IS: 2950 (Part I) -1981 (R eaffirmed 200 8 ) Indian Standard CODE OF PRACTICE FOR DESIGN AND CONSTRUCTION OF RAFT FOUNDATIONS PART I DESIGN (Second Revision) Fourth Reprint DECEMBER 2004 ( Including Amendment No.1) UD C 624.153.61 : 624.0 : 69.001.3 © Copyright 1982 BUREAU OF INDIAN STANDARDS MANAK BHAVAN, 9 BAHADUR SHAH ZAFAR M ARG NEW DELHI 110002 Gr 6 September 1982 IS: 2950 ( Part I ) · 1981 Indian Standard CODE OF PRACTICE FOR DESIGN AND CONSTRUCTION OF RAFT FOUNDATIONS PART I DESIGN ( Second Revision) Foundation Engineering Sectional Committee, BDC 43 Chairman PROF DINESII MOHAN Representing Central Building Research Roorkee Institute (CSIR), DR Members R. K. BHANDARI SHRI DeVENDRA SHARMA ( Central Building Research Institute (CSIR), Roorkee CHIEF ENGINEER Alternate) CaJcutta Port Trust. Calcutta SHRI S. GUHA ( Alternate) SHRJ M. O. DANDAVATE The Concrete Association of India, Bombay SHRI N. C. DUGOAL ( Alternate) SHR) R. K. DAS GUPTA Simplex Concrete Piles ( India) Pvt Ltd, Calcutta SHRt H. GUHA BISWAS ( Alternate) Smu A. O. DASTIDAR In personal capacity (5, Hungerford Road 121, Hungerford Street, Calcutta) SHRI V. C. DESHPANDE The Pressure Piling Co ( I ) Pvt Ltd, Bombay DIRECTOR ( CSMRS ) Central Water Commission, New Delhi DEPUTY DIRECTOR ( CSMRS ) ( Alternate ) SHRI A. H. DIVANJI Asia Foundations and Construction Co Pvt Ltd, Bombay SHRI A. N. JANGLE ( Alternate) SHRI A. GH05HAL Stup Consultants Ltd, Bombay PROF GOPAl RANJAN University of Roorkee, Roorkee DR JAGDISH NARAIN Indian Geotechnic Society, New DeW PROF SWAMI SARAN ( Alternate) ( Continued on pag~ 2 ) Copyright 1982 BUREAU OF INDIAN STANDARDS Thil publication is protected under the Indian Copyright Act (XIV of 19S7 ) and reproduction In whole or in part by any means except with written permission of the publisher shall be deemed to be an infrigement of copyright under the said Act. o IS : 2950 ( Part I ) - 1981 ( Continued from page 1 ) Members Representing SHRI G. S. JAIN G. S. Jain & Associates, Roorkee SHRI ASHOK KUMAR JAIN ( Alternate) JOINT DIRECTOR (.0 ) National Buildings Organisation, New SHRI SUNIL BERY ( Alternate) JOINT DIRECTOR RESEARCH ( SM ), Ministry of Railways Delhi RDSa JOINT DIRECTOR RESEARCH ( B & S ), ROSa ( Alternate) DR R. K. KATTI SHRI S. R. KuLKARNI SHRI S. Roy ( Alternate) SHRI O. P. MALHOTRA SHRI A. P. MATHUR SHIH V. B. MATHUR SHRI T. K. D. MUNSI SHRI M. IYEN(,AR ( Alternate) SHRI Y. V. NARASIMHA RAO Indian Instituteof Technology, Bombay M. N. Dastur & Co Pvt Ltd, Calcutta Public Works Department, Chandigarh Central Warehousing Corporation, New Delhi Machenzies Limited, Bombay Engineers India Limited, New Delhi Bokaro Steel Plant (Steel Authority of India), Bokaro Engineer-in-Chief's Branch, Army Headquarters, BRJO OMBIR SISGH New Delhi LT~COL K. P. ANAND ( Alternate ) SHRI B .K. PANTHAKY The Hindustan Construction Company Limited, Bombay SHRI V. M. MADGE ( Alternate) SHKI ~1. R. Pl:~UA Cemindia Co Ltd, Bombay SllRJ S. MUKHERJEE ( Alternate) The Braithwaite Burn & Jessop Construction Co SHHI N. E. V. RAGHVAN Ltd, Calcutta SBRI A. A. RAJU Vijayanagar Steel Plant ( SAl ), New Delhi DR V. Y. S. RAO Nagadi Consultants Pvt Ltd, New Delhi SHRI ARJUN RlJHSl:\GHANI Cement Corporation of India, New Delhi SHRIO. S. SR,VASTAVA ( Alternate ) DR A. SARGUNAN College of Engineering, Guindy SHRI S. BooMINATHAN ( Alternate) SHRI K. R. SAXENA Public Works Department, Government of Andhra Pradesh, Hyderabad United Technical Consultants Pvt Ltd, New Delhi DR S. P. SHRIVASTAVA DR R. KAPUR ( Alternate ) Gammon India Limited, Bombay SHRI T. N. SURBA RAO SHRI S. A. REDOI ( Alternate) SHRI N. SIVAGlJRL: Ministry of Shipping and Transport, New Delhi SHRI D. V. SIKKA ( Alternate) SUPERINTENDING ENG 1 N B E R Central Public Works Department, New Delhi ( DESIGNS) EXECU11VE ENGINEER (DESIGNS) V ( Alternate ) ( Continued on Pat' 24) 2 AMENDMENT NO. 1 TO DECEMBER 1988 IS I 2950 ( Part I ) - 1981 CODE OF PRACTICE FOR DESIGN AND CONSTRUCTION OF RAFT FOUNDATIONS PART 1 DESIGN ( Second Revision ] (Pagt 4, clause 3.I(g) ] - Substitute cIS: 1901-19lJ7t' for 'IS: 1904· 1978t'. ( Page 4,Joot-note marked with' for the existing foot-note: f t' mark) -- Substitute the following ion lC()(I" o f requira,n~nu rrnctko third "v'Jllln ).' for ( t " . l g n And c onvtr uct of fnunnRtiuna in loll.: "J G e n e r a ! 'K > [Page 0-5'. ( Pl1g~ 9, clause 5.2.1(a), lint 2] Substitute Substitute 'K 'St'8 < 0'5' for 16. clause C·2.1.1 ) - 5.1.1' for 'se« 5.2.1'. ( Page 19, clause E-I.4 ) matter: 'p 3 M. Pe, Substitute the following for the existing o--ca-y ( Page 19, claw, E-2.2 ) c Substitu te the following for the value of ( , )] ~if 'I [ Pl (I) + 4 Pm + Pl ' Substitute the folJowing for the [Page 21, claus, £.2.3 (b) ] eltilting matter: ( 4 Pe - Pm /1) C·' 4(,' + j-J-2. ( Page 21, clause F-1.1 ) ( Page 22, clause F-l.l, [.IllS Substitute ' 05 ( for evaluation of K, see Appendix C ). b) The column spacing is less than 1-75/>-. ( see Appendix C ). 5.1.2 The raft is analysed as a whole in each of the two perpendicular directions. The contact pressure distribution is determined by the procedure outlined in Appendix D. Further analysis is also based on statics. 5.1.3 In cases of uniform conditions when the variations in adjacent column loads and column spacings do not exceed 20 percent of the higher value. the raft may be divided into perpendicular strips of widths equal to the distance between midspans and each strip may be analysed as an independent beam with known column loads and known contact pressures. 8 ~.o IS : 2950 ( Part I ) - 1981 Such beams will not normally satisfy statics due to shear transfer between adjacent strips and the design may be based on suitable moment coefficients, or on moment distribution. NOTE - On soft soils. for example, normally consolidated clays, peat. muck, organic silts, etc. the assumptions involved in the conventional method are commonly justified. 5.2 Flexible Foundation 5.2.1 Simplified Method - In this method. it is assumed that the subgradc consists of an infinite array of individual elastic springs each of which is not affected by others. The spring constant is equal to the modulus of subgrade reaction ( k). The contact pressure at any point under the raft is, therefore, linearly proportional to the settlement at the point. This mcthoJ may be used when the following conditions are satisfied ( see Appendix E ): a) The structure ( combined action of superstructure and raft) may be considered as flexible ( relative stiffness factor K ·. O· 5, see Appendix C ). b) Variation in adjacent column load does not exceed 20 percent of the higher value. 5.2.1.1 General method - For the general case of a flexible foundation not satisfying the req uirements of 5.2. J. the method based on closed form solution of elastic plate theory may he used. This method is based on the theory of plates on winkler foundation which takes into account the restraint on deflection of a point provided by continuity of the foundation in orthogonal foundation. The distribution of deflection and contact pressure on the raft due to a column load is determined by the plate theory. Since the effect of a column load on an elastic foundation is damped out rapidly, it is possible to determine the total effect at a point of all column loads within the zone of influence by the method of super imposition. The computation of the effect at any point may be restricted to columns of two adjoining bays in all directions. The procedure is outlined in Appendix F. NOTE - One of the recent general methods based on the above mentioned theory is numerical analysis by either finite difference method or finite element method. This method is used for accurate analysis of the raft foundation. The details of this method could be covered at a later stage. 6. STRUCTURAL DESIGN 6.1 The general design for loads, shrinkage, creep and temperature effects and provision of reinforcement and detailing shall conform ot IS: 456-1978*, the foundation being considered as an inverted beam or slab. ·Code of practice for plain and reinforced concrete ( third "vision ). 9 IS : 2950 ( Part I ) - 1981 APPENDIX A [ Clause 3.1( f)] DETERMINATION OF MODULUS OF ELASTICITY ( E, ) AND POISSON'S RATIO ( I-' ) Arl. DETERMINATION OF MODULUS OF ELASTICITY (E.) A-I.t The modulus of elasticity is a function of the composition of the soil, its void ratio, stress history and loading rate. I n granular soils it is a function of the depth of the strata, while in cohesive soils it is markedly influenced by the moisture content. Due to its great sensitivity to sampling disturbance accurate evaluation of the modulus in the laboratory is extremely difficult. For general cases, therefore, determination of the modulus may be based 011 field tests ( A-2). Where a properly equipped laboratory and sampling facility arc available, E! may be determined in the laboratory ( sec A-3 ). A-2. FIELD DETEltI\llNATION A-2.1 The value of E, shall be determined from plate loan test given in lS : J R88-1982:\t. E. "::- a B · ~ } -- s ,u_~)_ i: where q -:- intensity of contact pressure, B =": least lateral dimension of test plate, s settlement, p. Poisson's ratio, L, Influence factor, and 0'82 for a square plate. A-2.1.1 The average value of E, shall be based on a. number of plate load tests carried out over the area, the number and location of the tests, depending upon the extent and importance of the structure. A-2.1.2 Effect of Size - In granular soils, the value of E, corresponding to the size of the raft shall be determined as follows: E· -- E -p _l!!- (BI Bf' 2B, +B p )2 · Method of load test on soils ( second revision ). 10 IS : 2950 ( Part I) - 1981 where BI, B" represent sizes of foundation and plate and E; is the modulus determined by the plate load test. A-2.2 For stratified deposits or deposits with lenses of different materials, results of plate load test will be unreliable and static cone penetration tests may be carried out to determine E·. A-2.2.1 Static cone penetration tests shall be carried out in accordance with IS : 4968 ( Part III )-1976*. Several tests shall be carried out at regular depth intervals up to a depth equal to the width of the raft and the results plotted to obtain an average value of E; A-2.2.2 The value of E. may be determined from the following relationship: E. = 2 where Ci« Ctd == cone resistance in kgf/cm 2 · A-3. LABORATORY DETERMINATION OF E, A-3.t The value of E, shall be determined by conducting triaxial test in the laboratory [ see IS : 2720 ( Part XI )-1971 t and IS : 2720 ( Part XII )-1981 ~ ] on samples collected with least disturbances. A-3.2 I n the first phase of the triaxial test, the specimen shall be allowed to consolidate fully under an all-round confining pressure equal to the vertical effective overburden stress for the specimen in the field. In the second phase, after equilibrium has been reached, further drainage shall be prevented and the deviator stress shall be increased from zero value to the magnitude estimated for the field loading condition. The deviator stress shall then be reduced to zero and the cycle of loading shall be repeated. A-3.3 The value of E. shall be taken as the tangent modulus at the stress level equal to one-half the maximum deviator stress applied during the second cycle of loading. -Method for subsurface sounding for soils : Part III Static cone penetration test ( first revision ). tMethods of test for soils: Part XI Determination of shear strength parameters of a specimen tested in unconsolidated undrained triaxial compression without the measurement of pore water pressure. tMethods of test for soils : Part XII Determination of shear strength parameters of soils from consolidated undrained triaxial compression test with measurement of pore water pressure (first revision ). 11 IS : 2950 ( Part I ) - 1981 APPENDIX B [ Clause 3.1( f) ] DETERMINATION OF MODULUS OF SUBGRADE REACTION 8-1. GENERAL B-l.1 The modulus of subgrade reaction I( k) as applicable to the case of load through a plate of size 30 x 30 em or beams 30 em wide on the soil is given in Table I for cohesionless soils and in Table 2 for cohesive soils, Unless more specific determination of k is done (see B-2 and B-3 ), these values may be used for design of raft foundation in cases where the depth of the soil affected by the width of the footing may be considered isotropic and the extrapolation of plate load test results is valid. TABLE 1 MODULUS OF SUDGRADE REACTION ( k ) FOR COHESIONLESS SOflS SOIL CKARACT£RISTIC r----------A..-------~ -MODULUS Of SUBGRADB REACTION ( k ) IN ka/cm l r----------.,A...-----~ Relative Density (I) Standard Penetration Test Value ( N ) (2) For Dry or Moist State (3) For Submerged State (4) Loose Medium Dense < 10 10 to 30 30 and Over 1'5 1-5 to 4-7 4'7 to 18-0 0-9 0'9 to 2'9 2'9 to 10·8 -The above value! apply to a square plate 30 x 30 em or beams 30 em wide. TABLE 2 i\IODULUS OF SUBGRADE REACTION (k ) FOR COHESIVE SOILS SOIL CHARACTERISTIC r - - - - - -----'---------~ Consistency (1) -MODULUS Of SUBGRADB REACTION ( k, ) IN kg/em' Unconfined Compressive Strength, ka/cm ' (2) to (3) Stit.' Vel v stiff I 2 2-7 . 2 to 4 2'7 to 5'4 HarJ 4 and over 5'4 to 10-8 -The values apply to a square plate 30 x 3D em. The above values are based on the assumption that the average loading intensity does not exceed half the ultimate burin. capacity. 12 IS : 2950 ( Put I) - 1981 B-2. FIELD DETERMINATION B-2 ·. 1 Incases where the depth of the soil affected by the width of the footing may be considered as isotropic, the' value of k may be determined in accordance with IS : 9214-1979*. The test shall be carried out with a plate of size not less than 30 em, 8-2.2 The average value of k shall be based on a number of plate load tests carried out over the area, the number and location of the tests depending upon the extent and importance of the structure. B-3. LABORATORY DETERMINATION B-3.1 For stratified deposits or deposits with lenses of different materials, evaluation of k from plate load test will be unrealistic and its determination shall be based on laboratory tests [see IS : 2720 (Part XI )-1971 t and IS : 2720 ( Part XII )-1981 t ]. B-3.2 In carrying out the test the continuing cell pressure may be so selected as to be representative of the depth of average stress influence zone (about O·SBtoB). 8-3.3 The value of k shall be determined from-the following relationship: " __ 0'65 12 I\, - \j r--E.E ~_~ I · 1 _ I"'J ~ _I · B where E, E ~ Modulus of elasticity of soil ( sec Appendix A ), Young's modulus of foundation material, Poisson's ratio of soil ( see Appendix A ), and = I Moment of inertia of structure if determined or of the foundation. 8-3.4 In the absence of laboratory test data, appropriate values of E. and 14 may be determined in accordance with Appendix A and used in B-3.2 for evaluation of k. · Method of determination of subgrade reaction ( k value) of soils in the field. tMethods of test for soils: Part XI Determination of shear strength parameters of specimen tested in unconsolidated undrained triaxial compression without the measurement of pore water pressure. ~ Methods of test for soils : Part X I I Determinat ion of shear strength parameters of soil from consolidated undrained triaxial compression test with measurement of pore water pressure (first revision ). 13 IS : 2950 ( Put I ) - 1981 8-4. CALCULATIONS 8-4.1 When the structure is rigid ( see Appendix C), the average modulus of subgrade reaction may also be determined as follows: k · Ill:: Averag~ contact pressure Average settlement of the raft APPENDIX C ( Clauses 5.1.1, 5.2.1 and B-4.1 ) RIGIDITY OF SUPERSTRUcrURE AND FOUNDATION c-r. DETERMINATION OF mE RIGIDITY OF THE STRUcrURE C-l.l The flexural rigidity £1 of the structure of any section may be estimated according to the relation given below ( see also Fig. 2): E~ I, bl EI=-2HS- +~E~/b ~ [ 1+ ( (-I',,+1',,+/'/)/i r, + I'~ )b 2 ] where E, = modulus of elasticity of the infilling material (wall material) in kg/emit I, b H = = moment of inertia of the infilling in em", length or breadth of the structure in the direction of bending, total height of the infilling in em, E, = modulus of elasticity of frame material in kg/eml, moment of inertia of the beam in em', ItJ , I" == = -,,;;' lu 14 IS : 2950 ( Part I ) - 1981 -/-, t, I h; spacing of the columns in em, length of the upper column in em, h, = :zs length of the lower column in em, -/-- r , I, 1M I, I, moment of inertia of the upper column in ems, moment of inertia of the lower column in ems, and moment of inertia of the foundation beam or raft in ems. NOTE - The summation is to be done over all the storeys, including the foundation beam of raft. In the case of the foundation, 1'/ replaces I' band" becomes zero, whereas for the topmost beam, l' u becomes zero . ..... - - - - - - b - - - - -....... FIG. 2 DETERMINATION OF RIGIDITY OF A STRUCTURE C-2. RELATIVE STIFFNESS FACTOR K C-2.1 Whether a structure behaves as rigid or flexible depends on the relative stiffness of the structure and the foundation soil. This relation is expressed IS IS : 2950 ( Part I ) - 1981 by the relative stiffness factor K given below: a) For the whole structure K = E,-baa El b) For rectangular rafts or beams K = . E ( d c) For circular rafts K == 12 E, 2 R f2~. (: r )3 where EI E, == flexural rigidity of the structure over the length (a) in kg/ern", modulus of compressibility of kg/ern", the foundation soil in b length of the section in the bending axis in em, a d R length perpendicular to the section under investigation in em, thickness of the raft Of beam in ern, and radius of the raft in em. e-2.1.1 For K ( see 5.2.1 ). > 0'5, the foundation may be considered as rigid C-3. DETERMINATION OF CRITICAL COLUMN SPACING C-3.1 Evaluation of the characteristics ,\ is made as follows: A= 4{ kB " 4E,1 where k B E, = modulus of subgrade reaction in kg/em' for footing of width B in em (see Appendix B ). modulus of elasticity of concrete in kgf/cm l = width of raft in em :=:: 1 :.::: moment of inertia of the raft in em' 16 IS : 2950 ( Part I ) - 1981 APPENDIX D ( Clause 5.1.2 ) CALCULATION OF PRESSURE DISTRIBUTION BY CONVENTIONAL METHOD n-i. DETERMINATION OF PRESSURE DISTRIBUTION 0-1.1 The pressure distribution ( q ) under the raft shall be determined by the following formula: q = ~ ± -J~' · Qe~ Qe~ Y::r "T. w x where Q A'· = total vertical load on the raft, e. , e', [', I' · ~ · , = = total area of the raft, eccentricities and moments of inertia about the principal axes through the centroid of the section, and I.', I' ~ e' , e' may be calculated from the following equations: , -. x, y ;:;:: co-ordinates of any given point on the raft with respect to the x and y axes passing through the centroid of the area of the raft. 12 l~ = I, e. h' In T elf, and ., , = e. - e~ = e, - I ·· - e. I, where I., /, =z moment of inertia of the area of the raft respectively about the x and y axes th rouah the centroid, 17 IS : 2950 ( Part I ) · 1981 I.e" ea, ~--=- f xydA for the whole area about x and y axes through the centroid, and e" :::: eccentricities ill the x and y. directions of the load from the centroid. For a rectangular raft the eq uation simplifies to: q =-== Q A (J ± 12~yY b2 ± 12ezX)' al where a and b the dimensions of the raft in the x and y directions respectively. NOTE - I f one or more of the values of ( q ) are negative, as calculated by the above formula. it indicates that the whole area of foundation is not subject to pressure and only a part of the area is in contact with the soil, and the above formula will still hold -good, provided appropriate values of /z' / v' /%11' e z and ell arc used with respect to the area in contact with the soil instead of the whole area. APPENDIX E ( Clause 5.2.1 ) CON1'ACT PRESSURE DISTRIBUTION AND MOl\'lENTS BELOW FLEXIBLE FOUNIJATION E-l. CONTACT PRESSURE DISTRIBUTION E-l.1 The distribution of contact pressure is assumed to be linear with maximum value attained under the columns and minimum at mid span. E-l.2 The contact pressure for the full width of the strip under an interior column load located at point i ( Pi ) can be determined as ( see Fig. 3B ): p. = 5P, + ±-~i\fi i where i~ i Pi M. ~ average length of adjacent span ( m ), = column load at point i ( t ), and = moment under an interior columns located at i. 18 IS : 2950 ( Part I ) - 1981 E-l.3 The minimum contact pressure for the full width of the strip at the middle of the adjacent spans pm' and pmr can be determined as ( see Fig. 3A ): pm, = 2P, J,-_ ILl I, Pi .1 t. pmr pm ~ 2P. - - p, /r/ I, I + pml = pmr -----2--- where l., I, as shown in Fig. 3A. E-l.4 If E-2.3( a) governs the moment under the exterior columns, contact pressures under the exterior columns and at end of the strip p. and p, can be determined as ( see Fig. 3C ): 6M, 4P, Pmll p,:.::= - - - C +--h----· + ---cp, - po c: -CI- - 3Me T where P" pm, M,. /1' C as shown in Fig. 3C. E-l.S If E-2.3 (b) governs the moment under the exterior columns, the contact pressures p. and P» are determined as ( see Fig. 3C ): v- ~ e- = -4('+ 4P, - pml} 11 E-2. BENDING MOMENT DIAGRAM E-2.1 The bending moment under an interior column located at i ( see Fig. 3A ) can be determined as: M4 = - 4I (0'24'\1 P. - + 0-16) E-2.2 The bending moment at midspan is obtained as ( see Fig. 3B ): M", = M, + M. where M, ~ moment of simply supported beam = 48 [ p, where is ( I) + 4p", + pc 19 (r ) ] 1, p.( I ), p.( r ). pm are as shown in Fig. 3B. IS : 2950 ( Part I ) - 1981 PI-I 1-1 'Wi\V4)+>.iC L I t ~1'12=t1r/2-tji.1 i'"- ml i --... ...- I . I , I, I P, P,·· _. N1 = · lr ~'J'. , I r . I,~HI~ I I . . -. . I. I I I. . I I &Ilrllttll .1 L 11~r i'" "IM" '~...,. f , I 1 i I :.J' I , . ~ I I i 3A Moment and Pressure Distribution at Interior Column PmI " (t) Pt It) --- Pmr J-l t 38 Pressure Distribution Over an Interlor Span '. ... ; III· i-lllllnl~llllll~ .L .. ... ", ' -- I.i."" ,..,_. 3C. Moment and Pr···ure Distribution at Ext.rior Column FlO. 3 MOMENT AND PRESSURB DlSTRlBtmON AT COLUMNS 20 IS : 2950 ( Part I ) · 1981 E-1.3 The bending moment M, under exterior columns can be determined as the least of ( see Fig. 3C ): a) b) :~ (0'13Ml + H)6.\C - 0'50) ( 4P. - p.ll) C' -. 4C--}-/ - - T 1 APPENDIX F ( Clause 5.2.1.1 ) FLEXIBLE FOUNDATION GENERAL CONDmON F-!. CLOSED FORM SOLUTION OF ELASTIC PLATE THEORY F-t.1 For a flexible raft foundation with nonuniform column spacing and load intensity, solution of the differential equation governing the behaviour of plates on elastic foundation ( Winkler Type) gives radial moment ( u. ) tangential moment ( Me ) and deflection ( w ) at any point by the following expressions: w ~ PL'I 4D %1 (r Y ) where P = column load; r = distance of the point under investigation from column load along radius; 21 IS : 2950 ( Part I ) - 1981 L = radius of effective stiffness; ~ -f k ~ modulus of subgradc reaction for footing of width B; D ~~ flexural rigidity of the foundation; F;(!. --~ -i2(J --=-7--it =-:: raft thickness; modulus of elasticity of the foundation material; functions of shear, moment and deflection ( see Fig. 4 ). E 2 1 , Z~, Z4 co-ord ina tes: M~ po =-~ poisson's ratio of foundation material; and F-I.2 The radial and tangential moments can be converted to rectangular = -= M, cos? ¢> M, sinl " M" where + M, sin" ,p + M, cos" 4> 4J :-:; is the angle with x axis to the line joining origin to the point under consideration. F-t.3 Tho shear Q per unit width of raft can be determined by: Q where =~ =- -~ z~ (~) = function for shear ( sec Fig. 4 ). F-l.4 When edge of the raft is located within the radius of influence, the following corrections are to be applied. Calculate moments and shears perpendicular to the edge of the raft within the radius of influence, assuming the raft to be infinitely large. Then apply opposite and equal moments and shears on the edge of the mat. The method for beams on elastic foundation may be used. F-l.5 Finally all moments and shears calculated for each individual column and walls are superimposed to obtain the total moment and shear values. 22 IS : 2950 ( Part I ) · 1981 . ----, I ·"1" , 0-5 - 0-4 Z, (r/l) , .......... ,,~ ...J .. N U) o z o z ~ G-1 o , ,'" /' I , ,t"') N - ()'2 - <, \, ,I ,.//''\.Z3 I I / .., I I..,"'''' (r/lJ I , , · f :"'-ZI, , , r. 1 (rIll o FIG. 4 FUNCTIONS FOR. SHEAR MOMENT AND DEFLECTION 23 IS : 29SO ( Part I ) - 1981 ( Continued from POle 2 ) Members SHRI M. D. TAMBU:AR DR A. V ARADARAJAN DR R. KAN1RAJ ( A lternate SHRIO. RAMAN, Represen: i", ) Bombay Port Trust Bombay Indian Institute ot TcchnoJoay. New Delhi Director General, B1S ( Ex-officio Member ) Director (Civ Eoa) Secretary K. M. MATHUR Deputy Director ( Civ Eng ). BIS SHRJ Bearing Capacity of Foundation Subcommittee, BDC 43 Convener SHJU S. GUllA Membn'8 DEPUTY DIRECTOR STANDAIlDS Calcutta Port Trust, Calcutta ~ r Desips LUCkDOW & ( B &: S ), CD-II StaDdar