CHAPTER8SPREAD FOOTING DESIGN18-1 FOOTINGS: CLASSIFICATION AND PURPOSEA footing carrying a single column is called a spread footing, since its function is to "spread"the column load laterally to the soil so that the stress intensity is reduced to a value that thesoil can safely carry. These members are sometimes called single or isolated footings. Wallfootings serve a similar purpose of spreading the wall load to the soil. Often, however, wallfooting widths are controlled by factors other than the allowable soil pressure since wall loads(including wall weight) are usually rather low. Foundation members carrying more than onecolumn are considered in Chapters 9 and 10. Concrete is almost universally used for footingsbecause of its durability in a potentially hostile environment and for economy.Spread footings with tension reinforcing may be called two-way or one-way dependingon whether the steel used for bending runs both ways (usual case) or in one direction (as iscommon for wall footings). Single footings may be of constant thickness or either steppedor sloped. Stepped or sloped footings are most commonly used to reduce the quantity ofconcrete away from the column where the bending moments are small and when the footingis not reinforced. When labor costs are high relative to material, it is usually more economicalto use constant-thickness reinforced footings. Figure 8-1 illustrates several spread footings.Footings are designed to resist the full dead load delivered by the column. The live loadcontribution may be either the full amount for one- or two-story buildings or a reduced value1This chapter will retain some Fps units as a reader convenience. This text is widely used as a reference work, andin remodeling/remedial work access to Fps units may be necessary. Also this chapter uses the standard AmericanInstitute of Steel Construction (AISC) terminology for rolled sections as given in their AISC (1989) publication formetric shapes based on the ASTM A 6M (SI) standard. For example, a W 360 X 79 is a rolled Wide flange shapeof nominal 360-mm depth (actual depth 354 mm), has a mass of 79 kg/m, and is usually used as a column.

ColumnColumnElevationColumn round or squareElevationElevationShoulderfor columnformsPlan(a)Plan(b)WallPlan(C)Bearing igure 8-1Typical footings, (a) Single or spread footings; (Jb) stepped footing; (c) sloped footing; (d) wallfooting; (e) footing with allowed by the local building code for multistory structures. Additionally the footing maybe required to resist wind or earthquake effects in combination with the dead and live loads.The footing loads may consist of a combination of vertical and horizontal loads (inclined resultant) or these loads in combination with overturning moments. The current ACI2 Codestrength design procedure uses reduced load factors for the several transient loading conditions in lieu of increasing the allowable material stresses.A pedestal (Fig. 8-Ie) may be used to interface metal columns with spread or wall footingsthat are located at the depth in the ground. This prevents possible corrosion of metal throughdirect contact with the soil.8-2 ALLOWABLE SOIL PRESSURESIN SPREAD FOOTING DESIGNThe allowable soil pressure for footing design is obtained as the worst case of bearing capacity and settlement as in Example 5-9. Where settlements control, the reported value is the net2American Concrete /nstitute Building Code 318-. This code is revised every four to eight years. The metric versionis designated 318M-. The latest (as of 1995) was issued in 1989 and revised in 1992 [the metric version beingdesignated ACI 318RM-89 (Revised 1992)].

increase in soil pressure that can be allowed. The reason is that settlements are caused byincreases in pressure over that currently existing from overburden.The allowable bearing capacity furnished to the structural designer by the geotechnicalengineer will have a suitable factor already applied. The safety factor ranges from 2 to 5 forcohesionless materials depending on density, effects of failure, and consultant caution. Thevalue may range from 3 to 6 for cohesive materials, with the higher values used where consolidation settlements might occur over a long period of time. Note that these safety factorsare larger than those cited in Table 4-9. Geotechnical caution should not be viewed as poorpractice unless it results in a different type of foundation that is several times more expensive.In general, reduction of qa from, say, 500 to 300 kPa will result in larger spread footings, butthe percent increase in total building cost will be nearly negligible. This can be considered insurance, since a foundation failure requires very expensive remedial measures and structuralrepairs, whereas a superstructure failure may be localized and easily repaired.The geotechnical consultant is not usually aware that the footing will be subjected to eccentric load and/or moment, so the allowable bearing pressure may not be found using theB' analysis of Chap. 4. Also if settlement controls, there is no reliable method to account foreccentricity. In these cases the best approach is to avoid any large differential pressure acrossthe base of the footing. Any footing rotation will have a marked effect on the column basemoment when the columns are rigidly attached to the footing. The footing rotation will be ina direction to reduce the base moment and may, in fact, reduce it to zero. Equation (5-17) canbe used to estimate moment loss due to footing rotation as in Example 5-8.Any increase in allowable soil pressure for transient load conditions should be verifiedwith the geotechnical consultant. Increasing qa by one-third as commonly found in designcodes for other materials may not be appropriate. Factors such as frequency of overload, soilstate, climatic conditions, and type of structure may disallow any large deviation from therecommended qa.8-3 ASSUMPTIONS USED IN FOOTING DESIGNTheory of Elasticity analysis [Borowicka (1963)] and observations [Schultze (1961), Barden (1962)] indicate that the stress distribution beneath symmetrically loaded footings is notuniform. The actual stress distribution depends on both footing rigidity and base soil. Forfootings on loose sand the grains near the edge tend to displace laterally, whereas the interiorsoil is relatively confined. This difference results in a pressure diagram qualitatively shownin Fig. 8-2(2. Figure 8-2fo is the theoretical pressure distribution for the general case of rigidfootings on any material. The high edge pressure may be explained by considering that edgeshear must occur before any settlement can take place. Since soil has a low rupture strength,and most footings are of intermediate rigidity, it is not very likely that high edge shear stressesare developed. The edge stress also depends on the thickness H of compressible soil as shownin Fig. 8-2fe.The pressure distribution beneath most footings will be rather indeterminate because ofthe interaction of the footing rigidity with the soil type, state, and time response to stress. Forthis reason it is common practice to use the linear pressure distribution of Fig. 8-2c beneathspread footings. The few field measurements reported indicate this assumption is adequate.Spread footing design is based almost entirely on the work of Richart (1948) and Moe(1961). Richart's work contributed to locating the critical section for moments; critical

Edge stressdepends onthe depth offooting DEdge stresses maybe very large(«)When:(C)(6)Figure 8-2 Probable pressure distribution beneath a rigid footing, (a) On a cohesionless soil; (b) generally forcohesive soils; (c) usual assumed linear distribution.sections for shear are based on Moe's work. The ACI, AASHTO, and AREA3 specificationsfor footing design are identical for locations of critical sections. AASHTO and ACI use thesame design equations and factors for strength design. AREA uses the alternative designmethod for footings but allowable concrete strengths are about 10 percent less than thoseallowed by ACI. Because of the similarity in the several codes the ACI code will be theprimary reference in this and the following two chapters.8-4 REINFORCED-CONCRETE DESIGN: USDThe latest revision of the ACI Standard Building Code Requirements for Reinforced Concrete(ACI 318-), hereinafter termed the Code, places almost total emphasis on ultimate strengthdesign (USD) methods. The older procedure, termed the Alternate Design Method (ADM), isstill allowed, and the basic elements are given in Appendix A of the ACI Code. The AASHTObridge code gives about equal emphasis to both the alternate and the strength design methods. For spread footings, even though the design is reasonably direct, the ADM procedure issimpler to use but produces a more conservative design. When one compares designs by thetwo methods the ADM will consistently compute a concrete footing thickness on the order of15 to 25 mm larger and reinforcing bar areas 30 to 50 percent larger. For these two reasonsAASHTO gives more emphasis to the ADM than does ACI.This text uses the ADM for the retaining wall design of Chap. 12—still a widely usedprocedure in practice—since the ACI code procedure does not give greatly different results3ACI American Concrete Institute, AASHTO American Association of State Highway and TransportationOfficials, AREA American Railway Engineering Association.

and there is much uncertainty with that design. We will use the USD for spread footingdesign; however, footing depth equations [Eqs.(8-5)-(8-9)] are also applicable for the ADM.The only difference is whether column loads are factored (USD) or unfactored (ADM).If you have difficulty factoring column moments for a spread footing design you should usethe ADM method. You should also use the ADM where the column loads are not well-defined.The basic procedure is given as previously stated in Appendix A of ACI 318-; select partsand most of the methodology are given in Sec. 12-16 [basic design equations and allowablestresses (in Tables 12-1 and 12-2)].All notation pertaining to concrete design used in this text will conform to the ACI Code.Where this conflicts with notation previously used, the reader should take note. Strengthdesign requires converting working design dead (D) and live (L) loads (see Table 4-10) toultimate loads through the use of load factors asPu IAD UL 0.75(1.4Z) UL UW) 0.9D 1.3 W(alternative with wind)(a)(b)(c)For earthquake loading substitute E for W (wind) as applicable. Other load combinations maybe used, but the user is referred to Art 9.2 of the Code for their application.The ultimate concrete strength / c ' in USD is reduced for workmanship and other uncertainties by use of (f) factors (Art 9.3) as follows:Design considerationMoment, without axial loadTwo-way action, bond, and anchorageCompression members, spiralCompression members, tiedUnreinforced footingsBearings on concrete j 0.900.850.750.700.650.70Concrete strain at ultimate stress is taken as 0.003 according to Art. 10.3.2, and the yieldstrength fy of reinforcing steel is limited to 550 MPa (80 ksi) per Art. 9.4. The most populargrade of reinforcing steel in current use has fy 400 MPa (Grade 400 or 60 ksi).ELEMENTS OF USD. For the partial development of the USD equations that follow, refer toFig. 8-3.From Fig. 8-3Z? the summing of horizontal forces, X FH 0, yields C T, and, takingthe compressive stress block as a rectangle of dimensions shown,C 0.85/c'fcaThe tensile force in the steel reinforcement T isT AJyEquating the latter quantities yields an expression for the depth of the compression block as(8-1)

Neutralaxis(b)(a)Figure 8-3(c)Assumptions used for the development of the ACI ultimate-strength-design equations.For beams, b width; for footings b 1 unit (m or ft). From statics and summing momentsat a convenient point (either T or C) we obtainrcH)-«- H)and solving for the ultimate resisting moment on a section and inserting the work qualityfactor (/ , we haveM11 4 Asfyld- \(8-2)Alternatively, if steel ratio terms p and q are defined as follows,PA1bdPf1UqEq. (8-2) can be written asMu f bd2fcq{\ - 0.59q)(8-2*)The steel ratio at a cross section has been defined as p As/bd and the ratio at balanced design will be designated as pb. To ensure a tensile failure rather than a sudden concrete compression failure pd is taken as not over 0J5pb (Art. 10.3.3) where the balancedreinforcement ratio is computed based on the concrete strain at ultimate stress of 0.003 andEs 200,000 MPa or 29 X 106 psi as0.85 1/;Pb fy600fy 600FpS*0.85JS 1 /;87,000fyfy 87,000Pb (8 3)"The factor /3i in the preceding equation is defined as follows:S I : 0i 0.85 - 0.008(/ c ; - 30 MPa) 0.65Fps : ft 0.85 - 0.05(/ c ' - 4 ksi) 0.65Footings for buildings seldom use / c ' 21 MPa (3 ksi); for bridge footings / c ; is not likely toexceed 30 MPa (4 ksi), so the factor pi will, in nearly all cases, be 0.85. The lower-strengthconcrete is somewhat less costly per cubic meter but, more importantly, will produce a morerigid footing as it will have to be made thicker (larger Dc of Fig. 8-3a). Table 8-1 providesvalues for /3i for a range of / c ', which may be of use here and for mat design (Chap. 10), where

TABLE 8-1Maximum allowable steel ratio p rf *Note: ASTM 615M and 615 now define only twogrades of rebars: Grade 300 (40 ksi) and Grade 400(60 ksi)fy, MPa (ksi)/;, MPa (ksi)prfGrade 300(40ksi)Grade 400(60 .0280.033Table ratios shown are 0.15 pb for ensuring a tensile rebarfailure per ACI Art. 10.3.3.!Values are slightly approximate for Fps units.higher-strength concrete may be used on occasion. Also given in Table 8-1 are the severalvalues of 0J5pb (limiting percentage of steel at a cross section), which as shown abovedepend on both f}c