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Pile design guide (Collected)

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Pile cap design and example solution.

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Pile design guide (Collected)

  1. 1. Design of piles & pi| e—cap I / ’/ '/ ‘I : :~4»~. a«-¢§¢x; ~-»; r¢~- A guide for the analysis and design of pile foundation with reference to code and illustrative examples KEUQR %§§‘“‘”§ NATIONAL ENGINEERING SERVICES PAKISTAN (Pvt. ) Limited : ;§](a . fi§§"“‘5
  2. 2. Design of pile & pile cap General Pile layout pattern: Pile underpile cap should be layout symmetrically in both directions. The column or wall on pile cap should be centered at the geometric center of the pile cap in order to transferred load evenly to each pile. Example of some typical pile layout pattern are shown below: El 00 000 000 00° 000 0+0 00 coo coo III: IE! IS: oooo oooo cocoa on-o oocoo do-O-co coco oooo coo Ifll up]: I‘lfI. l
  3. 3. Pile spacing, edge distance, and pile cap thickness: Pile spacing: - In general, piles should be spacing at 3 times ofpile diameter in order to transfer load effectively to soil. Ifthe spacing is less than 3 times of diameter, pile group settlement andbearing capacity should be checked. 4’-6” KKK Pile cap thicl<ness: - Pile cap thickness is normal determined by shear strength. For smaller pile cap, the thickness is normally governed by deep beam shear. For large pile cap, the thickness is governed by direct shear. When necessary, shear reinforcement may be used to reduced thickness pile cap. I mini. scum rm mm su-‘J9 ITIIIM. El! !! l'l3?H. IIG-KIEESIIEIF Edge distance: - The edge distance is normally governed by punching shear capacity of comer piles. According to AASI-{TO code, it shall not be less than 9 inches. (Refer next head)
  4. 4. References of the code Limitations/ Requirements for Pile Foundation Design: - AASHTO Specifications: 4.5.15 Spacing, Clearances, and Embedment 4.5.15.1 Pile Footings 4.5.15.l. I Pile Spacing Pile footings shall be proportioned such that the mini- mum center-to-center pile spacing shall exceed the greater of 2 feet 6 inches or 2.5 pile diameters/ widths. The dis- tance from the side of any pile to the nearest edge of the pile footing shall not be less than 9 inches. 4.5.15.1} Minimum Projection into Cup The tops of piles shall project not less than 12 inches into concrete after all damaged pile material has been re- moved. but in special cases. it may be reduced to 6 inches.
  5. 5. 4.5.l7 Cast-in-Place Concrete Piles 4.5. 11.1 Materials Cast-in-place concrete piles shall be. in general. cast in metal shells that shall remain pclTn: mcnll_' in place. How- ever. other types ot'cast—in-place pi lcs. plain or reinforced. cased or uncased. may be used if the soil conditions per- mit their use and if their design and method of placing are satisfactory. ' 45.17.: Shape C : isl—in-place concrete piles may have a uniform cross- section or may be tapered over any portion. 4.5.17.3 Minimum Area - The minimum area at the butt of the pile shall be I00 inches and the minimum diameter at the tip of the pile shall be 8 inches. Above the butt or taper. the minimum size shall be rt»: specified for precast piles. 4.5.17.-I‘ General Reinforcement Requirements Cast-in-place piles. carrying axial loads only where the possibility of lateraliorces being applied to the piles is in- significant need not be reinforced where the soil provides adequate lateral support. Those portions of cast-in-‘place concrete piles that are not supported laterally shall be de- signetl as reinforced concrete columns in accordance with Articles 8.154 and 8.16.4. and the reinforcing steel shall ‘extend 10 feet below the plane when the soil provides ad-
  6. 6. equate lateral restraint. Where the shell is smooth pipe and more than 0.12 inch in thickness. it may be considered as load carrying in the absence of corrosion. Where the shell is corrugated and is at least‘0.075 inch in thickness. it may be considered as providing confinement in the absence of corrosion. ' ' ' 4.5.17.5 Reinforcement into Superstructure ' Sufficient reinforcement shall be provided at the junc- tion of the pile with the superstructure to make a suitable connection. The cmbedment of the reinforcement IMO the cap shall be as specified for precn st piles. 4.5.17.6 Shell Requirements The shell shall be of sufficient thickness and strength so that it will hold its original form and show no hnmtful distortion after it and adjacent shells have been driven and the driving core. if any. has been withdrawn. The plans shall stipulate that alternative designs of the shell must be approved by the Engineer before any driving is done. 4.5.17.7 Splices Piles may be spliced provided the splice de velops the full strength ofthe pile. Splices should be detailed on the contract plans. Any altcmativc method of splicing pro- viding equal results may be considered for : tppro': .tl. d. S.l7.8 Reinforcement Cover The reinforcement shall be placed rt clear distance of not less than 2 inches from the cased or uncased sides. When piles are in corrosive or marine environments. or when concrete is placed by the water or slurry displace- ment methods. the clear distance shall not be less than 3 inches for ttncased piles and piles with shells not suffi- ciently corrosion resistant.
  7. 7. Uniform Building Code I 997: 1808.2 Uncased Cast-in-place Concrete Piles. 1808.2.l Maten'al. Concrete piles cast in place against earth in drilled or bored holes shall be made in such a manner as to ensure the exclusion of any foreign matter and to secure a full-sized shafi. The length of such pile shall be limited to not more than 30 times the average diameter. Concrete shall have a specified compressive strength ft of not less than 2,500 psi (17.24 D/ £Pa). EXCEPTION: The length of pile may exceed 30 times the diame- ter provided the design and installation of the pile foundation is in ac- cordance with an approved uivestigation report, 180 8.2.2 Allowable stresses. The allowable compressive stress in the concrete shall not exceed 0.33f'¢. The allowable compres- sive stress of reinforcement shall not exceed 34 percent of the yield strength of the steel or 25.500 psi (175. 7 MPa). Tie beams: 1807.2 Interconnection. Individual pile caps and caissons of every structure subjected to seismic forces shall be interconnected by ties. Such ties shall be capable of resisting, in tension or com- pression, a minimum horizontal force equal to 10 percent of the larger column vertical load. EXCEPTION: Other approved methods may be used where it can be demonstrated that equivalent restraint can be provided.
  8. 8. The0ry: - Punching shear The punching shear strength according to ACI-318 is qw, : Hf; where (I) = 0.85 is strength reduction factor, fc’ is compressive strength of concrete. The critical section of punching shear stress is at a distance, d/2, from edge of pile, d is the effective depth of pile cap. For corner pile, the critical section normally extends to the corner edge of pile cap since it gives less shear area. Direct shear or beam shear The critical section of direct shear is at a distance, d, from edge of column or pile. The direct shear strength according to AC1 is (l)V¢ :0.85[l.9/ f¢’+2500p(, ,(Vud/ Mu)] 2 0.85(2/ fc’) where pa, (m 0.002) is reinforcement ratio, V” is factored shear stress, Mn is factored moment at the critical section. For pa, m 0.002 and fc’ between 3000 psi and 4000 psi, ¢v, :0.85[1.9/ f¢’+0.1/ f., ’(Vud/ Mu)] 2 0.85(2vr; ) Deep beam shear Deep beam shear is evaluated at face of column when on < d and Vu*d/ Mu Z 1 The shear strength is calculated as follows: cbvc :0.85{(d/ co)[3.5-2.5(M, ,/Vud)][1.9/ fc’+2500pa, (Vu*d/ Mu)]} 2 0.85(10/ fc’) where 03 is the distance from face of column to the nearest pile. For pa, m 0.002 and fc’ between 3000 psi and 4000 psi, ¢v, =0.85{(d/ (n)[3.5-2.5(Mu/ V,, d)][1.9/ fc’+0. Hf, ’ (Vu*d/ M,, )]} 2 0.85(10/ fc’) Flexural reinforcement Design of flexural reinforcement is the same as spread footing design. The critical section is at face of column.
  9. 9. Pile load calculation Pile load can be calculated as pi = P/ n+Mx*dx/ Iy+ My*dy/ Ix where pi is axial load for individual pile, P is column load, M is moment from column moment and/ or from eccentricity between center of column and center of pile group, n is total number of piles, dx and dy are x and y distance from center of pile group, Ix and Iy are moment of inertia of pile group in x and y directions. Ix and Iy are calculated as 1,. : 2 df, 1, : 2 dx? Design procedure 1. Estimate number of pile needed(based on working design combination and allowable load carrying capacity of pile). Select pile layout pattem. Calculate individual pile load. The maximum pile load shall not exceed allowable pile capacity. 2. Calculate factored pile load. Assume a depth of pile cap (never forget to subtract the “embedded part of pile into the cap” for effective depth calculation), calculate factored moment and shear at critical section, check direct shear 3. Calculate moment and shear at face of column, check deep beam shear. 4. Check punching shear and edge distance. 5. Design flexural reinforcement. Design Examples Pile cap design example -1: Design Data: Column dead load: PD : 300 kip Column live load: PL : 350 kip Column dead load moment: MDX : 40 ft-kip, Mpy = 80 ft-kip Column Live load moment: MLX = 35 ft-kip, MLY = 65 ft-kip Column size: 18"x18" concrete column Type of pile: 16 in diameter concrete pile Allowable pile compression capacity: PC : 125 kip Allowable pile tension capacity: Pi : 50 kip Compressive strength of concrete: fc’ = 3000 psi Tensile strength of reinforcing steel: fy = 60 ksi Requirement: Design pile group and pile cap 1. Estimate number of pile and select pile layout pattem Total service pile vertical load: P : PD+PL : 650 kip Estimate number of pile: n = P/ PC = 5 .2
  10. 10. Try a six—pile layout pattem, n = 6 Minimum spacing ofpi1e: s = 16 in X 3 = 4 ft 2. Check pile capacity: dxi = —4 rt, d, ,2=-4£t, d, .3=0 ft, d, .4=o ft, d, .5=4ft, dx. -.=4£t I, .= d, ,i2+ d, ,22+ d,52+ dx42+ d,52+ dxf = 64 ft? dy1=-Zfli, dy2=2, ft, dy3=-2 fli, C1y4=Z ft, dy5=-2 R, dy5=2 fl, Ix = d, ,i2+ d, ,22+ d, a2+ d, ,., "+ d, .52+ d, i52 = 24 ft? Column service load moment: Mx = I/ IDX+I/ ILX = 75 M, =MD, ,+Mi, ,= 145 ft-kip Maximum pile compression load: Pi = Pln+(i/ I,, *d, i/I, i)+(IvI, *d, ii/ I,, ) = 93 kip P2 = P/ n+(M, ,*d, ,2/I, ,)+(1/ I,, *d, ,2/1,. ) = 105 kip P3 = P/ n+CM: x*dyjI, ,)+(I/ Iy*Clx3/Ty) = 125 kip P4 = P/ n+(M, ,* , ,)+(1/ I,, *d, ,4iI, ,) = 1 14.5 kip P5 = P/ n+(1vI, i*d, ,5/I, ,)+(1/ I,, *d, .5/1,. ) = 11 1.1 kip P5 = P/ 'n+(1/ Ix* , ,)+(1VIy*d, i5/'I, ,) = 123.6 kip 3. Assume a pile cap of 3'6" depth, the top ofpile is at 6" above bottom ofpile cap and the reinforcement is at 2" above top ofpile, the effective depth is d = 34 in Since the effective depth d is less than 4 it check direct shear in the longitudinal direction. Factored column load, Pu = 1.4*PD+1,7*Pi_ = 1015 kip Fa ctored column moment: Mix = l.4MDx+l.7MLx= 115.5 ft-kip Ivtuy = 1.4MDy+1.7Mi_, = 222. 5 ft—kip Factored pile load: Pui = Pufn+(1vIu, ,*d, .i/ I,i)-1-(1/ Iu, ,*d, ii/ I,, ) = 145. 6 kip Puz = Pu/ 'n+(1vIu, i*d, .gfI, i)+(1/ Iu, .*d, ,2fI, ,) = 164.8 kip Pug = Pu/ n+(I/ Iu, ,*d, ,3/Ix)+Cl/ Iu, .*d, i3/I, .) = 15 9. 5 kip Pu4 = P, ,!n+(14,, ,*d,4/I, ,)+(1/ I,, ,,*d, ,4lI, ) = 17 8.7‘ kip Pus = Pu/ n+(1/ I,i, .*d, .5/I, i)+(1/ l'u, ,*d, us/ I,, ) = 168.6 kip Pug = Pufn+(1/ Iu, i*d, ,5fI, i)+(1&, ,.*d, i5lI, ) = 192.6 kip The factored shear force at the critical section is Vu = Pu5+Pu5= 361.3 kip The factored moment at one d from face of column is Mu = (1>u; +Pus)(4 ft — d — 9 in) = 150. 5 ft-kip Assume an edge distance of 1'9", the width ofpile cap is b =75 ft 1’.
  11. 11. The shear strength of pile cap is ¢v, =o.85[1.9w'f, '+o.1«lg'(vudJ1v1.i)]bd= 367.5 kip > 3613 kip OK. 3. Check deep beam shear in the short direction. Factored shear force: Vu = P,,2+P, ,4+P, ,5 = 536. 3 kip The factored moment face of column is Mu = (Puzk Pu4+Pu5)(2 ft — 9 in) = 670.4 ft-kip The deep beam shear strength of concrete is as follows: The distance from pile to face of column, co = 24in — 9 in =15 in The length ofpile cap is b =11 ft The ratio, 'v‘u*d/ Mu = 2.26 > 1 W, =0. 85 { (d/ oo)[ 3. 5-2. 5(M, fV, ,d)][1 .9lf, ’+0. 1 xii“; O/ ',, *d: M,)] }bd=25 24 kip ¢Vc =0.85(10N'f, ’)bd = 2184 kip > 536.3 kip OK. 4. Design reinforcement in short direction: Mi = 670.5 ft—kip Factor: R, .= Mu/ (0.9*b*c12) = 56 ksi, m = f, .I0.85fg = 23. 5 Reinforcement ratio: pu, = (1/m)[1—i(1—2rnR, i/f, .)] = 000094 Check minimum reinforcement: p, ..i, i=pu, *4/3 = 0.0012 or p, .u, .= 0.002 Area of reinforcement: As = 0.002*b *d = 9.4 inz. Use 10#9 bar, A, = 10 inz. Design reinforcement in longitudinal direction: b = 7.5 ft Mu = (Pu5tP. ;6)(4 it — 9 in) = 1 174 ft-kip Factor: R, .= 1vt, l(0.9*b*d2) = 150.4 ksi Reinforcement ratio: pu, = (1/m)[1-i(1-2n1Ru»’fy)l = 0.0026 Check minimum reinforcement: p, ,.ui= pu, *41‘3 = 00034 Area of reinforcement: A, = 0.0034*b*-:1 =10.5 in”. Use 11:49 bar, A, =11 in? 11
  12. 12. P116 ca desi nexam le 2 (Referenced from Har1a'book0fConc. Engmeermg ByMARKFINTEL) M, , x 12,000 53.5 x 12.00:) / , ' 179 ' 423()= ton‘, ti’ = 423, I. = 20.5 in. . say 21 in. Sytrequtred) = 4210 12m. 24 tn. -1 Fig. 5-38 Two-way shear lfl strut-. u. 2. plain concrete footings. Check footing thickness for two-way shear (for illustrative pur- poses only). See Fig. 5-36. 33 ' AAV1 = (I-2) =7.5s rt’ AV, ,,- say, x 4,: 7.55 x 6.35 = as ktps 9., » Ar, ,= lStl —4t= llllkip _ tP. .- AP. ) |000 _t1uxtooo 1,04 4 x 33 x 21 "in = 40 psi n. permissible u, ,,=4ofi; =4 x 0115 x c/3ooo= 1147 psi 5.5 REINFORCED CONCRETE FOOTINGS WITH CONCENTRATED REACTIONS (FILE CAPS). 5.5.1 General Principles Where soil conditions do not favor the design or construc- tion of shallow foundations (spread footings), but a firm FOOTINGS 131 soil stratum can be found at greater depth, piles can be used to transfer. the loads from the superstructure down to the soil stratum, where the required resistance is available. The piles may develop this resistance by end bearing (bearing piles)on the firm stratum: or by skin friction (friction piles) developed by driving the piles into the firm stratum. Foun- dation piers or caissons can also be used for similar pur- poses but do not form a part of this discussion. Similar to the action of a spread footing, is fooling on piles (commonly called pile cap) has to distribute the col- umn load to the piles in each group, which in turn will transmit it to the subsoil. The main difference between the two types of footings lies in the application of the base re- : :-. ions winch. in the case of a footing on pit”, ""'wioN~ at a number of concentrated loads. if we *4 '1. . ‘ ' of all pile reactions in a group, just for reasons of comparison, by the base area of the pile cap, we obtain an equivalent bearing pressure caused by the beating capacities of the individual piles. Such an average bearing pressure would be quite high because of the large bearing capacities of the individual piles. These large pile capacities were brought about by great progress made in the theo- retical understanding of the soil resistance; by improvement in the quality of the materials mod; and by the higher power and reliability of modern driving procedures and equipment. The allowable bearing capacity that can be expected from a pile is usually based on the information gained from exploratory soil borings, and evaluated with the help of soil mechanicahprinciples; it should be confirmed, huw- ever, by performance tests made on the site to ascertain the actual conditions. Depending on the availability of rock, hardpan, or other firm soil stratum and on their dis- tance below grade, the engineer will decide whether bear- ing ptles can be used economically. Otherwise, he has to resort to friction piles of some sort to utilize the available soil condition. Lack of a firm soil stratum at reasonable depth can some- times be treated also with the help of floating (boatlike) foundations which do not form a part of this discussion. The structural design of a pile cap is, in principle, not af- fected by the type of pile to be used, because it is primarily dependent on the magnitude of the pile reaction; however, a few explanations are necessary for a better understanding in the evaluation of the basic design approach. 5.5.2 Number of Files Required in the case of a spread footing, the size of the footing is determined from the total load on the footing and the al- lowable bearing pressure; hence, the size of the footing is rather made to order. in the case of a pile load, however, the number of piles is determined from the total load and the allowable load bearing capacity of each individual pile. Since the addition of a pile will raise the capacity of the whole group by a considerable amount, some of the pile groups may have, in order to be on the safe side, a capacity that exceeds that of the column load by a substantial amount. Furthermore it is common practlge__g9_u_sg, reasons of stabili ' ‘mu o _,2il§_s_j_t1_a__f nw; . a . .minlm_um_ot. .twn. utles_lLa_£o. unda; . . . I _ . I p. t1e_' onLx_i. t‘ : .mmfld . itL. ttIu1.dire¢'. -. t. ions. _ These minimum requirements have to be satisfied even it’ the capacity provided by the pile group far exceeds the amount of the load to be supported. it is good practice to design the pile caps in any case for the full allowable capacity of the group. This is done whether required by the column load or not, and in spite of the waste that may
  13. 13. ‘I232 - HANDBOOK OF CONCRETE ENGINEERING be connected with it, to permit full utilization of the pile capacity under any circumstances. in the case of bearing piles, every pile in a group may be considered to act as an independent pier down to the hear- ing stratum and to share equally in the carrying of the load, in the case of friction piles, the number of piles in a group affects their carrying capacity, especially that of the in- terior piles. Although this deficiency is usually averaged over the entire pile group, as far as the capacity of the group is concemed, the variations in the capacity of each individual pile requires, sometimes, consideration in the design of the pile cap. in either case, whether we are dealing with bearing piles or friction piles, there is always a chance that some piles in the group may develop a smaller (or greater) resistance than others; a pile cap ought to be stiff enough to equalize this condition. It is therefore advisable not to keep the effective depth of a pile cap down to the minimum re- quired, but to increase it somewhat wherever possible. The design of a pile cap follows in general the sanw rul: -» and regulations as that of a spread footing, except that the base reactions (pile reactions) are applied as concentrated loads in the center of each pilefittention is drawn to sec- tio'n l5.5.5 of AC1 318-71 whic tales that “in com uti the external shear on__an_y se_cti9n_ _hroggh_. a,i_ooting sup- por e entire reaction £r. om. any. pile whose center is loiated d, ',/2 (d is th£jj_le_diameter. at the. upper end) or more outside Hie section shall be assumed as pro- ducing’ shear on _the‘. section. The_react. ion from any pile whose ceiiter is located. d,[2 or_mpr_e inside the section slTal1'be assumed as producing no shear_on the section-. For in‘tefiie‘a1aie positions‘ csrtarpiie cente‘r', the "portion the pile reaction to be assumed as producing shear on the sec- tion shall be based on straight line interpolation between full value at d, ,/2 outside the section and zero value at dg/ Zginside the section. " _ For evaluation of pile reactions under various loading conditions see'the following section. The considerable intensity of the concentrated pile reac- tions requires that more than usual attention be given to the design for shear in the concrete cap and the develop- ment (anchorage) of the reinforcement in the section. Due to the importance of a crack free entity ofa pile cap in the distribution of the column load to the supporting pile group, the use of plain concrete is not permitted for pile caps. .- 5.5.3 Evaluation of Pile Reactions -1. Concentric loading condi! ian. r—After the allowable pile reaction, RP, (often incorrectly call'ed “allowable _pile, Cafiacily"). has been determined o‘r evaluated by principles of soil mechanics, ‘ the minimum number of piles for each column load can be determined as follows: The effective pile reaction, RP, (kips), consists of the allowable pile reaction, R1,, (tons), less the weight of the pile cap per pile, W . Any eventual surcharge shall be added to the weight o the pile cap. R, ,, (in kips) = 2Rp, , - W’, The number of piles, n , required to support the unfac- tored total column load is then up = P/ R,, ,, where up is to be rounded up to the next whole number. 'Veriflcatlonof the validity of this “allowable pile reaction" la usually established by one or more pile loading tests performed at the site under actual driving conditions and at the beginning of con- atrucllon. A safe assumption of the allowable pile reaction. however. has to be made. at a much earlier date to enable the engineer to design the foundation ahead of the actual construction. Unless special conditions require a spreading of the piles, they are assembled in tight patterns to arrive at the most economical design for the pile caps. An often recommended spacing, cp, is about three times the butt diameter of the pile. usually not less than 2% ft. The most common spacing for piles of an average pile reaction ranging from 30 to 70 tons is 3 ft. -2. laading candilion or concentric loading with ma I a. te—To transform eccentric loading conditions into concentric loadings with moment at base proceed as follows: a_ find pile reaction R, for concentric loading condition b. find pile reaction RPM for moment at base c. superpose l and 2 R, +R, ,M < ZR” Vhere wind or earthquake are included, the R, ” can be increased by 33% if so allowed by the local building code. ‘. "i: -.- extra-me pile reaction due to a moment M is M [p6/zpG To calculate the moment of inertia of a pile group I, ,G, first find the centroid of the pile group and moment of inertia of all units in the group about the centroidal axis. '90 = :71 I RpM = where y is the distance of each pile in the group from the centroidal axis. Where a pile group consists of m equal, parallel rows of piles, the moment of inertia of the entire group is 1 . . . - 1 s 1,9 = .'p-1,, /Row = m ""—’(". -‘Ei cl :2 ' and the section modulus for the extreme piles in the group is H r(" r + 1) SP6 = m 4% cp However, if the parallel rows are not of the same configura- tion, sum up the moments of inertia for the various rows and find the section modulus of the extreme pile by divid- ing the moment of inertia of the entire group by the dis- tance of the extreme p‘le from the centroid, as S176 = [PG/ Z110 EXAMPLE 5-6: As discussed in section 5.3.2 for ordinary spread footings, the number of iles or their arran ement in the pile group depends only on the unlactorea loading conditions, as shown in Fig. 5-37, and the strength design of the pile cap has to be done by converting all loads and reactions to the factored conditions. column load: 1 D = 400 kip _ L = 520 R5: so tons total = 920 kip R, ,, = 2:2,, — w, = 2 x so - 6.5 - 93.5 kip 20 . np = % = 9.8 2 l0 piles - i J V K/ ‘ W, =/1P(Aq) = 3’(5o + 75 + 150 +450) = 6525 lb a 6.5 kip where Aq = |wL + slab + fill + cap]. See Fig. 5-37. 13
  14. 14. Sin slat: I l T 18 in. lill . i”i [36 in. pile cap : ___1|_L | I 1. _f_ __l A, = 3 n x 3 It Fig. 6-37 Pile cap. Conventional pile arrangement in ten~olle cap. r__¥ I I I _-_. _l EXAMPLE 5-7': lnvestrg' are ex. 5-6 for an additiottal wind moment of 450 kip-ft in the long direction of the pile group. The moment of inertia of the entire pile group can be considered as the sum of the moments of inertia of each row of piles or n, .,(n, ’,, —u _ 3(3’vi) ""’=2'_1T"2" 2x'72—+ 4(4’—1)_, _ 3 , +1x 12 13 81ft The section modulus of the extreme pile in longitudinal direction is then 1 S, g=l, ,'g/1.5 c, ,= 81/LS X 3 = 18 ft FOOTINGS 133 and the reaction on this pile due to the wind moment is M 450 R = ; = ——= 25 k’ P” Spg in "’ Summing up, we obtain a total maximum pile reaction under wind of a» RP + R, ,M= 93.5 + 25.0 = 123.5 kip Since the maximum allowable pile reaction under wind is. R, ,,(, ,,, = 1.33 x RP, = 1133 x too-133 > 123.5 kip no increase in the number of piles is required due to wind. EXAMPLE 5-8: Strength design of pile cap. The column load and allowable pile capacity is the same as in ex. 5-6. I". = 3000 psi. and I, = 60.000 psi Pier size is 22 X 22 in, , the butt diameter of the piles is 14 in. De- termine the thickness and reinforcement of the pile cap. The strength design of the pile cap is based on the R, " which is determ' d from the factored loading, similar to the q, for the spread fa and has also here no other significance. from dead load 400 X 1.4 ——— = 56.0 k‘ v‘ 10 ‘P from live load 520 X 1.7 T — 88,4 The factored. pile reaction is then 56.0 + 88.4 = 144.4 kips: it is, however, recommended to design the pile cap. for the maximum factored pile reaction based on the average load factor. average load factor 400 X 1.4 + 520 X 1.7 . ' or 1.6 920 maximum factored pile reaction due to column load is 93.5 X 1.6 a 150 kip Fig. 5-38 shows the layout for a ten-pile cap and the various ap- proaches that need to be followed in the evaluation of its strength design. Step I: For two-way shear section (a), as indicated in the lower left quadrant of Fig. 5-38, let us assume that the necessary depth has been evaluated with 30 in. and is checked herewith: the critical 1 * - Two - way shear lb) Two way shear (a) ‘—e—— 72 ill. ‘. _J Fig. 5-38 Stress evaluation in pile caps. 14
  15. 15. base size of the truncated pyramid is 22 + 2 X 30/2 = 52 in. The criiical shear force V1,, is then V2,, =6X l50.0+2X l6=932kip where the contribution of the outer piles located on the y -y axis is :1 ISO X I14:-=16 kip. d, ,= 14 in. . —f‘ < 5.5 = 1.5 in. U = VIII = 932xlt)O0 7" bodo (4 x 52)x aux 0.115 = l70 psi which is smaller than 4 / /f: 220 psi. Two-way shear action th). is indicated in the upper left quadrant of Fig. 5-38. It can be realized, by inspection of Fig. 5-38, that the actual shear distribution is unequal and will be much greater in the long direction. If we take an approach similar to ex. 5-3(b) we require a much. greater cap thickness. as evaluated in the approach (a) described above. In this respect we divide the shear action again into two portions separated by a 45" line placed at the corner of the truncated pyramid base. Let us assume again that the necessary thickness of 34 in. nas been evaluated before and is checked helow. The critical base size of the truncated pyramid is here 22 + 1 X 34/2 = 56 in. and the shear force for the most stressed quadrant becomes V', ,, =1x1so+ 2 x 107 = 364.0 kip where the contribution of the outer piles is l50X l(lIl4 = lU7.U KID. dp/ I + 5 = 10 in. V5,, 364 x iooo on = I = L I)gd¢ 56 X 34 X 0.85 but acceptable. The greater depth of 34 in. is. therefore, selected. = 225 > 220 psi Slep 2: One-way shear action as indicated in the upper right quadrant of Fig. 5-38. The critical line is 22/2 '» 34 = 45 in. away from the y ~ y axis. The critical shear rim: is than V, ,, = 150.0 kip. V“, 150 X 1000 II", = -—— = T = 56 ll, -do 92X 34 X 0. 5 which is smaller than 2/ f?= I10 psi. Step 3- The ». :-: 2:1 “‘7.‘{l'. ‘l'tS [or r1-mm-. , as indicated in the lower right quadrant of Fig. 5-38, are at the face of theipier; the moments and reinforcements are determined for these sections. critical section I: 7 2 25 43 M. = 150.0 = 1250 kip-ft 99 x 34‘ r= -17% - 9.6, 1<. , =1250I9.6 =13o, a, , = 4.37 M 1250 _ zoo A, = 73 = E7)? = 3.4 m. ’. p, ... ,. = 60 000- 0.0033 [4 I ' minimum trost~ tree depth A, ,,, .,, =o. oo33 x 99 x 34 = 11.3 in. ’. O! 1.33 x 11.4: ii.21ii. ’_ V which guvems critical section 2: M" = 3 X 150 X 20.5/12 = 7'70 ltip-i't 144 x 34’ 710 = jam. i<, , = l~1—7=56.a"= A.45 M 770 A, =—"— = — = s.1in. ’ cud 4.45 x 34 A, ,,. ,,, = p, ,,. ,, rm = -_o. oo33 144 x 34 = 16.] in. ’. or»- " ' 1.33 x s,1= as in. ’ which governs The selection and distribution of the bar: is done as described in Example 5-l. Step 4b. The maximum bar size that may be used has to he selected in such a way that the development (anchor) length of the bar is smaller or equal than the shortest available embedment length or the bar at either side of the critical section. 5.6 RETAINING WALLS 5.6.1 General A retaining wall is a structure designed for th_e purpose of providing one-sided lateral confinement of soil'or iill. All retaining walls, with the exception of true cantilever walls anchored to rock, are in principle gravity walls, i. e., their action depends primarily on their developed weight. In common practice, however, only those retaining walls are called gravity walls, where the dead weight required to make the resultant vector intersect the base within safe allowable limits is made up solely by the dead weight of the concrete. Such walls are usually designed unreinforced, Fig. 5-39a. The commonly called cantilever walls are in principle gravity walls where reinforcement is used to re- duce and modify the cross section of the concrete in such a way that portions of the soil or fill are utilized for devel- oping the necessary rightening moment, Fig. 5-39b. in every retaining wall design, regardless of the type used, three resultant forces, namely, the lateral confinement pres- sure, Q, the total developed weight, I‘, and the soil reaction ' or hearing resistance, R, have to be brought into_equilibn'um Fig. S-40a; in addition all internal stresses in the structure and all external soil reactions have to be within the per- missible limits. . Retaining walls of the commonly called cantilever type can be subdivided into two main groups: 1. Continuous walls of constant cross section, where every foot of wall length is providing its own equilib- rium, Fig. S-39b. 2. Sectional walls, where crosswalls introduced at certain looting at crosswalls only (al Fig. 5-39 Tvoes ot retaining walls. T3T‘ 15
  16. 16. Procedure for Three Dimensional Modeling of Piles and Pile-cap Arrangement Using Software Procedure: -. 1. W Define the modulus of sub-grade reaction 1:, of soil based on allowable bearing capacity q, as defined below: (Refer Fawtidarion Analysis & Design By BOWLES) as great as the soil stiffness as defined by k, . Recognizing this, the author has suggested the following for approximating it, from the allowable bearing capacity q, , furnished by the geotechnical consultant: SI: k, = 4o(sF)q. , kN/ m3 Fps: k, = l2(SF)q. , km’ (9.9) where q. is furnished in ksf or kPn. This equation is based on (ya - qua/ SF and the ultimate soil pressure is at a settlement AH = 0.0254 m or 1 in. (N12 ft) and k, is qu; /AH. For AH = 6. 12, 20 mm, etc. . the factor 40 (or I2) can be adjusted to 160 (or 48). 83 (or 24). 50 (or lo). etc. ; 40 is reasonably conservative but smaller assumed displacements can always be used. Select the dia ofpile and allowable pile capacity (From geotechnical investigation report). Determine the reaction of column (wall) under service load combinations. Multiply the maximum service reaction (enveloped combination) with 1. 2 (or u may enhance according to any other philosophy) and divide by the pile allowable capacity to get the number of piles required under each column (wall). (The enhancement of load will cater for the load moment interaction as Well as the backfill over the pile cap and weight of grade slab). Arrangement of the piles and pile cap wrt. the no of piles to be provided is shown in previous section of this document Arrange the piles accordingly or using any other arrangement that fits your requirement keep ing in View the stability of the assembly. While arranging and sizing the pile caps, the limitations of code for the minimum edge distance, center to center spacing between the piles and other limitations should be noted and must be taken in to consideration. For designing of piles provide the body constraints to all the meshed nodes of the pile cap except those nodes which contains column reaction and piles. Afterwards, there are two different approaches that can be followed. First approach is to consider the pile fixed after the length equal to 5 times dia of the pile (or u may extend it up to 8 times dia of pile or any other number) and then design it as column taking in to account the load moment interaction. 16
  17. 17. The second approach is to model the pile with its original length and provide lateral springs (k/ in or KN/ m) in both the local directions (lateral) throughout its entire length (Refer Foundation Analysis cl} Design By BOWLES). You may provide line springs or you may divide pile in to lft (lm) sections and provide point springs. Line spring can be calculated by multiplying the modulus of sub-grade reaction with the diameter (width) of pile. Point spring can be calculated by multiplying modulus of sub-grade reaction with the product of diameter (width) and length of segment of pile. Then design the pile as a column element. Make sure that every pile within a pile cap must be providing almost equal reaction. For designing a pile cap, remove the body constraint and then design it for flexure and check it against applicable shear (under ultimate load). (Author’s recommendation is to make two different models, one for the pile cap and other for the pile designing). For shear stress check it would be better to use the static methods to calculate the shear forces acting on the pile cap by taking column reaction and pile reactions from the software and performing calculation manually as explained in the examples. It is because of the difficulty in interpreting the stress contours resulting from the finite element analysis (although they must be correct if u have correctly modeled the structure) After finalizing the sizes and a preliminary estimate of steel in piles and pile caps (through the software) one should make sure that whether the reactions & the internal forces from the structure analysis program are comparatively same as that from the manual calculations. Different ways to check the credibility of your modeled structure is to pick one “column-pile cap-pile” assembly & check the summation of reaction of piles should equal the column reaction plus the load on pile cap, check deflected shapes under different load cases, check the average value of moment contour obtained from software to your manual calculation & repeat the same for shear forces. If the errors are insignificant, then you can trust the results of software and get the results for all other assemblies. On the other hand if not, then you must have made a mistake so perform rechecking. 17

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