finite element analysis of power transmission line tower

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FINITE ELEMENT ANALYSIS OF A POWERTRANSMISSION LINE TOWER

R. Todd Pettyjohn

September 15, !!"

#$%&'(b)r*, +r*n%, -SA



Introduction

The prob$em %t h%nd re)re( (tr)&t)r%$ %n%$y(( o/ % po0ertr%n(m((on$ne

to0er. Th( $%r*e tr)((, 0h&h (t%nd( 25 /t h*h %nd (p%n( 5! /eet ( (ho0n n /*)re 1.

E%&h member ( m%de /rom 1! n re&t%n*)$%r A3" Stee$, 0h&h h%( % mod)$)( o/

e$%(t&ty o/ "1!4 ⋅= E p(, % ye$d (tren*th o/ 3"= yS '(, %nd % Po((on( R%to o/

4.!=ν .

Figure 1 T0o dmen(on%$ tr)(( mode$ o/ % po0er tr%n(m((on $ne to0er.

The obje&t6e( o/ th( %n%$y(( %re to determne7

• The o6er%$$ beh%6or o/ the (tr)&t)re

• The 6%$)e %nd $o&%ton o/ m%8m)m de/$e&ton

• The $o%d %nd (tre(( n e%&h member

• The &rt&%$ member

• The &rt&%$ /%$)re mode

• The /%&tor( o/ (%/ety /or b)&'$n* %nd ye$d

Model Development

P%*e o/ 19



The tr)(( 0%( mode$ed n ANSYS 9.!. The tr)(( mode$ 0%( &omp$eted by

de/nn* 'eypont( %nd %ddn* the %ppropr%te $ne(. :ero d(p$%&ement &on(tr%nt( 0ere

%pp$ed %t pont( 1 %nd , %nd $o%d( 0ere %pp$ed %t pont( 11 %nd 1". F*)re %nd

F*)re 3 (ho0 the &omp$eted mode$ 0th the $o&%ton o/ %pp$ed $o%d( %nd bo)nd%ry

&ondton(, %( 0e$$ %( the e$ement n)mber(. E%&h e$ement n the tr)(( ( %ppro8m%ted %(

%

LIN;1 ANSYS e$ement, 0h&h ( % t0o dmen(on%$ )n%8%$ t0o /or&e member 0th

t0o de*ree( o/ /reedom %t e%&h node. The m%ter%$ 0%( mode$ed %( % $ne%r e$%(t&

(otrop& m%ter%$. T%b$e( 1 %nd ()mm%r<e the e$ement( %nd m%ter%$ mode$( )(ed.

P%*e 3 o/ 19

Figure 2 ANSYS mode$ (ho0n* the $o&%ton o/ %pp$ed $o%d( %nd bo)nd%ry &ondton(



Table 1 Type( o/ e$ement( )(ed

Element No. Element Type

A$$ E$ement( =14> LIN; 1

Table 2 M%ter%$ mode$( %nd m%ter%$ properte( o/ e%&h e$ement

P%*e 2 o/ 19

Element No. Material Type Material

Modulus of

Elasticity

Yield

trengt!

"oisson#s

$atio %rea

A$$ E$ement(

=14>

Lne%r E$%(t&

I(otrop& A3" Stee$ 4 8 1!" p( 3" '( !.4 1! n

Figure & ANSYS mode$ (ho0n* the e$ement n)mber(



%nalysis $esults

Pre(ented n th( (e&ton %re the re()$t( o/ the %n%$y((. T%b$e 3 $%be$( the &rt&%$

member( %nd the ye$dn* %nd b)&'$n* /%&tor( o/ (%/ety. T%b$e 2 (ho0( the ntern%$

/or&e, (tre((, %nd (tr%n n e%&h e$ement. T%b$e 5 (ho0( the b)&'$n* $o%d( o/ e%&h

member. ?%$&)$%ton( pert%nn* to b)&'$n* &%n be $o&%ted n Append8 #. F*)re( 2"

$$)(tr%te the ntern%$ member /or&e(, (tre((e(, %nd (tr%n( %nd ther e8%&t $o&%ton on the

(tr)&t)re. T%b$e " (ho0( the &omponent( %nd tot%$ m%*nt)de o/ de/$e&ton %t e%&h node.

F*)re 9 (ho0( the de/ormed (tr)&t)re p$otted %*%n(t %n )nde/ormed ed*e.

'verall (e!avior of t!e tructure)

• #)&'n* /%&tor o/ (%/ety o/ 155.1

• Ye$dn* /%&tor o/ (%/ety o/ 1"1

• The &rt&%$ member( %re member 12, 15, 1,

• The &rt&%$ member( %re %$$ n &ompre((on %nd 0$$ b)&'$e be/ore

ye$dn*

• The (tr)&t)re ( ()bje&t to $o%dn* 0e$$ be$o0 t( $mt(

• The m%8m)m de/$e&ton ( !.!!1!1@ %nd o&&)r( %t the )pper r*ht

e8treme o/ the (tr)&t)re =node 15>.

Table & ?rt&%$ member( %nd /%&tor( o/ (%/ety

*ritical (uc+ling Members 12,15,1,

*ritical Yielding Members 12,15,1,

(uc+ling Factor of afety ,nb- 155.1

Yielding Factor of afety ,ny- 1"1.!

P%*e 5 o/ 19



Table Intern%$ /or&e, (tre((, %nd (tr%n n e%&h member.

Element

No.

Member Force

,lb-

tress

,psi- train

1 1.!E1 1.!E13 3.5!E1

1!!! 1!! 3.25E!"

3 1.34E1 1.34E13 2.94E1

2 1!!! 1!! 3.25E!"

5 5! 5 ."E!9

" 1!31 1!3 3.55E!"

9 1!31 1!3 3.55E!"

2.3!E1 2.3!E13 1.2E!

4 5! 5 ."E!9

1! 1!!! 1!! 3.25E!"

11 1!!! 1!! 3.25E!"

1 1.1E11 1.1E1 ".3E!

13 !!! !! ".4!E!"

12 3" 2 9.91E!"

15 3" 2 9.91E!"

1" !!! !! ".4!E!"

19 !!! !! ".4!E!"

1 !!! !! ".4!E!"

14 !!! !! ".4!E!"

! !!! !! ".4!E!"1 3" 2 9.91E!"

3" 2 9.91E!"

3 9."E13 9."E12 .91E1

2 .95E11 .95E1 4.24E!

5 3.33E1 3.33E13 1.15E!

" ! ! !.!!EB!!

9 ! ! !.!!EB!!

9.!3E13 9.!3E12 .2E1

4 3.5E13 3.5E12 1.1E1

P%*e " o/ 19



P%*e 9 o/ 19

Table / Lo&%ton o/ e%&h pont o/ the member(, $en*th, ($enderne(( r%to(, b)&'$n* $o%d 6%$)e(, %nd /%&tor( o/ (%/ety



P%*e o/ 19

Figure ANSYS (o$)ton (ho0n* the ntern%$ /or&e n e%&h member



P%*e 4 o/ 19

Figure / ANSYS (o$)ton (ho0n* the (tre(( n e%&h member



P%*e 1! o/ 19

Figure 0 ANSYS (o$)ton (ho0n* the (tr%n n e%&h member



Table 0 ?omponent( o/ de/$e&ton %nd the tot%$ d(p$%&ement %t e%&h node

Node

No. ,in- Y ,in- 3 ,in-

Total

Displacement

,in-

1 5.5E! ! ! 5.5E!

! ! ! !

3 5.19E!5 5.19E!5 ! 9.315E!5

2 3.94E!5 5.19E!5 ! ".2""E!5

5 1.599E!5 4.2E!5 ! 4.493E!5

" .234E!5 .54E!5 ! .44E!5

9 1.2!2E!2 1.!2E!2 ! 1.5!E!2 9.12"E!5 1.33!E!2 ! 1.5!4E!2

4 1."!2E!2 .931E!2 ! 3.1"E!2

1! 5.3E!5 .425E!2 ! .4"1E!2

11 1.5!4E!5 .931E!2 ! .935E!2

1 .2!5E!5 1.!2E!2 ! 1.2"E!2

13 1.53!E!2 1.33!E!2 ! .!9E!2

12 .!E!2 3.1!4E!2 ! 3.!E!2

15 .41!E!2 4.595E!2 ! 1.!!1E!3

1" ".2!5E!5 3.1!4E!2 ! 3.192E!2

Ma4imum Displacement ,in- 1.!!1E!3

Node No. 15

P%*e 11 o/ 19



P%*e 1 o/ 19

Figure 5 ANSYS (o$)ton (ho0n* the de/ormed (h%pe =b$)e> %nd the or*n%$ (h%pe =b$%&'>



Discussion of %nalysis

From the %n%$y(( n pre6o)( (e&ton(, t ( )te e6dent th%t the (tr)&t)re

d(p$%y( % (o)nd de(*n. Wth the ye$dn* %nd b)&'$n* /%&tor( o/ (%/ety both o6er 15!,

t ( )n$'e$y th%t th( (tr)&t)re 0$$ e6er /%$ )nder the(e &ondton(. I/ the $o%d(

dr%(t&%$$y n&re%(e ho0e6er, the &rt&%$ member( 0$$ b)&'$e be/ore ye$dn*. The

d(p$%&ement ( % mere 1.2 E!2 C o/ the (tr)&t)re( he*ht, 0h&h ( ne*$*b$e /or th(

%pp$&%ton. I/ ne&e((%ry, th( (tr)&t)re &o)$d be (%/e$y rede(*ned 0th (m%$$er member(

or % 0e%'er m%ter%$. Th( %n%$y(( pro6e( th( po0er tr%n(m((on $ne to0er to be

(tr)&t)r%$$y %&&ept%b$e /or the pre(ent $o%dn* &ondton(, %( 0e$$ %( e8ten)%tn*

&r&)m(t%n&e( re()$tn* n n&re%(ed $o%dn*.

P%*e 13 o/ 19



%ppendi4 %) ample *alculations of Forces and tresses in elected Members

The /o$$o0n* &%$&)$%ton( n6o$6e %pp$yn* the method( o/ St%t&( %nd

Me&h%n&( o/ M%ter%$( to /nd the ntern%$ /or&e( %nd (tre((e( n (e$e&ted member(.

The(e re()$t( %re )(ed to &on/rm the Fnte E$ement An%$y(( re()$t(. F*)re A1 (ho0(

0here the (tr)&t)re 0$$ be %n%$y<ed.

F*)re A (ho0( % /ree body d%*r%m %( % re()$t o/ &)t 1.

P%*e 12 o/ 19

Figure %61 Lo&%ton o/ &)t( to %n%$y<e ntern%$ beh%6or o/ the member(.



T%'n* the po(t6e x dre&ton to the r*ht %nd the po(t6e y dre&ton )p,

%pp$yn* the e)%ton( o/ e)$br)m %t &)t 1 *6e(7

!1!!!5

1

=−⋅−=∑ F F y

3" =⇒ F lb =?ompre((on>

!5

1 =⋅+−=∑ F F F x

!!!1 =⇒ F lb =Ten(on>

!!1!

!!!1

1 −===

A

F σ psi

".31!

3"

−=−

==

A

F σ psi

F*)re A3 (ho0( % /ree body d%*r%m %( % re()$t o/ &)t .

P%*e 15 o/ 19



-(n* the (%me &oordn%te( %( be/ore, %pp$yn* the e)%ton( o/ e)$br)m

%t &)t *6e(7

!155.31!!!5.191!!!352

=⋅+⋅+⋅−=−∑ F M

1!!!3 =⇒ F lb =?ompre((on>

!

2 ==∑ F F x

!2 =⇒ F lb

!!!!53

=−−−=∑ F F F y

1!!!5 =⇒ F lb =?ompre((on>

1!!1!

1!!!

23 −=

−

=== A

F σ σ psi

!5 =σ

Sn&e %$$ 6%$)e( m%t&h tho(e &%$&)$%ted n ANSYS, t &%n be &on&$)ded the

%n%$y(( 0%( &omp$eted %&&)r%te$y.

%ppendi4 () Determination of *ritical Members and Factor of afety

Perh%p( the mo(t mport%nt p%rt o/ the %n%$y(( ( to $o&%te the &rt&%$

member %nd to determne the /%&tor o/ (%/ety o/ the (tr)&t)re %nd the potent%$ /%$)re

mode. T%b$e #1 (ho0( % ()mm%ry o/ the &rt&%$ member(, %( 0e$$ %( the /%&tor o/ (%/ety

o/ e%&h. T%b$e # (ho0( &rt&%$ n/orm%ton /or e%&h e$ement. ?%$&)$%tn* the ye$dn*

/%&tor o/ (%/ety 0%( r%ther (tr%*ht/or0%rd. Sn&e e6ery member h%( % onedmen(on%$

(t%te o/ (tre((, the ye$dn* /%&tor o/ (%/ety o/ e%&h member ( *6en byσ

y

y

S n = .

The b)&'$n* %n%$y(( re)re( determnn* the type o/ b)&'$n*, then

/ndn* the &rt&%$ /or&e. In order to determne the /%$)re mode, the ($enderne(( r%to,

k

, %nd t%n*ent ($enderne(( r%to,

P%*e 1" o/ 19



yS

A E

k

⋅⋅⋅=

1

π ,

m)(t be &%$&)$%ted. I/k

D 1!, the member /%$( n &ompre((6e ye$d r%ther th%n

b)&'$n*. For th( &%(e, the &rt&%$ $o%d ( *6en by

AS P ycr ⋅= .

The mo(t &ommon type o/ b)&'$n*, E)$erohn(on b)&'$n*, o&&)r( 0hen 1! Dk

D

1

k

. The &rt&%$ $o%d ( *6en by

−⋅=

1

k CE

S S A P y

ycr

π .

The thrd &%(e, 'no0n %( E)$er b)&'$n*, o&&)r( n $on*($ender &o$)mn( 0hen1

k

D

k

. The &rt&%$ $o%d /or th( &%(e ( *6en by

=

k

EAC P cr

π

.

-(n* the d%t% %bo6e, %n e8&e$ (pre%d(heet =T%b$e 5> 0%( de6e$oped 0h&h &ho(e the

&rt&%$ $o%d e)%ton to )(e b%(ed on 6%$)e( o/ the ($enderne(( r%to %nd t%n*ent

($enderne(( r%to.

P%*e 19 o/ 19

finite element analysis of power transmission line tower

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