+;#&! 'e e&(!)%(. E" e&(!)% *%&(#(e e& !,"#*! &! *!3! !H#!" 3!'!" ! "! ,%0e! =!(! ;e "! +e(! /!""e ,% *%+,e(#-& ,!! %0e&e e" e(/e$% 4"#+%. A'e+( ,!! *!"*"! e" +-'"% 'e e"!(#*#'!' (e 'e0e !,"#*! e(! *!3! ! #&e7!"%( 'e 3 ,!! +e'# 3!'!"+e&e ( 'e/%+!*#-&. C0*&$ 3'("4, - $( (&!/-$(: E" e(/e$% 4"#+% (e 'e0e *!"*"! +e'#!&e "! (#3#e&e /-+"!: σ ult =
F ult A
D%&'e: σ ult
: E(/e$% 4"#+% ! !**#-& ,e,e&'#*"! e& MP!
F ult
: C!3! 'e %! e& N
A: Áe! 'e "! (e**#-& !&(7e(!" 'e "! +e(!. P!! *!"*"! e" M-'"% 'e E"!(#*#'!' ! *%+,e(#-& 'e *!'! ,%0e! !&!"#$!'! (e 'e0e e!"#$! & *!'% ;e !&!"#*e "! *!3! ) 'e/%+!*#-& 'e "! ,%0e! ;e (e !&(/%+!! e& e(/e$% ) 'e/%+!*#-& !#!. Y *!"*"! +e'#!&e "! (#3#e&e /-+"! ;e eH,e(! "! "e) 'e %%e. σ = E∗ ε
D%&'e: σ
: E(/e$% e& MP!
E: M-'"% 'e E"!(#*#'!' e& MP! ε
: De/%+!*#-& !#!
COMPRESIÓN PERPENDICULAR A LA FIBRA:
Obj!"#$: Dee+#&! e" e(/e$% ) +-'"% 'e e"!(#*#'!' ! *%+,e(#-& ,e,e&'#*"! 'e" E*!"#,%.
A'//!$(: −
M;#&! e(!" 'e e&(!)%(
−
De/%+6+e% ,!! e" *"*"% 'e "! 'e/%+!*#-& !#!
E(')*"+, - '&b/: L! ,%0e! e( & ,#(+! e*!&3"! 'e (e**#-& H *+. ) & "!3% 'e 1 *+. A'e+( 'e0e+%( +!*! "! $%&! *e&!" 'e "! ,%0e! ,!! *%"%*! "! ,"!*! "! +#(+! ;e e*#0# ) e,!# "! *!3! e& "! +e(! 'e e&(!)%. P$*-"+",!$: T%+! "!( +e'#'!( 'e" !&*=% 'e "! +!'e! ) e" "!'% ;e *%"!0%! ,!! e" e&(!)%. I&3e(! e& e" '#(,%(##7% 'e *%+,e(#-& 'e "! +;#&! 'e e&(!)%( !'e+( (e 'e0e *%"%*! & 'e/%+6+e% e& "! 0!(e 'e" *#"#&'% ,!! +e'# e" 'e(,"!$!+#e&% 'e" +#(+%. P!! *!"*"! e" +-'"% 'e e"!(#*#'!' ! *%+,e(#-& ,e,e&'#*"! 'e "! ,%0e! (e 'e0e e!"#$! & *!'% ;e e&3! "! 'e/%+!*#-& ;e 7!6! 'e ! 2. ++ *%& I&e7!"%( 'e .1 ++. A'e+( 'e "! *!3! *%& ;e (e '! e(! 'e/%+!*#-&. P!! /#&!"+e&e *!"*"! e" +-'"% 'e e"!(#*#'!' E. C0*&$ 3'("4, - $( (&!/-$(: E" e(/e$% 4"#+% (e 'e0e *!"*"! +e'#!&e "! (#3#e&e /-+"!: σ ult =
F ult A
D%&'e: σ ult
: E(/e$% 4"#+% ! !**#-& ,e,e&'#*"! e& MP!
F ult
: C!3! 'e %! e& N
A: Se**#-& !&(7e(!" 'e "! +e(!.
P!! *!"*"! e" M-'"% 'e E"!(#*#'!' ! *%+,e(#-& 'e *!'! ,%0e! !&!"#$!'! (e 'e0e e!"#$! & *!'% ;e !&!"#*e "! *!3! ) 'e/%+!*#-& 'e "! ,%0e! ;e (e !&(/%+!! e& e(/e$% ) 'e/%+!*#-& !#!. Y *!"*"! +e'#!&e "! (#3#e&e /-+"! ;e eH,e(! "! "e) 'e %%e. σ = E∗ε
D%&'e: σ
: E(/e$% e& MP!
E: M-'"% 'e E"!(#*#'!' e& MP! ε
: De/%+!*#-& !#!
IV.
RESULTADOS:
ENSAYO DE COMPRESIÓN PARALELA A LA FIBRA:
Gráfca esuerzo vs. deormaciónEnsayo de compresión paralela a la fbra 350 300 250 Probeta 1
200
Esuerzo (Kg/cm2
Probeta 2 150
Probeta 3
100 50 0 0
0.01
0.01 0.02
0.02
0.03
Deormación
E(/e$% 4"#+%: P%0e!
σ ult =
σ ult
1
2
5
F ult
5.2 3*+2
522.9 3*+2
59.?? 3*+2
51.12 3*+2
A
2. MP!
51.9 MP!
5.1 MP!
5.8 MP!
M-'"% 'e e"!(#*#'!': Se %07% "#&e!"#$!&'% "! 3/#*! e(/e$% 'e/%+!*#-& e& "! $%&! e"(#*!. Ve !&eH% N 8 P%0e! E=
1
2
5
E ,%+
σ
289 3*+2
2892 3*+2
2211 3*+2
25?9@ 3*+2
ε
2.59 GP!
2.82 GP!
2.2 GP!
2.58 GP!
ENSAYO DE COMPRESIÓN PERPENDICULAR A LA FIBRA:
Gráfca esuerzo vs. deormaciónEnsayo de compresión perpendicular a la fbra 120.000
100.000
80.000
Probeta 1 Esuerzo (Kg/cm2 60.000
Probeta 2
Probeta 3
40.000
20.000
0.000 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018
Deormación
E(/e$% 4"#+%: P%0e!
σ ult =
σ ult
1
2
5
F ult
98.?8 3*+2
92.9 3*+2
91.9 3*+2
@.9@ 3*+2
A
8.@ MP!
.2 MP!
. MP!
9.9 MP!
1
2
5
E ,%+
σ
12@2 3*+2
1?21 3*+2
1? 3*+2
19? 3*+2
ε
1.2 GP!
1.@ GP!
1.2 GP!
1.92 GP!
M-'"% 'e e"!(#*#'!': Ve !&eH% N 5 P%0e! E=
V.
ANÁLISIS Y DISCUSIÓN DE RESULTADOS:
Se34& "%( e("!'%( "! e(#(e&*#! 'e "! +!'e! ! "! *%+,e(#-& ,!!"e"! ! "! /#0! e( +!)% (e34& "! 0#0"#%3!/6! *%&("!'! e" +-'"% 'e e"!(#*#'!' ,!! "! *%+,e(#-& ,e,e&'#*"! 7!6! 'e 8.22 M,! ! . MP! 85 ! @ 3*+2 +#e&!( ;e ,!! "! *%+,e(#-& ,!!"e"! 7!6! 'e 9.?@ GP! ! 11.? GP! @ ! 12 3*+ 2. L! 7!#!*#-& e&e &e(%( e("!'%( ) "%( 'e "!( e/ee&*#!( 0#0"#%3/#*!( (e 'e0e e& 3!& ,!e ! "! ,%*! ,e*#(#-& 'e "e*! 'e" !*%!+#e&% 'e "%( e(,e*6+e&e( 'e ,e0! '!&e e" e&(!)% ,e( &% (e *e&! *%& e" (%/
VI.
−
CONCLUSIONES Y RECOMENDACIONES:
E" +-'"% 'e Y%&3 *!"*"!'% 'e "! +!'e! 'e e*!"#,% (%+e#'! ! *%+,e(#-& ,!!"e"! ! "! /#0! e( 2.58 GP! ) (%+e#'! ! *%+,e(#-& ,e,e&'#*"! e( 'e 1.92 GP!.
−
A ,!# 'e "! 3/#*! e(/e$% 7(. 'e/%+!*#-& 'e "! $%&! e"(#*! %07#+%( e" +-'"% 'e
−
e"!(#*#'!' ,!! *!'! #,% 'e *!3! ,!!"e"! ) ,e,e&'#*"! ! "! /#0! N% /e ,%(#0"e *!"*"! e" *%e/#*#e&e P%#((%& ,e( &% *%&!+%( *%& e" e;#,% 'e e&(!)% ! !**#-&.
−
Se e*%+#e&'! ;e (e !';#e! e" (%/
VII.
BIBLIOGRAFÍA:
Gee J!+e(. 212. Resistencia de Materiales. e'. M!'#': P!!&/%.
P)e" A&'e< ) Fe'#&!&' S#&3e. 18. Resistencia de Materiales. 8 e'. MKH#*%: A"/!%+e3!
A3e""e( R!+-&. Estructuras de madera: diseño y cálculo. Re*,e!'% e" 1 'e % 21 'e =,(:0%%(.3%%3"e.*%+.,e0%%(#'78Z2'NT CYCW,3PA1?W",3PA1?W';*%+,e(#%&,!!"e"!,e,e&'#*"!/#0!+!'e!W(%*e0"W% (O="MEM%1W(#3HDGD1++DIB#X*LY=EW="e(W(!XWe# PZ
=,:<<<.*%,!&.%3#&'eH.,=,e(
VIII.
ANE5OS:
A&eH% N 1. P%*e(!+#e&% 'e '!%( 'e" e&(!)% 'e *%+,e(#-& ,!!"e"! ! "! /#0!. ÁREA P 3
2
*+2
P%0e! 1 'e/ "%&3# "#&e!" ' /#&!" \ 2
3*+2
1 1 2 2 5
2 8 9 ? 1 12
*+ .5 ? .@ 8 .1 1 .12 9 .18 9 .19 9
1.92
.1
1.29
.5@
1.?
.
1.?@8
.95
1.?8
.@5
1.?58
.?5
E ]\ 3*+2 129.51 ? 1?1.?1 ? 11??1.1?? 1 129?.812 @ 159?.95 1 188@.?51 5
.1
L%&3#' #*#!" P%0e! 2 'e/ E ]\ "%&3# "#&e!" 3*+2 ' /#&!" \ .8 1. 85.988 .98 921.5 1.?@1 .@@ @@81.58 1.?8 ?
.1@8
1.?29
.15
1.?@
.?@ .9
.2?
1.@2
.18
*+ .1 .12
1.825 1592.98 5 115?.891
2
*+ .12 ? .1 .19 ? .1@ .1? ? .1 9
*+ "%&3# ' /#&!" 2 1.?@2 1.? 1.?52 1.?21 1.?12 1.?8
'e/ "#&e!" \ . 9 . @ . ? . . .1
5 8 8 9 9 @ @ ?
18 19 1? 2 22 28 29 2? 5
.1? 5 .1 @ .21 1 .22 @ .28 2 .2 8 .2@ 8 .2 9 .58 2
1.?1@
.1
1.?5
.?
1.@?
.1
1.@@5
.118
1.@?
.121
1.@89
.12@
1.@29
.15@
1.@8
.18?
1.9?
.1@1
15.89 8 19285.98 ? 1@91.911 8 [email protected] 8 1?1?1.?1? 2 1??@.95@ ? 1?@?.12 2 1?1?.1? 1@85.? 9
52
.229
1.@@8
.115 .11
.25
1.@91
.29
1.@88
.29
1.@51
.12? .158
.2??
1.@12
.188
.58
1.99
.12
.512
1.9??
.551
1.99
.55
1.98@
.51
1.9
.19 .19 .1@9 .1
125?.5? 155?.121 5 1892. 18?9.??? 12@@.@@@ ? 1@?.8@5 @ 19999.999 @ 191?.82 19@.19@ 1 1959?.2?9 8
.2 5 .21 .22 .22 8 .25 8 .28 1 .2 2 .29 1 .2? 8
1.@@ 1.@ 1.@? 1.@@9 1.@99 1.@ 1.@8? 1.@5 1.@19
.1 .1 1 .1 1 .1 1 .1 2 .1 2 .1 5 .1 5 .1 8
A&eH% N 2. P%*e(!+#e&% 'e '!%( 'e" e&(!)% 'e C%+,e(#-& ,e,e&'#*"! ! "! /#0!. ÁREA P 3
@
3*+2 *+
*+2
L%&3#' #*#!"
P%0e! 1 'e/ "%&3# "#&e!" ' /#&!" \
9.99@
.58
8.992
.@
1
15.555
.5@
8.952
.@
1
2.
.5
8.91
.?
2
29.99@
.81
8.2
.?
2
55.555
.85
8.@2
.
5
8.
.8
8.
.
5
89.99@
.89
8.8
.
8
5.555
.8?
8.22
.1
8
9.
.
8.2
.1
99.99@
.2
8.8@?
.1
@5.555
.9
8.888
.11
9
?.
.91
8.5
.12
9
?9.99@
.9?
8.522
.18
@
5.555
.@9
8.288
.1
E ]\ 3*+2 ?9.152 8 1?11.82 298.12 9 529@.@5? 9 5?8.?1 8888.8888 8 @2.895@ @ @?.? 9 928.95 95?.99 8 98.@282 2 9@.5@@ 951.58@1 91@2.?5 1
*+
P%0e! 2 'e/ "%&3# "#&e!" ' /#&!" \
E ]\ 3*+2
.2?9
8.@18
.9
119.11@ 2198.21 9 51. 9 819.982 9 8@?.2@2 5 28.?91? ? 959.595 1 @8.9@5@ 2
.5?
8.92
.9
.522
8.9@?
.9
.552
8.99?
.@
.58?
8.92
.@
.592
8.95?
.@
.5@
8.95
.@
.5@?
8.922
.?
.5?8
8.919
.?
.5??
8.912
.?
.58
8.99
.?
.82
8.?
.?
.812
8.??
.?
@?12. ?1.92 59.29 ? .28?@ 9 11@.@ 8
.819
8.?8
.?
1121@.8?@
*+
*+
"%&3#' /#&!"
.29
8.@8
.2?
8.@2
.5
8.@
.5
8.@
.52
8.9?
.55
8.9@
.58
8.99
.5
8.9
.5
8.9
.59
8.98
.5@
8.95
.5@
8.95
.5?
8.92
.5
8.91
@
1.
.?8
8.19
.1@
?
19.99@
.8
8.9
.1
?
115.555
.1@9
8.?28
.22
12.
.1222
8.?@@?
.28
1 1
129.99@
.15@?
8.?922
.2?
155.555
.19
8.?88
.5
18.
.1?
8.?82
.52
11
189.99@
.1@?8
8.?219
.59
11 12 12 15 15 18 18 1 1 19 19 1@ 1@ 1? 1? 1 1 2 2 21 21 22 22 25
15.555
.19
8.?8
.8
19.
.221?
8.@@?2
.88
199.99@
.2818
8.@?9
.8?
[email protected]
.29
8.@88
.2
1?.
.2@98
8.@259
.
1?9.99@
.259
8.@98
.
15.555
.5??
8.912
.92
2.
.528
8.9@9
.9
29.99@
.55?
8.992
.9?
215.555
.58?
8.92
.@
22.
.5918
8.95?9
.@2
229.99@
.5@22
8.92@?
.@8
255.555
.5?2
8.91?
.@9
28.
.529
8.9@8
.@
289.99@
.81
8.
.?
25.555
.812
8.??
.?2
29.
.81@
8.?5
.?5
299.99@
.822
8.@?
.?8
[email protected]
.85
8.@
.?9
2?.
.85@
8.95
.?@
2?9.99@
.8822
8.@?
.??
25.555
.88?
8.2
.
5.
.8?
8.82
.
59.99@
.89
8.888
.1
2.5? 9@5.@?? @ 299.81?? 8 8.?59 5
.829
8.@8
.
.859
8.98
.
.882
8.?
.
.89?
8.52
.
89.52 8829.@5@8 885.5@@
.8@9
8.28
.1
.8?
8.2
.1
.181
8.?
.2?
811.912?9 5?81.15 9 599.?5 2 582.? 9 555?.898 8 529.1 1 51@?.2?2 515.5@2 8 5?9.81@ 5@.12 1 58.591 8 585.@1?? @ 588.@ 1 58.112 2
.192
8.?85?
.51
.1?8
8.?19
.59
.2@2
8.@2?
.81
.259?
8.@952
.8@
.2999
8.@558
.5
.2?2
8.@1?
.9
59.891 5@.9882 2 5?@.28 511@.9 51.@9 9 51@?.28 @ 525.9915 5 5281.59? 1 52@5.? 2 [email protected]@ 2 559.25 1
11@5@.?2 12252.81 12?2.12 ? 12?2.12 ? 155.522 1 15???.??? 898.5 1 898.?59 ? 828.?12 5 5?91.5? 9 51.1881 8 52.?12@ 51?.1?9
.8
8.9
.81
8.
.82
8.?
.85
8.@
.88
8.9
.8
8.1
.@
8.85
.@9
8.28
.9
8.8
.11
8.??1
.188
8.?9
.1?@
8.?15
.215
8.@?@ .25 .29
A&eH% N 5. L#&e!"#$!*#-& 'e "! $%&! e"(#*! e& e" '#!3!+! e(/e$% 7(. 'e/%+!*#-& 'e" e&(!)% 'e *%+,e(#-& ,e,e&'#*"! ! "! /#0!.
Gráfca esuerzo vs. deormación (zona elás!icaEnsayo de compresión perpendicular a la fbra 25.000 Probeta 1
"inear (Probeta 1 Probeta 2 "inear (Probeta 2 20.000 f(x ! 19585.25x 96.08 f(x ! 12720.16x - 79.61 f(x ! 18218.62x - 97.92
15.000
Esuerzo (Kg/cm2
Probeta 3
10.000 "inear (Probeta 3 5.000
0.000 0.005
0.006
0.006
0.007
0.007
0.008
0.008
Deormación
A&eH% N 8. L#&e!"#$!*#-& 'e "! $%&! e"(#*! e& e" '#!3!+! e(/e$% 7(. 'e/%+!*#-& 'e" e&(!)% 'e *%+,e(#-& ,!!"e"! ! "! /#0!.
Gráfca esuerzo vs. deormación ("ona elás!icaEnsayo de compresión paralela a la fbra 300 250
f(x ! 24064.8x - 72.66 f(x ! 24625.46x - 134.67
200 Probeta 1 "inear (Probeta 1 Esuerzo (Kg/cm2 150
Probeta 2
"inear (Probeta 2
Probeta 3
"inear (Probeta 3
100 f(x ! 22910.74x - 128.99
50 0 0.0040
0.0060
0.0080
0.0100
0.0120
0.0140
Deormación
I5.
PANEL FOTOGRÁFICO:
F%%3!/6! N 1. F!""! 'e "%( e(,e*6+e&e( ! *%+,e(#-& ,!!"e"! ! "! /#0!
0.0160