,-l *a.'-J.
, : , Y ) , t" { > * ; i " H G ;)/j.tt
,*--:,
-L
gloPes
of
€tob;l;ty
e2
,|
. \ , - ^ t q-.r J-r-f
-.j3
$or.
-/- rl
^ J,..1
;r"ti.'t
( sl'P's) :;r,Jt -ylr
t
;.p
,'p\,
i?-
' i)' ltr t5 itt (s/,pswlar)3v)vt i+ nJ:J\ ;i-Jt a--\.,jJt ="' z"r'Jr it --ry : Yi--+*)lJr -jr5,-,v-i :.,,-a;pt':}:-* l*J' +tr D?'; fj'C r'1r -J3 n'+ t . -^Jt :-,' .i,' i2), - <--r,*,Jt }5 -rjJ, e5.,t' t1.r{
/i .'/'
-
E lo/;"nJ
fiors/,'h;-J
Qp
fo-r-Io" s
of
S/oPcs :-
fir ce /- Gra,rz,l ali"no'( '; f t sc e Pz s e ,' to /,u ' ' i ;; . ' - du,
;- e:
iud/-n
5 - F o r c e s ,y'q, t
s/;P
oF s/aPe En'/*rt'
Caz4ea fi;/ore
3- Erotion of lle
- 6rt,r,/-t
g/;P
Qnpau*a/
st'7
,/an
S*'"jact
oT s/oP's du' f
FL' of '-s*f"
'5 s/'pc " Loeeriy oF r^sJc' Jtrazea* e*rlAQ un/<.s ( l )
----
a-rg
n
o"l /L
ShPs s h.r'U1. /2.
/3-
/e*'tn ;-
rreclnn;trn,
A- n*
y'
A;/a-*.
o/cte;/ee/ gr- Lr-lr3 C /l* Port
*
'/- / fu
fL
oF
-r/La
€ qut /; briu.t", ,l
D;s/ t'-rbi'3
lL
Arcc
(i*-rlr )-.,r\;Jl
(:!i-n
-i,-!--\\ slt.-..
L
5 hear
fr,
/"
Stte
Ura,*yoQ.r
gg
Sait:
/a 7rau,/-n 9 o ; l / +L he*A**r'r /n j/* 4*ry r f2/ott.u , i / i 5 bryr' tun-J94, e lJ af
9 /i6-
5lrcyt/
s Lun s/r"*g,l/
4*tQo,
Q/a,At-u
)
bu/oo.,
yd{onQ
flab;lity
"-s .
a-*a Le /,/;"rr'
tr.g. ie ro/ro s he-a She ss : Q-' + t'
fo;/tn
=r4 t ratb;' 2::'"*l 3::"*l | |
d;s/b/bl'yf
C
sdr -l
,ror/8.
For (e
E s :
s+re+y,lA -/
Ie;/*rp
y' *r,J1r;, is botry'on /,n;/./
fet /ra)a;L1
a^/
*f
SoFt/:-
fL ["4,+" t&t 4
/)*
J;s/r;bu.*.on
Frctth-t+
opera-l,ah*/
For/o,
50,
, //rc y'/1"-,7)
s/ol;/r/7 odJsis
.
(4t
r_
u*t
)t
/f
-,o.71.4
, 8.,
,a
2 -> )y
)
&ou.Jt.i, ' o/
fn;/t.,
.tr/ s/;.n
*"4
f/co,
D'r; de /L Gns; /et
(L
t/opc ;nt, y'-'ca
a. 5ca.1
dn eazL
t 42.
"y ,t/= UOr B
fl us,oP
/n fa_ oF rt6( 5lresrc_,i h) s;o B D;s /tnl;^1 Arrrc tT)' io r=u (T= -' C+d1a^4 - 4/ l* 4 f,rrtc ftafro*'orj = tJAu B f*^.P
.: f- s= M l a " 4 /-2-
t/Gs0{ar9 la,l 5;a B
E" e/g soit
( ,/a
ton Q
ton 0 9rr4A"
)
{f
f.-i
of
&,,J
Uo/.r
/r>. 9+wr, .Jj"C
( .4"
Jc'p*gc
asstt-t-tc/
I/oos
y'ap *f
/o-n
5 a*<
dalolL b.4,-, lL
ta..y'^<.e, fZ4 ,.-,,//infuo/a
t1- a/4i42h.4
oF s/,ce
a
y'*2,
-{ /A. 6n
L t /..-
u is lk P-r-t.P ./ lL /t*r, 4 t4-r..
ul fZ
nor,+^(
tu.az4>n ai
bnr.
{L
-/
s 4..
.1/ = /.s qs p fL
ztrt J
fJ. dftah;,. 5;n ce
oi:
s,lztsr
bor,+za-(
#=
Lr'CsB =t)ArP_!J6:p - a b 4 qB ,
51res7
q, =
dn -L/:td
t - 2 n ,
<-'s P
-
U
l.
U-- t.z.b ?n = ( t z Gr'fl - u)
n. Su4u 5ln,
resfra-t,tg Arrcc = A
b" d
= ({zdB-u)*o,Q
Sltest = J; sl,n Li"t :Arr. = af tt s;n B Csk - = _tJs;n D _ -(--
-!QsP \tt t
'
Z'-F lL-z
aa b,
Fs=( f2,',
et |-
urillat
, fra?'
/ -
/
[.2.r*:"l]
//* 9ea,--4
l-at B
Qt' '/;'y''";/ Z' ,n /L
{/'Pc'
ru= u,
Iz
. : F - t ' ( r - ! 1 )- . * ! ' Qs',f3 lon/3 b2 asrut'aiy2' Gn be 5i^1//;/f'e/ 6'+/ occt't4t paoilt( ,24't ,J"/t
Q gor..-/ (*'3;,;
*f
(L
groul
3u*/'"" '
'+-
/n.
F/o*, -(;,-
exc.g
at.{lu
{p...'4 /-
tF
-
p o r c ,-fq
h.-tl
be* ./ J.^r.tt
Qa.< t .4t-.-f
Grc,*"/ ^la-l<-r bt51,
*{
/, 5u-r..y'aza, 7,^>=
U" {_.Zu,G:P
r L - f . r=( , - + ) * ; t
X ' + o rra t V "l*nB
t l t
\ ) / -
C*rr.d
2-
&^
a:Jr-r.
P len. 72. =,.;
*rc ,f-,r/*
/ar*(
f s . =ta-r4' +*q B &'-a
3-
uJor
l.'-(
b-1.
Zu
E ./r-r- pbrre
Finc-9rq;n"j a neAJ'e So;l pir/rr.;^7 E;/t*roA (L Fb.o" , C/t4 I Cof;//ou
rL dx,
r
r
/ a,o*-,
\ , -
(/v
[.e
-) -
i l/a
.er
ry/"
S&^d/ dail . Q) uzL.^ d13 ,'--/
Lolgd tE
gla.Jy
u;/L
d'=
3d',
+*nB
o, EcAn .T s"-ft/
ta-112- per*'ist
C=a
(c ) c"-h,J-le
d=zo
d t;
d"./r.n,n,
Slopc i n {L
y'-/"-;1
tbl '-r1,.^ aut,-*E
,, p*ra//J
Sc.P$c t
Pow prestre f uzh'd4.
t-1u11-oO'
/t
=
i4
k
+l^< snr/nzc
/<,,u/rnr
.fL Es. 4 /L p,1,*..
a*/+
L.gqJ 5/.pc
ajq>,jl o L, o i4.r pGae e")ir.f t +l,z Su,y'^-:e , a'f nf,r4+l., aF (m, ,F o4 tLis {Lft- ii a 44^.i"..\3"r .{ Clr.zv',c.-folL--:iJr 1"tt4 -
+l-
J.-tt"-i3 C
/=
pngc,c*i
lZ /rrz/n? , 4'=
z{"
d "24 tL^/ht
,
9"'(, av)
.{L .fo,'/ i: /y
,-/,-"
[s
=
+r* g
. : B =2 6 H
()
s r, 1L4
*o.^a' fan
9;v;t
, / ,u
(? \ a*d'
\o"-
36
F-s l ' ) ( s 1g rz"t';o \ ' . z J (6 )
= o."8?r
'>
2''3
D ,/L
{L
50 {l*(,
.f '{l--s4azz
gn,.,
trE-.l*r, B =
{'
+o4.A'
f
)-.?p ( l-'?
tt ,fona'
'?-.o
[ f,s
8 = tlo (c ) /f (L
/k
/:s
t4pe
( s /./,
,rttc/,zd
Cl.yr're (ryo
s4 **4td
/{o,
"-/
o1 7 = (-o
/ ;
Za,'Z
=o.2/7
l-2
L
?).
,J'6ni/a;"'
t-,
c' t- ( {z- t-z-) Gs'g !o-^-&' f . 2 . 5 ; n BG B ,/2+(%xv-7.(txv
Ca? tf ,!a-"rzcr,"
2a, x c1 Y 5;4 /t/o
(7 )
= r'.Ss
CA lq.
S*ab,'/r'17 o F G h"
4hc.grtra
so,l
- E;rf;oh__,( so;L )c L) , o f ? t : t+tua,//y
ihvo/ue
aboa
s,trre aoh-
orc/a
. LL,t,/"rr,t)"cr"is s/rpe . ,-a /L /.eJarp
he-,t.u
n-orteaj
s/;p Eey'-ze
--r---27)
loe
14a44 f\ t-
.f
--fL/
a SS CLr, iryl
s /opc 5lorb;l;17 :
/a,noAle1;-*
ihu.thJ4-Ad-
4
Pru
o cealT-r
nn/
o s/,'P st'z-loe
b*rJon
, o bo',l"lLd^
a+ rtesrtzr.-r7'tt lL u,arct s /.P lL
Sur'y'aa ; s r'"*d.
\
\ -
-
,
- - - - l
cJrrl*-tzar/ O (r a
\
I
crilitle
;f- sL,,,/z/ be c)rc/e
z,j, /7".*
g4u
Gfr-(
glresr
Art
t-rclL/,
saht€
the s'-tel'
,4,"-n!s,r ' ir rzrq/ */,*"
no/L/
f, s;-p/"/tri,
;l ;t tuc* F r-oh-c
lL'r 4P/tet pore PrcsttbrE J,'st-;b,'-tin* roJ S/oPa ' s'2'b,'/.,'l)t ''n exa'dd 9l'zorf lvra ;n /L's l/n/ra-,a/ 11re'gJL '"';t/ bc we/ S lcx L;p'e: ,'. t 6o t^-4-l ir /r>,'/"/ a.t,-$*i
6rd
t-
?*4 f7;'
(Q =" ) a'z$rtr 4.r/ .r'u//f gJ*ra-/e/
Ch.-*,to ?t /,4
o
0^ lilz;^qruna,f
C u . ( € . f - C u ( ze
f < - rcStrd"iry'*"-d ) =
=
F.
O*
r*'dt
"/ry
oboJ(o)-
h/. e d;st prb iy
4 6
no-"-/
1 -6 /,/ 'J
5 Z'r.a
( g)
e
Cur'e l).e
Con bc 4"J
F*n
FFFe.j
of
fL
//i//
h t
44
/o ,lB' n c{rool;y
( "F
'
fen ercn Go.Ls
,1
uc /ea1/A Eo*, .4o
rdt e 4,
9/V
sary'*a.1. is /-d^J dh a C a,-/e Pagt-h'oa oP f Ugiht ?L E 4l, tL cro, i s ucr /tco/ ?v/ ha"4 a s/opc
h" = 2 C ^
t"
0
- -- ---'t
/ / . / t
0
J-.'
f-t=
C*r29' til'e
n(, Fl
br-4a
gir.,
/rlo./s
SoiL ai.ll^ Q=o
Qlrcs;m
oF a*t etrLor(nc^.f
a^-a/ C. )n
,l.z/r't.
*--/c u.r-'f
/k
"F
//e soil is lq L-r'/u3 oF sh-'.t,deleurn;r. lL {'a&. 8", l)e *n'o-.( z;tcl, '-rulAt /. lle sez.b.r is aSoinst r/,'A,'y .f)* */f7 .st/';y in f"r- 4l^e nl --a . eczentP;Ltty 4 3q6 k,1/. ec/''g r^tc,tjl*
.F
Cet,-lor oF rofoZLu^,
rf 4e fa botl
5Ld/e4 (a1q
1a//'-*
porlioa
tsovcA /'L tra-e.bn oT 5.,ft7
o F /Ae
ea Lo'',laeni
us"-re retnovt
a SSprte 14.-.rt ltzt y'enfz7n cra<*
(lo)
be
c/r-rt
.t
"/,-i
3n
t:4
314
9o ('
J
/73o
. 3 ? 5 x {=
m.mc,tf
D\ /,nrh'ra
k,/'t-, i
t q lr.-VtJ
- c
c r 2 e - 2 4 x fr9" t
r--a,nca-f :
/3o
= l? 2o k/'a
lq)a t73o
-t Fg. / ra. (
Pdyl,bn = / . f
nrr--r.-t
tJuyLt 4
/-rt7
=
(€ta-ave-d= 6 . 5 7 x t
prrhr,
6n-
Fccen-/.r,.eit,
= 3-3+
o
I
t?./r,-/
/
/rtt*-b
: Ft=
{. 6ea\
1
*cl. V 6
t2 7,r/ kat.
Q z
J)+
t,f
L l z ? - 4-
m oo-f ' f . 7 " ,rz-a
.J
7L?,
(-zd-
l/Bo
/77o*72{f
I \ .
l tt
t
I
I
k't-
t''-
5";L e;+a bo+h Ghe.sn.r, o""d Frl..&,on ( C- "t ro:t) , I A-'s su,l^.-!^-"^ cr.tis-t rf ltu
so]7"1''/
,ru
so,L is *
rL*' rn-'tll c- "^/ f,n'tt "4 * .uu:^'* ;n.fur^-P +;c/ion q sL*el be L^uA.x."t.
:1elL./ d ihple
-/
sh'r-
t*,it/ be ry.n/
p";ah
A /"^J s/,-p crrcft.
on th<
-
4
il-- t^)Ose
)flc.o= u
t1
n
D;s/u.bi=
t-z-ra$=
f
I (=
f,'
[?'s /r*,>,Y
nn-.^t
!'-
t
= r T-- , + r ft
z ty
I J + ---
E-r /*rlLd
"n"
+fti
= f ( Cure * .L M1-a*1 4r)
' t F t " Qr.9 + L M./o,4u f2.
r.-+,2t44-zc
lL
cra-<4 , s /t nt-,- b1
h " = 2C, -d"^ (*/"tVs) Y'
/2
"-/'j't
FJ
Ezn 72. e-J.ntL-a-y' ;n 5'1 L"Lu;s nu1-* c = 2a ttu./.nz - f)'< ,fail ,eilh Q =\3 -fu "
fA.
f ; tc h4 4 = V 5 oi L an u).z'L +A" em baaLneuf ad C = 7i Laz/t-,?. F* bo+l^ Sails Y. 9-7 /e.'t/n'7
De../c-nn"-a, +tJ. .f^2fr. 9/,/
c/rr-/1,
o F t$*-J
1fur 1)'. a-
5loun lo, ,
4,
cz2ohl4la
6<'''
1.ln
I .=?5 ka4rn z
4, 70
----
/r'.
fiu+' Vu('erh'c f). s/4^a gcJor oT s"it ;s /t'r;/c/;.2 f /,ra. fi J"{*n;r. is 5-1'cc ;1, nr./-L'ZL* r/ fq/'cu!*r b2 ;tt LteJt-L. aJ i9 tL ,*>.;ll4 ../ t4'r. trJapl,'s.r ( so;//enl;/y x.2-rezt)*J tel oFf *s a uect" balo;\ ( /l )
flr-*,
o/.o*,, /k (anpoae$ . +a,a-1rc*,f a*./ norne( prb ccd,& /L 1t reV a*4 /-",r ea-zA s -lr'cc / /./" a-(gebric a,,y' no,,t-terizu.( Su*-7 h, l-.y,e."ut;*{ tl*t.fL narrv-l is cLl-o..r'n./ '^d .J E'r.a/ T . hrr5 hrt
Avrn,
rt/ o,
h42
Ucigt^j ti c t<''v)
ti
3.7
2
8.7
7l t63
3
t/.5
2Lt/
7.7
ator,*t
/Cenp'
/v ( k^/t
Af fr'athh-l r (k/).
-7
7l /13 | ?t lar
tqg
L/2
t/6 to6 tLzEt
iM:52? Z t Jt * , $ = 5 L ? * o . 3 6 r
= /gz kr{.
Cu f g - 2z) x to-7 r< 76 xtf: lEo
h,,
zrdd. L r
A^
e. /.u*, Cu-rg
is a//..,, fu7. (4;+*)= 2/'
q9 at.t/3=2-?6,q-j
ig'
tL = Z
,[lg -
kN.
+73v= /-tr -_t 9 2 251
[ g - G . r a * L MP ' " 4 t Lr /F t"nfr>^
LEf
r. TI-= z 11 tz-rs.
/72+zr7 -/.ts zq7 (tq)
)-7 t't
A
't
/r/\x g 0,c y'o. I
2 3 q
4 ye-a /t'l
t)4|'f
I
loruJ
til (tr,tt)
'fd jc"/;*(
GnP'
r
N ( t'u)
/87 3Zo 57o
jr5 ) /-L
52 /86
IV- J
2V6
/ 62
?-2y
7t
E N louor
-33
)u,
Mt"rtO= /62xo.3dq+8Slxo.l23 Cu. r . O = V € u ? .tf * g f
tf'g?S
gE 3
= /68 /L'1/
T T + 2 o ,(9 .ttx E* r t\o
/3o
= tt{3
hJ.
f S_ lrds+/6s =3.3f 313
loh
Cra+tL /9 a//"u.J (,5)
G-p.
- sd
6t /8y
3.? 1.1 t6"6 /V-z
I. tt wpler lAcr.tlz
t
(kN)
'
F'<.,-.-ti// jc
L"cnitn
oT tn-os/ Cr;l;ca( c;rJc:
F"r n, t Jro.nar .C*;/t'-rz "tL /-/too;, t @,t/t" Ca4? Lc .7V L/ ,- rf /,1e 4te a*yr/c f etceJ, 5J" rL ar/e P*tut l),royA /), 4e io t-.a/r'cn ,^z/-.j lk tt*/-< ,/ Q^
2- /f lL si/ is E'c/r>t-.y' utilL Qo z i ui/l Sh7/ tArarTl {l- b. .
o, So, t'L ,;,c/,
(*s4 GhcEiut ( 4 ( 3') il" (;rc/e 3 - 17 +1. sotl is /r,// Pasr a lreo/ oF lA€ 6c .
q- f2. G1"-
c/rc-/c u/( J,"ta,2n iy' otte exl'Sts.
b c- fanl eaiia?
t
a ri y;d
hr-o1*c5 ,Q, Glu;nu oJ Soitr (),:tL &-- u , f).-.Fe/(eniu+ Tzropas./ G-n be ueed h, /o#,-in ?he
uPPn*'n-.* /nl/.
C-c^^*'. .F (L /-z-as/ cr;b-ca/ <-rrc/e. < -.*/ B a-az /"ler*;nd Ay ?) /],e sL.pealQ
uf ;,ry p ,-b4;s /r"a ta L/"-s, F
--lY--je' --_': i.rt
.,
L . l l c h. i. rr- q7 C etute+
l/6 t
; |
,
I
Q \
-
f-
^.1t-P't
Aty/, 'F g/ope p
f lopc
/*lL
11^1|tF'
*
lto.t
6o"
24
4o
l t I I: l.f
?5"
Lg
37
3s.8 z6.5 t B.t | /.3
z6
35
z{ zf
i{ 3t 5/
l : 2 t ; 3 l : f
b2 )tt*",y'r'i ha4 bc-a exl*tdd c- Q so\l et .84/o->s'
fL. n-/L/ {J* c-. 4 t- /;t"-at
|Ae
L5
Fe//eair-tt
Ccaier
x- Gnslnz-t a ;;;Z-;Ltn (r*' h*l ;/, ouluta.,r/ hr^
f-v,'
bu4u /)c cril:;u-1*'rz/'
c.*frn Sot-rc 'J/''-', o^ *l--s "/"'e. {/- Fey'/en;pt .
Poss,bk of
/f Qz o () =O\ n*
Cnet
O O'
c- 4
inczrez-a.-t
Locah'o.t H
A
is a*
inc-r<-o4e
rt7 )
O' .
6L
"4l lo'mc I
Dsfua1-;nofi-,.- oF €) fuv ay'za2-,4re7or7 f2a;/ I re1,'.!*r s/ope . (Ty hri f +a.b;/;/y tUr+"br,r) : t
7 o1/"" a
nt'a.
a Stnpl2
Pnpas./ F.S.
a S/op€
f*
(h
o./ /r-lo,-;*',y
mdlLl
o /aon
l/c pmch4 a Se,'ie-'s oF ottve't ,aL'oL rJole 91ab;/;/y ala,a|"n ('1/) 4 4he SloPeargle f .
Crg/.n 4L L*,',
"6
,+ -?J! la./. g
/t atr// fc
5o,
Seca {L--*
a-nd
L = k,H
.*d
L < t/
d=
/-./ 4{H'
L"tr/-J'
F = C''r' /"'/ Ya ' k z . e €;n re
Slal,zi/7 is /a/e^/al
a f s l V q'rcft S a ,
o,
y'.4, !e.me/',;
k z . e , e/Ln, ./ ;, I L
t/--
S/a 4;/t'ty ilu*r lon
f u,
6r*,
d.-,
/
f =
t
.
/{a (-
.
/ r ' '. f ir r h^. " ./a .
L*'
/
.:
^
/
,r
Cn t
,
/ s mobl'7.-/ 7J.
C^
ra (/8)
G/"-az'.t,
0.19 0.18 ' 0.17 ,:l\
n ra
tl
0.t5
?
3 =
u. l'+
E o.ts 6 0.12 0 . ' t1 0.10 0.09
2 Oeprhfactor,D
Whenrp,=oandD=c",
r u : o .t 8 l
(a)
0.8
a
0.20 0.181 0.15
=
0.10
tt{e
qii "?ir:',..|!'+:
g.')2.' ii^,.i(v
a
0.05
40
Slope angle, P (degrees)
2t
tJt*,
q<
/
6
721" a+-2/< {
a-.d
k NL slap< o.v6" p,
r.-L(.A
re4i5}e*r.g
SAe*7
dcp*L
*^r'
Q,
,fecfrr tD I . /4 ya-/ue
A^,
4
l-a.4 Q^
Fon
ab,t-o.-a a- ualrr,
6
iS
/)roccrt
[x,
)s t
/L.- 4-.
/)rac.r/u-*
tzr^/;//
/?,'
= +*'rg
a^d /1,.,^
Fe
tr" ut;y
4.-"
o4ri/e
alcr,Al<
.tL aL--/
F= /"= fe
,/),
.
n
,/4 f,ar/,U f n o 4).a,Ae SoiL l,*t o C/op. oyL jf o a..,-/ a uerhz^-( 1--.Sl,.9.o6 8 -. Ut ,ry Toy /o ri of aJ S./a'L;/;ly nr--r,lor. n?*.L./, /Jor1*rhe tfr h-t-Lr
oF s afu/ a) b)
a Sdosl shcq ful*t
Q","k,,t/r-," (o- z1q h.v/*,,
, ,
du=o' 4 . o
,
Q= r€"
(t -- zE hu/n"L
C)
5"(, 9 t,/L.
Dl F
61
,f,--tAL*/*,t,Dr;rl5 , t-- tg tr/n' , gr-- t.;.
l:- t[.< *,4^.i.
,'1 /a.;/r, B r 53' a"4f 4 u = " . fU
/-/ = o.t?t
b) 6,
y'.-r /L /11".,y c+-r-a,,
-
_
r-
.
r
=
Cc,
Cu
Ctu
/U f/4
D r ' ) . 5 . ( ?=3 i u
4'/ - a. / {B
c) 4v &d --/io
orP/ * rSx 8
On' o,Qun
o>d /t = 0-6
4'^-d
f= tr=
-- t.53
/o
= /-6f .
o ./6 t x tEx t
"//c,/
-/D,
uq/
;s h? aAU.
F.-n
2'J't fry /*tf* = 2'o /rtn oo, =+^f .: d2,. ,
6n
7.6
"
.-12-- a. /az
ry
a . / o z , rE . €
4)
z o'ttl
Fa'
/'7 '
o'/ o?
tB
*-a,24^= !n,
td
t.7f
4,U
= g.x 0'O3-6
=
2;
Fr=
= o-tr)
,z /.75f
c6g *ttr
o.o?dtrP-stP
9o
tr -- /-7i-
L-t,
' (=/Z'ril
. / ./ uerh'."'1 6 I Lr;t"*h'( )t opc ' l ' = /6 k ' u /n ) //' 3/ *t , , 4= 2 i
5ol'
-r-
-d s/"ytc -- /qa A^e/. f r y F' - -- / '.;fa u "
ltn. n d ! F
.'.Qrn=,l.iiL,,-6)
/= -:
-= 9!g /';
= o.zrr
o-oof fr-
l2ef
=5'ag
o' oo9 * 3t X/6
f,2 Eo- d,-./
F - /-c /:
ts.olJ
" :t? -l a -z Q m= tn o € n = -:
-- o ' l q z (o^--,,)
l- tr / ?-'€ = l'qy F . -6't/' \ 2a )
'(uis o'lz '
f //q/='"e
s,t'vess4*/1sr's fr", O"l*-iu.ZL-
/, /Lt o€ /4
l,lr//
//,u
Pore
aaltt , fl..,i>, /'a
anler
Gu1ut,ct-o,t pre ssLtre .
,T- ,t;.
sh.yA Para*tefers {dd ,.i/A same erti.,^-+z/e ,:F
A4e-/L/ oF ot4s,s ; fZu'ou ,z r't12. /J/->/ boe.a/ on lk at"tril/mrr/L/ hu{L/ fh;s m"lL/ is i--i/./;rot / t/,..s, (hrve ne(Lls Lcv^tn .73;rLp,, ..z"fL/r ay /^- ry Gnuu^rh'*-( t,r.f Ld 1/1. 2. 3 - f7.-
S,-r._t,6./'.d melL"4 (-4 oraclj neil-.o|.
/#*'*'r- 4a ,f+ abo*1 4nu
(>er;
ia {L br*,->..ur.,_s €i<.-t
Bo*;.
va-tiz,.- al
k
i
a'cfocz'pho4,
Ftr' -
{
\7
7 t. t. bt
-TI-
/ I
\L,
7
P
9att - Ja
*/,-il
b l ' <\ lrl
X n V -.---._>
T- frr-( S+r"^etL
S=sl (2tt
4 lv't
, 11,
ff.r
W"P
,Z-,j uF rnatqc^* ob"t
eTut/i bri,',*"
over q//
O Xiu4t
L b / . x= L s . R = L s a - R f c'4 r (P-u'() fonrQ' J
51 = L
F "
/".r (P-u-() = P' Rsin<
xz S o,
ablz.t7
utr
( L [ , ' - ( + P-u t) l o o Q ' )
F"
?-
l)
c-s
I
t-_
5o,
Z f l{.
t- 6, (^u^1f"1
(t)6t< -u4) b^ a' n.
nal/-o(,
t-csta-rzc
-x') s;nc)) +on4'= o f ( 1r*,-7 ) c.-t4 -(xn*,
rtu 6s<- u'() f* 4'J
f = J-L[c/
L tJr;n<
lF tt.
au =
iulra/uce
( Pore Fr"ts-re rart4 ) #
b-- J Gsn
,
u= Yhf u = L r u b
-i
U:.
F,
,-
(( 7o*,-rh)6s<-(*^r,-x^) s;a<)lanPt
Z t-/5;a a
so,
Bns,', %'
L LJ'sin<
{inrc
t/e
t1 .
[*PZ
/L
l/-fu
Q(=
Yu h)
fcc-{
-{c.s"<
f. Uin <
f[,'4*ta)
lzz)
( 6s< -ru Se,*) f*"dJ
fL,, nc/LJ
o6! aal7gi tu 1ttue errzq ,'n /1.< u./*..f f obtotnd.
r i'/
tr
t /.2 z- -
is ra*j.J
f ff..hlo
t-;
{h.r, 4,*!*
,4er-r/;^ir
€ Lry',
bt lL
c?2
lP
€zo^.aaT'
f.,
)
tr
J
fl iioroa
Me'll-'/ '
V
f' fttz 'x
la? na",-( -zfri.lrr. y'rzc f?cEoflt;g f-o* /o.-
,-?/f lrr--a4a
'
*P'oo* n
lD = 4 (ue< /-_
L/.
,*hd!
Fas
7's;n q
P = P/+u4 (c''{ +P/toora') + c'( F'tana'5;o4 + F F
n -
c'!t;a< r
+
P'= ( P- qz)
f f'(.
'.Gt
< t
,)aq
l-aa&t -. s;aq) =z-
s i n a ) +/ r ' ( G s * + ? ! ' r ; a * )
lJ -4 (-uc.s<. +
s;na)
Gs <- a tc*' b's;a< S
r
Stzbabl,,/e,2
P' 6,
CP-az) i'7 4c
Bo''' 7
s I c ' 4 + ( u ' t - L ( ( a s < -+ s ; a n ) t - " d
f u.x I .
Cas-<,EB?L ( 2 3)
] t
J
-1 '-9't 2- F.'
Gnsy'rou'hba oF a't eubaln*ttr' U= UorbU
[k/i/
rv
bt{ -- C/*,71e (Jo. ,[tlr'J
P'u.lo
du,
i n foi/
P't-''P
c/,o it, trtasr
ia f/terr'
b u = B f r g , n , 4( " 4 - o d t ) /.rL,.*t ,4/ B 'o'a F''t'P c--ufu/'u'tit' >Ll o4
l?r'r rl/cut
u
fa :
Yu
rh
Boa
'
Utt
-
+
th
th b6, - trh
/;tzce
l'u =
5o
Fx' '-:
,1
IL
Ib
CroEs sechon
a-r, imperr4u.{a/c on "/t".*S+*ii,1t,
',^7-iSJ.l'utig
{L*
Uo
"f
$
*6 c/-n
a'zz 4'/1A
bole'' nt
Sho'tn j"
A
ti/litj bJ'*t'
sLpe is +o be lL c/a'-')n3*ve'a-w't 3i''3 4k s('V orc/a sLan a4'41
fu//'-'g iofurr.n-f-"n : -
[t"-e= lq-t
k//m) . /=
1]' , R= q'6h'
/o L"z/],O"
g =- 8 7o. Pa/e,.2-,n, fL t- s. a) u,{h Gnuu,,ia7 /4a(L/' / U reSorat4 /'4c'A-d U ,'ft" d
ad
Lg sa,bshlu*;y
ub
___
I
{Z
'
lr"
t//sn<
I
|
L
5..< zfctt+tJ(rru1/o-.te'I ' 1 * L a a Q ' / a ]r 4 l | I ' F J I
, I
fL E^*( o^a./gy^ d ir bql Q-rr;e/ o"t 4
o !
\ \ \
\ {
s
v
-q
\
@
!
t.\
,t
q
-s
\
a-Ltr' on a uertj-rol s /;, *uo +4,bu.l-.d.,hal/,e CJr-Ua.
e@ $
$ \o
\
+'
I
U
t V v .U
s S
I \J
l'u = :!
Fn-
Yh
7 4re
a-rc fuo
hgikr
>€<<. --:-T
\n
t/ugfur
$
F=
F.
\
F-- E
( ru) Dey'c.rn,;na.h)a : /;l-ri1,;n
,nrrlL/,
4
pel.oft,n
r"-#..^ /-
@ F
-.a
\
Prcscr,-rE roi.
A
(!
"(
\
R.,
.J
u
5
t^"
X= p €;nt , b_-lorn
pom u-1.
f-j=
fron ft",-t ttJ
z(t---+-+^-
ru= tr-&
, /,(){, L/l
rh
l h //
E/o- 4q
(2qt
-9wV1la.l,'4 '{.1-<
E 2
<
e
6 c'i
14 E
\ t4
i
/\-r
@
:
d
. \
V
- \
\l----v-
t
O
4
.
E
ll
ir
5
F
z
.
r
8
:
'
6
,
*
'
K
"
f
X
g '
o ^
r
!
7
-'^
I
d
o
l!
'
c
1
^
E
d
!o 6
€o .
X
tr :
,^ :;
o.t $l
^e d
'
r
,
r* rf.,r .:lod
9l ;i
;" E- n
"
"
F a
-q
.
i
9
*.
:
rE t 6 E
:
E
3
6
H
€ ,
g F
F
V
; .')
rFd ZzB 6EB
sc t; :'I
\ ol1o6 ' ..,
qo E€
,- i .L'r ^i E ! '
:XE* , !:
AE* ;FP
o
H '
-
O
E * - r r g q ft
e Ei r ' o E t
=!
t
r
BE
Eb
EgiA
=
5€ s- . a3 ; r
^r / .f ) e= oi E
3
d\o
.^ i i
-.8 -:
b. z
d
-
.8
K
Fee E.Eh ? qt4
$ € *
3
€o .=E
E
S
-
4
3
E
X
€
! i
+ -
.o
.9
E E
E -r
ld r c
l
A
6g :x
o ; .o o.:
!l El tl'
; i : = x l a Ee H F l
r
s a i . t :r
r .d, € E
I
. X X c r l S 9 t t E E o -- oi l l N E r r .
- y 9 X =
5
I
r* r'- 7 c. , ex ;-
E E € i u.3 L 4 , .
b
:
F- =E . l E : t 1 €
R
\ ,
-
'
\ \___\z- F
\ v-.--\
o
.
-
o
H
i
o.
Efi
tr! . 4o )
Ei
]
t
g i
a
ot E
h
o
n
.i.,-
zx z< q 1 Y
v
s
9 F
F
; d
!
9 a
E.= {..8id z€ F \ 9 ,c-\4 2
_ ' {i
e
U -9 tr6
a1t- t,1: Eii o \ o..r.: r ilc .odl .t DR n I9..
S €E P-.,-e(T *-
X
b :
>,5 = ^
E 3S c€, \ . ..
4 8 9,=
! S 'r.l
.-lE .!o ,.'€ .!P oo q r q
I t-
-'A
o
e
o
c
E
;a€e 3c E;3
i:l
h
a C
< . od' q
$ e $g
g
x '
*-; a
(arc-()\t\
{ ' . ; 9
q to g
3
g : E
.Hst^ 5-
3P.e
.d'
; c {
36E5 e
o tr EY
6IHOC{-
\O O\ C4 0\ < N <
q.lqoqa (\
!
i EUI ;
e : rEs $;t.E E 3.€E : E
- E o o
^
E€g EaZ
'C
r{a
€ 'E *ae
E E EEE';EE
9 coOO\o rrl ( C.l
\ q q t tSQ c l 9 O-e{6lCt
.9 cg.r,E-9 o
.9.94
9\q
tr
4 l 4
rS
rpE 5E
E
oliD 9 Xi€ ir ;d:
5€E 5 €t* r!
qsqqe
5 E BE
E ..e q
E ts €
€t ' |g' ] =..q -x3 " ?
o 1'
lll @
nqqqe ooooo
o
? t
$ P -^-o,. ;EE.i i; ";g.EtrE
i
dic€
z (m)
o
b (m)
c
w (kN)
D I5
slice fn F
l-
z \.m)
6
J
l-
I .tl
F
M
w (kN)
J-
;
i)
Wsjna(l)
m
cb(2)
.o
b (rn)
5
o
I
d
I
|;
3
W(l - ru) tan O' (3
6-
2+3<4)
iJ
lJ
o
.l
cosd-tusecc
-=---
t
?-t
W (cos d - ru seca) ,an O,
rg I6
'',16.| 3 -a lr-lc ii I
b t,
? i-'r1
4x5
I
(6) i..r
!
J H ' t r T^
E SH f i g
i$$if$ #[ii$flFfiFEii*$
I;F 3 F:
t s- i F TE
99. 6 * s
=,F : iiE *y < 5 93
g$giEiiF'€$iFF*F* o
)46
e.
E-I E
6
3EEl SiriiliiF F ii
Ee
5 o
liE +9,
E
E E i a o
1 9 d o
iFii'gie ii* i is
_
E.fiS
fg
m
+ S\ : S
Ee
1 ?*a, # . , F K
3
d
=g
q
F
(tl i) (o
H g
g
5
{i
-a$H - rF €,Fs +
F F'?
3 3 Lt
:'.
6!t
x
*6 95
E
6
t 'i
'
!. ;
-
€
4
*
8
v)
^-i J r
, ' x i-E-ts E 9 o 3h
2
5
,
n
't !.'
YFi
E'
:
€H x
t l.1 tv
.e 4 s E Ee e **l : o !4bvi a uuuu
l€ ra o
,
' Ie
-
(
-
;
S .-
:
6
q
c
{
'., |lli - t a -
E V
.. Z-
I -' o,
1
r
! 5
E =
v
K
€
,:
E g
-s t
-
i
"'i
=
rr-
"
--E
.-
t;Ils fii;"'
53
$ i TF i
E.-'.
H:
7 c
o.l
.X
er
\o c]
o
i S
tl
c.l
e R L I a
? ;i I
;dh€ a:
igi:
€
x
o
t - l s ^i * E f r * " ll -E E ? s : _J i * q\q o ?. . l ; ; ; :.-=i .i .F ;=
r E
i ,:E-r." .g?f .-
o .
i A
rr
"l; ailx
ol
a' :
; = ; i ' . 3
r,
i
c
cr
'??
4
9
r ;
r g '" e I i' r ;-
9
x
x
(.1
a'
I d
-lg
l.-\OF
.i --: -;
I
= TFg ;s:"J tF53
s b- T ;
{a=-'
::
ll
lt
..r
E
c: lli
o a
tl
ll " l - .
O
(9)5Xt
t : l i l
\,
: l s
n F
( 9 rt x t
9 ; 9 0i9! .il{t
q.l
:l
:
:11
rJ., E
ro
o
3 r c :i
t't
ri
.9
^ 6 , : A - o.e
(t, t+a
(t, t+a
*
L
?
3
.
s
(t t+z (t),t|l||{trr-t)a
l
r
O r !
o-
9
o
l -r(lrlDs to J ol rDJ a\
|
o l . e
a vil{t
l!l WI'A
6
l o (\|a q
( 9 )t x t
a il.l"
F
r
l j m b X
:!-6r:e..
> T
*-
\
i =. " ' 6 2 d
-- Fi
o
:
: l -r:,Z
-l t
d o 3r'l
6 o.
ut /'\
.
>
irll
I
*==; r 'a)(< -:e N
.,N'
=5'
7 ?
=sqof,
.::
-n ,-'
=
.ql (lJ
6
e
g
-
.i
ll
;E
i z ; !
ll
o
.an -
2
{ rn
' - ;
F n =:e
o F
I
+
+ t) o\ I
H F o
I
A)E
t-)
=
o t
:
- v
5
< 'rl
{
d ;
-. P
di' i'' a
.n 6
g
E d i i
-
<
l
;
l
s
x :
6
n
t
o 1 r v
la
i,.r ir' i,l a
s : q
a
\
--*
cr t
5 6
;
t = r
3
6r a
F
E
a E '.j 3 E ? i o
6 i a ' 6
5
.
?
? 3 -
-'' -
r
.
A-i
6
'.4 l^
'
-:*
tl
'c
'
=
E
= - 3< 7-
*+o
/\ 3
*, . o X
i F :
l g
' E r 9 l !;\ a l (l tJ
l
= a o
\o
9c - 5
(, F,
g
o €
E
:$;igF iE[$$ :EF;$f,igrF 'FF*e *i Ii"5 €* isgfsil* iiilei a ig FsSi +i i ar:gegir sF3 iigiFgFi$iE;F 'n
c'l i,J l\)
m
t'l
\)
F F slHseF
ot
s 3
3 r
5 Y ! r =
: . q
F ':3 (!
t
:
u
X
d.E
\-J
E
€ , F . r o < i cr l-..r!o
-' bg l )
-C zor)3 'A:-
a.l\oOO\O r'r h F- a.J oo
>..
.n \o o .r \o
9E B \
F
.o
-t
: 1I i-o
\
tr
vl rt \n v.t r.)
99\q99 r)t,l')r)r|
T\
\t' (rJ
ro
re
uJ
;;
' !
p -o.ro+o
u-
\o
ir
"' o
';: rD 0) 'oD0 tidi
g $
;
d l o . 4 -
-
( N
/
I
r x .95
-8s
i4 .! " = S r , 3 S i Eki '< ::
;
o\ ll
"^
!, !
-o c.r
.:
olt''f
-
^ i 5
i *
g _
.:i ii
=.= a= .9^ la :
E';
E _ :' ' E E oor .-,ra
c d
r $_ ' r E
E
v_i F
E.E",i
E
tlt;BEfi-ie t
:pgIEEig
'=
"-: \o -
i
!
z
u,l rJ) a? gt
,:g/ (fi)
-:i-
--.=l-l--
;3Es3EEEg ='';*uii'i$ii€c : iil lgi*uis's
g{sissaisic*{di -$ :[i ill ; ' ':ut :ii Ea itE e$ f *=i EiFrFg: i tsEEFi ,i ; $ i 5 $ t : ; F ; ix i
ie+5i|l_F
i6i$€=Fgifi+
$ s $ i $ Ini r ir *$' ri iggi gf
iP 5eFi- $a: : s6* ri
F g
c:
€i
i
t
? z ut.f
\J
i 9PEF
Fr $ =g $'< b R
t
.si;
o
{;.i-
*
8+E
:::
c)@
r
f
9 '
t
d
Y
E
3 -
o .
|
. J
€
!
q t
r
s
:
-
F ! 4 3 .: o_ .o i X : +
O |
!
S q
;- ' { .i4
<
:P
.
b= t
3
E