ACI-336.2R-1988-R2002.pdf
ACI 336.2R-88 (Reapproved 2002) Suggested Analysis and Design Procedures for Combined Footings and Mats Reported by ACI Committee 336 Edward J. Ulrich Shyam N. Shukla Chairman Secretary Clyde N. Baker, Jr. Steven C. Ball Joseph E. Bowles Joseph P. Colaco XI. T. Davisson John A. Focht, Jr. M. Gaynor John P. Gnaedinger Fritz Kramrisch Hugh S. Lacy .Jim Lewis James S. Notch Ingvar Schousboe This report deals with the design of foundations carrying more than a single column of wall load. These foundations are called combined footings and mats. Although it is primarily concerned with the struc- tural aspects of the design, considerations of soil mechanics cannot be eliminated and the designer should focus on the important inter- relation of the two fields in connection with the design of such struc- tural elements. This report is limited to vertical effects of all loading conditions. The report excludes slabs on grade. Chapter 4-Combined footings, p. 336.2R-7 4. l-Rectangular-shaped footings 4.2-Trapezoidal or irregularly shaped footings 4.3-Overturning calculations Keywords: concretes; earth pressure: footings: foundations; loads (forces); mat foundations: reinforced concrete; soil mechanics; stresses; structural analysis; structural design. Chapter 5-Grid foundations and strip footings supporting more than two columns, p. 336.2R-8 5.l-General 5.2-Footings supporting rigid structures 5.3-Column spacing CONTENTS Chapter 1 -General, p. 336.2R-2 5.4-Design procedure for flexible footings 5.5-Simplified procedure for flexible footings 1.1-Notation 1.2-Scope 1.3-Definitions and loadings 1.4-Loading combinations 1.5-Allowable pressure 1.6-Time-dependent considerations 1.7-Design overview Chapter 6-Mat foundations, p. 336.2R-9 Chapter 2-Soil structure interaction, p. 336.2R-4 2.1-General 2.2-Factors to be considered 2.3-Investigation required to evaluate variable factors Chapter 3-Distribution of soil reactions, p. 336.2R-6 3.1-General 6.1-General 6.2-Finite difference method 6.3-Finite grid method 6.4-Finite element method 6.5-Column loads 6.6-Symmetry 6.7-Node coupling of soil effects 6.8-Consolidation settlement 6.9-Edge springs for mats 6.10-Computer output 6.11-Two-dimensional or three-dimensional analysis 6.12-Mat thickness 6.13-Parametric studies 6. 4-Mat foundation detailing/construction 3.2-Straight-line distribution 3.3-Distribution of soil pressure governed by modulus of subgrade reaction Chapter 7-Summary, p. 336.2R-20 ACI Committee Reports, Guides, Standard Practices, and Commentaries are intended for. guidance in designing, plan- ning, executing, or inspecting construction and in preparing specifications. Reference to these documents shall not be made in the Project Documents. If items found in these documents are desired to be part of the Project Documents they should be phrased in mandatory language and incorporated into the Project Documents. This report supercedes ACI 336.2R-66 (Reapproved 1980). Copyright 0 2002, 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 any 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 de- vice, unless permission in writing is obtained from the copyright proprietors. John F. Seidensticker Bruce A. Suprenant Jagdish S. Syal John J. Zils 336.2R-1 336.2R-2 MANUAL OF CONCRETE PRACTICE Chapter 8-References, p. 336.2R-21 8.1 -Specified and/or recommended references 8.2-Cited references CHAPTER 1-GENERAL 1.1-Notation The following dimensioning notation is used: F = force;e=length; Q = dimensionless. A = b = B = Bm = Bp = c = D = Do = Df = base area of footing, e2 width of pressed edge, l Dst = e = ei = E = Ec = E = Es = Fvh = G = hw = H = Hci = AH = I = IB = IF = Iw = i = J = kp = ksi = k'si = ks = foundation width, or width of beam column element, 4 mat width, P plate width, ! distance from resultant of vertical forces to overturning edge of the base, ! dead load or related internal moments and forces, F dead load for overturning calculations, F the depth Df should be the depth of soil measured adjacent to the pressed edge of the combined footing or mat at the time the loads being considered are applied stage dead load consisting of the unfactored dead load of the structure and foundation at a particular time or stage of construction, F eccentricity of resultant of all vertical forces, P eccentricity of resultant of all vertical forces with respect to the x- and y-axes (ex and ey, respectively), ! vertical effects of earthquake simulating forces or related in- ternal moment or force, F modulus of elasticity of concrete, F/e2 modulus of elasticity of the materials used in the superstruc- ture, F/l? soil modulus of elasticity, F/e2 vertical effects of lateral loads such as earth pressure, water pressure, fill pressure, surcharge pressure, or similar lateral loads, F shear modulus of concrete, F/e height of any shearwalls in structure, e settlement of foundation or point, ! consolidation (or recompression) settlement of point i, l magnitude of computed foundation settlement, t plan moment of inertia of footing (or mat) about any axis x(Ix) or y(Iy) , f” moment of inertia of one unit width of the superstructure, t” moment of inertia per one unit width of the foundation, t” base shape factor depending on foundation shape and flexi- bility, e4 vertical displacement of a node, t! torsion constant for finite grid elements, e4 coefficient of subgrade reaction from a plate load test, F/l3 coefficient of subgrade reaction contribution to node i, F/E revised coefficient of subgrade reaction contribution to node i, F/4”, see Section 6.8 q/6 = coefficient (or modulus) of vertical subgrade reac- tion; generic term dependent on dimensions of loaded area, F/f” kvl = K = Kr = L = Ls = Lst = M' = ME = basic value of coefficient of vertical subgrade reaction for a square area with width B = 1 ft, F/4 spring constant computed as contributory node area x ks, F/l relative stiffness factor for foundation, Q live load or related internal moments and forces produced by the load, F sustained live loads used to estimate settlement, F. A typical value would be 50 percent of all live loads. stage service live load consisting of the sum of all unfac- tored live loads at a particular stage of construction, F bending moment per unit length, F l overturning moment about base of foundation caused by an earthquake simulating force, F 4 MF = Mw = Mo = MR = n = P = q = qa = qu = qult = qi = _ q = Rv = R v min S = SR = tw = W = Xi = Z = Z' = s = = ; = p = v = c = Y = overturning moment about base of foundation, caused by Fvh loads, F f overturning moment about base of foundation, caused by wind loads, blast, or similar lateral loads, F l largest overturning moment about the pressed edge or cen- troid of the base, F ! resultant resisting moment, F ! exponent used to relate plate kp to mat ks, Q any force acting perpendicular to base area, F soil contact pressure computed or actual, F/P2 allowable soil contact pressure, F/P2 unconfined (undrained) compression strength of a cohesive soil, F/e2 ultimate soil bearing capacity; a computed value to allow computation of ultimate stregth design moments and shears for the foundation design, also used in overturning calcula- tions, F/e2 actual or computed soil contact pressure at a node point as furnished by the mat analysis. The contact pressures are evaluated by the geotechnical analysis for compatibility with qa and foundation movement, F/f2 average increase in soil pressure due to unit surface contact pressure, F/f2 resultant of all given design loads acting perpendicular to base area, F least resultant of all forces acting perpendicular to base area under any condition of loading simultaneous with the over- turning moment, F section modulus of mat plan area about a specified axis; Sx about x-axis; Sy about y-axis, t3 stability ratio (formerly safety factor), Q thickness of shearwalls, e vertical effects of wind loads, blast, or similar lateral loads, F the maximum deflection of the spring at node i as a linear model, P foundation base length or length of beam column element, ! footing effective length measured from the pressed edge to the position at which the contact pressure is zero, e vertical soil displacement, k torsion constant adjustment factor, Q footing stiffness evaluation factor defined by Eq. (5-3), l/t? Poissons ratio, Q distance from the pressed edge to Rv min (see Fig. 4-l and 4-2, e summation symbol, Q unit weight of soil, F/e 1.2-Scope This report addresses the design of shallow founda- tions carrying more than a single column or wall load. Although the report focuses on the structural aspects of the design, soil mechanics considerations are vital and the designer should include the soil-structure interac- tion phenomenon in connection with the design of combined footings and mats. The report excludes slabs- on-grade. 1.3-Definitions and loadings Soil contact pressures acting on a combined footing or mat and the internal stresses produced by them should be determined from one of the load combina- tions given in Section 1.3.2, whichever produces the maximum value for the element under investigation. Critical maximum moment and shear may not neces- sarily occur with the largest simultaneously applied load at each column. ANALYSIS AND DESIGN OF COMBINED FOOTINGS AND MATS 336.2R-3 1.3.1 Definitions Coefficient of vertical subgrade reaction ks-Ratio be- tween the vertical pressure against the footing or mat and the deflection at a point of the surface of con- tact k, = q/6 Combined footing-A structural unit or assembly of units supporting more than one column load. Contact pressure q-Pressure acting at and perpendic- ular to the contact area between footing and soil, produced by the weight of the footing and all forces acting on it. Continuous footing-A combined footing of prismatic or truncated shape, supporting two or more columns in a row. Grid foundation-A combined footing, formed by in- tersecting continuous footings, loaded at the inter- section points and covering much of the total area within the outer limits of assembly. Mat foundation-A continuous footing supporting an array of columns in several rows in each direction, having a slablike shape with or without depressions or openings, covering an area of at least 75 percent of the total area within the outer limits of the assem- bly. Mat area-Contact area between mat foundation and supporting soil. Mat weight-Weight of mat foundation. Modulus of subgrade reaction-See coefficient of ver- tical subgrade reaction. Overburden-Weight of soil or backfill from base of foundation to ground surface. Overburden should be determined by the geotechnical engineer. Overturning-The horizontal resultant of any combi- nation of forces acting on the structure tending to rotate the structure as a whole about a horizontal axis. Pressed edge-Edge of footing or mat along which the greatest soil pressure occurs under the condition of overturning. Soil stress-strain modulus-Modulus of elasticity of soil and may be approximately related (Bowles 1982) to the coefficient of subgrade reaction by the equation Es = k(1-p2)/. Soil pressure-See contact pressure. Spring constant-Soil resistance in load per unit de- flection obtained as the product of the contributory area and k,. See coefficient of vertical subgrade re- action. Stability ratio (SR)-Formally known as safety factor, it is the ratio of the resisting moment MR to the over- turning moment Mo. Strip footing: See continuous footing definition. Subgrade reaction: See contact pressure and Chapter 3. Surcharge: Load applied to ground surface above the foundation. 1.3.2 Loadings-Loadings used for design should conform to the considerations and factors in Chapter 9 of ACI 318 unless more severe loading conditions are required by the governing code, agency, structure, or conditions. 1.3.2.1 Dead loads-Dead 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 volume. 1.3.2.2 Live loads-Live load L consisting of the sum of: a. Stationary or moving loads, taking into account allowable reductions for multistory buildings or large floor areas, as stated by the applicable building code. b. Static equivalents of occasional impacts. Repetitive impacts at regular intervals, such as those caused by drop hammers or similar machines, and vi- bratory excitations, are not covered by these design recommendations and require special treatment. 1.3.2.3 Effects of lateral loads-Vertical effects of lateral loads Fvh such as: a. Earth pressure. b. Water pressure. c. Fill pressure, surcharge pressure, or similar. d. Differential temperature, differential creep and shrinkage in concrete structures, and differential settle- ment. Vertical effects of wind loads, -blast, or similar lat- eral loads W. Vertical effects of earthquake simulating forces E. Overturning moment about base of foundation, caused by earthquake simulating forces ME. Overturning moment about base of foundation, caused by FVH loads MF. Overturning moment about foundation base, caused by wind loads, blast, or similar lateral loads Mw. Dead load for overturning calculations Do, consist- ing of the dead load of the structure and foundation but including any buoyancy effects caused by parts presently submerged or parts that may become sub- merged in the future. The influence of unsymmetrical fill loads on the overturning moments Mo, as well as the resultant of all vertical forces Rv min, shall be investi- gated and used if found to have a reducing effect on the stability ratio SR. Service live load Ls, consisting of the sum of all un- factored live loads, reasonably reduced and averaged over area and time to provide a useful magnitude for the evaluation of service settlements. Also called sus- tained live load. Stage dead load Dst, consisting of the unfactored Dead Load of the structure and foundation at a partic- ular time or stage of construction. Stage service live load Lst, consisting of the sum of all unfactored Live Loads up to a particular time or stage of construction, reasonably reduced and averaged over area and time, to provide a useful magnitude for the evaluation of settlements at a certain stage. 336.2R-4 MANUAL OF CONCRETE PRACTICE 1.4-Loading combinations In the absence of conflicting code requirements, the following conditions should be analyzed in the design of combined footings and mats. 1.4.1 Evaluation of soil pressure-Select the combi- nations of unfactored (service) loads which will pro- duce the greatest contact pressure on a base area of given shape and size. The allowable soil pressure should be determined by a geotechnical engineer based on a geotechnical investigation. Loads sh
