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R e l i a b i l i t y - B a s e d D e s i g n o f T r a n s m i s s i o n L i n e S t r u c t u r e s- D i r e c t A p p r o a c h U s i n g th e I n v e r s e R e l i a b i l i t y M e t h o d

H on g L i I and G our i Bhuy a n 2

A b s t r a c tA r e l i a b i l i t y - ba s e d de s i gn p r oc e du r e u s i ng t he i nve r s e r e l i a b i l i ty m e t hod i s p r opo s e di n t h i s pa pe r f o r de s i gn o f ove r he a d t r a ns m i s s i on s t r uc t u r e s . T he p r oc e du r e a l l ow sd i r e c t a nd f a s t de t e r m i na t i on o f de s i gn pa r a m e t e r s s uc h a s w i nd s pa n a nd po l eg r ound l i ne c i r c um f e r e nc e , i n o r de r t o m e e t p r e - s pe c i f i e d ta r ge t r e l i a b il i ti e s . T w ode s i gn a pp l i c a t i ons a re i l l u s tr a te d : 1 ) c a l c u l a t ion o f t he d e s i gn w i nd s pa n o f a l a tt i c es t e e l s u s pe ns i on t ow e r s o t ha t a t a r ge t r e l i a b i l i t y i s a c h i e ve d i n a c o m p r e s s i onpe r f o r m a nc e c r i t e r i on ; a nd 2 ) de t e r m i na t i on o f de s i gn w i nd s pa n o f a n H - f r a m et a nge n t w oo d po l e s t ruc t u r e t o a c h i e ve t a r ge t r e l ia b i l i ti e s a s s oc i a t e d w i t h de s i gnc r i t e ri a i n t i p de f l e c t i on ( s e r v i c e a b i l i t y c r i te r i on ) a nd be nd i ng ( u l ti m a t e de s i gnc r it e r ion ) . T he a dva n t a ge s a nd i m p l i c a t i ons o f t he s e a pp r oa c he s a r e d i s c us s e d .Keyw ords: inverse reliability, structural analysis, woo d pole, steel lattice tower, reliab ility-base d designI n t r o d u c t i o nT he m a i n o b j e c t i ve i n e ng i ne e r i ng de s i gn i s t o e ns u r e tha t the r e qu i r e d pe r f o r m a nc ec a n be m e t du r i ng s e r v i c e li fe . T he pe r f o r m a nc e o f a de s i gne d s ys t e m de pe n ds on t hei n t e r a c ti on o f m a ny i n t e r ve n i ng r a ndom va r i a b l e s, p l u s t he design parameters t ha t thede s i gne r ha s c hos e n on t he ba s i s o f s a f e ty a nd s e r v i c e a b i l i t y c r it e ri a . G i ve n t heunc e r t a i n t y a s s oc i a t e d w i t h i n t e rve n i ng va r i a b l e s , t he pe r f o r m a nc e c r i t e ri a c a n o n l ybe s a t i s fi e d w i t h i n a c e r t a in p r ob a b i l it y . T he ob j e c t i ve o f r e l i a b i l i t y - ba s e d de s i gn i s t ode t e r m i ne t he de s i gn pa r a m e t e r s ne e de d s o t ha t t he p r oba b i l i t y o f pe r f o r m a nc e , c a l l e dre l i ab i l i ty , w i l l ach ieve the des ign c r i t e r ion wi th in a spec i f i ed t a rge t l eve l .

Structural & Re liabilityEngineer, Powertcch Labs. Inc ., 12388-88 h A ve., Surrey,BC, CanadaV3W 7R 7; pho ne 604-590-7463, Fax 604-590-5347; hong.li@pow ertechlabs.comz S pecialistEngineer, Pow ertechLab s. Inc., 12388-88 h Ave., Surrey,BC, CanadaV3W 7R7; phone604-590-7407, Fax 604-590-5347; gouri.bhuyan@pow ertechlabs.com357

Electrical Transmission in a New Age

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358 ELECTRICAL TRANSMISSION N A NEW AGE

I f t he de s i gn pa r a m e t e r s a r e g i ve n , the r e l i a b i l i t y o f a s y s t e m c a n be e va l ua t e d f o r ac e r t a in c on d i t i on a nd pe r i od o f ti m e t h r ough r e l i a b i l i t y a s s e s s m e n t . This i s a f o r w a r dr e l i a b i l i t y pr ob l e m . O n t he o t he r ha nd , w he n t he de s i gn pa r a m e t e r s ne e d to bede t e r m i ne d i n o r de r t o a c h i e ve p r e - s pe c i f i e d t a r ge t r e l ia b i l i t y l e ve ls , t he p r ob l e mb e c o m e s o n e o f i n v e r s e r e l i a b i l i t y . T hi s i nve r s e r e l i a b i l it y p r ob l e m de f i ne s t he n a t u r eo f r e l i a b i l i t y - ba s e d de s i gn .Re l i a b i l i ty - ba s e d de s i gn ha s be e n s t ud i e d and a pp l i e d t o ov e r he a d s t ruc t u re d e s i gn f o rthe l a s t two decad es (Peyro t e t . a l , 1984, Kr i shna sanm y, 1991 , AS CE -74, 1991 andI E C 60826 , 1991 ). S e ve r a l m e t hod o l og i e s ha ve be e n p r opos e d , inc l ud i ng : 1 ) t heL oa d / Re s i s t a nc e F a c t o r D e s i gn ( L RF D ) f o r m a t , i n w h i c h t he l oa d f a c t o r s a ndres i s t ance fac tor a re ca l ib ra ted to m ee t t a rge t re l i ab i l i ty , and 2) d es ign nom ina l loa dwi th a ce r t a in re turn pe r iod and charac te r i s t i c s t rength wi th a low exc lus ion l imi t , i nw h i c h t he l oa d r e t u rn pe r i od i s u s e d t o s p e c i f y i nd i r e c t ly t he t a r ge t a nnua l r e l i a b i l i t yleve l .T r a d i t i ona l l y , r e l i a b i l it y - ba s e d de s i gn o r L RF D de s i gn i s i m p l e m e n t e d t h r ough ades ign equa t ion conta in ing load fac tors and res i s t ance fac tor tha t a re in tended form e e t i ng a s pe c i f i e d r e l i a b il i ty . H ow e ve r , t he de s i gn e ng i ne e r s do no t ge ne r a l l y knowthe ra t io na le behind the fac tors chosen and the re l i ab i l i ty or s a fe ty l eve l tha t i s rea l lya c h i e ve d . I f the no m i na l l oa d ha s a r e t u r n pe r i od o f T ye a r s , a nd a s t re ng t h e xc l u s i onl i m i t o f 10% i s u s e d a s t he c ha r a c t e ri s ti c s tr e ng th , t he a c h i e ve d a nnua l p r oba b i l i t y o ff a i lu r e is i n t he o r de r o f P f = 1 / 2T . F o r e xa m p l e , i f t he r et u r n pe r i od w e r e 50 ye a r s ,t he a nnu a l p r oba b i l i t y o f f a i l u re w o u l d be i n t he o r de r o f 1 .0%. L oc a l w e a t he rs t a t i s t i c s c a n be u s e d t o de t e r m i ne t he nom i na l de s i gn l oa d f o r a s pe c i f i e d r e t u r npe r i od .A n o t he r m e t hod i s t ha t o f i nve r s e re l i a b i li t y , w he r e t he de s i gn pa r a m e t e r s a r e d i r e c t l yca lcu la te d to a ch ieve a spec i f i ed t a rge t re l i ab i l i ty . Us in g th i s approach , an eng ineerc ou l d w or k on a c us t om i z e d o r c a s e - by - c a s e ba s i s, ta k i ng i n to a c c oun t l oc a l w e a t he rs t a ti s ti c s w i t h t he a s s i st a nc e o f r e l i a b i l i t y s o f tw a r e . T he de s i r e d pe r f o r m a n c e c r i te r i ac a n be m e t w i t h t he c o r r e s pond i ng t a rge t r e li a b i l it y .In th i sfor thew i l l be

pa pe r a d i r e c t a pp r oa c h , ba s e d on t he i nve r s e r e l i a b i l it y m e t hod , i s p r opo s e dr e l i a b i l i t y - ba s e d de s i gn o f t r a ns m i s s ion s tr uc tu r e s. T w o de s i gn a pp l i c a t i onsde m ons t r a t e d :

1.

2.

Ca l c u l a t i on o f t he de s i gn w i nd s pa n o f a l a t t i c e s t e e l s u s pe ns i on t ow e r t oa c h i e ve a t a r ge t r e l i a b i l i t y a s s oc i a t e d w i t h t he c o m p r e s s i on pe r f o r m a nc ecr i t e r ion for a c r i t ica l m em ber ; an dC a l c u l a ti o n o f t h e d e s ig n w i n d s p a n o f a n H - f ra m e t a n g en t w o o d p o l es t ruc ture so tha t t a rge t re l i ab i l i t i e s a s soc ia ted wi th d es ign c r i t e r i a in bo thde f l e c t i on and be nd i ng c a n be a c h i e ve d .


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ELECTRICAL TRANSMISSION N A NEW AGE 359

R e v i e w o f In v e r se R e l ia b i li ty

D u r i ng t he p a s t f e w ye a r s , t he i nve r s e r e li a b i l i t y m e t ho d ha s b e e n d i s c us s e d bo t h i nt he c on t e x t o f a s i ng l e de t e r m i n i s ti c de s i gn pa r a m e t e r ( D e r K i u r e gh i a n e t a l , 1994 ) o ri n t he c on t e x t o f m u l t i p l e pa r a m e t e r s a s s oc i a t e d w i t h r a ndom va r i a b l e s ( L i a ndFosc hi , 1998). I t has been show n through se vera l appl i ca t ions tha t the inverser e l i a b i l i t y m e t hod i s s upe r i o r t o t he t r a d i ti ona l a pp r oa c h o f tr i a l -a nd - e r r o r , i n w h i c ht he f o r w a r d r e l i a b i l i t y m e t ho d i s r e pe a t e d l y a pp l i e d t o i n t e rpo l a t e t he de s i gnpa r a m e t e r s m e e t i ng t a r ge t re l i a b i l it y .T he i nve r s e r e l i a b i l i t y p r ob l e m a r is e s w he n i t is ne c e s s a r y to f i nd t he va l ue s o f de s i gnpa r a m e t e r s t ha t c o r r e s pon d t o s pe c i f ie d r e l ia b i l i t y l e ve ls . A ge ne r a l m e t hod w a sde ve l ope d t o a pp r oa c h t he i nve r s e r e l ia b i l i t y p r ob l e m f o r e i the r s i ng l e o r m u l t i p l edes ign va r i ab les by L i and Fo schi (1998). In genera l , t hese va r i ab les a re a l so rega rdeda s r a ndom , w i t h c o r r e s pond i ng m e a n va l ue s a nd s t a nda r d de v i a t i ons . T he p r ob l e mm a y i nc l ude t he de t e r m i na t i on o f bo t h t he m e a n va l ue s a nd s t a nda r d de v i a t ions , o r them e a n va l ue s a l one w he n t he c oe f f i c i e n t s o f va r i a t i on a r e s pe c i f i e d , o r t he s t a nda r dde v i a t i ons w he n t he m e a n va l ue s a r e g ive n . A de t a i l e d de s c r i p t i on o f t he m e t hod i sg iven e l sewhere (L i and Foschi , 1998 and L i , 1999) . The method for a s ing le des ignpa r a m e t e r ha s be e n a pp l i e d in t h i s pa pe r , u s ing t he f r a m e w or k d e s c r i be d be l ow .S upp os e t ha t t he l i m i t - st a t e f unc t ion G i n t he S t a nda r d N or m a l , unc o r r e l a t e d s pa c e i sG (U , d ) = g (X , d ) ................................................................................................... (1 )w he r e U i s t he r a ndom , S t a nda r d N o r m a l ve c t o r w i t h c om pone n t s u~. c o r r e s pond i ng t ot he r a ndom va r i a b l e ve c t o r X w i t h c om p one n t s x i i n t he o r i g i na l, ba s i c s pa c e, d i s thede s i gn pa r a m e t e r .Fo r a t a rg e t re l i ab i l i ty index 13, the inv erse re l i ab i l i ty pro blem can be s t a t ed as :Given: 13,F in d : a d e si g n p a ra m e te r d ....................................................................................... (2 )S u b j e c t t o : r n i n ( U r U ) = ~ 2 a n d G ( X , , d ) = OT he m a pp i ng o f U i n t o X i s a c h ie ve d t h rough t he t ra ns f o r m a t ions

-1x i = F i ( q ~ ( u , ) ) i = 1 , 2 . . .. n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3 )


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360 ELECTRICALTRANSMISSION N A NE W AGE

w h e r e F t i s t h e c u m u l a t i v e d i s tr i b u t i o n f u n c t i o n f or t h e v a r i a b l e x i , an d qb( .) i s theS t a n d a r d N o r m a l f u n c t i o n .F r o m r e l i a b i l i t y i n d e x [ 3 , t h e p r o b a b i l i t y o f f a i l u r e P f a n d t h e r e l i a b i l i t y P ~ c a n b ee s t im a t e d a p p r o x i m a t e l y a s s h o w n i n (4 ) a n d ( 5 ), b y u s e o f t h e S t a n d a r d N o r m a lp r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n q b (.) .P f = qb (-[3 ) ................................................................................................................ (4 )a n d P r : 1 - ~ [ 3 ) = ~ ( ~ ) .. .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. .. . .. . . (5)

T w o b a s i c f o r m u l a e w e r e d e r i v e d t o i te r a te t h e d e s i g n p a r a m e t e r f o r a g i v e n ta r g e tr e l i a b i l i t y i n d e x [3.

U = - ~ V v G( V v G r V v G ) I/2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 )

d = d o G ( U o , d o )O G ( U o , d ) ) [~d d~

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 )

F o r a n i n i t i a l p a i r ( d o , U o ) , a n d t h e c o r r e s p o n d i n g g r a d i en t V v G ( U , d ) l u o .a o , (6 ) and( 7 ) a r e u s e d t o g e t h e r to o b t a i n b o t h t h e v e c t o r U a n d t h e d e s i g n p a r a m e t e r d b y m e a n so f a N e w t o n - R a p h s o n i te r at io n .C a s e S t u d i esC a s e S t u d y 1 : D e s i g n o f a L a t t ic e S t e e l T o w e rA t y p i c a l s u s p e n s i o n la t t ic e st e e l t o w e r w a s c h o s e n f o r t h e c a s e s t u d y ( s e e F i g u r e 1 ).S i x c o n d u c t o r s a r e a t t a c h e d a n d t h e l e g m e m b e r i s c o n s i d e r e d a s t h e c r i t i c a lc o m p o n e n t . I t i s a s s u m e d t h a t t h e c o n f i g u r a t i o n a n d t h e m e m b e r s i z es o f t h e t o w e r a r ef i x e d . W i n d s p a n i s c h o s e n a s t h e d e s i g n p a r a m e t e r t o r e f l e c t t h e d e s i r e d t a r g e tr e l i a b i l i t y . C o m p r e s s i o n f o r c e o f t h e l e g m e m b e r i s c o n s i d e r e d i n t h e l i m i t - s t a t ef u n c t i o n f o r t h e r e l ia b i l it y - b a s e d d e s ig n , a s s u m i n g th a t f a i l u re o f t h e l e g m e m b e r w i l lc a u s e t h e f a i l u r e o f e n t i r e s tr u c t u r e. T h e o b j e c t i v e o f th i s a p p l i c a t i o n i s to f i n d t h ed e s i g n w i n d s p a n s o t h a t th e t a r g e t r e l i a b i l i t y c o r r e s p o n d i n g to t h e c o m p r e s s i o nd e s i g n c r i t e r i o n o f t h e l e g m e m b e r w i l l b e a c h i e v ed f o r t w o l o a d c a s es d u r i n g t h ese rv ice l i fe .


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ELECTRICALTRANSMISSION N A NEW AGE 361

Figure 1: The suspension lattice steel tower

In reliability-based analysis, an analytical model formulated either as a close-formequation or as a computational program is needed to evaluate the effect of loadsconsidered in the limit-state functions, such as deflection, bending moment andcompression force. For this case study, it is assumed that the tower has a linearbehavior in compression, thus the influence coefficient (effect of unit loads) can beused to calculate the structural response. To obtain the influence coefficient,structural analysis software ATADS (BPA, 2000) was used to calculate the effect(compression force of the leg member) of the unit vertical group loads and unithorizontal group loads as well as unit wind pressure. If a combined stress level due toapplied vertical and transverse loads exceeds the compression capacity of themember, the structure will fail.For the reliability calculations, the limit state functions corresponding to compressionfailure of the leg member are written as follows, considering two load cases:


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362 ELECTRICALTRANSMISSION N A NEW AGE

Wind + ice: G = R A - e f f e c t o f ( T S + ( V + D ) S p + d + P ) . . .. . .. . .. . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . (8)

Wind only: G = R A - e f f e c t o f ( T S + D S p + d + P ) . . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . (9)where:S = design wind spanT = transverse load (function of wind velocity and/or ice thickness) per unit length

of conductorsp = ratio of weight span to wind spanV = vertical load (function of ice thickness) per unit length of conductorsD = dead load per unit length contributed by the weight of conductorsd = dead load contributed by the weight of membersP = wind pressure applied on the structureRA = compression capacityThe effect is the compression force of the leg member. Three random variables areconsidered: compression capacity RA, wind velocity, and ice thickness. For specifiedtarget reliability, the design wind span S can be calculated based on the algorithmdescribed above.Statistics of wind velocity, ice thickness, and compression capacity (treated asrandom variables) are assumed and shown in Table 1 for this case study.

Table 1: Statistics of Random VariablesComponent

Compression capacity RAExtreme wind*

Mean890 kN (200.0 kips)78 km/h (44.7 mph)

Wind during ice 43 km/h (26.7 mph)Ice * 8.6 mm (0.34 inch)

COV Type0.10 Lognormal0.10 Gumbel0.4 Gumbel0.8 Gumbel

* Annual maximumThe inverse reliability procedure was carried out for three target reliability levels, 13 =3.0, 2.5 and 2.0, corresponding to a probability of failure of 0.14%, 0.62% and 2.3%respectively, in a 50-year window. The results are shown in Table 2. The design isgoverned by the wind with ice case. The corresponding target reliability is achievedexactly, and the target reliability for the wind-only case is satisfied, thus providing asatisfactory design for both load cases. It should be noted that different design spanscould be obtained if the weather statistics change due to change of tower location.Ideally, if the weather statistics for all design sites are available, such reliability-baseddesign could lead to a nearly uniform design across the board.


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ELECTRICALTRANSMISSION N A NEW AGE 363

Table 2: Design Span and Achieved Reliabilit, IndexTarget ReliabilityIndex (50 years)Wind Wind +only ice3.02.52.0

3.0

Design Span ControllingSpanWind only Wind + ice223m 106m733 (fi) 347 (~)297m 187m976 (if) 614 (~)380m 307m

1249(ft) 1008(~)

106m347(fi)187 m

614 (fl).5307 m2.0 1008 (ft)

AchievedReliability IndexWind Wind +only ice3.98 3.003.28 2.502.44 2.00

C a s e S t u d y 2." D e s i g n o f a n H - f r a m e W o o d S tr u c t u r eA typical tangent H-frame wood structure was chosen as a reference structure, withthree conductors attached (see Figure 2). It is assumed that the configuration of the H-frame and the sizes of the poles are fixed. A critical section A at the bottom of thecross braces is considered in the design. If a combined stress level due to appliedvertical and transverse load exceeds the bending strength capacity, the structure willfail.Wood poles are, in general, slender structures subjected to horizontal and verticalloads, and wood behaves nonlinearly n compression and brittle tension. This allowedthe nonlinear finite element program POLE (Powertech Labs Inc. 1998) to be used inconjunction with the inverse reliability method to perform reliability-based design,taking the P-A effect into account. Two limit states corresponding to serviceabilityand ultimate design criteria were considered:Ultimate: G I = R - Ef f e c t o f (TS +( V+ D) S p +P ) . . . .. . .. . .. . . .. . .. . .. . .. . . .. . .. . .. . . .. . .. . .. . .. . . (1 O)Serviceability: G2 = Ao - E f f e c t o f ( T S + ( V+ D ) S p +P) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (11)where:S = design wind spanp = ratio of weight span to wind spanT = transverse load (function of wind velocity and/or ice thickness) per unit length

of conductorsV = vertical load (function of ice thickness) per unit length of conductorD = dead load per unit length contributed by the weight of conductorsP = wind pressure applied on the structureR = bending strengthAo = allowable tip deflection of the wood pole, assuming 2% of the height of the pole


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F i g u r e 2 : A t yp i c a l t a nge n t H - f r a m e w ood s t ruc t u reT hr e e r a ndom va r i a b l e s a r e c ons i de r e d i n t he l i m i t s ta t e func t ions : be nd i ng s t re ng t hR , t r a ns ve r s e l oa d T ( f unc t ion o f w i nd ve l oc i t y ) , a nd ve r t i c a l loa d V ( f tm c t i on o fr a d i a l i c e t h i c kne s s ) . M e a n , c oe f f i c i e n t o f va r i a t i on a nd t ype o f d i s t r i bu t i on o f t hebe nd i ng s t r e ng t h a re g i ve n i n T a b l e 3 . W i nd a nd i c e s ta t is t ic s w e r e u s e d f o r t he s a m el oc a t i on a s Ca s e S t udy 1 (s e e T a b l e 1 ), bu t on l y t he w i nd d u r i ng i c e loa d c a s e w a sc ons i de r e d .

T a b l e 3 : S t a ti s ti c s o f Be nd i ng S t r e ng t hM e a n C O V T y p e

45.5 M Pa (6600 ps i ) 0 .15 Lo gn orm alU s i ng t he i nve r s e r e l i a b i l i t y m e t hod , t he r e l i a b i l i t y - ba s e d de s i gn w a s c a r r i e d ou t f o rva r io us t a rge t re l i ab i l i t i e s for each d es ign c r i t e r ion . The resu l t s a re show n in Tab le 4 .Fo r u l t im a te an d se rv ice abi l i ty l imi t s t a tes , two d i f fe ren t t a rge t re l i ab i l i t i e s a res pe c i f i e d . T he de s i gn i s c on t r o l l e d by t he u l t i m a t e l i m i t s t a t e . T he c o r r e s pond i ngr e l i a b i l i t y i nde x i s a c h i e ve d e x a c t l y , a nd t he t a r ge t r e l ia b i l i t y c o r r e s pond i ng t ose rv iceab i l i ty i s a l so sa t i sf i ed .


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ELECTRICAL TRANSMISSION N A NEW AGE 365

Target Reliabil i ty IndexT a b l e 4 : R e s u l t s (W i n d w i th I c e C a s e

3.02.52.0

(50 years),. Q

c1 3

2.01.51.0

Design Span

1 6 3 m 1 8 4 m535 (ft) 603 (ft)239 m 262 m785 (ft) 861 (ft)339 m 363 m1111 fit)

e~

.E=Or..)

163 m535 (ft)239 m785 fit)3 3 9 m1193 (ft ) l l l l ( ft )

Achieved ReliabilityIndex

'EY ~3.00 2.162.50 1.632.00 1.11

D i s c u s s io n a n d C o n c l u s i o n sA n a l t e r na t i ve de s i gn a pp r oa c h f o r t r a ns m i s s i on l i ne s t r uc t u r e s u s i ng t he i nve r s er e l i a b i l i t y m e t ho d i s p r opos e d i n t h i s pape r . T w o c a s e s t ud ie s w e r e c a r r i e d ou t, onefor a l a t t i ce tow er s t ruc ture mad one for an H-f ram e woo d s t ruc ture . De s ign sp an w asc hos e n a s t he de s i gn pa r a m e t e r t o r e f l e c t va r ious t a r ge t r e l i a b i l i ty l e ve ls . I t s hou l d beno t e d t ha t a ny o t he r pa r a m e t e r c ou l d ha ve be e n c hos e n , s uc h a s t he g r ound l i ned i a m e t e r o f t he w o o d p o l e o r t h e c o m p r e s si o n c a p a c i ty o f a l e g m e m b e r o f th e s te e ltow er when th e span i s f ixed . In cont ras t to the t rad i t iona l de te rm in i s t i c o r re l i ab i l i ty -c a l i b r a t e d f a c t o r e d de s i gn a pp r oa c h , t he a pp r oa c h de ve l ope d i n t h i s pa pe r pe r m i t sd i r e c t de t e r m i na t i on o f the d e s i gn pa r a m e t e r to m e e t de s i r e d pe r fo r m a nc e . S i nc e t hede s i r e d pe r f o r m a nc e i s w e l l de f i ne d by l i m i t - s t a t e f unc t i on a nd a s s oc i a t e d t a r ge tr e l i a b i l it y , t he a c h i e ve d pe r f o r m a nc e w i l l be t r a ns pa re n t t o t he d e s i gn e ng i ne e r s . T heunc e r t a in t i e s i nvo l ve d i n l oa ds a nd m a t e r i a l p r ope r t i e s a r e a u t om a t i c a l l y t a ke n i n t oa c c oun t du r i ng t he p r oc e du r e . L i ne i m por t a nc e , l oc a l w e a t he r c ond i t i ons , m a t e r i a lp r ope r t i e s , a nd m u l t i p l e de s i gn c r i t e r i a c a n be e a s i l y c ons i de r e d , a l l ow i ng f o r ac us t om i z e d de s i gn . I n a dd i t ion , t h is r e l i a b i l i t y - ba s e d de s i gn a pp r oa c h o f f e r s t heo p p o r t u n i ty t o u s e w e l l - d e v e l o p e d r e li a b i li t y t h e o r y a n d c o m p u t e r t e c h n o l o g y t oc om pl e m e n t s t r uc tu r a l m e c h a n i c s a nd c om pu t a t i ona l t oo l s.R e f e r e n c e sA d v a n c e d T o w e r A n a l y s i s an d D e s i g n S y s t e m ( A T A D S ) S o f tw a r e, B o n n e v i l l e P o w e rA d m i n i st r a ti o n ( B P A )A S CE - 74 . ( 1991 ) . Guidelines or Transmission Line Structural LoadingDe r Kiureg hian , A . , Zhang , Y , and L i , C .C. (1994). " Inverse re l i ab i l i ty pro blem " , J .of Engineering Mechanics,ASCE, 120(5) , p . 1154-1159.


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IEC 60826 - Des ign Cri ter ia o f Ov erhead Transm ission Lines. (1991) . (Also theprevious ly publ i shed guide l ines : Lo ading and S t rength o f Overhead Transm iss ionLines) , IE C-T C1 1 -Pu b l ica t ion 826.Kris hnas am y, S . G. , Hathou t , I . An d Tabatabai , M. (1991). "Reliabil i ty-based designof overhe ad transm ission structures- a cri t ica l review". P r o c . In t . C o n f . o nP r o b a b i l is t i c M e t h o d s A p p li e d t o E l e ct r i c P o w e r S y s t e m s , Londo n, UK , p. 86-91Li, H. (1999) . "An inv erse re liabi l i ty method and i ts applicat ions in engineer ingdesign", P h .D . t h e s is , D e p a r t m e n t o f C i v i l E n g i n e e r i n g , Univers i ty o f Br i ti shColum bia , Vancouver , Canada.Li , H. and Foschi , R.O . (1998). "An inverse re l iabi li ty me thod and i ts application" ,S t ru c tu ra l S a f e t y , Elsevier, 20(3), p. 257-270.Peyrot , A.H . and Dagh er , H.J . (1984) . "Reliabil i ty-based design o f t ransmissionlines" J o u r n a l o f s t ru c tu r a l e n g i n e e r i n g A SC E , Vo l. 110, No. 11, p. 27 58-2777 .POLE : A C om pute r P rogram to Car ry Out Re l iab i li ty Ana lys is of Pole S t ruc tures .(1998) . Powertech Labs.

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