Me hodology o he elabo a ion o he design able o GFRP s uc u es
subjec ed o i e
Ha kai z Ga cía1*, Mikel Zubiza e a2 and Iñaki Ga mendia1
1Mechanical Enginee ing Depa men , Facul y o Enginee ing Gipuzkoa, Uni e si y o he Basque Coun y
UPV/EHU, Plaza de Eu opa, 1 20018) Donos ia-San Sebas ián, Spain
*a kai z.ga ci[email p o ec ed]us
2Bussines O ganiza ion Depa men , Facul y o Enginee ing Gipuzkoa, Uni e si y o he Basque Coun y
UPV/EHU, Plaza de Eu opa, 1 20018) Donos ia-San Sebas ián, Spain
“This is an accep ed manusc ip o an a icle published by Taylo & F ancis
in Mechanics o Ad anced Ma e ials and S uc u es on 16 Oc obe 2021,
a ailable a : h ps://doi.o g/10.1080/15376494.2021.1980924.”
“This is an Accep ed Manusc ip e sion o he ollowing a icle, accep ed o publica ion in Mechanics o Ad anced Ma e ials and
S uc u es. H. Ga cía, M. Zubiza e a & I. Ga mendia (2022) Me hodology o he elabo a ion o he design able o GFRP s uc u es
subjec ed o i e, Mechanics o Ad anced Ma e ials and S uc u es, 29:27, 6495-6504, DOI: 10.1080/15376494.2021.1980924 . I is
deposi ed unde he e ms o he C ea i e Commons A ibu ion-NonComme cial-NoDe i a i es License (h p://c ea i ecommons.o g/
licenses/by-nc-nd/4.0/), which pe mi s non-comme cial e-use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal
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ARTICLE TEMPLATE
Me hodology o he elabo a ion o he design able o GFRP
s uc u es subjec ed o i e
H. Ga c´ıaa, M. Zubiza e aband I. Ga mendiaa
aMechanical Enginee ing Depa men , Facul y o Enginee ing Gipuzkoa, Uni e si y o he
Basque Coun y UPV/EHU, Plaza de Eu opa, 1 20018) Donos ia-San Sebas i´an, Spain;
bBussines O ganiza ion Depa men , Facul y o Enginee ing Gipuzkoa, Uni e si y o he
Basque Coun y UPV/EHU, Plaza de Eu opa, 1 20018) Donos ia-San Sebas i´an, Spain
ARTICLE HISTORY
Compiled Sep embe 1, 2021
ABSTRACT
The main objec i e o his s udy is o es ablish a i e p o ec ion design me hod o
pul uded Glass Fibe Rein o ced Polyme (GFRP) s uc u es exposed o i e. The
me hod is based on he de elopmen o ables simila o hose al eady a ailable o
s eel s uc u es. The s uc u al designe may use hese ables o de e mine he min-
imum equi ed hickness (o any ype o insula ion), so ha he s uc u e main ains
i s mechanical p ope ies abo e he o e -dimensioning coe icien . The me hod used
o d aw up hese ables ollows ou s eps; i) Fi s , he limi empe a u es a e de e -
mined o he empe a u e anges wi hin which he applica ion o pul uded GFRP
is pe mi ed; ii) Second, he beha io o ce ain physical p ope ies (densi y, speci ic
hea , he mal conduc i i y, emissi i y...) a e de ined as a unc ion o he empe -
a u e; iii) Thi d, he me hod o de e mine he i e esis ance empe a u e o he
pul uded p o ile sec ions is de ined; i ) Finally, he mechanical p ope ies and ul i-
ma e esis ance alues o hese p o iles a di e en empe a u es a e also es ima ed.
The beha io o he mechanical p ope ies is analyzed as a unc ion o he massi i y
o each sec ion and he a io be ween he he mal conduc i i y o he insula ion
and i s hickness. In addi ion, a p ac ical example is gi en o he applica ion o he
ables o a pul uded GFRP s uc u e.
KEYWORDS
Pul uded elemen s; Fi e p o ec ion; dimensioning me hod
1. In oduc ion
One main limi a ion o pul uded Glass Fibe Rein o ced Polyme (GFRP) p o iles in
building and b idge s uc u es is hei poo pe o mance when exposed o i e Wong,
Da ies, and Wang (2004); Rosa e al. (2018, 2019). The au ho s o his pape ne e -
heless belie e ha he e should be some ules o s anda ds o i s design, as is indeed
he case o o he s uc u al ma e ials.
Among he cha ac e is ics o pul uded GFRP p o iles is ha mos o hem should
be classi ied as class 4 sec ions, as in Eu ocode 3, i analyzed in a simila way o s eel
CEN (2005).
A oom empe a u e, Class 4 sec ions ha e di e en and mo e complex cha ac e is-
ics han Class 1, 2 and 3 sec ions, mainly due o he likelihood o local buckling wi hin
CONTACT H. Ga c´ıa. Email: a kai z.ga [email protected]
he sec ion. A beha io ha necessi a es speci ic design ules and hei co esponding
design me hods, which a e al eady well es ablished in he case o s eel CEN (2005).
Design me hods a e likewise unde de elopmen o pul uded componen s Ascione
e al. (2016).
A highe empe a u es ( i e si ua ions), Class 4 s eel sec ions a e usually o e sized
in mos buildings Cou o e al. (2016); Knobloch e al. (2012); Cou o e al. (2018);
Maia e al. (2016), due o he ac ha , in p ac ice, hey a e limi ed o he c i ical
empe a u e o 350ºC CEN (2005), when, in eali y, hey could con inue o wo k a
highe empe a u es F anssen, Zhao, and Ge nay (2016); Jande a, P achaˇ , and Wald
(2020); P acha e al. (2015).
Up un il now, di e en coun ies ha e had hei own design guidelines o Fibe
Rein o ced Polyme (FRP) s uc u es, i.e., Ge many BUE (2010), I aly Council e al.
(2007), he Ne he lands CUR Commission C124 (2003) and he Uni ed S a es Associa-
ion e al. (2012). No speci ic p ocedu es ha e been p oposed o design a ele a ed em-
pe a u es in hese guidelines, while design ules a e a ailable o s eel Eu ocode (1993),
conc e e del Ho mig´on Es uc u al (2008) and wood o S anda diza ion (CEN). Mo e-
o e , he e a e no speci ic i e p o ec ion design p ocedu es in he d a e sions o he
u u e Eu ocode o FRP Ascione e al. (2016). This u u e s anda d needs o make a
con ibu ion in his espec Ma a eas, Miamis, and V akas (2012)
In his s udy, a design me hod is p oposed o pul uded GFRP componen s. A
able is p esen ed o ob ain he minimum insula ion hickness necessa y o achie e
he mechanical p ope ies equi ed o each sec ion o he s uc u e.
The ables we e calcula ed o i e esis ance imes o less han 60 minu es. While
in es iga ing hese alues, i was concluded ha longe exposu e imes we e no iable
o coa ings o easonable hickness. The ables we e he e o e no limi ed o he
s anda d in e als o 30, 60, and 90 minu es. Ins ead, hey we e o ganized in o sho e
pe iods, om 5 o 60 minu es, in 5-minu e inc emen s.
The disc e iza ion o ime pe iods can be use ul o op imiza ion o he i e design
o s uc u es, al hough i equi es speci ic calcula ions and he adjus men o he ” e-
ques ed s anda d imes”. The equi alen ime equa ion is one sugges ed me hod ha
could be used Eu ocode (2002).
2. Me hodology
The s eps aken o ob ain he ables p esen ed in he design me hod p oposed in his
a icle a e explained below (Figu e 1):
The symbols used in his a icle a e p esen ed below:
•Tg:glass ansi ion
•Td:decomposi ion empe a u e
•Em: modulus o elas ici y
•Eg: glassy modulus
•E : ubbe y modulus
•αg :con e sion deg ee o he glass ansi ion
•ρ:densi y
•cp: speci ic hea
•: emissi i y
•λ: he mal conduc i i y
•d: coa ing hickness
2
Limi empe a u es Tg
and Td o GFRP ma e ial
S ep 1A ailable Guides
esea ch in scien i ic a icles
Beha io o he physical
p ope ies o he GFRP (ρ,
cp, ε...) up o Td
S ep 2
esea ch in scien i ic a icles
Equa ion o empe a u e o
p o ec ed sec ions
S ep 3Eu ocode 3 + FEM + TLP
Equa ions o mechanical
p ope ies a di e en
empe a u es
S ep 4 esea ch in scien i ic a icles
Table o he design o FRP
elemen s a ele a ed
empe a u es
S ep 5
Figu e 1. Me hodology o he de elopmen o he able
3
•λp: e ec i e he mal conduc i i y o he coa ing
2.1. S ep 1: Limi empe a u es o pul uded GFRP ma e ial.
In his i s s ep, ou aim was o de e mine he empe a u e ange in which he pul-
uded GFRP ma e ial may be used in s uc u es. To do so, a bibliog aphical sea ch
o a icles and exis ing guides was pe o med.
Bai e al. Bai and Kelle (2007) s a ed ha he elas ic Young’s modulus unde wen
a conside able (al hough eco e able) dec ease du ing i s glass ansi ion a Tg em-
pe a u e. They also s a ed ha , al hough he moduli o longi udinal and ans e se
elas ici y we e di e en in his ype o ma e ial, he dec ease was simila o alues
be ween he glass ansi ion empe a u e, Tg and he decomposi ion empe a u e, Td
Bai e al. (2008). These easons explain why he exis ing guidelines limi he use o
GFRP o empe a u es close o Tg. Taking he da a o common pul uded GFRP
ma e ial used in he wo k o Mo gado e al. Mo gado e al. (2018); Mo gado, Sil es e,
and Co eia (2018a,b) (Tg=141ºC, Td=370ºC) as a e e ence, he limi empe a u es
o some guides migh be as ollows:
•ASCE Associa ion e al. (2012): Tg-22 = 141 – 22= 119 ºC
•Ge man guideline BUE (2010): Tg-15 = 141 – 15= 126 ºC
•Du ch CUR Commission C124 (2003): Tg-20 = 141 – 20= 121 ºC
Using a mean Tg ≃120ºC
In he speci ic design p ocedu e o pul uded GFRP s uc u es discussed in his
a icle, h ee design anges a e p oposed depending on he empe a u e o he sec ion:
•Zone 1 (whi e): θ < 120ºC
•Zone 2 (ligh g ey): 120ºC≤θ≤370ºC
•Zone 3 (da k g ey): θ > 370ºC
In Zone 1 i is possible o calcula e he s uc u es wi hou modi ying hei elas ic
moduli. In Zone 2 he elas ic moduli should be co ec ed using hose alues co espond-
ing o he eal empe a u e o he sec ion. he equa ion p esen ed by Bai e al. Bai,
Kelle , and Vall´ee (2008) (1) is p oposed o ob ain he modulus o elas ici y. Finally, i
is no ad isable o design pul uded GFRP s uc u es wi hin he ange co esponding
o Zone 3.
Em=Eg·(1 −αg) + E ·αg·(1 −αg) (1)
whe e, Em is he modulus o elas ici y, Eg and E a e he glassy and ubbe y
modulus, espec i ely, and αg·is he con e sion deg ee o he glass ansi ion.
Figu e 2 shows he h ee zones o di e en sec ion sizes.
2.2. S ep 2: Beha io o he physical p ope ies o pul uded GFRP
ma e ial.
In S ep 2, a bibliog aphic sea ch was conduc ed o da a ha e lec he beha io o
he ma e ial p ope ies as a unc ion o he empe a u e: densi y ρ, speci ic hea cp,
emissi i y and he mal conduc i i y λ, o he pul uded GFRP ma e ials up o he
limi empe a u es ob ained in S ep 1.
4
50 m¯ ¹ 200 m¯ ¹
d/λp 5 10 15 20 25 30 35 40 45 50 55 60 d/λp 5 10 15 20 25 30 35 40 45 50 55 60
0.05
338
512
613
673
708
732
757
802
855
891
917
936
0.05
557
709
783
880
923
946
960
970
977
983
987
992
0.1
185
347
453
529
586
630
663
688
706
720
734
748
0.1
319
541
653
710
748
800
854
891
917
936
951
962
0.15
98
237
342
420
480
530
571
605
633
657
676
691
0.15
124
362
504
596
658
699
727
753
786
825
856
880
0.2
50
154
252
330
393
444
487
525
557
585
610
631
0.2
34
188
347
457
537
598
645
680
706
727
746
767
0.25
34
92
177
252
315
368
413
452
486
516
543
567
0.25
34
56
187
309
402
475
533
581
620
653
680
701
0.3
34
53
116
185
246
299
345
385
421
452
480
506
0.3
34
34
60
158
257
341
409
465
513
554
589
619
0.35
34
35
71
127
183
235
281
322
359
391
421
447
0.35
34
34
34
48
116
198
273
337
393
441
482
519
0.4
34
34
43
81
129
177
221
262
299
333
363
391
0.4
34
34
34
34
36
73
134
199
260
315
363
406
0.45
34
34
34
50
84
125
167
206
243
277
308
336
0.45
34
34
34
34
34
34
41
76
126
180
231
279
0.5
34
34
34
36
53
83
118
155
190
223
254
283
0.5
34
34
34
34
34
34
34
34
39
65
103
146
0.55
34
34
34
34
37
53
79
109
141
172
203
231
0.55
34
34
34
34
34
34
34
34
34
34
35
48
0.6
34
34
34
34
34
37
51
73
99
127
155
182
0.6
34
34
34
34
34
34
34
34
34
34
34
34
100 m¯ ¹ 250 m¯ ¹
d/λp 5 10 15 20 25 30 35 40 45 50 55 60 d/λp 5 10 15 20 25 30 35 40 45 50 55 60
0.05
450
629
705
746
812
879
917
941
957
969
977
984
0.05
588
728
832
904
935
953
964
972
978
984
988
992
0.1
254
450
564
638
685
714
737
761
802
846
878
903
0.1
335
564
674
727
774
838
882
911
932
948
960
970
0.15
121
310
433
519
583
632
668
694
713
729
745
764
0.15
114
370
519
613
675
714
743
777
818
851
877
898
0.2
47
190
316
409
480
536
582
619
649
674
693
708
0.2
34
171
343
461
545
608
656
692
718
740
763
790
0.25
34
95
208
304
381
442
492
535
571
603
629
652
0.25
34
39
158
290
392
471
533
584
625
660
687
709
0.3
34
41
116
205
284
349
404
450
490
525
556
583
0.3
34
34
37
116
222
313
389
451
503
547
585
618
0.35
34
34
53
118
191
257
315
365
409
447
480
511
0.35
34
34
34
34
68
145
225
298
360
414
460
501
0.4
34
34
34
56
110
170
227
279
325
366
403
436
0.4
34
34
34
34
34
37
73
134
199
259
314
363
0.45
34
34
34
34
53
95
145
195
242
285
324
359
0.45
34
34
34
34
34
34
34
35
58
102
153
205
0.5
34
34
34
34
34
46
78
118
161
203
243
280
0.5
34
34
34
34
34
34
34
34
34
34
39
63
0.55
34
34
34
34
34
34
39
60
92
128
165
201
0.55
34
34
34
34
34
34
34
34
34
34
34
34
0.6
34
34
34
34
34
34
34
35
46
68
96
128
0.6
34
34
34
34
34
34
34
34
34
34
34
34
150 m¯ ¹ 300 m¯ ¹
d/λp 5 10 15 20 25 30 35 40 45 50 55 60 d/λp 5 10 15 20 25 30 35 40 45 50 55 60
0.05
514
682
742
829
895
930
950
963
973
980
985
990
0.05
611
743
860
916
941
956
966
973
979
985
989
993
0.1
294
506
620
686
722
753
799
850
886
912
931
946
0.1
345
581
689
741
802
860
897
922
941
954
965
973
0.15
128
345
478
568
632
676
706
728
749
776
812
844
0.15
100
371
526
623
686
724
757
798
836
866
889
908
0.2
39
196
341
443
518
577
623
659
687
708
725
741
0.2
34
148
331
457
546
612
662
699
725
749
776
805
0.25
34
78
206
316
401
468
523
568
606
637
664
685
0.25
34
34
123
263
374
459
526
580
624
660
690
713
0.3
34
34
91
190
280
355
416
468
512
549
582
611
0.3
34
34
34
74
176
276
359
428
485
533
574
609
0.35
34
34
35
84
162
238
305
362
411
454
492
525
0.35
34
34
34
34
37
88
167
246
315
376
428
473
0.4
34
34
34
35
67
126
191
251
305
352
395
432
0.4
34
34
34
34
34
34
36
69
126
190
250
306
0.45
34
34
34
34
34
49
90
142
195
245
291
332
0.45
34
34
34
34
34
34
34
34
34
41
73
119
0.5
34
34
34
34
34
34
36
58
95
139
183
226
0.5
34
34
34
34
34
34
34
34
34
34
34
34
0.55
34
34
34
34
34
34
34
34
38
58
88
124
0.55
34
34
34
34
34
34
34
34
34
34
34
34
0.6
34
34
34
34
34
34
34
34
34
34
36
50
0.6
34
34
34
34
34
34
34
34
34
34
34
34
ime (min) ime (min)
ime (min)
ime (min)
ime (min)
ime (min)
Figu e 2. Design ables, zones 1, 2 and 3 o di e en sec ion sizes
5
Acco ding o Co eia e al. Co eia, Bai, and Kelle (2015), he he mo-physical
p ope ies (densi y, speci ic hea and he mal conduc i i y) emain s able un il he
decomposi ion empe a u e o he ma e ial (Td). Howe e , Bai e al. p oposed equa-
ions as a unc ion o empe a u e ha de ine he beha io o he he mal conduc i i y
λBai e al. (2008), he speci ic hea a io and he densi y Yu, Till, and Thomas (2007).
Al hough Kelle e al. also analyzed and p oposed a linea p og ession o he emis-
si i y coe icien Kelle , T acy, and Zhou (2006), i was decided o use he equa ions
o Bai e al. o ob ain he ables p esen ed in his a icle.
2.3. S ep 3: Tempe a u e calcula ion o pul uded GFRP beams exposed
o i e.
Eu ocode 3, pa s 1-2 is only applicable o s eel s uc u es exposed o i e Eu ocode
(1993). The o mulae ha appea in ha con ex a e he e o e limi ed o hese me al
componen s. Howe e , i appea s highly desi able o ha e a se o equi alen o mulae
ha could be used o pul uded GFRP beams and columns. The me hod ollowed o
de elop such a se o o mulae was o in es iga e he basic assump ions o he EC-3
no m, in o de o es ablish whe he hey a e applicable o he case o pul uded GFRP.
2.3.1. Assump ions o s eel sec ions
The main assump ion o he EC-3 no m is ha , i he exposu e and he insula ion
a e equal on all exposed su aces, hen he empe a u e o an insula ed s eel s uc u e
exposed o i e may be es ima ed by a one-dimensional analysis. A he same ime,
he co ne e ec s a e neglec ed. In addi ion, as he he mal di usi i y o s eel is e y
high, i can be assumed ha he hea will be uni o mly dis ibu ed h oughou he
s eel Wicks ¨om (1985).
An HEB-300 s eel sec ion was used as a case s udy o e i y hese assump ions. The
s eel sec ion was insula ed wi h a 25 mm ock wool laye . Th ee di e en nume ical
me hods we e used o calcula e he empe a u es dis ibu ion o e ime: he TLP
(The mal Lumped Pa ame e ) me hod Associa es (2019); Ga mendia e al. (2016), he
o mula (4.27) om EC-3 Eu ocode (1993) and he well-es ablished Fini e Elemen
Me hod. The empe a u e o he i e was aken om he ISO 834 cu e S anda d
(1999), as shown in (2):
θg= 20 + 345 ·log (8 + 1) (2)
whe e, is exp essed in minu es and θg in ºC.
The i s me hod, he TLP me hod, assumes a wo-node ne wo k model (gas node
numbe 1 and s eel node numbe 2) wi h a single linea conduc ance be ween bo h
(GL(1,2)=0.71120 W/ºC). This linea conduc ance is he in e se alue o he he mal
esis ance ha is p esen due o he insula ion laye . The s eel is assumed o ha e
a single empe a u e (a node 2) wi h a he mal ine ia o M2C2=16817.055 J/ºC.
The empe a u e a node 1 is imposed as a bounda y condi ion and as a unc ion o
ime. The p og am (called TK) calcula es empe a u e a node 2 as a unc ion o ime,
p oducing a nume ical solu ion o he di e en ial equa ion (3):
6
GL (1,2) (T1−T2) + M2C2
dT2
d = 0 (3)
The second me hod in eg a es he equa ion in Eu oCode-3 CEN (2005) o e ime
(4):
∆θa, =λpAp/V (θg, −θa, )
dpcaρa(1 + φ/3) ∆ −eφ/10 −1∆θg, (4)
ollowing he me hod sugges ed in F anssen, Kodu , and Zaha ia (2009).
Finally, he Fini e Elemen Me hod was used o model a qua e o he HEB sec ion,
which is su icien due o geome y and loads symme ies. The mesh shown in Figu e
3 was used whe e he di e en ma e ials (s eel and insula ion) a e colo coded.
The esul s o he h ee me hods a e summa ized below in Figu e 4.
The esul s o he h ee me hods compa e well. Fo he FEM me hod, a empe a u e
dis ibu ion on he sec ion (di e ences lowe han 12 ºC, see Figu e 5) was calcula ed
wi h he FEM me hod and a mean empe a u e alue was used o he compa isons.
F om hese esul s, i is possible o s a e ha he h ee me hods could be used
o es ima e he s eel empe a u e and ha he assump ion o a single empe a u e
ep esen ing he he mal s a e o he s eel is app op ia e.
2.3.2. Assump ions o pul uded GFRP ma e ial
The idea is now o use he h ee p e iously men ioned me hods o es ima e he GFRP
empe a u e as a unc ion o ime, so as o e alua e whe he he assump ion o a single
empe a u e ha ep esen s he he mal s a e o he GFRP is app op ia e.
Pul uded GFRP ma e ial p ope ies we e used as a unc ion o he empe a u e,
ob ained om he p ospec o new guidance Ascione e al. (2016). The esul s a e
summa ized in Figu e 6.
Reasonable compa isons be ween he h ee cu es we e e iden wi h empe a u e
alues ha we e highe han hose assumed o he s eel sec ion. The pul uded GFRP
sec ion p esen ed qui e la ge g adien s, as can be seen in Figu e 7.
The mean alue o he FEM esul s e lec ed in Figu e 6 p o ided a easonable
ep esen a ion o he he mal s a e o he whole pul uded GFRP sec ion. Howe e ,
i he maximum empe a u e in he sec ion is analyzed, i is a o he mean alue
( hose calcula ed wi h any o he h ee me hods); a di e ence ha was la ge as he
exposu e ime inc eased.
2.3.3. Rela ion be ween TEC-3 and Tmax FEM
The he mal conduc i i y o pul uded GFRP is much lowe han s eel. This ac e-
sul s in di e ences be ween he maximum and he mean empe a u es o he GFRP
sec ions. This di e ence is mo e e iden o sec ions wi h he ewes aces exposed
o i e whe e he low conduc i i y o GFRP plays an impo an ole. The ewe he
numbe o aces exposed o i e, he la ge he di e ence be ween he maximum em-
pe a u e wi hin he sec ion and ha ob ained wi h eq. (4).
The numbe o di e en cases ha can be de ised wi h di e en sec ion geome ies
and he numbe o aces exposed o i e is ex emely high. As a consequence, i was
7
Figu e 3. Mesh and ma e ials o a HEB-300 case s udy
8
d/λ=0.4 d= 0.08m
I-BEAM 152X76X10 Massi i y 200 m-1 RF 30 min
d/λ=0.35 d=0.07m
Figu e 10. Applica ion o he able o p ac ical example
15
Some eal cases o GFRP s uc u es a e p esen ed in Figu e 11.
5. Conclusions
•Ha ing de eloped he i e design able and a e sea ching o all es s pe o med
o da e, an impo an conclusion was ha wi h he mos common insula ion
hicknesses a ailable o he ype o applica ion, GFRP + insula ion sec ions
canno main ain hei mechanical p ope ies o exposu e imes longe han 60
minu es.
•I he empe a u e sec ion emains be ween he glass ansi ion, Tg, and he
decomposi ion empe a u e, Td (Zone 2), he s uc u e will p obably be alid,
bu he modulus o elas ici y o he sec ion mus be co ec ed (1).
•In con as wi h he s eel sec ions, he empe a u e wi hin he GFRP sec ion
canno be conside ed cons an (due o i s much lowe he mal conduc i i y). A
co ec o equa ion (eq. 5) is p oposed o GFRP sec ions exposed om he ou
sides, in o de o ob ain he maximum sec ion empe a u e.
•A e he calcula ion o dimensioning o a pe sis en si ua ion and wi h he
o e sizing coe icien s o he ex ao dina y i e si ua ion, i is a s aigh o wa d
ask o ob ain he necessa y insula ion hicknesses using he design able ha
has been p oposed in his s udy.
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