npgeocalc piles theory v2.1

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GeoCalc

Pile Calculation TheoryVianova Systems Finland Oy

Versio 2.13.9.2010


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Vianova Systems Finland Oy Vaisalantie 6 Tel +358 9 2313 2100 [email protected] Espoo Fax +358 9 2313 2250 www.vi anova.fi

Table of Contents

Table of Contents .......................................................................................................................................... 2Version History .............................................................................................................................................. 31. Background ............................................................................................................................................ 42. Bearing resistance of pile ....................................................................................................................... 4

2.1. Level of safety ............................................................................................................................... 42.2. Design value for geotechnical bearing capacity of the pile ........................................................... 5

2.2.1. Static method for bearing capacity of pile which supports to soil layer ................................. 62.2.2. Method based on sounding to define bearing capacity of pile which supports to soil layer .. 9

3. Lateral stress displacement behaviour ............................................................................................. 113.1. Introduction .................................................................................................................................. 113.2. Cohesionless soil......................................................................................................................... 11

3.2.1. Effective stress Coulomb earth pressures........................................................................... 123.2.2. Total stress Coulomb earth pressures ................................................................................ 123.3. Cohesive soil ............................................................................................................................... 12

3.4. Introduction to the Calculation Model .......................................................................................... 143.4.1. Input Data for Geometry ...................................................................................................... 153.4.2. Generation of Nodes and Elements .................................................................................... 163.4.3. Loads ................................................................................................................................... 17

4. Structural calculations /3/ ..................................................................................................................... 184.1. Basis of design ............................................................................................................................ 18

4.1.1. Buckling of initially straight piles .......................................................................................... 184.2. Bearing capacity of piles with initial curvature ............................................................................. 21

4.2.1. Behaviour of a pile under axial loading ............................................................................... 214.2.2. Resistance of the soil .......................................................................................................... 224.2.3. Structural resistance of the pile ........................................................................................... 22


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Version History

Version Date Writer Changes0.1 06.02.2006 Markku Raiskila

0.2 14.2.2006 Timo Ruoho Layout changes

1.0 26.3.2006 Markku Raiskila picture updates, text checks


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1. Background

The purpose of this document is to explain the theory behind the pile calculations in No-vapoint GeoCalc.

The calculation model for the pile calculations has been developed in Tampere Universityof Technology by Markku Raiskila and Tim Lnsivaara.

The calculation engine itself has been implemented and programmed by Vianova SystemsFinland Oy based on the calculation model.

This document is written and maintained by Tampere University of Technology / Tim Ln-sivaara and Markku Raiskila.

2. Bearing resistance of pile

2.1. Level of safety

Definition of bearing capacity for pile the partial safety factors fromTable 1 are used,.

Table 1 /1/ Partial safety factors for definition of calculation value in ultimate limit state.

Factor b s t

Driven pile 1,3 1,3 1,3

Bored pile 1,6 1,3 1,5

Partial safety factors b and s from table 1 are used to define design valueto

base resistance and shaft resistance of the pile.Partial safety factors t may be used in the case when it isnt possible to define base resis-tance and shaft resistance separately.

With grouted piles are total safety factors used according to table 2 /2/

Table 2 /2/ Total safety factors for grouted piles

Factor b s t

Grouted pile 2,2 1,8 2,0

Characteristic value for geotechnical bearing capacity is evaluated from theoreticalultimate bearing capacity by dividing with factor (equation 1)

cm

ck

RR = (1)

Rck characteristic value for geotechnical bearing capacity of the pile.

Rcm is geotechnical bearing capacity which is evaluated with analytical orempirical calculations or measured in test loading


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Rbd

Rbk

b

=

is obtained from table 3 /1/ when static or dynamic tests are used,otherwise is 1,6.

Table 3

2.2. Design value for geotechnical bearing capacity of the pile

If formulas which are used bases to strength properties of soils, the geotechnical bearingcapacity R cd, is evaluated from equation 2:

sdbdcd RRR += (2)

Rbd design value for base resistance of the pile.

Rsd design value for shaft resistance of the pile.

Design value for base and shaft resistances of the pile are evaluated from correspondingcharacteristic values of bearing capacities dividing by partial safety factors (equations 3and 4)

(3)


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Rsd

Rsk

s

=

Rsk

1

n

i

qsikAsi( )=

=

Rbk qbkAb=

qbk

v Nq

=

(4)

Rbk is characteristic value for base resistance of the pile,Rsk is characteristic value for shaft resistance of the pile,

Yb,Y s is partial safety factors from tables 1 and 2.

Characteristic values for base resistance and shaft resistance of the pile are evaluatedfrom equations 5 and 6.

(5)

(6)

Ab is area of pile base cross section,

Asi is area of the pile shaft in soil layer i,

qbkis characteristic value of base resistance of the pile due to unit of area

qsik is characteristic value of shaft resistance of the pile due to unit of area in soil layer i.

2.2.1. Static method for bearing capacity of pile which supports to soillayer

Bottom zone of pile is defined with the soil layer which starts 5 D above pile base and ends3D below pile base and D is diameter of the pile. User may change default values 5 and 3.

The characteristic value for base resistance of the pile due to unit area in cohesionlesssoils is evaluated from equation 7.

(7)

Nq is bearing factor of the pile base from figure1,

v is effective vertical stress at the level of pile base.

is 1,6 (table 3) /1/

Calculation of effective vertical stress on pile shaft bases on the effective weights ofthe soil layers above the pile base presented as amount of diameters of pile.Amountof pile diameters defines the measure up from inspection point from inside which theeffective weights of soil layers are taken into consideration when the effective stressis calculated to inspection point. Effective vertical stress v at the level of pile basebases to same parameter.


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qsik

v Ks tan ( )

=

Figure 1 Bearing factor Nq.

Characteristic value for shaft resistance due to unit area in cohesionless soils is evaluatedfrom equation 8.

(8)

Kstan() is factor for shaft resistance which depends on material of the pile, driv-ing method and friction angle of soil (figure 2),

v is effective vertical stress at shaft of pile.

is 1,6 (table 3) /1/


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suik

sui

=

Figure 2 Factor for shaft resistance Kstan() 2a) displacement piles, 2b) re-placement piles

Characteristic value for shaft resistance of the pile in cohesive soils is adhesion be-tween pile and soil. Adhesion is estimated with undrained shear strength su of soil andadhesion factor with equation 9.

(9)

adhesion factor corresponding to material of the pile (figure 3),


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sui undrained shear strength in soil layer i.

is 1.6 or from table 3 /1/

Figure 3 Adhesion factor between pile and cohesive soil.

2.2.2. Method based on sounding to define bearing capacity of pilewhich supports to soil layer

Ultimate bearing capacity due to unit area of base resistance of the pile is evaluated from

sounding results by using average driving resistance from figure 4a or 4b.The base resistance of the pile is defined due to average sounding resistance in the soillayer which reaches the distance of 5 D above and 3 D below the pile base.

The ultimate shaft resistance capacity per area unit of the pile is defined due to averagesounding resistance as presented in figures 4a and 4b.

Characteristic values are evaluated from ultimate bearing capacity by dividing withfactor 1,6. /1/


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Figure 4 Base and shaft resistances of the pile


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k nh zD=

nh M

z=

Ed

z=

3. Lateral stress displacement behaviour

3.1. Introduction

Soil support reaction to the pile is modelled with springs. The deformation behaviour of the

springs, starting from the initial stress state and going towards the limiting earth pressures,is described with two different kind of models. The models can be used both with effectiveand total stress analysis.

3.2. Cohesionless soil

In cohesionless soil, it is assumed that the lateral subgrade reaction increases linearly tothe depth z=10*D and thereafter remains constant. Under static loading the subgrade reac-tion is obtained from equation 10.

(10)

The coefficient of subgrade reaction, nh, is obtained according to the equation 11 deter-mined under drained conditions from the compressibility modulus, M, of the soil or from themodulus of elasticity, Ed.

(11)

0,74 (according to Terzaghi),

1,0 (according to Poulos),

0,83 ... 0,95; for sand, while Poissons ratio varies between 0.25...0.15, re-spectively.

Lateral pressure-displacement relationship in the case of cohesionless soils is presented inFigure 5


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ks 50...150su

D=

Figure 5 subgrade reaction of cohessionless soil.

In the case of cohesionless soils, the corresponding ultimate earth pressure is obtainedfrom the equation 12.

+== 2'

45tan'4.43'4.432

pm Kp (12)

where is the effective overburden pressure and is the angle of internal friction of thesoil.

3.2.1. Effective stress Coulomb earth pressures

Vertical stress at depth h in soil is calculated from equation 13.

( ) ( ) ( )( ) +=h

wvpdxxxh

0

( 13 )

where )(x = weight of soil at depth h

)(xw

= weight of water 10 kN/m3 below ground water level

0 kN/m3 above ground water level

p = possible uniform load

3.2.2. Total stress Coulomb earth pressures

Vertical stress at depth h in soil is calculated from equation 14

( ) ( ) +=h

v pdxxh0

( 14 )

where )(x = weight of soil at depth h

p = possible uniform load

3.3. Cohesive soil

In cohesive soils the subgrade reaction depends on loading time and the diameter of pile.

In temporary loading, the subgrade reaction of cohesive soil is expected according to fig-ure 6 to be in the range in equation (15)

(15)


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ks 20...50su

D=

Figure 6 subgrade reaction of cohesive soil in temporary loading

In long-term loading, the subgrade reaction of cohesive soil is expected according to figure7 to be in the range in equation 16.

(16)

Figure 7 subgrade reaction of cohesive soil in long-term loading

In the case of cohesive soils, the ultimate earth pressure is normally in the range of six tonine times the undrained shear strength, su, of the soil (equation 17).

pm = 6...9 cu (17)


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ks M

D=

In the case of long-term loading, the subgrade reaction of the cohesive soil can be deter-mined more accurately with the compressibility modulus M from equation 18.

(18)

on 0,46 ... 0,74; for clay, where Poissons ratio varies between 0,4 ... 0,3, re-spectively

on 0,62 ... 0,83; for silt, where Poissons ratio varies between0,35 ... 0,25,respectively

Figure 8 Definition of horizontal subgrade modulus between soil layers /1/.

3.4. Introduction to the Calculation Model


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The single pile is modelled using common 2D beam elements with three degrees of free-dom (DOF) per node. Interaction between soil and wall is taken into account with support-ing springs as can be seen in figure 9. In the non-linear iterative solution the relationshipbetween displacements and earth pressure based spring stiffness value variation betweeninitial and passive value at each node of the model is solved.

Figure 9 Illustration of the mathematical model

3.4.1. Input Data for Geometry

Basic geometry of the wall to be calculated is defined according to Figure 10.

- distances to top end and bottom end of pile are given in meters measured from ter-rain surface.

In input data up to ten soil layers can be defined. For each layer bulk density, friction angleand drained shear strength parameters needs to be defined. There are also parametersdepending on the calculation method for each soil layer. It should be decided should thesoil layer be calculated in drained or undrained condition. Definitions of soil layer thick-nesses are described in picture 10.


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Figure 10 Definition of soil layers

3.4.2. Generation of Nodes and Elements

Generation of calculation model is based on user defined amount of beam elements permeter. Total number of elements em is calculated from equation 19.

em 1 floor H( ) 1+( ) em+:= (19)

in which emm is a user defined parameter identifying beam elements per meter andfloor(H) is the greatest integer less than or equal to embedded depth H of pile. Totalnumber of nodes is the number of elements added by one. The node number two is alwayslocated on terrain surface and first node is above surface on height of top end of the pile.

The largest node number is at the bottom end of the pile. The length of beam elementsfrom three upwards are equal and calculated from the equation 20.

LeH

em 1.5:=

(20)

Length of element two is Le divided by two and length of first element is equal to distancefrom terrain surface to top end of pile.


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After the generation of nodes and elements the borders of soil layers are adjusted to ele-ment divisions. First the borders are calculated from user defined thicknesses of soil layersand then placed to nearest midpoint of beam element of the pile. One adjusted layer bor-der can be seen in Figure 9.

3.4.3. Loads

Earth pressure from soil layers

The vertical pressure due to soil weight is calculated from the weight of soils over the nodepoints in the wall. Vertical pressure is converted to horizontal nodal loads according towhat is described in chapters 2.4 and 2.5

Concentrated loads at top of the pile

Bending moment and horizontal and vertical loads can be defined to top of the pile.

Figure 11 Loads to pile top


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4. Structural calculations /3/

4.1. Basis of design

Figure 12 Alternative drilled pile cross sections. Casing tube can also be with-drawn, when required.

A drilled pile is nearly always resting on the bedrock in Scandinavia. In the case of solidbedrock, the strength of the bedrock is commonly in excess of the design loads. Then themain task in dimensioning is to determine the structural resistance of the pile cross sectionin relation to the prevailing actions. The most important procedures related to the geotech-nical capacity are the appropriate working methods and their verification procedures in theexecution phase.

In dimensioning, the safety level against failure has to be chosen in every case dependingon the structure in question, prevailing conditions and the accuracy of available informationused in calculations. The safety factors applied in dimensioning are chosen according tonational or CEN-dimensioning codes.

A drilled pile is dimensioned either as a steel structure or as a composite steel and con-

crete structure depending on the shape of the cross section and the proportions of thesteel and concrete sections. The dimensioning can be carried out as a composite structureon the condition that the structure fulfills the requirements presented in national /15, 16/ orCEN-dimensioning codes /6/ for composite structures.

In the case of a drilled pile, where the steel section is located in the outer edge of the crosssection, the influence of corrosion during the entire life span has to be taken into account.

The most common practice is the corrosion allowance for the wall thickness.

The bearing capacity of a pile can be determined by the calculation method in both cohe-sive and cohesionless soils. In the case of cohesionless soils, the surrounding soil givesnotable lateral support to a pile so that the increase of the curvature of a pile, caused bythe applied load, is negligible.

The presented calculation model is applicable only to axially loaded piles. In the case ofbridge structures, for instance, more advanced computer-based calculation methods,which take into account the bending actions from the superstructure, have to be used.

4.1.1. Buckling of initially straight piles

When a straight pile is subjected to purely axial compressive forces of increasing magni-tude, at a certain critical value of the compression, a sudden lateral deflection of the pilewill take place. This process is called buckling and the value of that compressive force isknown as a critical load /9/.

When determining the buckling load of a pile, it is assumed that an elastic medium sur-rounds the pile completely. Therefore, whenever the pile deflects laterally, a correspondingdeformation in the medium will be generated /9/.


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The analysis of the bending of beams on an elastic foundation is usually based on the as-sumption that the reaction forces of the foundation are proportional at every point to thedeflection of the beam at the same point. This theory should be regarded only as a practi-cal approximation. The physical properties of soils are of a much more complicated naturethan that which could be accurately represented by such a simple mathematical relation-ship /9/.

However, in spite of the simplicity of this theory, it may often represent more accurately theactual conditions existing in soil foundations than some of the more complicated analyses/9/.

If we consider an initially straight pile with hinged ends (Fig. 13) which is supported byequally spaced elastic supports of equal rigidity, their action on the buckled pile can be re-placed by the action of a continuous elastic medium. The reaction of the medium, p, at anycross section of the pile is proportional to the deflection, y, at that section according to therelationship 21 /13/:

p=ksy (21)

The spring constant, ks, is referred to as the lateral subgrade reaction.

Figure 13 Reacion of elastic medium and the deflected shape of the buckled pile

For the elastic curve of the pile, the following differential equation can be deduced:

(22)E I 4x

y

d

d

4

P 2xy

d

d

2

+ ks D y+ 0=


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Pcr n2

2E I

L2

ksD L

2

n2

2

+=

This differential equation implies that the intensity of the load perpendicular to the axis ofthe pile is equal to the sum of the reaction pressure, ksDy, from the medium plus an addi-

tional amount,2

2

dx

ydP , due to the axial load and curvature of the pile /8/. D is the diame-

ter and EI is the bending stiffness of a pile.

On the basis of the boundary conditions, the following expression for the critical load, P cr,producing failure of a pile by buckling is obtained:

(23)

The ultimate strength is thus determined as the sum of two terms. The first term dependson the stiffness of the pile and is equal to the buckling load according to Euler. The secondterm depends only upon the properties of the medium and the length of the pile. The firstterm is dominant for short piles, but for increasing length of the pile, the additional strengthobtained on account of the support from the medium becomes more significant /8/.

In every case, for given values ofks, D and EI, n must be determined in such a way as tofind the least value ofPcr. Differentiating dPcr/dn=0 gives:

(24)

The integer number which is nearest to the value ofn determined from equation (24) issubstituted into equation (23), to obtain the minimum value of the critical load /9/:

IEDkP scr = 2 (25)

It is interesting to note that the minimum value ofPcrdoes not depend upon the pile length,but is determined solely by the modulus of horizontal subgrade reaction, Mh =ksD, and thebending stiffness, EI, of the pile. However, in the case of a pile having a length, L, lessthan a value of critical length, Lc, corresponding to n=1 in equation (24),

4

Dk

IEL

s

c

= (26)

the minimum critical load, Pcr, will be influenced by the length of the pile. In other words,when the length of the pile is smaller than the corresponding critical buckling length, Lc,which expresses the distance between deflection of zero in a buckled pile, the value of thecritical load increases and it then can be determined according to equation (23) /8/.

The quantity, n, that represents the number of halfbays formed by the pile must always bean integer. For values that are not integers, the ultimate load will always be greater thanthe minimum critical buckling load /8/.

A greatest practical significance is, however, the minimum load determined according toequation (25). The minimum load, the elastic buckling load, is a parameter which is used indetermining the second order moment for a pile.

nL

4ks D

E I=


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4.2. Bearing capacity of piles with initial curvature

4.2.1. Behaviour of a pile under axial loading

Very often the design load of a pile is determined according to the smallest value of eitherthe buckling load of an ideal straight elastic pile supported by linear elastic springs, or the

axial battering capacity of the pile cross section, both incorporating large safety margins(cf. Finnish code for driven piles /12/, for instance).

However, a pile in the ground always has imperfections and deviations compared to theideal case. In reality, a pile will have at least a slight initial curvature after installation in theground before loading is applied. Bearing capacity of piles with initial curvature has beeninvestigated, for example, by Broms /5/ and Bernander and Svensk /4/.

Axial loading tends to increase the curvature of a pile, resulting in both bending stresses inthe pile and lateral stresses in the soil. The maximum load carrying capacity of an axiallyloaded pile is obtained when either the maximum structural capacity of the pile cross sec-tion is reached or when the maximum soil reaction along the pile reaches the maximumcapacity of the soil surrounding the pile.

The maximum load for an initially deformed pile decreases as the magnitude of the initialdeformations increase. Under no conditions can the failure load exceed the elastic bucklingload, which represents the upper bound to the failure load of the pile. In determining thefailure load of a pile, the analyses generally include the elastic buckling load as a parame-ter which is used in determining the second order moments for slender structures.

Generally the influence of the initial shape of the pile on the buckling length is assumed tobe represented by a sinus curve (Fig. 14). The initial deflection can be obtained from theequation:

cL

x=

sin

0 (27)

The maximum lateral deflection, o, for the unloaded pile can be determined in the field

with an inclinometer. It should be measured as the maximum deviation of the pile axis froma straight line between two points located at the critical length, Lc, apart. The correspond-ing maximum lateral deflection of the loaded pile can be calculated from the relationship:

00001

1 =

=+ a

PP

y

cr

(28)

where magnification factor a is,

PP

P

PP

acr

cr

cr

=

=

1

1(29)


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Figure 14 The assumed curvature of the pile on the buckling lengh.

4.2.2. Resistance of the soi l

The resistance of the soil to lateral movement of the pile is limited. The unit lateral earthpressure can be calculated from:

p(x) =ks(a -1)(x) (30)

The maximum soil reaction can then be calculated from:

pmax ks(a -1)0 (31)

Because the maximum value of the soil reaction must be smaller than the correspondingultimate earth pressure, pm, the ultimate load, P, of the pile with respect to soil resis-tance can be obtained from:

P =Pcr/(1+ks0 /pm ) (32)The subgrade reaction is assumed to be constant regardless of the depth. The evaluationof the subgrade reaction is dependent on the deformation level prevailing in the ground,whereas the predicted deformation depends on the safety margins used in the calcula-tions.

4.2.3. Structural resistance of the pile

Broms /5/ as well as Bernander and Svensk /4/ have presented methods for calculatingbending actions in piles with initial curvature. According to Broms /5/, the maximum bend-ing moment, M, in the loaded pile will be proportional to the initial bending moment in the

pile,


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M = aM0 (33)

where M0is the maximum initial bending moment in the unloaded pile and a is the previ-ously mentioned magnification factor. According to Broms the maximum bending momentcan be calculated based on the assumption that every initial deflection of the pile inducesbending stresses in the pile according to the equation:

R

IEM =

0(34)

The termR refers to the radius of curvature corresponding to the maximum initial deflec-tion, 0, over the buckling length, Lc. The radius of curvature can be obtained according tothe equation:

0

2

8 = c

LR (35)

According to Bernander and Svensk, when the second order moment is taken into consid-eration, the applied load, P, induces the bending moment which is half of that for a column

with the same initial deviation /4/:

crP

P

PMaM

==

1

5.00

(36)

Respectively, the initial bending moment is obtained from:

= PM 5.00

(37)

Bernander and Svensk have proposed that the effect of residual stresses in the pile mate-rial has to be taken into consideration in calculations. Swedish Commission on Pile Re-search /7/ has proposed that the effect of residual stresses is considered as the fictive ini-tial curvature, f, in addition to the actual geometric curvature, g.

To consider the fictive initial curvature, pile cross sections are divided into three groups ac-cording to the manufacturing method and dimensions.

The fictive initial curvature to consider the effect of residual stresses in the pile material ispresented as follows /7/:

group a: f=0.0003Lc

group b: f=0.0013Lc

group c: f=0.0025Lc

Cold-formed steel pipes belong to group b or c and rolled steel bars to group b or c accord-ing to the reference in question.

Taking into account both the geometric and the fictive initial curvatures, the maximum ini-tial deviation is then obtained from:

0=

g+

f(38)

Axial res is tance of s teel st ructure

The axial plastic resistance to compression, Nu, of a steel cross section in ultimate limitstate is obtained from:

Nu=Asfyd (39)

The bending resistance is obtained from:

Mu =Welfyd (40)


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is the form factor depending on the classification of cross sections into different classes.Welis the elastic section modulus of cross section.

In the case of the drilled pile cross section including two separate steel parts, steel coreand casing tube, either the axial resistance and the bending resistance can be calculatedby adding the resistances of both components on condition that the separating con-crete/grout section is able to hold the steel sections in their place.

Axial res is tance of composi te s teel and concrete s tructure

The axial plastic resistance to compression, Nu, of a composite cross section in ultimatelimit state is calculated by adding the plastic resistances of each of its components:

Nu=Acfcd +As1fyd 1+As2fyd 2 (41)

where, Ac, As1, As2 arethe cross-sectional areas of the concrete and the structural steels,respectively, fcd, fyd1, fyd2 the design strengths of the materials.

The concrete contribution ratio, c, indicates the proportion of concrete section of the over-all axial plastic resistance:

u

c

u

ccd

cN

N

N

Af=

= (42)

In the case of concrete filled steel section, the prerequisite for composite structure dimen-sioning is that the concrete contribution ratio varies between 0.1 c0.8 and for concretesurrounded steel core 0.2c0.8, respectively /11/.

The bending resistance of composite cross section is determined according to the dimen-sioning codes for composite steel and concrete structures

The flexural stiffness of the cross section of a composite pile should be calculated from:

EI = EcdIc+ Es1Is1+ Es2Is2 (43)

where, Ecdthe secant modulus of the concrete (=500K according to the Finnish codes),Es1, Es2 the elastic moduli for the structural steels,Ic, Is1, Is2the second moments of area for the bending plane of the concrete (assumed to beuncracked) and the structural steels, respectively.

Resistance of cross section in combined compression and bending

The ultimate load, P, of the pile with respect to the structural resistance of the pile can beobtained under the condition that combined compression (P) and bending (M) actions donot exceed the structural capacity (Nu, Mu) of a pile cross section.

Variations in the resistance to combined actions provided by steel structures versus com-posite steel and concrete structures are illustrated in Fig. 15.


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Figure 15 Principle comparison of the interaction curves to combined actions ofsteel cross section versus composite steel and concrete cross section.

Steel structure

In the case of a pile cross section in which only the steel structure is dimensioned as abearing structure, the resistance of the cross section to combined actions is determinedfrom the equation:

1


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According to Bernander and Svensk, after substituting equation (36) into equation (49), isobtained:

( )( ) 05.00

2 =+++ ucrucucrucr NPMNNPNPPP (50)

The failure load, P, of the pile with respect to struc tural resistance of the compositepile cross section can be obtained from:

CBBP =42

2

(51)

where,

( ) ucucrucr MNNPNPB ++= 05.0 (52)

ucr NPC = (53)

The principle illustration of the structural bearing capacity of a slender pile as the functionof the shear strength of the surrounding soil is presented in Fig. 16.

Figure 16 Principle presentation of structural bearing capacity as the function of theshear strength of surrounding soil. The ruled area implies the upper bound

for the failure load of pile

REFERENCES


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/1/ Suurpaaluohje 2001. RIL 212-2001 Suomen Rakennusinsinrien Liitto r.y. Suo-men geoteknillnen yhdistys r.y.

/2/ RR-CSG-paalujen suunnittelu ja asennusohje 5.12.2002. Rautaruukki

/3/ Sami Eronen. Publication 52. Drilled steel pipe piles in underpinning and bridgefoundations. Tampere University of Technology, Laboratory of foundation andEarth Structures 2001

/4/ Bernander, S., Svensk, I., Plars brfrmga i elastiskt medium underhnsynstagande till initialkrkning och egensspnningar i plmaterialet. Stockholm1970. IVA, Plkommissionen. Srtryck och preliminra rapporter, Nr 23.

/5/ Broms, B., Allowable bearing capacity of initially bent piles. J ournal of the Soil Me-chanics and Foundations Division, Proceedings of the American society of civilengineers (ASCE), Vol. 89, no. SM 5, September 1963.

/6/ ENV 1994-1-1 Eurocode 4: Design of composite steel and concrete structures -Part 1-1: General rules and rules for buildings. European Committee forStandardization CEN, 1992.

/7/ Fredriksson, A., Bengtsson, P-E., Bengtsson, ., Berkning av dimensionerandelastkapacitet fr slagna plar med hnsyn till plmaterial och omgivande jord.Linkping 1995. IVA, Plkommissionen, Rapport 84a.

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