Deformacion Alivianada 1d Ronald Fx

8/20/2019 Deformacion Alivianada 1d Ronald Fx

1/205

FLEXION.

fc

fy

r

LO"# 2#$O%O &

M4= '.()' [KN-m/m]

µ ‗ 534.48=

1.667 * 1 * 18 !

" = 1.#5 * $ 1 - $ 1 - # * .%8%78 &' .5& = .1353%

N(= 31.3#%4 [KN]

31.3#%4 [KN]

31.3#%4=

.%734.8

#rm!d*r! M+,+m!-.4 * 1.667 * 5 * #

34.78

M 4-7= 2.(

)e= ) + ,o

)e= 5. + 3.665 5

)ds 0 5.73

Ns1= N(=

0s1 = [(m!]

0s1 =

1#MO &3E

[N-m/m]

)e 2

As1

As2 Ndcg

Mdcg

hf

be

bw

d1

h


2/205

) / 5 #

#rm!d*r! $r+,c+!4-omo

µ = .7%183 1.#5* " = .13#4# 1.86 6.#5 [(m]9= .%5751= 1.858355 E: D.;. esta en :a mesa de (omres?a re(tan?@:ar&

#$O%O E

ME= '.()' [KN-m/m]

µ ‗ 534.48=

1.667 * 1 * 18 !

" = 1.#5 * $ 1 - $ 1 - # * .%8%78 &' .5& = .1353%

N(= 31.3#%4 [KN]

31.3#%4 [KN]

31.3#%4=

.%734.78

#rm!d*r! M+,+m!-.4 * 1.667 * 5 * #

34.78

MOMENTO [KN-m/m] µ α β zNc εs1 σs1

[kN] [‰] [kN/cm2]

Md & 5.34483#3 .%8%784 .1353%# .%456%57 17.##5#3 31.3#%3%8 1 34.8Md &3E #1.38 .7%18#7 .13#41% .%57514 17.##6%#4 1#3.8%3# 1 34.8

Md E 5.34483#3 .%8%784 .1353%# .%456%57 17.##5#3 31.3#%3%8 1 34.8

5+sos+c+6,#re!

[cm2/m]#A1# #.33A16 6.3

#A1# #.3

En e: (aso de B@e se dson?a de )arras re(tas C do):adas se ana:a e: area a:tante a reor

Ns1= N(=

0s1 = [(m!]

0s1 =

f7 #M#58# "8$LE"


3/205

#$O%O#s # s* 9 !do N: de Es!c.

5I"$O"I&I[cm2] [cm2] [mm] ;!rr!s [cm]

; 1.%# 1.%# 8. 3.81 #6.#3 18 (/#6& 1.%# .14 8. .#7 37.3 F,N FGHIE

rese(to de :a armad@ra rn(a: $:on?t@dna:&J es de(r

.#* #.#6.45

Hara tramos C aoCos

MOMEN1O#s !do #< #< !do 9 !do N: de Es!c.

5I[cm2/m] [cm2/m] [cm2/m] [mm] ;!rr!s [cm]

Md ; #.#6 .45 1.#1 8 #.4 41.67Md ;3& 6.3 1.#1

Md & #.#6 .45

1r!mos &3E y E3F

#s= 5e=

5 6=

.86#5Cd 347.8#61

Hara 9 .86#5

=3.8 [eas] 1 [m]

.#8 3.8 [eas]0dotar

9 c/((

>&o,c4*s+o,es-

g7 #M#58# 1#N"?E"#L

Ia norma e?e B@e se (o:oB@e armad@ra trans>ersa: en @na roor(on de: # rese(to d

Hara Md )@ se tene0t=0t= [(m!/m]

g7 M#LL# "8$EIO

L-L Fe rea:< e: (a:(@:o de :os F@:esJ esto en e: (aso de @sar )arras do):adas.

&=( .#∗_


4/205

Datos de Entrada [kN/cm2]= 1.667

[kN/cm2]= 34.78yd [‰]= #.17b [cm]= 5w [cm]= 1h [cm]= #hf[cm]= 5

eom[cm]= #d [cm] 18

s [M!]= #

.%8%78

=1.%# [(m!]

=5.73 [m]

2 5. erO(a


5/205

/ d18

µ = .7%183.13#4#.%5751

N(= 1#3.8%30s1= 3.56#

.%8%78

=1.%# [(m!]

As1 As1 min As1 adop

[cm2/m] [cm2/m] [cm2/m]

.%7 1.%# 1.%#3.5618 1.%# 3.56

.%7 1.%# 1.%#

ar

"re(t =9 re(t =

[(m!]


6/205

N

"$O"I&ION

18 (/35

[(m#/m]

=.3#4638

:a armad@ra rn(a:


7/205


8/205


9/205


10/205

D,FEPQ 0 RIES,QNDATOS DE ENTRADA

fck = 25 [Mpa] e [(m] 5fyk = 500 [Mpa] .# 0rmad@ra s@eror

1.5 .575 T .461.15

n ϕ Disposiciónfcd= 1.667 [cm2]

fyd= 43.48 434.783 3 6 0.85 MALLA6c/332.174

0.6169

Geometria Prop

Tramo lo [m] br [cm] be [cm] h [cm] hf [cm] d1 [cm]

L O " #

Apoyo 01 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

L O " #

2

A-B 2.73 50.00 50.00 10.00 20.00 5.00 2.00 2.00 400.00

B-C 2.87 50.00 50.00 10.00 20.00 5.00 2.00 2.00 400.00

C-E 4.16 50.00 50.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo A 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo B 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo C 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

L O " #

(

A-B 2.54 50.00 50.00 10.00 20.00 5.00 2.00 2.00 400.00

B-C 3.72 50.00 50.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo A 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo B 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00Apoyo C 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

L O " #

)

A-B 2.73 50.00 50.00 10.00 20.00 5.00 2.00 2.00 400.00

B-C 3.28 50.00 50.00 10.00 20.00 5.00 2.00 2.00 400.00

C-C! 1.39 50.00 37.80 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo A 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo B 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo C 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo C! 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

L O " #

'

B-C 3.74 50.00 50.00 10.00 20.00 5.00 2.00 2.00 400.00

C-C! 1.20 50.00 34.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo B 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo C 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo C! 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

L O " #

=

A-B 2.73 50.00 50.00 10.00 20.00 5.00 2.00 2.00 400.00

B-C 2.87 50.00 50.00 10.00 20.00 5.00 2.00 2.00 400.00

C-E 4.16 50.00 50.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo A 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo B 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo C 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

γ c =

γ " =

As[#$/c%2]

[#$/c%2]

εy= [o/

oo]

α 3&'%

=

bw[cm]

d2[cm]

Area[cm2]


11/205

Apoyo E 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

L o s !

A

Apoyo 5-6 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

L O " #

/

B-C 2.92 50.00 50.00 10.00 20.00 5.00 2.00 2.00 400.00

C-E 4.16 50.00 50.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo B 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

Apoyo C 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00Apoyo E 50.00 10.00 10.00 20.00 5.00 2.00 2.00 400.00

fck = 25 [Mpa] e [(m] 5fyk = 00 [Mpa] 0rmad@ra s@eror

1.5 .7188 T .5751.15

n ϕ Disposiciónfcd= 1.667 [cm2]

fyd= 34.78 3 6 0.85 MALLA6c/33

1.739

0.6680

Beome


12/205

L O " # Apoyo B 50.00 10.00 10.00 25.00 5.00 2.00 2.00 450.00

Apoyo B! 50.00 10.00 10.00 25.00 5.00 2.00 2.00 450.00


13/205

A s!p min

MALLA 0.58

edades Geometricas "olicitaciones

13.75 12708.3 -2.99 0.00 2.9898297 0 1.28 ---------- ----------

13.75 12708.3 9.21 0.00 9.21 0.00 0.78 0.0341 0.0434

13.75 12708.3 10.32 0.00 10.32 0.00 0.88 0.0382 0.0487

13.75 12708.3 21.38 0.00 21.38 0.00 1.86 0.0792 0.1032

13.75 12708.3 -2.30 0.00 2.30 0.00 0.98 ---------- ----------

13.75 12708.3 -14.38 0.00 14.3840028 0 7.12 ---------- ----------

13.75 12708.3 -22.30 0.00 22.30 0.00 13.11 ---------- ----------

13.75 12708.3 -5.34 0.00 5.34 0.00 2.35 ---------- ----------

13.75 12708.3 8.01 0.00 8.01 0.00 0.68 0.0297 0.0376

13.75 12708.3 17.06 0.00 17.06 0.00 1.47 0.0632 0.0816

13.75 12708.3 -2.00 0.00 2.00 0.00 0.85 ---------- ----------

13.75 12708.3 -19.26 0.00 19.2630506 0 10.46 ---------- ----------13.75 12708.3 -4.26 0.00 4.26 0.00 1.85 ---------- ----------

13.75 12708.3 9.21 0.00 9.21 0.00 0.78 0.0341 0.0434

13.75 12708.3 13.48 0.00 13.48 0.00 1.15 0.0499 0.0640

13.75 12708.3 2.41 0.00 2.41 0.00 0.27 0.0118 0.0148

13.75 12708.3 -2.30 0.00 2.30 0.00 0.98 ---------- ----------

13.75 12708.3 -14.38 0.00 14.38 0.00 7.12 ---------- ----------

13.75 12708.3 -11.62 0.00 11.6213849 0 5.52 ---------- ----------

13.75 12708.3 -0.60 0.00 0.60 0.00 0.25 ---------- ----------

13.75 12708.3 17.21 0.00 17.21 0.00 1.48 0.0637 0.0824

13.75 12708.3 1.89 0.00 1.89 0.00 0.23 0.0103 0.0130

13.75 12708.3 -4.30 0.00 4.30 0.00 1.87 ---------- ----------

13.75 12708.3 -17.65 0.00 17.65 0.00 9.26 ---------- ----------

13.75 12708.3 -0.47 0.00 0.47345392 0 0.20 ---------- ----------

13.75 12708.3 9.21 0.00 9.21 0.00 0.78 0.0341 0.0434

13.75 12708.3 10.32 0.00 10.32 0.00 0.88 0.0382 0.0487

13.75 12708.3 21.38 0.00 21.38 0.00 1.86 0.0792 0.1032

13.75 12708.3 -2.30 0.00 2.30 0.00 0.98 ---------- ----------

13.75 12708.3 -14.38 0.00 14.38 0.00 7.12 ---------- ----------

13.75 12708.3 -22.30 0.00 22.30 0.00 13.11 ---------- ----------

(c)[cm]

*[cm]

+dc) [,-m]

-dc)[,-]

+d [,-m]

-d[,-]

$[cm]

µ

f α

f

As

1 As2 Ndc

g

Mdcg

hf

be

b

w

d1

h


14/205

13.75 12708.3 -5.34 0.00 5.34483231 0 2.35 ---------- ----------

13.75 12708.3 -1.38 1.00 1.33791283 1 0.56 ---------- ----------

13.75 12708.3 10.63 0.00 10.63 0.00 0.90 0.0394 0.0502

13.75 12708.3 21.38 0.00 21.38 0.00 1.86 0.0792 0.1032

13.75 12708.3 -11.77 0.00 11.77 0.00 5.60 ---------- ----------

13.75 12708.3 -22.30 0.00 22.301033 0 13.11 ---------- ----------13.75 12708.3 -5.34 0.00 5.34 0.00 2.35 ---------- ----------

A s!p min

MALLA 0.72

!des Beome


15/205

16.94 24548.6 -15.76 1.00 15.70 1.00 5.68 ---------- ----------

16.94 24548.6 -2.22 0.00 2.21769351 0 0.73 ---------- ----------


16/205

"i# $ % 1.25 & d "i# $ % 1.25 & d

'n las Alas 'n el -er/io

-cf [,-]

---------- ---------- ---------- 2.9898297 0.05536722 0.07123902 0.97150439 17.0973648 2.9898297 0

0.9826 52.05 9.21 ---------- ---------- ---------- ---------- ---------- ---------- ----------

0.9805 58.50 10.32 ---------- ---------- ---------- ---------- ---------- ---------- ----------

0.9587 123.89 21.38 ---------- ---------- ---------- ---------- ---------- ---------- ----------

---------- ---------- ---------- 2.30 0.0426 0.0545 0.9782 13.07 2.30 0.00

---------- ---------- ---------- 14.3840028 0.26637042 0.39554554 0.84178179 94.9309288 14.3840028 0

---------- ---------- ---------- 22.30 0.4130 0.6169 0.7533 148.05 20.07 2.23

---------- ---------- ---------- 5.34 0.0990 0.1305 0.9478 31.33 5.34 0.00

0.9849 45.17 8.01 ---------- ---------- ---------- ---------- ---------- ---------- ----------

0.9673 97.95 17.06 ---------- ---------- ---------- ---------- ---------- ---------- ----------

---------- ---------- ---------- 2.00 0.0371 0.0472 0.9811 11.34 2.00 0.00

---------- ---------- ---------- 19.2630506 0.35672316 0.58086614 0.76765355 139.407873 19.2630506 0---------- ---------- ---------- 4.26 0.0790 0.1029 0.9588 24.71 4.26 0.00

0.9826 52.05 9.21 ---------- ---------- ---------- ---------- ---------- ---------- ----------

0.9744 76.85 13.48 ---------- ---------- ---------- ---------- ---------- ---------- ----------

0.9941 13.46 2.41 ---------- ---------- ---------- ---------- ---------- ---------- ----------

---------- ---------- ---------- 2.30 0.0426 0.0545 0.9782 13.07 2.30 0.00

---------- ---------- ---------- 14.38 0.2664 0.3955 0.8418 94.93 14.38 0.00

---------- ---------- ---------- 11.6213849 0.21521083 0.30661983 0.87735207 73.5887584 11.6213849 0

---------- ---------- ---------- 0.60 0.0111 0.0140 0.9944 3.36 0.60 0.00

0.9670 98.88 17.21 ---------- ---------- ---------- ---------- ---------- ---------- ----------

0.9948 10.58 1.89 ---------- ---------- ---------- ---------- ---------- ---------- ----------

---------- ---------- ---------- 4.30 0.0797 0.1039 0.9584 24.94 4.30 0.00

---------- ---------- ---------- 17.65 0.3268 0.5143 0.7943 123.44 17.65 0.00

---------- ---------- ---------- 0.47345392 0.00876767 0.01100805 0.99559678 2.64193258 0.47345392 0

0.9826 52.05 9.21 ---------- ---------- ---------- ---------- ---------- ---------- ----------

0.9805 58.50 10.32 ---------- ---------- ---------- ---------- ---------- ---------- ----------

0.9587 123.89 21.38 ---------- ---------- ---------- ---------- ---------- ---------- ----------

---------- ---------- ---------- 2.30 0.0426 0.0545 0.9782 13.07 2.30 0.00

---------- ---------- ---------- 14.38 0.2664 0.3955 0.8418 94.93 14.38 0.00

---------- ---------- ---------- 22.30 0.4130 0.6169 0.7533 148.05 20.07 2.23

β

f +cf

[,-m]+dw

[,-m] µ

w α

w β

w

-cw[,-]

+cw[,-m]

+dw[,-m]


17/205

---------- ---------- ---------- 5.34483231 0.09897838 0.13053916 0.94778434 31.3293981 5.34483231 0

---------- ---------- ---------- 1.33791283 0.02477616 0.03136368 0.98745453 7.52728233 1.33791283 0

0.9799 60.26 10.63 ---------- ---------- ---------- ---------- ---------- ---------- ----------

0.9587 123.89 21.38 ---------- ---------- ---------- ---------- ---------- ---------- ----------

---------- ---------- ---------- 11.77 0.2179 0.3112 0.8755 74.68 11.77 0.00

---------- ---------- ---------- 22.301033 0.41298209 0.61685824 0.7532567 148.045977 20.0729925 2.22804054---------- ---------- ---------- 5.34 0.0990 0.1305 0.9478 31.33 5.34 0.00

"i# $ % 1.25 & d "i# $ % 1.25 & d

, 4!s #4!s E, e4 Ner+o

-cf [,-]

0.9841 60.80 13.76 ---------- ---------- ---------- ---------- ---------- ---------- ----------

0.9964 10.51 2.41 ---------- ---------- ---------- ---------- ---------- ---------- ----------

---------- ---------- ---------- 11.77 0.1335 0.1798 0.9281 55.13 11.77 0.00

---------- ---------- ---------- 11.6213849 0.13181155 0.17734493 0.92906203 54.3857771 11.6213849 0

---------- ---------- ---------- 0.60191382 0.006827 0.00856308 0.99657477 2.6260113 0.60191382 00.9810 72.78 16.42 ---------- ---------- ---------- ---------- ---------- ---------- ----------

---------- ---------- ---------- 19.03 0.2158 0.3076 0.8770 94.33 19.03 0.00

---------- ---------- ---------- 4.10516615 0.04656143 0.05962379 0.97615049 18.284628 4.10516615 0

0.9906 36.18 8.24 ---------- ---------- ---------- ---------- ---------- ---------- ----------

0.9817 69.97 15.80 ---------- ---------- ---------- ---------- ---------- ---------- ----------

---------- ---------- ---------- 2.06 0.0234 0.0296 0.9882 9.07 2.06 0.00

---------- ---------- ---------- 18.26 0.2071 0.2933 0.8827 89.94 18.26 0.00

---------- ---------- ---------- 3.95 0.0448 0.0573 0.9771 17.58 3.95 0.00

0.9904 36.92 8.41 ---------- ---------- ---------- ---------- ---------- ---------- ----------

0.9827 66.18 14.96 ---------- ---------- ---------- ---------- ---------- ---------- ----------

---------- ---------- ---------- 2.10 0.0238 0.0302 0.9879 9.25 2.10 0.00

---------- ---------- ---------- 17.61 0.1997 0.2812 0.8875 86.25 17.61 0.00

---------- ---------- ---------- 3.74 0.0424 0.0542 0.9783 16.62 3.74 0.00

0.9743 98.56 22.09 ---------- ---------- ---------- ---------- ---------- ---------- ----------

---------- ---------- ---------- 5.52 0.0626 0.0809 0.9676 24.81 5.52 0.00

---------- ---------- ---------- 5.5216513 0.06262742 0.08090236 0.96763906 24.8100564 5.5216513 0

0.9898 38.96 8.87 ---------- ---------- ---------- ---------- ---------- ---------- ----------

0.9858 54.34 12.32 ---------- ---------- ---------- ---------- ---------- ---------- ----------

---------- ---------- ---------- 2.22 0.0252 0.0318 0.9873 9.77 2.22 0.00

β

f +cf

[,-m]+dw

[,-m] µ

w α

w β

w

-cw[,-]

+cw[,-m]

+dw[,-m]

As

1 As2 Ndcg

Mdcg

hf

be

b

w

d1

h


18/205

---------- ---------- ---------- 15.70 0.1780 0.2469 0.9012 75.73 15.70 0.00

---------- ---------- ---------- 2.21769351 0.02515342 0.03184748 0.98726101 9.76656188 2.21769351 0


19/205

'n la "ección

-c [,-] -s -s

17.10 17.10 0 0 17.10 -0.43 10.00 -8.59 43.48 0.00

52.05 52.05 0.00 52.05 0.00 10.00 -0.71 43.48 -14.16 1.20

58.50 58.50 0.00 58.50 0.00 10.00 -0.66 43.48 -13.11 1.35

123.89 123.89 0.00 123.89 0.00 10.00 -0.09 43.48 -1.76 2.85

13.07 13.07 0.00 0.00 13.07 -0.60 10.00 -11.98 43.48 0.00

94.93 94.93 0 0 94.93 2.52 5.35 43.48 43.48 0.00

148.05 161.97 13.93 13.93 161.97 2.87 2.17 43.48 43.48 0.32

31.33 31.33 0.00 0.00 31.33 0.22 10.00 4.47 43.48 0.00

45.17 45.17 0.00 45.17 0.00 10.00 -0.76 43.48 -15.27 1.04

97.95 97.95 0.00 97.95 0.00 10.00 -0.32 43.48 -6.42 2.25

11.34 11.34 0.00 0.00 11.34 -0.67 10.00 -13.41 43.48 0.00

139.41 139.41 0 0 139.41 2.83 2.53 43.48 43.48 0.0024.71 24.71 0.00 0.00 24.71 -0.09 10.00 -1.82 43.48 0.00

52.05 52.05 0.00 52.05 0.00 10.00 -0.71 43.48 -14.16 1.20

76.85 76.85 0.00 76.85 0.00 10.00 -0.50 43.48 -10.06 1.77

13.46 13.46 0.00 13.46 0.00 10.00 -0.98 43.48 -19.55 0.31

13.07 13.07 0.00 0.00 13.07 -0.60 10.00 -11.98 43.48 0.00

94.93 94.93 0.00 0.00 94.93 2.52 5.35 43.48 43.48 0.00

73.59 73.59 0 0 73.59 2.23 7.91 43.48 43.48 0.00

3.36 3.36 0.00 0.00 3.36 -0.98 10.00 -19.70 43.48 0.00

98.88 98.88 0.00 98.88 0.00 10.00 -0.31 43.48 -6.26 2.27

10.58 10.58 0.00 10.58 0.00 10.00 -0.99 43.48 -19.89 0.24

24.94 24.94 0.00 0.00 24.94 -0.08 10.00 -1.60 43.48 0.00

123.44 123.44 0.00 0.00 123.44 2.74 3.31 43.48 43.48 0.00

2.64 2.64 0 0 2.64 -1.01 10.00 -20.24 43.48 0.00

52.05 52.05 0.00 52.05 0.00 10.00 -0.71 43.48 -14.16 1.20

58.50 58.50 0.00 58.50 0.00 10.00 -0.66 43.48 -13.11 1.35

123.89 123.89 0.00 123.89 0.00 10.00 -0.09 43.48 -1.76 2.85

13.07 13.07 0.00 0.00 13.07 -0.60 10.00 -11.98 43.48 0.00

94.93 94.93 0.00 0.00 94.93 2.52 5.35 43.48 43.48 0.00

148.05 161.97 13.93 13.93 161.97 2.87 2.17 43.48 43.48 0.32

-s1 [,-] -s

2 [,-]

εs1

[ooo

]εs

2

[ooo

] σ

s1 [,-cm2]

σ

s2 [,-cm2] As

1[cm2]


20/205

31.33 31.33 0 0 31.33 0.22 10.00 4.47 43.48 0.00

7.53 8.53 0 0 8.53 -0.82 10.00 -16.47 43.48 0.00

60.26 60.26 0.00 60.26 0.00 10.00 -0.64 43.48 -12.82 1.39

123.89 123.89 0.00 123.89 0.00 10.00 -0.09 43.48 -1.76 2.85

74.68 74.68 0.00 0.00 74.68 2.25 7.75 43.48 43.48 0.00

148.05 161.97 13.9252534 13.9252534 161.97 2.87 2.17 43.48 43.48 0.3231.33 31.33 0.00 0.00 31.33 0.22 10.00 4.47 43.48 0.00

1

E, 4! "ecc+6,

-c [,-] -s -s

60.80 60.80 0.00 60.80 0.00 10.00 -0.49 43.48 -9.85 1.40

10.51 10.51 0.00 10.51 0.00 10.00 -0.79 43.48 -15.72 0.24

55.13 55.13 0.00 0.00 55.13 1.13 10.00 22.63 43.48 0.00

54.39 54.39 0 0 54.39 1.10 10.00 21.97 43.48 0.00

2.63 2.63 0 0 2.63 -0.79 10.00 -15.81 43.48 0.0072.78 72.78 0.00 72.78 0.00 10.00 -0.41 43.48 -8.29 1.67

94.33 94.33 0.00 0.00 94.33 2.51 7.88 43.48 43.48 0.00

18.28 18.28 0 0 18.28 -0.29 10.00 -5.81 43.48 0.00

36.18 36.18 0.00 36.18 0.00 10.00 -0.65 43.48 -12.98 0.83

69.97 69.97 0.00 69.97 0.00 10.00 -0.43 43.48 -8.66 1.61

9.07 9.07 0.00 0.00 9.07 -0.59 10.00 -11.83 43.48 0.00

89.94 89.94 0.00 0.00 89.94 2.46 8.43 43.48 43.48 0.00

17.58 17.58 0.00 0.00 17.58 -0.31 10.00 -6.29 43.48 0.00

36.92 36.92 0.00 36.92 0.00 10.00 -0.64 43.48 -12.89 0.85

66.18 66.18 0.00 66.18 0.00 10.00 -0.46 43.48 -9.15 1.52

9.25 9.25 0.00 0.00 9.25 -0.59 10.00 -11.71 43.48 0.00

86.25 86.25 0.00 0.00 86.25 2.42 8.94 43.48 43.48 0.00

16.62 16.62 0.00 0.00 16.62 -0.35 10.00 -6.93 43.48 0.00

98.56 98.56 0.00 98.56 0.00 10.00 -0.24 43.48 -4.85 2.27

24.81 24.81 0.00 0.00 24.81 -0.07 10.00 -1.32 43.48 0.00

24.81 24.81 0 0 24.81 -0.07 10.00 -1.32 43.48 0.00

38.96 38.96 0.00 38.96 0.00 10.00 -0.63 43.48 -12.63 0.90

54.34 55.34 0.00 55.34 0.00 10.00 -0.53 43.48 -10.68 1.27

9.77 9.77 0.00 0.00 9.77 -0.57 10.00 -11.38 43.48 0.00

-s1 [,-] -s

2 [,-]

εs1

[ooo

]εs

2

[ooo

] σs

1 [,-cm2] σs

2 [,-cm2] As

1[cm2]


21/205

75.73 76.73 0.00 0.00 76.73 2.12 10.00 42.49 43.48 0.00

9.77 9.77 0 0 9.77 -0.57 10.00 -11.38 43.48 0.00


22/205

Armad!ra as!mida

n ϕ n ϕ

0.39 0.97 0.97 1 10 1 10 1.57QK

1

0.00 0.44 1.20 1 10 1 10 1.57 QK 1 0.00 0.44 1.35 1 10 1 10 1.57 QK 1 0.00 0.44 2.85 2 12 1 12 3.39 QK # 0.30 0.97 0.97 1 10 1 10 1.57 QK 1 2.18 0.97 2.18 1 12 1 12 2.26 QK 1 3.73 0.97 3.73 2 12 2 10 3.83 QK # 0.72 0.97 0.97 1 10 1 10 1.57 QK 1 0.00 0.44 1.04 1 10 1 10 1.57 QK 1 0.00 0.44 2.25 1 12 1 12 2.26 QK 1 0.26 0.97 0.97 1 10 1 10 1.57 QK 1

3.21 0.97 3.21 2 12 1 12 3.39 QK # 0.57 0.97 0.97 1 10 1 10 1.57 QK 1 0.00 0.44 1.20 1 10 1 10 1.57 QK 1 0.00 0.44 1.77 1 12 1 12 2.26 QK 1 0.00 0.44 0.44 1 10 1 10 1.57 QK 1 0.30 0.97 0.97 1 10 1 10 1.57 QK 1 2.18 0.97 2.18 1 12 1 12 2.26 QK 1 1.69 0.97 1.69 1 12 1 12 2.26 QK 1 0.08 0.97 0.97 1 10 1 10 1.57 QK 1 0.00 0.44 2.27 2 10 1 10 2.36 QK # 0.00 0.44 0.44 1 8 1 8 1.01 QK 1 0.57 0.97 0.97 1 8 1 8 1.01 QK 1 2.84 0.97 2.84 2 12 1 10 3.05 QK # 0.06 0.97 0.97 1 10 1 10 1.57 QK 1 0.00 0.44 1.20 1 10 1 10 1.57 QK 1 0.00 0.44 1.35 1 10 1 10 1.57 QK 1 0.00 0.44 2.85 2 10 2 10 3.14 QK # 0.30 0.97 0.97 1 8 1 8 1.01 QK 1 2.18 0.97 2.18 1 12 1 12 2.26 QK 1 3.73 0.97 3.73 2 12 2 12 4.52 QK #

As2

[cm2] Asmin

[cm2] As [cm2]

Asreal

[cm2] O ; " .


23/205

0.72 0.97 0.97 1 8 1 8 1.01 QK 1

0.20 0.97 0.97 1 8 1 8 1.01QK

1

0.00 0.44 1.39 1 10 1 10 1.57 QK 1 0.00 0.44 2.85 2 12 1 10 3.05 QK # 1.72 0.97 1.72 1 12 1 12 2.26 QK 1

3.73 0.97 3.73 2 12 2 12 4.52 QK # 0.72 0.97 0.97 1 8 1 8 1.01 QK 1

5

n ϕ n ϕ

0.00 0.56 1.40 1 10 1 10 1.57 QK 1 0.00 0.56 0.56 1 8 1 8 1.01 QK 1 1.27 1.17 1.27 1 10 1 10 1.57 QK 1 1.25 1.17 1.25 1 10 1 10 1.57 QK 1

0.06 1.17 1.17 1 10 1 10 1.57 QK 1 0.00 0.56 1.67 1 12 1 12 2.26 QK 1 2.17 1.17 2.17 1 12 1 12 2.26 QK 1 0.42 1.17 1.17 1 10 1 10 1.57 QK 1 0.00 0.56 0.83 1 8 1 8 1.01 QK 1 0.00 0.56 1.61 1 12 1 12 2.26 QK 1 0.21 1.17 1.17 1 10 1 10 1.57 QK 1 2.07 1.17 2.07 1 12 1 12 2.26 QK 1 0.40 1.17 1.17 1 10 1 10 1.57 QK 1 0.00 0.56 0.85 1 8 1 8 1.01 QK 1 0.00 0.56 1.52 1 10 1 10 1.57 QK 1 0.21 1.17 1.17 1 10 1 10 1.57 QK 1 1.98 1.17 1.98 1 12 1 12 2.26 QK 1 0.38 1.17 1.17 1 10 1 10 1.57 QK 1 0.00 0.56 2.27 2 10 1 10 2.36 QK # 0.57 1.17 1.17 1 10 1 10 1.57 QK 1 0.57 1.17 1.17 1 10 1 10 1.57 QK 1 0.00 0.56 0.90 1 8 1 8 1.01 QK 1 0.00 0.56 1.27 1 10 1 10 1.57 QK 1 0.22 1.17 1.17 1 10 1 10 1.57 QK 1

As2

[cm2] Asmin

[cm2] As

[cm2]As

real

[cm2]


24/205

1.76 1.17 1.76 1 12 1 12 2.26 QK 1 0.22 1.17 1.17 1 10 1 10 1.57 QK 1


25/205

UQ0VF MUQ 0VF #

1 + 1 1 + 6.15 6.15

1 + 1 1 + 6.15 6.151 + 1 1 + 6.15 6.151# + 1 1# + 17.7 8.851 + 1 1 + 6.15 6.151# + 1 1# + 8.85 8.851# + # 1 + 17.7 1#.#%1 + 1 1 + 6.15 6.151 + 1 1 + 6.15 6.151# + 1 1# + 8.85 8.851 + 1 1 + 6.15 6.15

1# + 1 1# + 17.7 8.851 + 1 1 + 6.15 6.151 + 1 1 + 6.15 6.151# + 1 1# + 8.85 8.851 + 1 1 + 6.15 6.151 + 1 1 + 6.15 6.151# + 1 1# + 8.85 8.851# + 1 1# + 8.85 8.851 + 1 1 + 6.15 6.151 + 1 1 + 1#.#% 6.158 + 1 8 + 3.%3 3.%3

8 + 1 8 + 3.%3 3.%31# + 1 1 + 17.7 6.151 + 1 1 + 6.15 6.151 + 1 1 + 6.15 6.151 + 1 1 + 6.15 6.151 + # 1 + 1#.#% 1#.#%8 + 1 8 + 3.%3 3.%3

1# + 1 1# + 8.85 8.851# + # 1# + 17.7 17.7


26/205

8 + 1 8 + 3.%3 3.%3

8 + 1 8 + 3.%3 3.%3

1 + 1 1 + 6.15 6.151# + 1 1 + 17.7 6.151# + 1 1# + 8.85 8.85

1# + # 1# + 17.7 17.78 + 1 8 + 3.%3 3.%3

1 + 1 1 + 6.15 6.15 .8 + 1 8 + 3.%3 3.%3

1 + 1 1 + 6.15 6.151 + 1 1 + 6.15 6.15

1 + 1 1 + 6.15 6.151# + 1 1# + 8.85 8.851# + 1 1# + 8.85 8.851 + 1 1 + 6.15 6.158 + 1 8 + 3.%3 3.%3

1# + 1 1# + 8.85 8.851 + 1 1 + 6.15 6.151# + 1 1# + 8.85 8.851 + 1 1 + 6.15 6.158 + 1 8 + 3.%3 3.%3

1 + 1 1 + 6.15 6.15

1 + 1 1 + 6.15 6.151# + 1 1# + 8.85 8.851 + 1 1 + 6.15 6.151 + 1 1 + 1#.#% 6.151 + 1 1 + 6.15 6.151 + 1 1 + 6.15 6.158 + 1 8 + 3.%3 3.%3

1 + 1 1 + 6.15 6.151 + 1 1 + 6.15 6.15


27/205

1# + 1 1# + 8.85 8.851 + 1 1 + 6.15 6.15


28/205

5I"EO # FLEXION7 Beome


29/205

L O8

. 1. .11 . #0 .17.8% 1. .11 .87% #0 .115#36.#7 1. .11 .178# #V .#47#

%. 1. .11 . #0 .

#3.46 1. .11 .1153 #V .15354.% 1. .11 .#1 #0 .#54

1 . 1. .11 . #0 .#8.6 1. .11 .137% #V .186#

1113.%1 1. .11 .684 #0 .886#6.%1 1. .11 .13## #V .178

1#14.# 1. .11 .6%8 #0 .%5#5.47 1. .11 .1#5# #V .1677

13 37.74 1. .11 .1855 #V .#586

1415.# 1. .11 .738 #0 .%5%#1.## 1. .11 .143 #V .138

5I"EO 5E #M#58#" EN LO" #$O%O"NH

Md b d 5om+,+o

J[kN3m] [m] [m] [ ] [ ]

L O S A

1 5.11 1. .11 .#51 #0 .3

#

3.%1 1. .11 .1%# #0 .##4.58 1. .11 .1#8 #V .1638.11 1. .11 .1873 3a .#6%.7 1. .11 .446 #0 .6

33.38 1. .11 .166 #0 .#

3#.%# 1. .11 .1618 #V .##

7.#7 1. .11 .357 #0 .5

4

3.%1 1. .11 .1%# #0 .##4.58 1. .11 .1#8 #V .161%.86 1. .11 .%76 #0 .131.# 1. .11 .5 #0 .1

57.35 1. .11 .361 #0 .5

3.16 1. .11 .148# #V .#.77 1. .11 .38 #0 .

6

3.%1 1. .11 .1%# #0 .##4.58 1. .11 .1#8 #V .1638.11 1. .11 .1873 3a .#6%.7 1. .11 .446 #0 .6

7 #.36 1. .11 .116 #0 .1

8

. 1. .11 . #0 .#.11 1. .11 .%88 #0 .1338.11 1. .11 .1873 3a .#6%.7 1. .11 .446 #0 .6. 1. .11 . #0 .

#.11 1. .11 .%88 #0 .13


30/205

1%.86 1. .11 .%76 #0 .131.# 1. .11 .5 #0 .1

1. 1. .11 . #0 .

3#.51 1. .11 .15%8 #V .##7.# 1. .11 .345 #0 .4

11

3.48 1. .11 .171 #0 .#

31.#1 1. .11 .1534 #V .#16.73 1. .11 .331 #0 .4

1#3.55 1. .11 .174 #0 .#

3.% 1. .11 .147% #V .#6.37 1. .11 .313 #0 .4

13%.44 1. .11 .464 #0 .6%.44 1. .11 .464 #0 .6

143.76 1. .11 .185 #0 .#

#6.%3 1. .11 .13#3 #V .185.31 1. .11 .#61 #0 .3


31/205

[ ] [m]

1 .115 . 1.%8% 1.47 1.%% ; C D1 .161 3.3% 1.%8% 1.47 3.3% ; C D1 .156 3.75 1.%8% 1.47 3.75 ; C D1 .%%6 8.38 1.%8% 1.47 8.38 ; C D1 .167 #.%1 1.%8% 1.47 #.%1 ; C D1 .11% 6.56 1.%8% 1.47 6.56 ; C D1 .161 3.3% 1.%8% 1.47 3.3% ; C D

1 .13% 5.6 1.%8% 1.47 5.6 ; C D1 .1%4 .86 1.%8% 1.47 1.%% ; C D1 .118 6.63 1.%8% 1.47 6.63 ; C D1 .1%7 .65 1.%8% 1.47 1.%% ; C D1 .161 3.3% 1.%8% 1.47 3.3% ; C D1 .156 3.75 1.%8% 1.47 3.75 ; C D1 .%%6 8.38 1.%8% 1.47 8.38 ; C D1 .115 . 1.%8% 1.47 1.%% ; C D

#s

#sMIN B

#sMIN M

#s#5O$

[cm2] [cm2] [cm2] [cm2]


32/205

1 .115 . 1.%8% 1.47 1.%% ; C D1 .154 3.% 1.%8% 1.47 3.% ; C D1 .%%6 8.38 1.%8% 1.47 8.38 ; C D1 .115 . 1.%8% 1.47 1.%% ; C D1 .137 5.# 1.%8% 1.47 5.# ; C D1 .1%4 .86 1.%8% 1.47 1.%% ; C D

1 .115 . 1.%8% 1.47 1.%% ; C D1 .1#3 6.31 1.%8% 1.47 6.31 ; C D1 .166 3. 1.%8% 1.47 3. ; C D1 .1#6 6.3 1.%8% 1.47 6.3 ; C D1 .165 3.7 1.%8% 1.47 3.7 ; C D1 .131 5.68 1.%8% 1.47 5.68 ; C D1 .%%1 8.76 1.%8% 1.47 8.76 ; C D1 .163 3.#5 1.%8% 1.47 3.#5 ; C D1 .144 4.67 1.%8% 1.47 4.67 ; C D

[ ] [m]

1 .1%1 1.8 1.%8% 1.47 1.%%1 .1%4 .8# 1.%8% 1.47 1.%%1 .134 5.47 1.%8% 1.47 5.471 .%8% 8.86 1.%8% 1.47 8.861 .18 1.%3 1.%8% 1.47 1.%%1 .1%6 .71 1.%8% 1.47 1.%%1 .17 7.5# 1.%8% 1.47 7.5#

1 .185 1.54 1.%8% 1.47 1.%%1 .1%4 .8# 1.%8% 1.47 1.%%1 .134 5.47 1.%8% 1.47 5.471 .148 4.36 1.%8% 1.47 4.361 .11# .#1 1.%8% 1.47 1.%%1 .185 1.56 1.%8% 1.47 1.%%1 .116 6.83 1.%8% 1.47 6.831 .113 .16 1.%8% 1.47 1.%%1 .1%4 .8# 1.%8% 1.47 1.%%1 .134 5.47 1.%8% 1.47 5.471 .%8% 8.86 1.%8% 1.47 8.861 .18 1.%3 1.%8% 1.47 1.%%1 .1%% .4% 1.%8% 1.47 1.%%1 .115 . 1.%8% 1.47 1.%%1 .147 4.4# 1.%8% 1.47 4.4#1 .%8% 8.86 1.%8% 1.47 8.861 .18 1.%3 1.%8% 1.47 1.%%1 .115 . 1.%8% 1.47 1.%%1 .147 4.4# 1.%8% 1.47 4.4#

#s

#sMIN B

#sMIN M

#s#5O$ 5+sos+c+o

,[cm2] [cm2] [cm2] [cm2]

φ 1 (/#4φ 1 (/#4φ 1 (/#5φ 1# (/17φ 1 (/#4φ 1 (/#4φ 16 (/16

φ 1 (/#4φ 1 (/#4φ 1 (/#5φ 16 (/14φ 1 (/#4φ 1 (/#4φ 1 (/#5φ 10 (/#4φ 10 (/#4φ 10 (/#5φ 10 (/#6φ 10 (/#4φ 10 (/#4φ 10 (/#4φ 1# (/#1φ 12 (/#1φ 1 (/#4φ 1 (/#4φ 1# (/#1


33/205

1 .148 4.36 1.%8% 1.47 4.361 .11# .#1 1.%8% 1.47 1.%%1 .115 . 1.%8% 1.47 1.%%1 .18 7.4# 1.%8% 1.47 7.4#1 .186 1.4% 1.%8% 1.47 1.%%1 .1%5 .73 1.%8% 1.47 1.%%

1 .113 7.% 1.%8% 1.47 7.%1 .186 1.4# 1.%8% 1.47 1.%%1 .1%5 .75 1.%8% 1.47 1.%%1 .116 6.81 1.%8% 1.47 6.811 .187 1.35 1.%8% 1.47 1.%%1 .17% #.1 1.%8% 1.47 #.11 .17% #.1 1.%8% 1.47 #.11 .1%5 .7% 1.%8% 1.47 1.%%1 .1#6 6.4 1.%8% 1.47 6.41 .1% 1.1# 1.%8% 1.47 1.%%

φ 1 (/#1φ 1 (/#4φ 1 (/#4φ 1# (/#φ 1 (/#4φ 1 (/#4

φ 1# (/#1φ 1 (/#4φ 1 (/#4φ 1 (/#5φ 1 (/#4φ 1 (/#4φ 1 (/#4φ 1 (/#4φ 1 (/#5φ 1 (/#4


34/205

#,

5+sos+c+o,mm

. . . ZD,/3.%3 .7% 5 1 3.%3 A1/#3.%3 .7% 5 1 3.%3 A1/#%.5 1.81 8 1# %.5 A1#/1#3.14 .63 4 1 3.14 A1/#56.7% 1.36 6 1# 6.7% A1#/163.%3 .7% 5 1 3.%3 A1/#

5.5 1.1 7 1 5.5 A1/14#.1 .4 4 8 #.1 A8/#56.7% 1.36 6 1# 6.7% A1#/16#.1 .4 4 8 #.1 A8/#53.%3 .7% 5 1 3.%3 A1/#3.%3 .7% 5 1 3.%3 A1/#%.5 1.81 8 1# %.5 A1#/1#. . . ZD,/

#sE#L

#s1#N"

#sE#L

[cm2] [cm2] [cm2]


35/205

. . . ZD,/3.%3 .7% 5 1 3.%3 A1/#%.5 1.81 8 1# %.5 A1#/1#. . . ZD,/5.5 1.1 7 1 5.5 A1/14#.1 .4 4 8 #.1 A8/#5

. . . ZD,/6.7% 1.36 6 1# 6.7% A1#/163.14 .63 4 1 3.14 A1/#56.1% 1.#4 7 1# 7.%# A1#/143.14 .63 4 1 3.14 A1/#55.65 1.13 5 1# 5.65 A1#/#%.5 1.81 8 1# %.5 A1#/1#3.%3 .7% 5 1 3.%3 A1/#4.71 .%4 6 1 4.71 A1/16

#,

φ

5+sos+c+o,mm

#.1 .4 4 8 #.1 A8/#5#.1 .4 4 8 #.1 A8/#55.5 1.% 7 1 5.5 A1/14%.5 1.77 8 1# %.5 A1#/1##.1 .4 4 8 #.1 A8/#5#.1 .4 4 8 #.1 A8/#57.%# 1.5 7 1# 7.%# A1#/14

#.1 .4 4 8 #.1 A8/#5#.1 .4 4 8 #.1 A8/#55.5 1.% 7 1 5.5 A1/144.71 .87 6 1 4.71 A1/16#.1 .4 4 8 #.1 A8/#5#.1 .4 4 8 #.1 A8/#57.%# 1.37 7 1# 7.%# A1#/14#.1 .4 4 8 #.1 A8/#5#.1 .4 4 8 #.1 A8/#55.5 1.% 7 1 5.5 A1/14%.5 1.77 8 1# %.5 A1#/1##.1 .4 4 8 #.1 A8/#5#.1 .4 4 8 #.1 A8/#5. .4 . ZD,/4.71 .88 6 1 4.71 A1/16%.5 1.77 8 1# %.5 A1#/1##.1 .4 4 8 #.1 A8/#5. .4 . ZD,/4.71 .88 6 1 4.71 A1/16

#sE#L

#s1#N"

#sE#L

[cm2] [cm2] [cm2]


36/205

4.71 .87 6 1 4.71 A1/16#.1 .4 4 8 #.1 A8/#5. .4 . ZD,/7.%# 1.48 7 1# 7.%# A1#/14#.1 .4 4 8 #.1 A8/#5#.1 .4 4 8 #.1 A8/#5

7.%# 1.4# 7 1# 7.%# A1#/14#.1 .4 4 8 #.1 A8/#5#.1 .4 4 8 #.1 A8/#57.%# 1.36 7 1# 7.%# A1#/14#.1 .4 4 8 #.1 A8/#5#.36 .4 3 1 #.36 A1/33#.36 .4 3 1 #.36 A1/33#.1 .4 4 8 #.1 A8/#56.7% 1.#1 6 1# 6.7% A1#/16#.1 .4 4 8 #.1 A8/#5


37/205

/ro?rama area rea:

(m# F$(m& n om)na(on7φ6 1.%8 ZD,/ + 3φ12 3.3% # 5 # 1 + # 3φ8+2φ12 3.77 # 5 # 1 + # 5φ10+4φ12 8.45 1#.5 8 # 1# + 3 1φ8+3φ10 #.86 #5 4 # 1 + # 4φ12+1φ16 6.53 16.666667 6 # 1# + # 3φ12 3.3% # 5 # 1 + # 5φ10+1φ12 5.6 14.#85714 7 # 1 + 3 7φ6 1.%8 #5 4 # 8 + # 2φ8+5φ12 6.66 16.666667 6 # 1# + # 7φ6 1.%8 #5 4 # 8 + # 3φ12 3.3% # 5 # 1 + # 3φ8+2φ12 3.77 # 5 # 1 + # 5φ10+4φ12 8.45 1#.5 8 # 1# + 3 7φ6 1.%8 ZD,/ +


38/205

7φ6 1.%8 ZD,/ + 5φ10 3.%3 # 5 3 1 + # 5φ10+4φ12 8.45 1#.5 8 # 1# + 3 7φ6 1.%8 ZD,/ + 1φ16+1φ20 5.15 14.#85714 7 # 1 + 3 7φ6 1.%8 #5 4 # 8 + #

7φ6 1.%8 ZD,/ + 2φ12+2φ16 6.#8 16.666667 6 # 1# + # 6φ8 3.# #5 4 # 1 + # 3φ16 6.3 14.#85714 7 # 1# + 3 3φ8+2φ10 3.8 #5 4 # 1 + # 5φ8+4φ10 5.65 # 5 # 1# + # 4φ10+5φ12 8.8 1#.5 8 # 1# + 3 2φ8+2φ12 3.#7 # 5 # 1 + # 6φ10 4.71 16.666667 6 # 1 + #

/ro?rama area rea:

(m# F$(m& n om)na(on7φ6 1.%8 #5 4 # 8 + # 7φ6 1.%8 #5 4 # 8 + # 7φ10 5.5 14.#85714 7 # 1 + 3 2φ16+1φ25 8.%3 1#.5 8 # 1# + 3 7φ6 1.%8 #5 4 # 8 + # 7φ6 1.%8 #5 4 # 8 + # 3φ12+2φ16 7.41 14.#85714 7 # 1# + #

7φ6 1.%8 #5 4 # 8 + # 7φ6 1.%8 #5 4 # 8 + # 7φ10 5.5 14.#85714 7 # 1 + 3 4φ8+3φ10 4.37 16.666667 6 # 1 + # 7φ6 1.%8 #5 4 # 8 + # 7φ6 1.%8 #5 4 # 8 + # 3φ10+4φ12 6.88 14.#85714 7 # 1# + 3 7φ6 1.%8 #5 4 # 8 + # 7φ6 1.%8 #5 4 # 8 + # 7φ10 5.5 14.#85714 7 # 1 + 3 2φ16+1φ25 8.%3 1#.5 8 # 1# + 3 7φ6 1.%8 #5 4 # 8 + # 7φ6 1.%8 #5 4 # 8 + # 7φ6 1.%8 ZD,/ + 1φ8+5φ10 4.43 16.666667 6 # 1 + # 2φ16+1φ25 8.%3 1#.5 8 # 1# + 3 7φ6 1.%8 #5 4 # 8 + # 7φ6 1.%8 ZD,/ + 1φ8+5φ10 4.43 16.666667 6 # 1 + #


39/205

4φ8+3φ10 4.37 16.666667 6 # 1 + # 7φ6 1.%8 #5 4 # 8 + # 7φ6 1.%8 ZD,/ + 3φ12+2φ16 7.41 14.#85714 7 # 1# + 3 7φ6 1.%8 #5 4 # 8 + # 7φ6 1.%8 #5 4 # 8 + #

9φ10 7.7 14.#85714 7 # 1# + 3 7φ6 1.%8 #5 4 # 8 + # 7φ6 1.%8 #5 4 # 8 + # 6φ12 6.7% 14.#85714 7 # 1# + 3 7φ6 1.%8 #5 4 # 8 + # 1φ16 #.1 33.333333 3 # 1 + 1 1φ16 #.1 33.333333 3 # 1 + 1 7φ6 1.%8 #5 4 # 8 + # 3φ16 6.3 16.666667 6 # 1# + # 7φ6 1.%8 #5 4 # 8 + #


40/205

Mto 0)s. $KN-m& Mto 0)s. $KN-m& Mto 0)s. $KN-m&rmad@ra1 + . . . ;e>sar1 + 1 1 7.#1 7.#1 3.61 Ven1 + 1 1 7.18 7.18 3.5% Ven1# + 3 1# %.75 14.6# 14.6# Ven1 + 7.#5 7.#5 . Ven1# + # 1# %.%8 %.%8 %.%8 Ven1 + 1 1 7.#1 7.#1 3.61 Ven

1 + # 1 7.6 1.6 7.6 Ven8 + 4.76 4.76 . Ven

1# + # 1# %.%7 %.%7 %.%7 Ven8 + 4.77 4.77 . Ven

1 + 1 1 7.#1 7.#1 3.61 Ven1 + 1 1 7.18 7.18 3.5% Ven1# + 3 1# %.75 14.6# 14.6# Ven

+ . . . ;e>sar


41/205

+ . . . ;e>sar1 + 1.75 7.17 . Ven1# + 3 1# %.75 14.6# 14.6# Ven

+ . . . ;e>sar1 + # 1 7.5 1.58 7.5 Ven8 + 4.76 4.76 . Ven

+ . . . ;e>sar1# + # 1# 1.1 1.1 1.1 Ven1 + 7.#5 7.#5 . Ven1 + # 1 1.5 1.47 6.%8 Ven1 + 7.#4 7.#4 . Ven1# + 1 1# 1.% 1.% 5.5 ;e>sar1# + 3 1# %.7 14.55 14.55 Ven1 + 1 1 7.## 7.## 3.61 Ven1 + # 1 7.1 7.1 7.1 Ven

Mto 0)s. $KN-m& Mto 0)s. $KN-m& Mto 0)s. $KN-m&rmad@ra8 + 4.75 4.75 . Ven8 + 4.76 4.76 . Ven

1 + # 1 7.3 1.54 7.3 Ven1# + 3 1# %.6% 14.53 14.53 Ven8 + 4.7 4.7 . Ven8 + 4.77 4.77 . Ven

1# + 3 1# %.86 %.86 14.7% Ven

8 + 4.7# 4.7# . Ven8 + 4.76 4.76 . Ven1 + # 1 7.3 1.54 7.3 Ven1 + # 1 7.13 7.13 7.13 Ven8 + 4.8 4.8 . Ven8 + 4.7# 4.7# . Ven

1# + # 1# %.%5 14.%# %.%5 Ven8 + 4.8 4.8 . Ven8 + 4.76 4.76 . Ven

1 + # 1 7.3 1.54 7.3 Ven1# + 3 1# %.6% 14.53 14.53 Ven8 + 4.7 4.7 . Ven8 + 4.78 4.78 . Ven

+ . . . ;e>sar1 + # 1 7.1# 7.1# 7.1# Ven1# + 3 1# %.6% 14.53 14.53 Ven8 + 4.7 4.7 . Ven

+ . . . ;e>sar1 + # 1 7.1# 7.1# 7.1# Ven


42/205

1 + # 1 7.13 7.13 7.13 Ven8 + 4.8 4.8 . Ven

+ . . . ;e>sar1# + # 1# %.87 14.81 %.87 Ven8 + 4.7# 4.7# . Ven8 + 4.77 4.77 . Ven

1# + # 1# %.%1 14.87 %.%1 Ven8 + 4.73 4.73 . Ven8 + 4.77 4.77 . Ven

1# + # 1# %.%5 14.%# %.%5 Ven8 + 4.73 4.73 . Ven

1 + 7.33 3.67 . Ven1 + 7.33 3.67 . Ven8 + 4.76 4.76 . Ven

1# + # 1# 1.5 1.5 1.5 Ven8 + 4.74 4.74 . Ven


43/205

. .3.%3 18.33.%3 17.%5%.5 38.%%3.14 14.516.7% #%.%43.%3 18.3

5.5 #4.7##.1 %.5#6.7% #%.%1#.1 %.543.%3 18.33.%3 17.%5%.5 38.%%. .

0;E0 DE0E;Q ;E0I

(m#

momentoa)s tota:


44/205

. .3.%3 17.%#%.5 38.%%. .5.5 #4.68#.1 %.5#

. .6.7% 3.43.14 14.4%6.1% #7.4%3.14 14.485.65 #5.#3%.5 38.83.%3 18.64.71 #1.#%

MUQ UQU0I#.1 %.4%#.1 %.5#5.5 #4.6%.5 38.75#.1 %.4#.1 %.547.%# 34.5

#.1 %.44#.1 %.5#5.5 #4.64.71 #1.38#.1 %.5%#.1 %.447.%# 34.81#.1 %.6#.1 %.5#5.5 #4.6%.5 38.75#.1 %.4#.1 %.56. .4.71 #1.36%.5 38.75#.1 %.4. .4.71 #1.36

0;E0 DE0E;Q ;E0I

(m#


45/205

4.71 #1.38#.1 %.5%. .7.%# 34.55#.1 %.45#.1 %.53

7.%# 34.6%#.1 %.45#.1 %.537.%# 34.8##.1 %.46#.36 11.#.36 11.#.1 %.536.7% 3.14#.1 %.4%


46/205

D*"' A 34T' Materiales:

fck = 2' [Ma] fcd= 1.67

fyk = 'DD [Ma] fyd= 43.48

.' ey= #.17.'

0

Propiedades Geometricas "olicitación 3lc!los

LOSA Tramo h [cm] d [cm] ρ β 6c!

1 0-1 10.0 20.0 2.0 2.0 18.0 2.99 2.05 2.00 1.57 0.0087 25 1.00 10

2

A 10.0 20.0 2.0 2.0 18.0 13.45 2.05 2.00 1.57 0.0087 25 1.00 10

B 10.0 20.0 2.0 2.0 18.0 21.56 2.05 2.00 2.26 0.0126 25 1.00 11

C 10.0 20.0 2.0 2.0 18.0 28.59 2.05 2.00 3.83 0.0213 25 1.00 13

E 10.0 20.0 2.0 2.0 18.0 20.53 2.05 2.00 1.57 0.0087 25 1.00 10

3A 10.0 20.0 2.0 2.0 18.0 12.57 2.05 2.00 1.57 0.0087 25 1.00 10

B 10.0 20.0 2.0 2.0 18.0 26.43 2.05 2.00 3.39 0.0188 25 1.00 13

C 10.0 20.0 2.0 2.0 18.0 18.32 2.05 2.00 1.57 0.0087 25 1.00 10

4

A 10.0 20.0 2.0 2.0 18.0 13.45 2.05 2.00 1.57 0.0087 25 1.00 10

B 10.0 20.0 2.0 2.0 18.0 22.96 2.05 2.00 2.26 0.0126 25 1.00 11

C 10.0 20.0 2.0 2.0 18.0 22.03 2.05 2.00 2.26 0.0126 25 1.00 11

C! 10.0 20.0 2.0 2.0 18.0 6.88 2.05 2.00 1.57 0.0087 25 1.00 10

5B 10.0 20.0 2.0 2.0 18.0 18.41 2.05 2.00 1.01 0.0056 25 1.00 8

C 10.0 20.0 2.0 2.0 18.0 26.08 2.05 2.00 3.05 0.0169 25 1.00 12

C! 10.0 20.0 2.0 2.0 18.0 6.11 2.05 2.00 1.57 0.0087 25 1.00 10

6

A 10.0 20.0 2.0 2.0 18.0 13.45 2.05 2.00 1.01 0.0056 25 1.00 8

B 10.0 20.0 2.0 2.0 18.0 21.56 2.05 2.00 2.26 0.0126 25 1.00 11

C 10.0 20.0 2.0 2.0 18.0 28.59 2.05 2.00 4.52 0.0251 25 1.00 13E 10.0 20.0 2.0 2.0 18.0 20.53 2.05 2.00 1.01 0.0056 25 1.00 8

[KN/(m#]

[KN/(m#]

γc = [o

/oo]γs =

ρ m!

b[cm]

d1[cm]

d2[cm]

6d[,-]

ξ

calc ξ

as!m

Asl[cm2]

fc/[+pa]

( )1/3

c( & c)* 0.10 100 f + d = ⋅ ξ ⋅ ⋅ ρ ⋅ ⋅β ⋅ ⋅


47/205

7 5!-6 10.0 20.0 2.0 2.0 18.0 1.38 2.05 2.00 1.01 0.0056 25 1.00 8.6

8

A! 10.0 20.0 2.0 2.0 18.0 -6.19 2.05 2.00 2.26 0.0126 25 1.00 11.3

B 10.0 20.0 2.0 2.0 18.0 20.98 2.05 2.00 0.00 0.0000 25 1.00 0.0

C 10.0 20.0 2.0 2.0 18.0 28.59 2.05 2.00 4.52 0.0251 25 1.00 13.2

E 10.0 20.0 2.0 2.0 18.0 20.53 2.05 2.00 1.01 0.0056 25 1.00 8.6

%

A! 10.0 20.0 2.0 2.0 18.0 -6.19 2.05 2.00 0.00 0.0000 25 1.00 0.0

B 10.0 20.0 2.0 2.0 18.0 22.38 2.05 2.00 1.57 0.0087 25 1.00 10.0

C 10.0 20.0 2.0 2.0 18.0 22.16 2.05 2.00 1.57 0.0087 25 1.00 10.0

10.0 20.0 2.0 2.0 18.0 6.88 2.05 2.00 1.57 0.0087 25 1.00 10.0

1A! 10.0 20.0 2.0 2.0 18.0 -12.47 2.05 2.00 0.00 0.0000 25 1.00 0.0

B 10.0 20.0 2.0 2.0 18.0 26.38 2.05 2.00 2.26 0.0126 25 1.00 11.3

C 10.0 20.0 2.0 2.0 18.0 17.97 2.05 2.00 1.57 0.0087 25 1.00 10.0

11A 10.0 20.0 2.0 2.0 18.0 12.75 2.05 2.00 1.57 0.0087 25 1.00 10.0

B 10.0 20.0 2.0 2.0 18.0 25.57 2.05 2.00 2.26 0.0126 25 1.00 11.3

B! 10.0 20.0 2.0 2.0 18.0 17.63 2.05 2.00 1.57 0.0087 25 1.00 10.0

1#A 10.0 20.0 2.0 2.0 18.0 12.87 2.05 2.00 1.57 0.0087 25 1.00 10.0

B 10.0 20.0 2.0 2.0 18.0 24.99 2.05 2.00 2.26 0.0126 25 1.00 11.3

B! 10.0 20.0 2.0 2.0 18.0 17.63 2.05 2.00 1.57 0.0087 25 1.00 10.0

13 B 10.0 20.0 2.0 2.0 18.0 20.84 2.05 2.00 1.57 0.0087 25 1.00 10.0

B! 10.0 20.0 2.0 2.0 18.0 20.84 2.05 2.00 1.57 0.0087 25 1.00 10.0

14A 10.0 20.0 2.0 2.0 18.0 13.21 2.05 2.00 1.57 0.0087 25 1.00 10.0

B 10.0 20.0 2.0 2.0 18.0 23.21 2.05 2.00 2.26 0.0126 25 1.00 11.3

B! 10.0 20.0 2.0 2.0 18.0 15.66 2.05 2.00 1.57 0.0087 25 1.00 10.0


48/205

5.40

"olicitación

bser/ación Tramo ϕ

"ma$ [cm] 6!7[mm]

$o ,c"'"a a%ad(a d co 0-1 2.99 10.06 -7.07 5.40 8 13 41.65 51.71

$c"'a a%ad(a d co A 13.45 10.06 3.39 5.40 8 13 41.65 51.71

$c"'a a%ad(a d co B 21.56 11.36 10.20 10.20 8 13 41.65 53.01

$c"'a a%ad(a d co C 28.59 13.26 15.33 15.33 8 13 41.65 54.91

$c"'a a%ad(a d co E 20.53 10.06 10.47 10.47 8 13 41.65 51.71

$c"'a a%ad(a d co A 12.57 10.06 2.51 5.40 8 13 140.87 150.93 $c"'a a%ad(a d co B 26.43 13.00 13.43 13.43 8 13 350.26 363.27

$c"'a a%ad(a d co C 18.32 10.06 8.26 8.26 8 13 215.50 225.56

$c"'a a%ad(a d co A 13.45 10.06 3.39 5.40 8 13 140.87 150.93

$c"'a a%ad(a d co B 22.96 11.36 11.60 11.60 8 13 302.63 313.99

$c"'a a%ad(a d co C 22.03 11.36 10.67 10.67 8 13 278.37 289.72

$o ,c"'"a a%ad(a d co C! 6.88 10.06 -3.18 5.40 8 13 140.87 150.93

$c"'a a%ad(a d co B 18.41 8.67 9.74 9.74 8 13 254.12 262.79

$c"'a a%ad(a d co C 26.08 12.55 13.53 13.53 8 13 353.07 365.61

$o ,c"'"a a%ad(a d co C! 6.11 10.06 -3.95 5.40 8 13 140.87 150.93

$c"'a a%ad(a d co A 13.45 8.67 4.78 5.40 8 13 140.87 149.54

$c"'a a%ad(a d co B 21.56 11.36 10.20 10.20 8 13 266.10 277.46

$c"'a a%ad(a d co C 28.59 13.26 15.33 15.33 8 13 399.85 413.11

$c"'a a%ad(a d co E 20.53 8.67 11.86 11.86 8 13 309.42 318.09

6s! min[,-]

6d[,-]

6c![,-]

6s!calc [,-]

6s![,-]

6s![,-]

6![,-]

( )1/3

c( & c)* 0.10 100 f + d = ⋅ ξ ⋅ ⋅ρ ⋅ ⋅β ⋅ ⋅

%', cd*"( 0.018 f + d= ⋅ ⋅ ⋅


49/205

$o ,c"'"a a%ad(a d co 5!-6 1.38 8.67 -7.29 5.40 8 13 140.87 149.54 #

$o ,c"'"a a%ad(a d co A! -6.19 11.36 -17.55 5.40 8 13 140.87 152.23 #

$c"'a a%ad(a d co B 20.98 0.00 20.98 20.98 8 13 547.30 547.30 #

$c"'a a%ad(a d co C 28.59 13.26 15.33 15.33 8 13 399.85 413.11 #

$c"'a a%ad(a d co E 20.53 8.67 11.86 11.86 8 13 309.42 318.09 #

$o ,c"'"a a%ad(a d co A! -6.19 0.00 -6.19 5.40 8 13 140.87 140.87 #

$c"'a a%ad(a d co B 22.38 10.06 12.32 12.32 8 13 321.41 331.47 #

$c"'a a%ad(a d co C 22.16 10.06 12.10 12.10 8 13 315.67 325.73 #

$o ,c"'"a a%ad(a d co 6.88 10.06 -3.18 5.40 8 13 140.87 150.93 #

$o ,c"'"a a%ad(a d co A! -12.47 0.00 -12.47 5.40 8 13 140.87 140.87 #

$c"'a a%ad(a d co B 26.38 11.36 15.02 15.02 8 13 391.84 403.20 #

$c"'a a%ad(a d co C 17.97 10.06 7.91 7.91 8 13 206.37 216.43 #

$c"'a a%ad(a d co A 12.75 10.06 2.69 5.40 8 13 140.87 150.93 #

$c"'a a%ad(a d co B 25.57 11.36 14.21 14.21 8 13 370.71 382.07 #

$c"'a a%ad(a d co B! 17.63 10.06 7.57 7.57 8 13 197.50 207.56 #

$c"'a a%ad(a d co A 12.87 10.06 2.81 5.40 8 13 140.87 150.93 #

$c"'a a%ad(a d co B 24.99 11.36 13.63 13.63 8 13 355.58 366.94 #

$c"'a a%ad(a d co B! 17.63 10.06 7.57 7.57 8 13 197.50 207.56 # $c"'a a%ad(a d co B 20.84 10.06 10.78 10.78 8 13 281.24 291.30 #

$c"'a a%ad(a d co B! 20.84 10.06 10.78 10.78 8 13 281.24 291.30 #

$c"'a a%ad(a d co A 13.21 10.06 3.15 5.40 8 13 140.87 150.93 #

$c"'a a%ad(a d co B 23.21 11.36 11.85 11.85 8 13 309.15 320.51 #

$c"'a a%ad(a d co B! 15.66 10.06 5.60 5.60 8 13 146.11 156.17 #


50/205

8samos

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13


51/205

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13

E8c/13E8c/13

E8c/13

E8c/13

E8c/13

E8c/13


52/205

'"TAD 9:+*T' D' ;*"84A3*


53/205

Determna(on de 0n(o de Rs@ra.

Fe?@n :a EWE.

Donde ^m = 0n(o medo de Rs@ras.

Determinacion del Coeficiente β

Es e: redondeo de 1.64 (orresondente a: (@ant: %5 en :a dstrde an(os de Os@ras. Hara a((ones dre(tas.

Determinacion de la separacion media de Fisuras.

Ia EWEJ s?@endo a: .E.V. a adotado :a orm@:a.

=1475.68

= 37.68 [KN/(m#].% . 11 . 4.#

k "%9/ %/ : ;= β ⋅ ε ⋅

1.7β =

2

" " ""% 2

" " "

1 k 0.4E E

σ σ σε = − ≥ ⋅ σ

k "

< "

M

k d Aσ =

⋅ ⋅c9%

"

< "

f :

k d A

⋅σ =

⋅ ⋅

( )3

ck c 28E 8500 f 8= ⋅ +

(

(

(

3

+

2= +

+ > ,

12

⋅ ⋅ +=

⋅ +

⋅= +

23c9% ck

f 0.30 f = ⋅

>:

==

( )

"

c 28

E,

E=


54/205

P9A-*99A# '"TAD 9*+*T' D' ;*"84A3*-.

5.67

Para la suracion.

0.5

1

1

6.67

Determinacion de la Relacion

(= = 1.755

LO"#"o4+c+

Mome,


55/205

V-V_ Md= 1#.47 M= 7.11

@(on ?a@ssana

) ( )

) ( )

) ( )

"1

"1

2

"1

, 1 A d

, 1 A

1 A d y

− ⋅ ⋅

− ⋅

− ⋅ −


56/205

#

Para E.L.U.Co

BEOME1I# de l1.5 + [c%] 11.6 [c%] 13

#11.71 d [c%] 11

r! re!4 `s C , ^ (tJm `sr#re!.cm2 [KN/(m#] (m (m4 (m3 Ma [KN/(m#]

. .8 ZD,/ 6.5 #%7.51 45.8 .% Z0IGE Z1.57 .8 37.%53854 6.4# 766.15 11%.3 #.565 .% 1.%71.57 .8 4#.55%14% 6.4# 766.15 11%.3 #.565 .% 1.%73.3% .8 4.83% 6.33 1#8%.#8 #3.7 #.565 .% 1.561.57 .8 33.131%4 6.4# 766.15 11%.3 #.565 .% 1.%7#.#6 .8 48.8#5%5% 6.3% %67.1 151.5 #.565 .% 1.731.57 .8 37.%53854 6.4# 766.15 11%.3 #.565 .% 1.%7#.#6 .8 38.587767 6.3% %67.1 151.5 #.565 .% 1.73

1.57 .8 %.%#53578 6.4# 766.15 11%.3 #.565 .% 1.%7#.36 .8 47.33664 6.38 %%4.#6 155.8 #.565 .% 1.711.1 .8 1#.1%858% 6.45 5%%.37 %#.% #.565 .% #.41.57 .8 37.%53854 6.4# 766.15 11%.3 #.565 .% 1.%71.57 .8 4#.55%14% 6.4# 766.15 11%.3 #.565 .% 1.%73.14 .8 44.67#5 6.34 1#18.3% 1%#.1 #.565 .% 1.58. .8 ZD,/ 6.5 #%7.51 45.8 #.565 .% ZD,/ Z. .8 ZD,/ 6.5 #%7.51 45.8 #.565 .% ZD,/ Z1.57 .8 43.8#315 6.4# 766.15 11%.3 #.565 .% 1.%73.5 .8 45.43154 6.35 11%1.7 187.8 #.565 .% 1.6. .8 ZD,/ 6.5 #%7.51 45.8 #.565 .% ZD,/ Z

1.57 .8 56.7#%11 6.4# 766.15 11%.3 #.565 .% 1.%71.1 .8 15.5837# 6.45 5%%.37 %#.% #.565 .% #.4. .8 ZD,/ 6.5 #%7.51 45.8 #.565 .% ZD,/ Z#.#6 .8 47.8%# 6.3% %67.1 151.5 #.565 .% 1.731.1 .8 53.18%# 6.45 5%%.37 %#.% #.565 .% #.4#.#6 .8 45.#331# 6.3% %67.1 151.5 #.565 .% 1.731.57 .8 61.668136 6.4# 766.15 11%.3 #.565 .% 1.%71.57 .8 -8.66664#% 6.4# 766.15 11%.3 #.565 .% 1.%7#.36 .8 6.71#4 6.38 %%4.#6 155.8 #.565 .% 1.711.1 .8 57.13%1# 6.45 5%%.37 %#.% #.565 .% #.4

% [c%]

d [#$/%]

k <

k <

d # 6 # 78 4= ⋅ γ + ⋅ γ

23c 9% ck

f 0.30 f = ⋅

c 9%

"/

< "

f :

k d A

⋅σ =

⋅ ⋅

"%ε


57/205

1.57 .8 51.411#8 6.4# 766.15 11%.3 #.565 .% 1.%7


58/205

probacion del alargamiento relatio

a armadura respecto al !ormigon "ue lo rodea

0.50

sm Dsos(ons [mm]

0rmad@ra.,/ ZD,/ ZD,/ A A .1#5 # ZD,/

.# .75% QK # A 1 3 A 1 .1#5 15 #.

.# .851 QK # A 1 3 A 1 .1#5 15 #.

.# .816 QK # A 1# 6 A 1# .1#5 14 1#.5

.# .66 QK # A 1 # A 1 .1#5 15 #5.

.# .%77 QK # A 1# 4 A 1# .1#5 14 16.667

.# .75% QK # A 1 3 A 1 .1#5 15 #.

.# .77# QK # A 1 5 A 1 .1#5 15 14.#86

. .1%% QK # A 8 # A 8 .1#5 16 #5..# .%46 QK # A 1# 4 A 1# .1#5 14 16.667

.1 .#44 QK # A 8 # A 8 .1#5 16 #5.

.# .75% QK # A 1 3 A 1 .1#5 15 #.

.# .851 QK # A 1 3 A 1 .1#5 15 #.

.# .881 QK # A 1# 6 A 1# .1#5 14 1#.5,/ ZD,/ ZD,/ A A .1#5 # ZD,/,/ ZD,/ ZD,/ A A .1#5 # ZD,/

.# .876 QK 3 A 1 # A 1 .1#5 15 #.

.# .%% QK # A 1# 6 A 1# .1#5 14 1#.5,/ ZD,/ ZD,/ A A .1#5 # ZD,/

.3 .1135 QK # A 1 5 A 1 .1#5 15 14.#86

.1 .31 QK # A 8 # A 8 .1#5 16 #5.,/ ZD,/ ZD,/ A A .1#5 # ZD,/

.# .%4 QK # A 1# 4 A 1# .1#5 14 16.667

.3 .16# QK # A 1 # A 1 .1#5 15 #5.

.# .%5 QK # A 1# 5 A 1# .1#5 14 14.#86

.3 .1#33 QK # A 1 # A 1 .1#5 15 #5.

. -.173 NQ GMHIE # A 1# 3 A 1# .1#5 14 #.

.3 .1#14 QK # A 1# 6 A 1# .1#5 14 1#.5

.3 .1143 QK # A 1 3 A 1 .1#5 15 #.

k 2

omro)a(on de0:ar?amento medo

de: 0ok

1 @&. (a

Es.re(. (.mm [

2

" " "2

" " "

1 k 0.4E E

σ σ σ= − ≥ ⋅ σ

"

"

0.4E

σ⋅ =

1%9

k ; 2 c 0.2 " 0.4

⋅ φ= ⋅ + ⋅ + ⋅

ρ


59/205

.3 .1#8 QK # A 1 4 A 1 .1#5 15 16.667


60/205

1.7

0n(o Rs@ras

^ [mm]# # . ZD,/ ZD,/ ZD,/%5 %5 .# 336.3% .18 QK %5 %5 .# 336.3% .1## QK

11 11 .3 ##5.# .78 QK %5 %5 .# 337.3% .%5 QK

11 11 .# 3#3.1# .134 QK %5 %5 .# 336.3% .18 QK %5 %5 .# #4#.85 .8 QK

8 8 .# #4.7# .# QK 11 11 .# 311.45 .1#5 QK 8 8 .1 355.31 .36 QK %5 %5 .# 336.3% .18 QK %5 %5 .# 336.3% .1## QK

11 11 .3 #4.58 .% QK # # . ZD,/ ZD,/ ZD,/# # . ZD,/ ZD,/ ZD,/%5 %5 .# 336.3% .1#5 QK

11 11 .3 #47.8 .%5 QK # # . ZD,/ ZD,/ ZD,/

%5 %5 .# 335.#5 .16# QK 8 8 .1 355.31 .46 QK # # . ZD,/ ZD,/ ZD,/

11 11 .# 3#3.1# .1#% QK %5 %5 .1 57.4% .##% QK

11 11 .# 3##.64 .1#4 QK %5 %5 .# 337.3% .177 QK

11 11 .1 45#.17 -.3# QK 11 11 .# 31.61 .16 QK %5 %5 .1 56.4% .#46 QK

emm]

0(eO(a[mm#] br

FmJr[mm]

0n(o ma.Os@ras

.4 mm

k "% %9 : ;= β ⋅ ε ⋅


61/205

%5 %5 .# 335.73 .147 QK


62/205

E"1#5O LPMI1E 5E 5Beomeano [m] (.)) 1.57

1 # 3 4 5 6 7 8 %

Estado de carga <

,dG!s M! M! cm2 cm2 cm cm

peso propio #8 #5 1. #7#64.418 7.336 18318.#% 18318.3 6.5341% 6.53tabiquería 6 #7.61 1.8 #8365.681 7.51 18317.84 18317.8 6.53#66 6.53#66

solado 1# #8.44% 1.14 #%83.%%#8 6.877 18317.56 18317.6 6.53 6.53173

sobrecarga 1E+## 3#.16 1.#8 38%4.#68 6.474 18316.%3 18316.% 6.53 6.5#%57

Momento de R?@ra(


63/205

dG!s M! M! cm2 cm2 cm cm


solado 1# #8.44% 1.14 #%83.%%#8 6.877 18317.56 18317.6 6.53 6.53173

sobrecarga 1E+## 3#.16 1.#8 38%4.#68 6.474 18316.%3 18316.% 6.53 6.5#%57

Momento de R?@ra(ano [m] (.)) 1.57

1 # 3 4 5 6 7 8 %

Estado de carga <


peso propio #8 #5 1. #7#64.418 7.336 18318.#% 18318.3 6.5341% 6.53

tabiquería 6 #7.61 1.8 #8365.681 7.51 18317.84 18317.8 6.53#66 6.53#66solado 1# #8.44% 1.14 #%83.%%#8 6.877 18317.56 18317.6 6.53 6.53173

sobrecarga 1E+## 3#.16 1.#8 38%4.#68 6.474 18316.%3 18316.% 6.53 6.5#%57

Momento de R?@ra(


64/205

.8 .%#

D.1.6#

WaC Os@ra(


65/205

λ

e(D.)A

Beomeano [m] ).C 1.57

1 # 3 4 5 6 7 8 %

Estado de carga <



solado 1# #8.44% 1.14 #%83.%%#8 6.877 18317.56 18317.6 6.53 6.53173

sobrecarga 1E+## 3#.16 1.#8 38%4.#68 6.474 18316.%3 18316.% 6.53 6.5#%57

Momento de R?@ra(


66/205

1 # 3 4 5 6 7 8 %

Estado de carga <



solado 1# #8.44% 1.14 #%83.%%#8 6.877 18317.56 18317.6 6.53 6.53173

sobrecarga 1E+## 3#.16 1.#8 38%4.#68 6.474 18316.%3 18316.% 6.53 6.5#%57

Momento de R?@ra(


67/205

.816#*0/@ 173.33 W; 7

eso .8 .%#

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68/205

.&8M$LE e(a derda [mm]

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1 # 3 4 5 6 7 8 %

Estado de carga <



solado 1# #8.44% 1.14 #%83.%%#8 6.877 18317.56 18317.6 6.53 6.53173

sobrecarga 1E+## 3#.16 1.#8 38%4.#68 6.474 18316.%3 18316.% 6.53 6.5#%57

Momento de R?@ra(ano [m] 2.() 1.57

L/2'D

ξ(

dJ #8J6e(a tota: or eso

roo tJ 6 [mm] dJ

$ro+ed!desBeomS


69/205

1 # 3 4 5 6 7 8 %

Estado de carga <


peso propio #8 #5 1. #7#64.418 7.336 18318.#% 18318.3 6.5341% 6.53

tabiquería 6 #7.61 1.8 #8365.681 7.51 18317.84 18317.8 6.53#66 6.53#66solado 1# #8.44% 1.14 #%83.%%#8 6.877 18317.56 18317.6 6.53 6.53173

sobrecarga 1E+## 3#.16 1.#8 38%4.#68 6.474 18316.%3 18316.% 6.53 6.5#%57

Momento de R?@ra(


70/205

Momento de R?@ra(


71/205

.' ξ

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1 # 3 4 5 6 7 8 %

Estado de carga

<



solado 1# #8.44% 1.14 #%83.%%#8 6.877 18317.56 18317.6 6.53 6.53173

sobrecarga 1E+## 3#.16 1.#8 38%4.#68 6.474 18316.%3 18316.% 6.53 6.5#%57

Momento de R?@ra(


72/205

d1 [(m] 2 #7#64 13 0c 0oCod [(m] 11 'DD :@ de: >ano [m] (.)) 1.57

1 # 3 4 5 6 7 8 %

Estado de carga <

,

dG!s M! M! cm2 cm2 cm cmpeso propio #8 #5 1. #7#64.418 7.336 18318.#% 18318.3 6.5341% 6.53tabiquería 6 #7.61 1.8 #8365.681 7.51 18317.84 18317.8 6.53#66 6.53#66

solado 1# #8.44% 1.14 #%83.%%#8 6.877 18317.56 18317.6 6.53 6.53173

sobrecarga 1E+## 3#.16 1.#8 38%4.#68 6.474 18316.%3 18316.% 6.53 6.5#%57

Momento de R?@ra(


73/205

Momento de R?@ra(


74/205


75/205


76/205


77/205


78/205


79/205


80/205


81/205


82/205

EFOM#&IQN 0 VLO"# ( ?#NO #3;

&*!,


83/205


84/205

#.%6 #.7%3 3.77%aC Os@ra(


85/205

λ

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.%#a derda [mm] e(a derda [mm]

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86/205

1 11 1# 13 14 15 16 17

cm) cm) cm cm cm) cm) cm( cm(

1858.3 1858.331 1.48111# 1.48111#1 115#.37% 115#.37%4 #58.4474 #58.4474184%%.4 184%%.47 1.4541#5 1.4541#5 1111.71% 1111.7185 #48.85478 #48.85478184%4 184%3.%51 1.437318 1.4373177 186.746 186.7464 #43.#143 #43.#143

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#,!4+s+s de 4! deform!c+6, e, e4 6J1# dJ 1#J dtJ+t+so:+s( [mm]

ceme,


87/205

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88/205

1.8 # ξ

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= D [dG!s] ano [N/m]eso roo + ta)B@era +

so:adoeso roo + ta)B@era +

so:ado + so)re(ar?a

[N/m] M?J+t+so: [N/m] M?J+t+so:+s( [N/m]

m4] ,e [(m4] ,e [(m4]

[mm] J+t+so: 1# [mm] J+t+so:+s( [mm]

[mm] Jso: 1# [mm] Js( [mm]ξ 60) ξ(120) 1o

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89/205

. . s = D.2' (.(

1 11 1# 13 14 15 16 17

cm) cm) cm cm cm) cm) cm( cm(

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#,!4+s+s de 4! deform!c+6, e, e4


90/205

nto de R?@ra(

1e,s+6, de c!4c*4o! e+6,

ρ1 = ρ1 =

ρ2 = ρ2 = (tJe

Ih3!,o Ih3!oyo XYs3!,o XYs3!oyo IYs3!,o IYs3!oyo ZYs3!,o ZYs3!oyo

= D [dG!s] ano [N/m]eso roo + ta)B@era +so:ado

eso roo + ta)B@era +so:ado + so)re(ar?a

[N/m] M?J+t+so: [N/m] M?J+t+so:+s( [N/m]

m4] ,e [(m4] ,e [(m4]

[mm] J+t+so: 1# [mm] J+t+so:+s( [mm]


91/205

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92/205


93/205

#,!4+s+s de 4! deform!c+6, e, e4


94/205


95/205


96/205


97/205


98/205


99/205


100/205


101/205


102/205

4.#5 5.#5

NQ UQ0; IQF

3.#5 4.#5


103/205


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121/205


122/205

6.87 8.87

IQ;EF UQM0DQF

5.67 7.67


123/205


124/205


125/205


126/205


127/205


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142/205

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143/205

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145/205

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146/205

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147/205

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148/205

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149/205

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150/205


151/205


152/205

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153/205

15 8 # .8% 1 17

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154/205

Nc φ Nc nombre area rea: (m#

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# 6 2φ6 .5654866776

3 6 3φ6 .848#3165

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5 6 5φ6 1.4137166%41

6 6 6φ6 1.6%6463#%

7 6 7φ6 1.%7%#33718

8 6 8φ6 #.#61%46716

% 6 9φ6 #.5446%4%4

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11 6 11φ6 3.111767#71

1# 6 12φ6 3.3%#%#65%1 8 1φ8 .5#6548#46

# 8 2φ8 1.53%64%1

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6 8 6φ8 3.15%#8%474

7 8 7φ8 3.51858377#

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# 1 2φ10 1.577%63#68

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11 1 11φ10 8.63%37%7%74

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1 1# 1φ12 1.13%733553

# 1# 2φ12 #.#61%46716


155/205

3 1# 3φ12 3.3%#%#65%

4 1# 4φ12 4.5#38%34#1#

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6 1# 6φ12 6.785841318

7 1# 7φ12 7.%16813487

8 1# 8φ12 %.4778684#3

% 1# 9φ12 1.178761%8

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11 1# 11φ12 1#.4476%8

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3 16 3φ16 6.318578%4%

4 16 4φ16 8.4#4771%3#

5 16 5φ16 1.53%64%1

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% 16 9φ16 18.%5573685

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1# 16 12φ16 #4.1#743158

1 # 1φ20 3.1415%#6536

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4 # 4φ20 1#.56637614

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% # 9φ20 #8.#7433388#

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3 #5 3φ25 14.7#6#15564

4 #5 4φ25 1%.634%5485

5 #5 5φ25 #4.5436%#66

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7 #5 7φ25 34.36116%64%

8 #5 8φ25 3%.#6%%817


156/205

% #5 9φ25 44.1786466%1

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11 #5 11φ25 53.%%61#3734

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6 3# 6φ32 48.#5486315%

7 3# 7φ32 56.#%73435#

8 3# 8φ32 64.33%817546

% 3# 9φ32 7#.38##%473%

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1# 3# 12φ32 %6.5%7#63181 4 1φ40 1#.56637614

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5 4 5φ40 6#.8318537#

6 4 6φ40 75.3%8##3686

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8 4 8φ40 1.53%64%1

% 4 9φ40 113.%733553

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11 4 11φ40 138.#37676

1# 4 12φ40 15.7%644737

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1 8 # 1 1φ8+2φ10 #.734511514

1 8 3 1 1φ8+3φ10 #.85884%3148

1 8 4 1 1φ8+4φ10 3.644#47478#

1 8 5 1 1φ8+5φ10 4.4#%6456416

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3 8 4 1 3φ8+4φ10 4.64%5571#73


157/205

3 8 5 1 3φ8+5φ10 5.434%55#%7

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4 8 # 1 4φ8+2φ10 3.5814156#51

4 8 3 1 4φ8+3φ10 4.3668137885

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5 8 1 1 5φ8+1φ10 3.#%867##863

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# 1 1 1# 2φ10+1φ12 #.7176%68#1


158/205


159/205

5 1# 4 16 5φ12+4φ16 13.6%7343%7

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3 16 3 #5 3φ16+3φ25 #.7587345%

3 16 4 #5 3φ16+4φ25 #5.666811%8

3 16 5 #5 3φ16+5φ25 3.5755551


160/205

4 16 1 #5 4φ16+1φ25 1#.%51#15714

4 16 # #5 4φ16+2φ25 17.85%%54#36

4 16 3 #5 4φ16+3φ25 ##.7686%#757

4 16 4 #5 4φ16+4φ25 #7.677431#78

4 16 5 #5 4φ16+5φ25 3#.58616%7%%

5 16 1 #5 5φ16+1φ25 14.%6183513

5 16 # #5 5φ16+2φ25 1%.87573534

5 16 3 #5 5φ16+3φ25 #4.77%31#55

5 16 4 #5 5φ16+4φ25 #%.6885576

5 16 5 #5 5φ16+5φ25 34.5%678%%8

1 # 1 #5 1φ20+1φ25 8.53311748

1 # # #5 1φ20+2φ25 1#.%5%6%6%6

1 # 3 #5 1φ20+3φ25 17.86788#17

1 # 4 #5 1φ20+4φ25 ##.77654673%

1 # 5 #5 1φ20+5φ25 #7.685#85#6

# # 1 #5 2φ20+1φ25 11.1%1%#38#8# # # #5 2φ20+2φ25 16.166#35

# # 3 #5 2φ20+3φ25 #1.%4871

# # 4 #5 2φ20+4φ25 #5.%1813%3%#

# # 5 #5 2φ20+5φ25 3.8#6877%13

3 # 1 #5 3φ20+1φ25 14.33351648#

3 # # #5 3φ20+2φ25 1%.#4##553

3 # 3 #5 3φ20+3φ25 #4.15%%35#4

3 # 4 #5 3φ20+4φ25 #%.5%73#46

3 # 5 #5 3φ20+5φ25 33.%6847567

4 # 1 #5 4φ20+1φ25 17.4751%136

4 # # #5 4φ20+2φ25 ##.383847657

4 # 3 #5 4φ20+3φ25 #7.#%#586178

4 # 4 #5 4φ20+4φ25 3#.#13#46%%

4 # 5 #5 4φ20+5φ25 37.1163##1

5 # 1 #5 5φ20+1φ25 #.6167178%

5 # # #5 5φ20+2φ25 #5.5#54431

5 # 3 #5 5φ20+3φ25 3.43417883#

5 # 4 #5 5φ20+4φ25 35.34#%17353

5 # 5 #5 5φ20+5φ25 4.#516558741 #5 1 3# 1φ25+1φ32 1#.%51#15714

1 #5 # 3# 1φ25+2φ32 #.%%36%#%8

1 #5 3 3# 1φ25+3φ32 #%.361711

1 #5 4 3# 1φ25+4φ32 37.78647#%4

1 #5 5 3# 1φ25+5φ32 45.1#11#4487

# #5 1 3# 2φ25+1φ32 17.85%%54#36

# #5 # 3# 2φ25+2φ32 #5.%#4314#%


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# #5 3 3# 2φ25+3φ32 33.%44%86##

# #5 4 3# 2φ25+4φ32 41.%87385815

# #5 5 3# 2φ25+5φ32 5.#%8638

3 #5 1 3# 3φ25+1φ32 ##.7686%#757

3 #5 # 3# 3φ25+2φ32 3.81116%%5

3 #5 3 3# 3φ25+3φ32 38.853647143

3 #5 4 3# 3φ25+4φ32 46.8%61#4336

3 #5 5 3# 3φ25+5φ32 54.%386153

4 #5 1 3# 4φ25+1φ32 #7.677431#78

4 #5 # 3# 4φ25+2φ32 35.71%%8471

4 #5 3 3# 4φ25+3φ32 43.76#385665

4 #5 4 3# 4φ25+4φ32 51.8486#858

4 #5 5 3# 4φ25+5φ32 5%.8473451

5 #5 1 3# 5φ25+1φ32 3#.58616%7%%

5 #5 # 3# 5φ25+2φ32 4.6#8646%%3

5 #5 3 3# 5φ25+3φ32 48.6711#41865 #5 4 3# 5φ25+4φ32 56.7136137%

5 #5 5 3# 5φ25+5φ32 64.7567857#

1 #5 1 4 1φ25+1φ40 17.4751%136

1 #5 # 4 1φ25+2φ40 3.4147%75

1 #5 3 4 1φ25+3φ40 4#.6785364

1 #5 4 4 1φ25+4φ40 55.174##%7%

1 #5 5 4 1φ25+5φ40 67.745%15%3

# #5 1 4 2φ25+1φ40 ##.383847657

# #5 # 4 2φ25+2φ40 34.%5#18#71

# #5 3 4 2φ25+3φ40 47.516588886

# #5 4 4 2φ25+4φ40 6.8#%5%5

# #5 5 4 2φ25+5φ40 7#.64%33114

3 #5 1 4 3φ25+1φ40 #7.#%#586178

3 #5 # 4 3φ25+2φ40 3%.858%567%#

3 #5 3 4 3φ25+3φ40 5#.4#53#747

3 #5 4 4 3φ25+4φ40 64.%%16%8#1

3 #5 5 4 3φ25+5φ40 77.55868635

4 #5 1 4 4φ25+1φ40 3#.#13#46%%

4 #5 # 4 4φ25+2φ40 44.7676%53144 #5 3 4 4φ25+3φ40 57.33465%#8

4 #5 4 4 4φ25+4φ40 6%.%43654#

4 #5 5 4 4φ25+5φ40 8#.46687157

5 #5 1 4 5φ25+1φ40 37.1163##1

5 #5 # 4 5φ25+2φ40 4%.676433835

5 #5 3 4 5φ25+3φ40 6#.#4#8444%

5 #5 4 4 5φ25+4φ40 74.8%17564


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5 #5 5 4 5φ25+5φ40 87.375545678

1 3# 1 4 1φ32+1φ40 #.6884788

1 3# # 4 1φ32+2φ40 33.175#184##

1 3# 3 4 1φ32+3φ40 45.74158%36

1 3# 4 4 1φ32+4φ40 58.37%5%651

1 3# 5 4 1φ32+5φ40 7.87433#65

# 3# 1 4 2φ32+1φ40 #8.6513#51

# 3# # 4 2φ32+2φ40 41.#176%5615

# 3# 3 4 2φ32+3φ40 53.78466##%

# 3# 4 4 2φ32+4φ40 66.35436844

# 3# 5 4 2φ32+5φ40 78.%1687458

3 3# 1 4 3φ32+1φ40 36.6%38#1%4

3 3# # 4 3φ32+2φ40 4%.#617#88

3 3# 3 4 3φ32+3φ40 61.8#65434#3

3 3# 4 4 3φ32+4φ40 74.3%#%1437

3 3# 5 4 3φ32+5φ40 86.%5%#846514 3# 1 4 4φ32+1φ40 44.736#7%387

4 3# # 4 4φ32+2φ40 57.3#651

4 3# 3 4 4φ32+3φ40 6%.86%#616

4 3# 4 4 4φ32+4φ40 8#.4353%1#3

4 3# 5 4 4φ32+5φ40 %5.1761845

5 3# 1 4 5φ32+1φ40 5#.77875658

5 3# # 4 5φ32+2φ40 65.3451#71%5

5 3# 3 4 5φ32+3φ40 77.%114%78%

5 3# 4 4 5φ32+4φ40 %.4778684#3

5 3# 5 4 5φ32+5φ40 13.44#3%4

.#8#74333% 1φ6

.5#6548#5 1φ8

.565486678 2φ6

.7853%8163 1φ10.848#316 3φ61.53%64% 2φ8

1.13%73355 4φ61.13%73355 1φ121.4137166%4 5φ61.57%64474 3φ81.577%63#7 2φ101.6%64633 6φ61.%7%#337# 7φ6#.161%#%8 4φ8#.161%#%8 1φ16


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#.#61%46711 8φ6#.#61%46711 2φ12

#.3561%44%3φ10#.513#741#3 5φ8#.5446%4% 9φ6#.8#7433388 10φ6

3.15%#8%47 6φ83.111767#7 11φ63.1415%#654 4φ103.1415%#654 1φ203.3%#%#66 12φ63.3%#%#66 3φ123.51858377# 7φ83.%#6%%817 5φ104.#1#385%7 8φ84.#1#385%7 2φ164.5#38%34#1 4φ12

4.5#38%34#1 9φ84.71#388%86φ10

4.%87385#1 1φ255.#6548#46 10φ85.4%7787144 7φ10

5.5#%#3711φ85.654866776 5φ126.318578%5 12φ86.318578%5 3φ166.#8318537 8φ106.#8318537 2φ206.7858413# 6φ127.68583471 9φ107.853%81634 10φ107.%16813487 7φ128.4#4771%3 4φ168.4#4771%3 1φ328.63%37%7%7 11φ10%.4778684# 8φ12%.4#4777%61 12φ10%.4#4777%61 3φ20

%.8174774# 2φ251.53%64% 5φ161.17876#9φ12

11.3%73355 10φ121#.637157% 6φ161#.4476%1 11φ121#.5663761 4φ201#.5663761 1φ4013.57168#6 12φ12


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14.74335% 7φ1614.7#6#1556 3φ2515.77%63#7 5φ2016.84%543% 8φ1616.84%543% 2φ3218.%557368 9φ16

18.84%555%# 6φ201%.634%548 4φ25#.161%#%8 10φ16#1.%%114858 7φ20##.11681##8 11φ16#4.1#743158 12φ16#4.1#743158 3φ32#4.5436%#61 5φ25#5.13#741#3 8φ20#5.13#741#3 2φ40#8.#7433388 9φ20

#%.45#43113 6φ2531.415%#654 10φ203#.16%%877 4φ3234.36116%65 7φ2534.55751%1% 11φ2037.6%%11184 12φ2037.6%%11184 3φ403%.#6%%817 8φ254.#1#385%7 5φ3244.1786466% 9φ2548.#5486316 6φ324%.87385#1 10φ255.#6548#46 4φ4053.%%61#373 11φ2556.#%73435 7φ3258.%486##5 12φ256#.8318537 5φ4064.33%81755 8φ327#.38##%474 9φ3275.3%8##36% 6φ408.4#4771%3 10φ32

87.%645%437φ4088.467#4%13 11φ32%6.5%7#63# 12φ321.53%64% 8φ40113.%73355 9φ401#5.663761 10φ40138.#3768 11φ4015.7%64474 12φ40


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1.13%73355 1φ12#.161%#%8 1φ16#.#61%46711 2φ123.1415%#654 1φ203.3%#%#66 3φ12

4.#1#385%7 2φ164.5#38%34#1 4φ124.%87385#1 1φ255.654866776 5φ126.318578%5 3φ166.#8318537 2φ206.7858413# 6φ127.%16813487 7φ128.4#4771%3 4φ168.4#4771%3 1φ32%.4778684# 8φ12

%.4#4777%61 3φ20%.8174774# 2φ251.53%64% 5φ16

1.17876#9φ1211.3%73355 10φ121#.637157% 6φ161#.4476%1 11φ121#.5663761 4φ201#.5663761 1φ4013.57168#6 12φ1214.74335% 7φ1614.7#6#1556 3φ2515.77%63#7 5φ2016.84%543% 8φ1616.84%543% 2φ3218.%557368 9φ1618.84%555%# 6φ201%.634%548 4φ25#.161%#%8 10φ16#1.%%114858 7φ20##.11681##8 11φ16

#4.1#743158 12φ16#4.1#743158 3φ32#4.5436%#61 5φ25#5.13#741#3 8φ20#5.13#741#3 2φ40#8.#7433388 9φ20#%.45#43113 6φ2531.415%#654 10φ203#.16%%877 4φ32


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34.36116%65 7φ2534.55751%1% 11φ2037.6%%11184 12φ2037.6%%11184 3φ403%.#6%%817 8φ254.#1#385%7 5φ32

44.1786466% 9φ2548.#5486316 6φ324%.87385#1 10φ255.#6548#46 4φ4053.%%61#373 11φ2556.#%73435 7φ3258.%486##5 12φ256#.8318537 5φ4064.33%81755 8φ327#.38##%474 9φ3275.3%8##36% 6φ40

8.4#4771%3 10φ3287.%645%437φ40

88.467#4%13 11φ32%6.5%7#63# 12φ321.53%64% 8φ40113.%73355 9φ401#5.663761 10φ40138.#3768 11φ4015.7%64474 12φ40


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V@s(ar 0rmad@ra !sc"r Are")@s(ar aB@ )@s(a

F, F,;E .#8#74333% 1φ6 10φ10

F, F,;E .5#6548#5 1φ8 10φ12F, F,;E .565486678 2φ6 10φ16F, F,;E .7853%8163 1φ10 10φ20

F, F,;E .848#316 3φ6 10φ25F, F,;E 1.53%64% 2φ8 10φ32

F, F,;E 1.13%73355 4φ6 10φ40F, F,;E 1.13%73355 1φ12 10φ6

F, F,;E 1.#885#%88 1φ8+1φ10 10φ8F, F,;E 1.4137166%4 5φ6 11φ10F, F,;E 1.57%64474 3φ8 11φ12

F, F,;E 1.577%63#7 2φ10 11φ16F, F,;E 1.6336#818 1φ8+1φ12 11φ20

F, F,;E 1.6%64633 6

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Deformacion Alivianada 1d Ronald Fx