Buckling Of Raker Piles

International Conference on Coastal Engineering

1. Proceedings of the International Conference on

ENGINEERING
FOR

OCEAN &
OFFSHORE
STRUCTURES

AND

COASTAL
ENGINEERING
DEVELOPMENT

18—20 December 2001
SINGAPORE

ISBN: 981-04-2515-5

Wost-Conteranc edition}

|
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Official Support Organisations
+ PSA Corporation Limited, Singapore

+ PACON International, USA

« Technical University of Lisbon, Portugal
+ University of Porto, Portugal

Organised by
+ Cl-Premier Conference Organisation, Singapore

iE

2. > —miemalional Conference on |
Engineering for Ocean and Offshore Structures

‘and Coastal Engineering Development
18-20 December 2001, Singapore _ BE

Table of Contents

auorPaper Page

Keynote Papers

lan poema tly fg mars ner vessel under 1
niches a Posto arbour
Redo Banos

Eng coved ring 1090044 vera hatin Geo Dome fer Compressed 12

‘ar cay Storage (CAES)
a Y lang, M Sakurado,F ou and in Sato

Uncetaity in precios of os jeta 20
9 Soares and? Sabato

‘echnical Papers

<tc bucking Id fo rr ple by physical approximation model approsch =
Sehaheaboriy

(Character aspects conceming Bick Sea Cosat erosion ac ES
Sr &liea. © Come, D Pacalo and G Coralvan

“Canari coking waves wih Gaussian wave pockets 40
700.6 7 Lleonar and V Roullard

Sustrucu on tne dynanic response los on gravity shoe luce base sa
Sad sand subject oe and crtquake fac
Si Younimoto,¥ Yamane, 7 Fu, K Kamasakl and Y Yorauch

to succcsion fr vate environment on Ihe e fa cata in ban 0

conso
Pit, Morata, Tak and H Tatsumoto

gan o uste pl of underground suche ws Sea m

ie ai
‘Sivoo, toto, Orense ond! Towrata

A Eotaton mal or stay coastal src Ground system sueco 7

oe force

'SKawamore, 5 Mira and S Yokohama

Por of Kapor ratur the function opti processes. a

plis and JPotar

3. AuthouPaper

Laboratory mode testing and casero of clon plo nsotaon in sand
T Preber, 5 Bang, S Boyle, Y Cho, God and K Park

Probl of tio exterior ith cracks opened by heated wedge loas bso,
ges are noma to ecc
[2

Hydrodynamic I force on oscila yes rif fa
Mi Shottetar en

metal simulation ot nearshore cents und bach changes on
the Gnawa Coos,
‘A Shaliooar and AR Khoddam

Y oneroso, our vin
LS, Fra, À art and Pan

Goastal engineering probleme in Indonesia
Syamsudin, Yat Mule and € Pond

ist and socond our wave forces ical study
A Umar and TK Datta

‘Theo use o geocontainors fr e Southem Indo eclumaion project
dei K Chun, K Q Ho, WH No, 8K Cheng, MK Send,
FW Yan ond RS Ccncah

Iran of offshore jack up rg raie sol ayers
DY Yu, E Mustapa ond EM Syed

Pos lm modal for ho reconstruction of habia const tweturs
A CAS Anwarat stam and Nur Yazdanı

‘Neural network based identácain o foco palm by ambient bralen ata
1 Facchin, O Spadaceln and À Vigil

osa bote Beach erosion dling by anal water equations
© Glarusso, EP Carat ma À Dentalo

Index of authors

it Odin

CLPREMIER PTE LTD.
190 Orchard Road 30-14, Orehar Plazo, Singapore 238841
Te: [phone] Fax [phone] E Male opromie@ingnelLcom se

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4. rc n rar sem & Ola te ntl xiang Da

Peer
Date 01, Sog

CRITICAL BUCKLING LOAD FOR RAKER PILE
BY PHYSICAL APPROXIMATION MODEL APPROACH

‘schatraborty, Calcuta Port Tus, oia

Iutraducb
11 Bekgrou

towards a

à phenomenon, mit wit th xl sabi fhe pl, eo
ela in a coum lt svete ees, amounting eat
on of anil and lateral Join in ease of ker il,
cit appa nine ral Duckling dor et Toad is reached
being mine ener cames paar. The sis ME 10d plays an
ole o assesses of loud cin coc 0 Su “rien buckling
For ie under vera! nd Ita oi bas es decana en this sudy,
lo crec! modelo psa aproximan by sing e ile ito (wo members,
y ri o and he ler ane ony esse lor demas

petite discusion on Us behavior of iles subjected. roma! de inlined toads
Dee eect ups fo say oli compostion Se med by
enel al 3) wea concep of Toad or or ds ail load acting,
Tenino?) ve elit th pp and do bound fs So ‘by aplitng the
in col der member ad oe xa ma, AM was Oe the nodal
mei ao lens conside two ap frech vi de able of retaining Ihe
pa impad y an array Ita Todt he pen Sy ‘Calculation for the
efor gg land 2 bas Been ited o he ina vole SIR boulling lod by
aia eri ee len considering he fet ofa lo

“the caracte mai on for rita baling oad Ls a pS Y h axial loud has
Toe ro spat codi i, ese ad Inc aed ES “The length
tee side rom the pit of tn Fy he UP ot pile. (21. The ful FD
RS tati a op) fs à ing condition The oT ‘of fixity at the (op has been
Ce he ey in he pie ps been placed are em ss capable of
pete and on ton spring capa o satin he tation atthe tp

1.2 Methodology
LM cc vi raking pile ls bcn one analysis. The most

A pial dole ning pls wo resi Te odin 1 ve Pl piles raking in
Se ductos. A simple 2 sation wher eo De be subjected o axial and
expos dco arca load on tho pl np ea e presse DY 3 ‘ial Ar
Frame Pied Dolphin. ho present dy

5. a “The inclined pile has been analysed us a venially loaded strut due to the axial lol
develope because of the applied horizontal loa

a The statically indoterminac) of the structure duo to the fixity at hath ends has been
replenished by sehematising the situation in a static scheme.

The axial loads on te pile re calculated from the triangle of forces,

& The behavior of a single mker pile under horizontal loading condition has been
chematized in ree body diagram,

fa A model represents the actual steuctwe, A physical approximation Das been assumed with
{he concept of spliing die st into (Figure 2):

1 A rigid rocker member (Le. pin junte st Doll ends) o transmit the normal (direct
axial) force on the member. The rocker member only roles about the hinges at the
joints

2, A Nexura member, without extensional igdiy, which resists the bending moments
‘and shear forces and takes the deformations

& For the purpose of analysis, the length of the pile has been considered fom the point af
vital fixity upto the Gp of Ue pile fixed at the fixed end tp

a The concept of a reaction load capable of resisting the developed defleetions on the
Aexible member has been introduced in the same fashion as done in reference [3]

& The support condition for one pile atthe tip due lo the elec of the other pile has been
seplacod by two springs (Figure 3),

3" Spring capable of restraining the revetion developed by newtlizing the effect of
‘placement (assumed in the fon of a spring dflection) arising out of the applied
Joad, which isthe result ofthe applied horizontal Ion.

u Spring capable of restraining the reactionary moment a the tip by neulrlizing the
‘leveloped rotation, which i the resul of the applied load

‘he resctiomry moment andthe resclion is calculated as a product ofthe spring sli and

the rotation and displacement respectively asthe eas may be,

da. he Inert stifess of the member assunied in the form of Lateral spring stiffness. as
been calculated fom the rescion fo resist the (estensiowshotening ) deformation in axial
direcion

© Rotational Stiffness K has been calulated by assum
atthe point of vital City and pined at de op and the rest
pied end is borne by the pr

In dhe deformed position, the axial force acting, on the rocker member and the vertical
fon acting on the exible member ac not in equilibrium with each other, Consequently,
a horizontal force as reaction (Figure 4) is considered o be developed in between the two
split members.

e ir senction R and resistance (0 rotation(Moment) M has been considered as Ihe
respective force Kyx5 and moment Ka $ borne by the springs(Figure à). The deflection of
the flexible member at the nodal comection points u uy arising out of the reaction
funds FFF at the joints as heen calculated by using the concept of superimposition
(e mazas euch considered separately for Pia. and then added)

là The st of simultaneous equations has been developed and solved by Matrix Method o
Find ou the value of eriial buckding load AP.

y an isolated pile a a bean Fixed
moment acting a the

2.0 Characteristic Equation aud the Solution
2.1 Schomatization and Free Body Dingen

The pie ln been considered as fixed at its lower end atthe point of vitua fixity. The upper
end ls embedded inside the pile cap. Thus i represents a column with both end fixed. The
Saically indetemninaey ofthe structure due tothe fixity at both ents has been replenished by

7. schemaiing the situation in a stale scheme and the fixity in the support condition for ene
pile atthe tip de to the ellec of the other pile has been replaced by

ess KUK2. In the Physiol model the rocker member and the flexible member are
assumed to be connected by strings a joins and when they ate separated an acta For is
‘developed to resist he defletion

22 Cateul
LS

ion of sttiues or springs
plified Model

= a

2. Determination of spring süss

Fiat

= HAS)

pr

1 Stifness uf spring assumed o reis lateral deflection

rom the triangle of forces, the resolved components of forces acting on the members as
eompressive und tensile force along the axis ofthe member re enlerdated as

© 7 = $72 Sina The elongation or shortening of the members can be calculated es

Buna” (Force x length} / AB,whore A isthe area of eross-section, and is dhe modulus of

lastcty. 30, sae te ee ete” C2 Sina) x AL

Deformation in lateral direction = Ga dope / SI
I there is any sping to tesis the developed deformation, the stiffness oF the spring

«calculated from the relation, Force=Stihessx deformation

a

8. 0, K along pil = 2 Sina Si

Ses Ky= Kant ® Kante Cos(90- 0)

2.2.2 Stiffness of spring assumed to resist rotation

gray" Me BEL, on = Ma LSE, “ar Ma LE gy Ma 1/60
Since Ma /9EL= My ORL, Ma= Mol?

‘on™ aut one = My LEI - Ma 1/04 = Mn DEL M LA = My LE
Rotational Sine Ka = Mip= Fi

2.3 Characteristic Equation for buckding load.
AA Case L: For Only Vertical load for avoluum with one end free,

Relation between forces nd deletions fiom lic body dingrum
{From the fee body diagean for he members as slow in (Figure).
2:V=0,211=0 & EM=0, the following equations an be writen,
1. aP= Ve, 2 FytF2+He=0, 3. APW3tan 01-F1U3=0, 4. Ve
5. E ytitar llc 6 Vel tan Oot eV 0,7. Var Var OB. Ma + Hor
9. Vy lion 051 Hy V3 0.
Solution of above 9 equations yield
DP tan a" Abktan Oy tan Du Fy ln Oy tan 0 Where 5
an G-Qara 3, tan O4 (us) am Os us 3.
‘The deflections uu u, for the concentrated loads at a distance of 19, 243 and L can be
ond from fist principles by superposition u,
Uy FPR EL BL PET AST E
ABLE PILAS Pa DY E AS PAE
e PAR + SG PTE IP ET
Rearanging the above equations by substituting values OFF sin. u ar

= Ve
0

implfication

thedeveloped st of simullancous equations can be vite in Mati form as,
M a an} fu] - fo
a1 m ||| - fe
ja 02 wm] ]o |] - Lo

POS

¡EE E Eg

9. where al = (13272Q 1),ald« (11920), a13-(2/9 20)
421-219 AQ, a22> (e 154 AQ), 423° U9AQ , 1 = 1/1BAQ,a32- 0 &

a33=(- 1/54 0-1) , Where Q=PP VFL

‘This is he characteristic equation fr solution of rtical buckling load AP ‚where is the kad
factor To determine the solution of the equation it is mandatory that the set of linear
homogeneous equation for us, uz and w il have mon zero solutions only if the determinant
ofthe coefficient mauris [ A | zero. Acconlingy,

ALL (022s 483-2324023)- a2I(ol2x a33-a32x 913) + 031(212x323-022x013) = Oiom the
determinant which is a eubieal equation for AQ. the three posible values uf the roots are
obtained as,

AQ =2.5267, 269247, and 90.17856

‘which means luce posible values of 2. can be found from AQ x EMPL? as

Au 2.5267 BIN”, k= 26.9247 BIN, hy=90.1 7856 KIA?

The lowest val i the erica! buckling lad

23,2 Case Ik, For axial load with effect of springs.

rom the fice body dingra forthe members as shown in Figure 822 V=0,H 0 &

EM = 0, similar equations can be formulated.

‘The deflections usta ty for the concentrated Jonds at a distance of V3, 243 and Y can be
Found (rm fist principles by superposition a,

FL RE + ABER PILLS P/E
use By AB PAR AS FPL
ae AL PIE AG FPE ISP

Rearanging he above. sauntions by subsiving expressions for 1° sin ws the characters

equation an be expressed in Matrix form as,

alt ald a3} | w Jo

EN om alu) 0
EN a #3) fe + o

5718) 101 =101

where,

ae [13127 1 Kx WO-(BN LC el; a1 (119) LAON K à €]

13e (29) 5 21 (29) (14181) Ke (619) K 3 €
CAD GS) K à 3230 [C40 a]; 931 = [(/18)a-(481) Kb-(U6) K ¿e
A (116) Ke; A330] (SEQ)

Where, a PIEL, N= PPE, es MEL

Dra

10. ‘The set of linear homogeneous equation ‚which is the characteristic equotion for solution of
citcal buckling load AY in u, u and uy Wil have non zero solutions ony if the determinant
ofthe coefficient marx [A } is zero, Or,

AUN (22x a33-aA21023)- a21(ul2x a33-092x a13) + a31(a12x020-22xa13) =0,
From the determinant which wil be a enbieal equ the thre possible values of
the roots can be obtained in terms of Ky and K 3 „But in absence of numerical values of Ky
and K 2, as solution to the algcbr expression forthe cubie equation becomes cumbersome

xica values for real fe pile dimension has hocn assumed to find the oo

Assumed values +
{= length of pie, say=15 M ‚D= External Diameter of Pile say = 0.762 M

Internal diameter of Pile = D-2 t,t = Thickness of Pie say, = 16 mm =0,016 M

1 = Moment of Inertia = nd + 078M,

= Modulous of Blsicity of steel = 200 G Pa =2 x 10 "Newman ?

Kı= Súlimes of lateral sping= ALL Sin 2.4, Ka = ABUL

Putting the above values in a Spreadsheet , from solver menu of Excel programme ,the
solution is found o be a=APÉAEI-19.2084 , when the determinant ts zero. The sane has
‘been checked and found that when Ky and Ko valves have heen put as zero, the solution i
(obtained from the same matrix as 2.5267 similar to what har been obtained in fre end coso

3.0 CONCLUSION AND RECOMMENDATION
3.1 Diseussion on Result,

‘The solution fora column with one end fixed and on ed ie the result has been found close
lo exact solution. 2 2.52. This is comparable with the values obtained by taking bo.
elements (3jicA= 2.59 BIN ?, 3= 31.6 EU * Por column with one end fixed amd one
nd fre the critical load x EL AKL) 22.47 E 11.3, when k= 2.The obtained value cons
that taking more numbers of elements will converge the value to the value obtained by exact
solution fom Euler form:

‘he solution for critical Jod as obtained in Section 3.2 fiom the characteristic equation
is"AP = 19.2084 EVI? The actual solution for a column with one end fixed and one end
pinned the value of critical lond is “AP = 20.19 EME,

2 Conclas
From the above study ud thatthe physical approximation model considered in
the cases above can be applied in ease ofa pile with ono ead fixed atthe point of vitally
fixed and the oer end fre,

The critical bucking load is = 2.5267 B®

Tie rest y 19-2084 BIN? is alo close o the exact solution in case of incline ple with
axial load when one end is fied and the other end pinned) which intealia means thatthe
‘behaviour ofthe pile tip is like tht of in part it. In eae of pinned end top column with
list at base the value of AP is found inthe text book as 20. OEM The result isin betwee
{hat of fix and fee, and close (opined end tip, I realty this may happen, although the
‘wsuniptions were pot 50.The possibl cause in the difference may be due to not considesig,
the reaction from another spring in the direction axial o pile which is actually acting along,
th pile and in this ease incloded within AP. Other limitation of the adopted method les
within tht the indeterminate suuetue js simplified asa determinate structure

e]

| es ee ee)

11. has also been found in text books that buckling equations can bo trascendental equation,
the characteristic equation formed in the described manner may have its imitation us the
indeteuninat case has been approximated as determinate onc, This lis been done fr the
sake of ense of ealenation and to take the advantage of applying method of superposition,
The deflection equation for buckling when considered as tigonomelie, logar,
‘exponential and other such functions more secure results can be found. However the
structure ofthe set of equations are receptabl asthe determinant of he mt alo Found
zero, when the value of spring cuelicients are substituted as zero

‘The outcome ofthe study leaves scope fr many Further studies taking into consideration t
Tnads from Waves, Current and Ship's load, Seismie lads ete

40 Acknowledgement
‘The author deeply ucluowlede the guidance help and encouragement received during the
lod of study from Ir, Aud Q.C.sau der Horst_& Mr. Leon AM. Grocnewegen of Delt
Marine Consultans_by, Hi Nederhorssirai J, PO.Dax 20 2800AG Gau,
Norherlands

5.0 Notations

Except olerwise specified the following symbols will cary’ the meanings as mentioned
hereundert

A ‘Area of Cross section. à Coefficient
b Cot A

€ Compressive farce D External diameter of pile

a Interna diameter of pile Modulous of Elasticity

F Force Horizontal load

1 Moment of Inertia Critica) length factor

Kr Stiess oF spring Stltness"uF Rotation spring
1 Length Length

Le tive length Lond factor for eitia! load
P Axial loa Critica toad

a Kenction t Thickness of Pile

0 Anglo of rotation “ Lateral displacement

60 References:

1. Gere,l.M and Timoshenko, $.P." Mechanics o Materials”

1, Tomlinson, MI, Pile Design and Construction Practice”

2. Vronwenvelder.Adr and Wiueven.Jlr ; Lower bound approximation for lis
buckdine lous HERON,vol 20, no. 4,1975 (STEVIN-Labortory ofthe Department
of Civil Engineering of the Delf University of Technology, Del The Netherlands
And 1.8.1.€ ING for Building Materials and Building Structures, Riswiik(2H), Ihe
Netherlands

12. 70 Appendices

sult for Oral buckling Lond

Length 16 tere
Ex 0702
Tis 0016 Me
tn 0746 Nee
Area of Che no1svan he
Moment of natin o.t7ootsacs MA
Modulus ol lec 2000000 nz
“ue 024978003 Rain
Sping Süéss. Tim NAN
Retail Sets. Corel
ama? 102004523798
©
Pal bosse
ves © Saints

ait dotes
12 3043505205
Free 02
a 0498866
22191005808
2 213272085
ast Dress
ase Doom
m9 ara
Determinant Det 2 33715E:07 Chose to

Cttest Buckling Load AT HA 1620845298 =o apa
Crivcationgth 1 = - ony
Son for Fi Pinned Col ATLA 2m 2 202
Cite! Length - oo
‘Obained Salon Close to Fed
Planea
Solution for Fica Fined Colne AR 12
‘Call Leng - (0.809,

osu for Critical buckling Load When
‘here no spring

Length 15 meo
Goa 0762

Thiness 901 ae

in ia CRE

feos ot Ce Doro M2

einen of nee DR]

Modufows of Easy 20000000 Ton?
“Angle Ab 0244078008

A

13. 4. Result

Swing Silos
Rolatona Sons
Camda?

Pe

el

Determinant

Criteat Buckling Load to

m Solver for Cria! buckling Load
"When there ls no spring

Leng
Eo

neos

Int de

areal le
Moment of nea
oto of Easily
“ang

Spring Sas
Rotations Since
toma?

SE

wa

Determinant

Kia

o
0
25007

D osgssreos

on
a
as
EJ
=
=
E]
=
ES
Dat

ana mt

AATGE OS
0216660268
020070000
0661400008
sera
04678074
‘00744

oneusrz22
4.04s700745
40805804

2.8267

o7e2

0746
ote
0.100100
20000000
0244972063
°

o
ana
Sos O4
AATI2GE 06
0215390000
aig 0200474086
ana 0200040373
Pier)
507 AAA
523 “Oza0aracas
an 0140237343,
a o
39 -tonsraszat
Det 13301000

tica Buckling Load tem ATA 1208 2524272477

a

1

0016 —

Neue

ewe

Mote
pee?
Mao
Ton

coco to