls— Girders, supported by a reinforced concrete wall located in the plane of the frame, should continue along the full horizontal wall length. Girder width should not be less than wall thickness. Where girders are supported by walls perpendicular to the longitudinal axis of the girder, a beam should run along the full horizontal wall length at the same level and have the same height as the girder. Beam width should not be less than wall thickness or 8 in. (200 mm). Vertical reinforcement of the wall should pass through the girder or beam, as indicated in Chapter 12. 8.7.2.4 Lateral support—For girders not continuously laterally supported by the floor slab or secondary beams, the clear distance between lateral supports should not exceed 50 times the least width b of compression flange or face. 8.7.2.5 Restrictions—The following restrictions should be in effect for girders of frames designed under 8.7: (a) There are two or more spans (b) Spans are approximately equal, with the shorter of two adjacent spans greater than or equal to 80 percent of the larger span (1.3) (c) Loads are uniformly distributed and adjustments for concentrated loads are performed (d) Unfactored unit live load wℓ does not exceed three times unfactored unit dead load wd (e) Girders should not have a slope exceeding 15 degrees 8.7.3 Required moment strength 8.7.3.1 Factored positive and negative moment—Factored positive and negative moment Mu (required moment strength) for girders and beams that are part of a frame whose vertical members are columns and concrete structural walls should be calculated using equations in Table 8.7.3.1, where ∑Pu is the sum of all factored concentrated loads that act on the span. 8.7.3.2 Girders parallel to one-way joist systems—For girders parallel to joists, the assumed tributary width for the calculation of girder factored loads should be twice the joist spacing plus the girder width. 8.7.3.3 Use of frame analysis—Frame analysis, meeting [Show More]

Last updated: 2 years ago

Preview 1 out of 132 pages