1、ACI 336.2R-88 supersedes ACI 336.2R-66 (Reapproved 1980).Copyright 1988, American Concrete Institute.All rights reserved including rights of reproduction and use in any form or by anymeans, including the making of copies by any photo process, or by electronic ormechanical device, printed, written, o
2、r oral, or recording for sound or visual reproductionor for use in any knowledge or retrieval system or device, unless permission in writingis obtained from the copyright proprietors.336.2R-1ACI Committee Reports, Guides, Manuals, StandardPractices, and Commentaries are intended for guidance inplann
3、ing, designing, executing, and inspecting construction.This document is intended for the use of individuals who arecompetent to evaluate the significance and limitations of itscontent and recommendations and who will acceptresponsibility for the application of the material it contains.The American C
4、oncrete Institute disclaims any and allresponsibility for the stated principles. The Institute shall notbe liable for any loss or damage arising therefrom.Reference to this document shall not be made in contractdocuments. If items found in this document are desired by theArchitect/Engineer to be a p
5、art of the contract documents, theyshall be restated in mandatory language for incorporation bythe Architect/Engineer.Suggested Analysis and Design Proceduresfor Combined Footings and MatsReported by ACI Committee 336ACI 336.2R-88(Reapproved 2002)This report deals with the design of foundations carr
6、ying more than asingle column of wall load. These foundations are called combined footingsand mats. Although it is primarily concerned with the structural aspects ofthe design, considerations of soil mechanics cannot be eliminated and thedesigner should focus on the important interrelation of the tw
7、o fields inconnection with the design of such structural elements. This report islimited to vertical effects of all loading conditions. The report excludesslabs-on-grade.Keywords: concretes; earth pressure; footings; foundations; loads (forces);mat foundations; reinforced concrete; soil mechanics; s
8、tresses; structuralanalysis; structural design.CONTENTSChapter 1General, p. 336.2R-21.1Notation1.2Scope1.3Definitions and loadings1.4Loading combinations1.5Allowable pressure1.6Time-dependent considerations1.7Design overviewChapter 2Soil structure interaction, p. 336.2R-52.1General2.2Factors to be c
9、onsidered2.3Investigation required to evaluate variable factorsChapter 3Distribution of soil reactions,p. 336.2R-63.1General3.2Straight-line distribution of soil pressure3.3Distribution of soil pressure governed by modulus ofsubgrade reactionChapter 4Combined footings, p. 336.2R-74. 1Rectangular-sha
10、ped footings4.2Trapezoidal or irregularly shaped footings4.3Overturning calculationsChapter 5Grid foundations and strip footings supporting more than two columns, p. 336.2R-85.1General5.2Footings supporting rigid structures5.3Column spacing5.4Design procedure for flexible footings5.5Simplified proce
11、dure for flexible footingsChapter 6Mat foundations, p. 336.2R-96.1General6.2Finite difference method6.3Finite grid methodClyde N. Baker, Jr. John A. Focht, Jr. Hugh S. Lacy John F. SeidenstickerSteven C. Ball M. Gaynor Jim Lewis Bruce A. SuprenantJoseph E. Bowles John P. Gnaedinger James S. Notch Ja
12、gdish S. SyalJoseph P. Colaco Fritz Kramrisch Ingvar Schousboe John J. ZilsM. T. DavissonEdward J. UlrichChairShyam N. ShuklaSecretaryThis document has been approved for use by agenciesof the Department of Defense and for listing in theDoD Index of Specifications and Standards.336.2R-2 ACI COMMITTEE
13、 REPORT6.4Finite element method6.5Column loads6.6Symmetry6.7Node coupling of soil effects6.8Consolidation settlement6.9Edge springs for mats6.10Computer output6.11Two-dimensional or three-dimensional analysis6.12Mat thickness6.13Parametric studies6.14Mat foundation detailing/constructionChapter 7Sum
14、mary, p. 336.2R-19Chapter 8-References, p. 336.2R-208.1Specified and/or recommended references8.2Cited referencesCHAPTER 1GENERAL1.1NotationThe following dimensioning notation is used: F = force;l = length; and Q = dimensionless.A=base area of footing, l2b=width of pressed edge, lB=foundation width,
15、 or width of beam columnelement, lBm= mat width, lBp= plate width, lc = distance from resultant of vertical forces to over-turning edge of the base, lD=dead load or related internal moments and forces, FDf= the depth Dfshould be the depth of soil measuredadjacent to the pressed edge of the combinedf
16、ooting or mat at the time the loads being consideredare appliedDo= dead load for overturning calculations, FDst= stage dead load consisting of the unfactored deadload of the structure and foundation at a particulartime or stage of construction, Fe=eccentricity of resultant of all vertical forces, le
17、i= eccentricity of resultant of all vertical forces withrespect to the x- and y-axes (exand ey, respec-tively), lE=vertical effects of earthquake simulating forces orrelated internal moment or force, FE = modulus of elasticity of the materials used in thesuperstructure, F/l2Ee= modulus of elasticity
18、 of concrete, F/l2Es= soil modulus of elasticity, F/l2Fvh= vertical effects of lateral loads such as earthpressure, water pressure, fill pressure, surchargepressure, or similar lateral loads, FG = shear modulus of concrete, F/l2hw= height of any shearwalls in structure, lH=settlement of foundation o
19、r point, lHci= consolidation (or recompression) settlement ofpoint i, lH= magnitude of computed foundation settlement, lI = plan moment of inertia of footing (or mat) aboutany axis x(Ix) or y(Iy), l4IB= moment of inertia of one unit width of the super-structure, l4IF= moment of inertia per one unit
20、width of thefoundation, l4Iw= base shape factor depending on foundation shapeand flexibility, l4i = vertical displacement of a node, lJ=torsion constant for finite grid elements, l4kp= coefficient of subgrade reaction from a plate loadtest, F/l3ks=q/ = coefficient (or modulus) of vertical subgradere
21、action; generic term dependent on dimensionsof loaded area, F/l3ksi= coefficient of subgrade reaction contribution tonode i, F/l3ksi = revised coefficient of subgrade reaction contribu-tion to node i, F/l3, see Section 6.8kv1= basic value of coefficient of vertical subgradereaction for a square area
22、 with width B = 1 ft, F/l3K=spring constant computed as contributory nodearea xks, F/lKr= relative stiffness factor for foundation, QL=live load or related internal moments and forcesproduced by the load, FLs= sustained live loads used to estimate settlement,F. A typical value would be 50% of all li
23、ve loads.Lst= stage service live load consisting of the sum of allunfactored live loads at a particular stage ofconstruction, FM = bending moment per unit length, FlME= overturning moment about base of foundationcaused by an earthquake simulating force, FlMF= overturning moment about base of foundat
24、ion,caused by Fvhloads, FlMo= largest overturning moment about the pressededge or centroid of the base, FlMR= resultant resisting moment, FlMW= overturning moment about base of foundation,caused by wind loads, blast, or similar lateralloads, Fln=exponent used to relate plate kpto mat ks, QP=any forc
25、e acting perpendicular to base area, Fq=soil contact pressure computed or actual, F/l2qa= allowable soil contact pressure, F/l2qi= actual or computed soil contact pressure at a nodepoint as furnished by the mat analysis. The contactpressures are evaluated by the geotechnical analysisfor compatibilit
26、y with qaand foundation movement,F/l2qu= unconfined (undrained) compression strength of acohesive soil, F/l2qult= ultimate soil bearing capacity; a computed valueto allow computation of ultimate strength designmoments and shears for the foundation design,also used in overturning calculations, F/l2AN
27、ALYSIS AND DESIGN PROCEDURES FOR COMBINED FOOTINGS AND MATS 336.2R-3Rv= resultant of all given design loads acting perpen-dicular to base area, FRv min= least resultant of all forces acting perpendicular tobase area under any condition of loading simulta-neous with the overturning moment, FS = secti
28、on modulus of mat plan area about a specifiedaxis; Sxabout x-axis; Syabout y-axis, l3SR = stability ratio (formerly safety factor), Qtw= thickness of shearwalls, lv = distance from the pressed edge to Rv min(see Fig. 4.1and 4.2), lW=vertical effects of wind loads, blast, or similarlateral loads, FXi
29、= the maximum deflection of the spring at node i asa linear model, lZ = foundation base length or length of beam columnelement, lZ = footing effective length measured from thepressed edge to the position at which the contactpressure is zero, l = vertical soil displacement, lq= average increase in so
30、il pressure due to unitsurface contact pressure, F/l2 = footing stiffness evaluation factor defined byEq. (5-3), 1/l = Poissons ratio, Q = summation symbol, Q = unit weight of soil, F/l3 = torsion constant adjustment factor, Q1.2ScopeThis report addresses the design of shallow foundationscarrying mo
31、re than a single column or wall load. Althoughthe report focuses on the structural aspects of the design, soilmechanics considerations are vital and the designer shouldinclude the soil-structure interaction phenomenon inconnection with the design of combined footings and mats.The report excludes sla
32、bs-on-grade.1.3Definitions and loadingsSoil contact pressures acting on a combined footing or matand the internal stresses produced by them should bedetermined from one of the load combinations given inSection 1.3.2, whichever produces the maximum value forthe element under investigation. Critical m
33、aximum momentand shear may not necessarily occur with the largestsimultaneously applied load at each column.1.3.1 Definitionscoefficient of vertical subgrade reaction ksratiobetween the vertical pressure against the footing or mat andthe deflection at a point of the surface of contactks= q/combined
34、footinga structural unit or assembly of unitssupporting more than one column load.contact pressure qpressure acting at and perpendicularto the contact area between footing and soil, produced by theweight of the footing and all forces acting on it.continuous footinga combined footing of prismatic ort
35、runcated shape, supporting two or more columns in a row.grid foundationa combined footing, formed by inter-secting continuous footings, loaded at the intersection pointsand covering much of the total area within the outer limits ofassembly.mat foundationa continuous footing supporting anarray of col
36、umns in several rows in each direction, having aslab-like shape with or without depressions or openings,covering an area of at least 75% of the total area within theouter limits of the assembly.mat areacontact area between mat foundation andsupporting soil.mat weightweight of mat foundation.modulus
37、of subgrade reactionsee coefficient ofvertical subgrade reaction.overburdenweight of soil or backfill from base of foun-dation to ground surface. Overburden should be determinedby the geotechnical engineer.overturningthe horizontal resultant of any combinationof forces acting on the structure tendin
38、g to rotate the struc-ture as a whole about a horizontal axis.pressed edgeedge of footing or mat along which thegreatest soil pressure occurs under the condition of overturning.soil stress-strain modulusmodulus of elasticity of soiland may be approximately related (Bowles 1982) to thecoefficient of
39、subgrade reaction by the equationEs= ksB(1 2)Iwsoil pressuresee contact pressure.spring constantsoil resistance in load per unit deflectionobtained as the product of the contributory area and ks. Seealso coefficient of vertical subgrade reaction.stability ratio (SR)formally known as safety factor, i
40、t isthe ratio of the resisting moment MRto the overturningmoment Mo.strip footingsee continuous footing.subgrade reactionsee contact pressure and Chapter 3.surchargeload applied to ground surface above thefoundation.1.3.2 LoadingsLoadings used for design shouldconform to the considerations and facto
41、rs in Chapter 9 ofACI 318 unless more severe loading conditions are requiredby the governing code, agency, structure, or conditions.1.3.2.1 Dead loadsDead load D consisting of the sum of:a. Weight of superstructure.b. Weight of foundation.c. Weight of surcharge.d. Weight of fill occupying a known vo
42、lume.1.3.2.2 Live loadsLive load L consisting of the sum of:a. Stationary or moving loads, taking into account allowablereductions for multistory buildings or large floor areas, asstated by the applicable building code.336.2R-4 ACI COMMITTEE REPORTb. Static equivalents of occasional impacts.Repetiti
43、ve impacts at regular intervals, such as thosecaused by drop hammers or similar machines, and vibratoryexcitations, are not covered by these design recommenda-tions and require special treatment.1.3.2.3 Effects of lateral loadsVertical effects oflateral loads Fvh, such as:a. Earth pressure.b. Water
44、pressure.c. Fill pressure, surcharge pressure, or similar.d. Differential temperature, differential creep andshrinkage in concrete structures, and differential settlement.Vertical effects of wind loads, blast, or similar lateralloads W.Vertical effects of earthquake simulating forces E.Overturning m
45、oment about base of foundation, caused byearthquake simulating forces ME.Overturning moment about base of foundation, caused byFvhloads MF.Overturning moment about foundation base, caused bywind loads, blast, or similar lateral loads MW.Dead load for overturning calculations Do, consisting ofthe dea
46、d load of the structure and foundation but includingany buoyancy effects caused by parts presently submergedor parts that may become submerged in the future. The influ-ence of unsymmetrical fill loads on the overturning momentsMo, as well as the resultant of all vertical forces Rv min, shallbe inves
47、tigated and used if found to have a reducing effect onthe stability ratio SR.Service live load Ls, consisting of the sum of all unfactoredlive loads, reasonably reduced and averaged over area andtime to provide a useful magnitude for the evaluation ofservice settlements. Also called sustained live l
48、oad.Stage dead load Dst, consisting of the unfactored dead loadof the structure and foundation at a particular time or stageof construction.Stage service live load Lst, consisting of the sum of allunfactored live loads up to a particular time or stage ofconstruction, reasonably reduced and averaged
49、over area andtime, to provide a useful magnitude for the evaluation ofsettlements at a certain stage.1.4Loading combinationsIn the absence of conflicting code requirements, thefollowing conditions should be analyzed in the design ofcombined footings and mats.1.4.1 Evaluation of soil pressureSelect the combinationsof unfactored (service) loads that will produce the greatestcontact pressure on a base area of given shape and size. Theallowable soil pressure should be determined by a geotech-nical engineer
