RESISTENCIA DE MATERIALES EVALUACION A DISTANCIA 1-2015
CARLOS ALBERTO GUERRERO RUALES
UNIVERSIDAD SANTO TOMAS VICERRECTORIA DE UNIVERSIDAD ABIERTA Y ADISTANCIA
CONSTRUCCION EN ARQUITECTURA E INGENIERIA CENTRO DE ATENCION UNIVERSITARA PASTO (N) SAN FRANCISCO (P), MAYO MAYO DE 2015 RESISTENCIA DE MATERIALES EVALUACION A DISTANCIA 1-2015
CARLOS ALBERTO GUERRERO RUALES CODIGO: 21771 PRESENTA PRESEN TADO DO A: PROF! "IMMY YANDAR
UNIVERSIDAD SANTO TOMAS VICERRECTORIA DE UNIVERSIDAD ABIERTA Y ADISTANCIA
CONSTRUCCION EN ARQUITECTURA E INGENIERIA CENTRO DE ATENCION UNIVERSITARA PASTO (N) SAN FRANCISCO (P), MAYO DE 2015 TABLA DE CONTENIDO
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! 00J%'
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$! 1000*%'
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CONCLUCIONES BIBLIOGRAFIA
INTRODUCCION
E' *# #$6#*%# * %9+%4'#' +#4**4 94*#$%4'#* .# %'#4 *# %''4#$%&' $'4*&%$# *# $4'+6$$%&', '%'4 ' $6'# *#+ '$+%#+ *# +4$%#H *# $6#* .# +%4 4*%## # 4%%$# *# 4$69#$%&' * +9#$%4 *4 86 .# 9%%4 86 *# %''%# @ *# #86%$6# +#4**' %%$#$%4'+ 4# %$#* $44 +4' *4+ %%$%4+ $4' 6' #*4 '?4 '%*+ 4 9%+4+! D +# 4# + .#' +#*$%4 ' 44 6'4 '4#+ $'%$#+ +%+4+%+'$%#, '%'4 ' $6'# +6%4+ 4$'%$4+ @ %''%# 9## 86 *#+ %%$#$%4'+ 94+#' +6$6#+ +%+'+, $4' $#9#$%# +494# $6#*86% '&'4 '#6#* @ +6 949%4 9+4! E' + ##4 + 9+'# 6' +6%4 %'+%#$%&' 94 %4 *# $4'+6*# 6'+ %*%4=%$#+ $4' * 6+4 .#%'#+ 4%=%$#+ +#*$%#+ ' *#+ TIC+, 9## 4#*$ * $4'4$%%'4 *4+ +6%#'+! E+4+ +6%4+ +#*$' *4+ %'+ $4'$94+ *4+ 9%'$%9%4+ *# +=%$# @ *# $='%$# 86 +4' *#+ #%#+ 86 + '$##' * +6%4 *4+ '&'4+ +%$4+ *# #%# @ *4+ $694+, 94 #* #;&' + .#$ 6' #'=*%+%+ @ +#4**4 *# 9+' #*6#$%&' # %+#'$%# 86 '4+ 9% #86%% $4'4$%%'4+ &%$4+ +?' *#+ %'%$%4'+ *# %'4*4# $'%$# @ *# $#9#$%# +4* $%$%4+ #=%$4+ @ +%$4+ #$4 $4' *# =%$# 6;#+, &6*4+ *#+%$%# *4+ #%#*+ @ =+ 9%'$%9%4+ #=%$4+ 86 '4+ 9%' %'# *4+ +6;4+ # *4+ 86 + +4 6' #%#* $44 94 9*4 ' $4'$4, * #$4 @ *# ##! E' * +#4**4 * 9+' ##4 + %'# *# %94#'$%# *# #%# +%+'$%# #%#*+, *# $6#* '4+ .# %'#4 $4'4$%%'4+ &%$4 9=$%$4+ 9## 9*#'# @ +4*6$%4'# 94*#+ #=%$4+, #+#4+ ' *4+ 9%'$%9%4+ 6'#'#*+ *# $='%$# @ *# +=%$# ' * %+4 @ $=*$6*4 *#+ 6;#+ 86 96' #$# # 6' $694 +&*%4!
OBJETIVOS
OB"ETIVO GENERAL C4'4$ %'%%$# %#' * +6%4 +# #%#, *4+ 9%'$%9%4+ +%$4+ (+=%$# @ $='%$#) 9## %'# * $494#%'4 *#+ +6$6#+ '%'4 ' $6'# +6 4#, %94 #%#*+ ' # *4+ +6;4+ @ $##+ # *4+ $6#*+ +4' +4%#+!
OB"ETIVOS ESPECIFICOS #! C4'$96#*%;#$%&' 9+4'#* *4+ 9%'$%9%4+ +%$4+ +6*#'+ * $494#%'4 6'# +6$6# # *#+ $##+! ! C4'+6*# #%#!
%*%4=%$# 9## #9*%# @ 4#*$ * #9'%;# +#
$! R+4* *4+ 94*#+ 4# $6#'%#%# 9## 4' +6*#4+ *#+ $##+ $%#+ ' *4+ *'4+ +6$6#*+ 6'# %%$#$%&'! ! E+6%4 @ 946'%;#$%&' *#+ '4#+ +#*$%#+ ' *# NSR-10, +4 * %+4 +6$6#* %%$#$%4'+ @ 4#+ $%%*+ '%'4 ' $6'# *# +%+4+%+'$%#! ! F6'#'#$%&' %#' $4'4$%%'4+ $'%$4+ 9## ' * +94 94+%4'#* %&'4 ' * +#4**4 *4+ %'+ %94+ $4'+6$$%4'+!
DESARROLLO DE LA ACTIVIDAD
1! L# #$$%&' *#+ $##+ .#$ /###3 *4+ *'4+ +6$6#*+, #. 86 + 9+'#' +#4+ '+%4'#*+, 4 +# +6;4+! E'?'$%*4+ @ 6'# %'%$%&' +6;4!
1!1 ESFUERZOS DE CORTANTE: S4' #86**4+ 86 #$?#' 99'%$6*#+ #* *4'%6%'#* * *'4! S %' ' $6'# 86 6'# 9#$6*# + +*%;# $4' +9$4 # 4# #* + +4%# # 6' 9# 6;#+ %' %$$%&' @ +'%4 $4'#%4!
Grafica 1. Esfuerz cr!a"!e
1!2 ESFUERZOS A#IALES: S4' #86**4+ 86 #$?#' 9##**4+ #* *4'%6%'#* * *'4! D'4 +4+ %+' 4+ %94+ +6;4+ %#4+ * +'%4 * 86 + #9*%$#' *#+ 6;#+ ' *# %+# %$$%&': 1!2!1 E+6;4 C49+%&': C6#'4 4+ 6;#+ $4''+ ($49+%&') +'%4 $4'#%4 + #9*%$#' # 6' *'4 +6$6#* +4 *# %+# %$$%&' #$$#'4 # *#+ 9#$6*#+ @ '#'4 #$4#%'4 * *'4!
Grafica $. Esfuerz a c%&resi'"
1!2!2 E+6;4 T#$$%&': S # $6#'4 4+ 6;#+ %'+ +'%4 $4'#%4 + #9*%$#' # 6' *'4 +6$6#* +4 *# %+# %$$%&' #*#'4 *#+ 9#$6*#+ @ '#'4 #*##%'4 * *'4 +6$6#*!
Grafica (. Esfuerz a !racci'"
E* #6'4 ' *4'%6 946$4 * +%#%'4 %94' 6'# 6$$%&' ' * +9+4 * $694 9486 *# #%# '4 + $#! 1!2! E+6;4 F*%&': S 946$ $6#'4 6' *'4 +6$6#* + +4%4 # +6;4+ 86 %'' # $6#*4 $44 + * $#+4 6'# %# 86 +4 **# + $ +6;4+ $4#', #$$%&' @ $49+%&' #* %+4 %94 @ +# %' *# $#9#$%# #'+%% %$.4+ +6;4+ # +6+ 96'4+ #94@4! L# %# + 4# *$='4+ '#'4 +6;4+ $49+%&' @ #$4#%'4 ' +6 $## +69%4 @ +6;4+ #$$%&' @ #*##%'4 ' *# %'%4! 1
Grafica ). Esfuerz *e f+e,i'" $. TI-OS DE A-OO
1 .9+:!@466!$4#$.>9%I.9
L#+ #$$%4'+ +4 6'# +6$6# 96' + %%%#+ ' + %94+ $4'%4'+ 4 #94@4+! 2!1 F6;# $4' *'# A$$%&' C4'4$%# (A94@4+ M&%*+ 4 9% #4)! U' *'4 +6$6#* +$#'+# +4 44 #94@#4 +4 6' *'4 86 * 9% +6 #+*#$%&' @ 4#$%&' 94 %# 86 + 6# ' %$$%&' 99'%$6*# # +6 ! E' $4'$*6+%&' *4+ #94@4+ 86 4%%'#' #$$%4'+ + %94, 96' %9% * 4%%'4 ' 6'# +4*# %$$%&'! (R4%**4+, #*#'$%'+, +*#4'+ 4 %*#+)
Grafica /. Ti&s *e a&0s
2!2 F6;# #'%6 @ %$$%&' +$4'4$%# (A94@4+ A%$6*#4+)! P%' #* *'4 +6$6#* *# 4#$%&' #*4 +6 , %#'4 *# #+*#$%&' +?' +6 @ ' *# %$$%&' 99'%$6*# #* %+4H +%'' 4+ #4+ *%# E+4 86% $% 86 %9%' *# #+*#$%&' * $694 %4 ' 4#+ *#+ %$$%4'+ 94 '4 96' %9% *# 4#$%&' * %+4 (9'4+, 4%%$%4+, #%$6*#$%4'+ 4 %+##+)
Grafica . A&0s ar!icu+a*s
2! F6;# @ 9# (#94@4+ %4+ $ #4 4 94#%'4+)! I'4%*%;#' 4#*' #* *'4 +6$6#* +%'%'4 + #4+ *%#! E+#+ #$$%4'+ + 4%%'#' 94 #94@4+ %4+ *#+ $6#*+ + 494'' # $6#*86% 4%%'4 * $694 *% 94 *4 #'4 *4 +%'' 94 $49*4! 2
Grafic 2. A&0 fuerza 0 &ar
! 2 .9+:!@466!$4#$.>K'NYM*9D$
E* &6*4 *#+%$%# 6' #%#* + *# *#$%&' ' * +6;4 #* 86 += +4%4 * #%#* @ +6 4#$%&' 6'%#%#! R9+'# *# %%; * #%#* #' 6'# $## %96+# +4 * %+4! S %'# 94 %4 * $4$%' ' * +6;4 #9*%$#4 (6;# 86 $%) @ *# 4#$%&' 86 *4 946$ @ + *4 9+'# *# +%6%' 4#: M46*4 *#+%$%#
+6;4 4#$%&'
C6#'4 *# *#$%&' ' * +6;4 @ *# 4#$%&' 6'%#%# # *# 86 += +4%4 * #%#* + *%'#*, $4'+#' @ *4+ +6;4+ #9*%$#4+ '4 #*$#';#' * *% 9494$%4'#*%#, * #%#* %' 6' $494#%'4 *=+%$4 86 $69* $4' *# L@ 44J!
!1 E* &6*4 *#+%$%# ' * $4'$4! R9+'# *# %%; + #%#* #' 6'# $## %96+# +4 * %+4! E* '+#@4 9## *# %'#$%&' * &6*4 *#+%$%# +=%$4 * $4'$4 + .#$ 94 %4 *# N4# $'%$# C4*4%#'# 025 86 %' $44 #'$' *# ASTM C K @ %' $44 9%'$%9%4 *# #9*%$#$%&' $## +=%$# @ *# $4+94'%' 4#$%&' 6'%#%# 946$%#!
L# 9%# #+ + *# ;4'# *=+%$#, 4' * +6;4 @ *# 4#$%&' 6'%#%# 96' '+ #94%##' ' 0 #* 0 @ 5 *# +%+'$%# # *# $49+%&' * $4'$4 !
U'# +6'# #+, 9+'# 6'# *'# $6# $44 $4'+$6'$%# 6'# %$4%+6#$%&' 86 + 946$ ' * $4'$4 #* $%% 6'# $##, +#+ %+6#+ + 6%$#' ' *# %'#+ ##4- 9#+# @ += $49'%# ' * 5 @ K *# +%+'$%# * $4'$4!
Grafica 3. Grafica esfuerz 0 *efr%aci'"
E' *# %6# + 96 86 * %'4 &6*4 *#+%$%#, 96 #9*%$#+ +%$#' ' *# 9# $#! E' +6'4 *6#, * %'$'4 ' *# 4#$%&' 6'%#%#, %'#+ #$?# *# $## 6#' * '+#@4, + ' 9# # #*4 *#+%$%# @ ' 9# # *# *6'$%# * $4'$4, ' $4'+$6'$%# + %'# 86 * $4'$4 '4 + 6' #%#* $49*#' *=+%$4! 3
Grafica 4. Defr%aci"es u"i!arias
.9:*4!0#4+'$4'$4!$486-+-*-46*4--*#+%$%#-'-*$4'$4
!2 M&6*4 *#+%$%# *# ##! S?' *# '4# NSR-10 + # ' 4+ $#+4+! #! M&6*4 *#+%$%# *4'%6%'#* #%+%*! E+ * &6*4 *#+%$%# 6' *'4 ## %4 ' *# %$$%&' 9##**# #* #'4, 6*%9*%$#4 94 *4+ $4%$%'+ 4%%$#$%&' 86 *4 #$'! ! M&6*4 *#+%$%# '%4 *4'%6%'#* #%+%*! E+ * #'%4 46*4, **#4 #* 86%'4 9$'%*, # *%&' 96# @ %'#*' 94 6' #$4 +6%#
! M&6*4 *#+%$%# * #$4! R*#$%&' ' * +6;4 '4#* @ *# 4#$%&' 6'%#%# $4+94'%', 9## +6;4+ #$$%&' 4 $49+%&' '4+ 86 * *% 9494$%4'#*%# * #%#*!
! T'%'4 ' $6'# *# N4# S%+4+%+'$%# C4*4%#'# (NSR-10), 86 +#*$ ' +6 T6*4 C!!5!2, 86 * &6*4 *#+%$%#, Es , 9## * #$4 6;4 '4 9+4;#4 96 4#+ $44 200 000 MP#! E+ #*4 + .# %'#4 %#' '+#@4+ *#4#4%4 @ *4+ #%$#'+ + %'4# # *4+ $49#4+ %#' %$.# $'%$# * #%#*! E* &6*4 *#+%$%#, E&, 9## * #$4 9+4;#4 %'#+ %#' '+#@4+ 4 + %'4#4 94 * #%$#'!
MINISTERIO DE AMBIENTE Y DESARROLLO TERRITORIAL! 2010! R*#'4 C4*4%#'4 C4'+6$$%&' S%+4 R+%+' NSR-10! B44=: A+4$%#$%&' C4*4%#'# I''%# S+%$#, 2010! T%6*4 C-!5! P!12
5! S% 94 6'# $4*6'# += ##'4 6'# $## 50 4', %'$*6@'4 * 9+4 949%4 *# ;#9## @ *# $#9#$%# =%# * +6*4 + 10 4'2, <$6=* + * *#4 6'# ;#9## $6### 9## 86 '4 .#@# #+'#%'4> W $#9#$%# =%# * +6*4 P $## A X# %+%6$%&' $## L S$$%&' ;#9## P
WADM
A
A
P δ
! A
50 ton 10 ton
/m2
=5 m ²
L √ 5 m = 2.2 m 2
R#*%;#'4 * $=*$6*4 *# %+%6$%&' *# $## 46%4+ 86 *# ;#9## ' 6'# +$$%&' ;#9## 2!2 4+ 9## +494# 6'# $## 4#* 5Z 4'*##+ *#+ $6#*+ +4' #'+%%#+ # 6' +6*4 $4' $#9#$%# 94#' 10 4'!
! E9+ *#+ 6'%#+ ' 86 + 9+'#' $## 6'# *#+ 9+%4'+ +%6%'+ ' * +%+# %''#$%4'#*>! #! F6;# ! I'$%# V*4$%#
! E+6;4 ! X#
$! M4'4! A%#* ! $4#' .! V4*6' %! T4+%&' !
−
7! C6=* + * 4'4 %'$%# 6'# +$$%&' $#'6*# 86 %' 0!0 #'$.4 94 0!70 #*6#> #! !0 ! 0!005
! 5!0 ! 2!505
$! 1!50
E* 4'4 %'$%# + $#*$6*# # 9#% *# &6*#:
h=0.70m
I
b∗h
I
b∗h
3
12
3
12
b=0.30m 0.30∗0.7³ 4 =0.008575 m 12
! U'# ?# += *#'#'4 6'# %# $4'$4 86 %' 0!0 #'$.4H 0!0 #*4 @ 6'# *4'%6 !0, * 9+4 * $4'$4 + 2!0 4'! S% * $#* %;#4 %' %=4 1%', #! 200*%'
! 00J%'
! 25!1J$
! 251!714'
P
3m
$! 1000*%'
0.6m 0.3m
D'+%# 4 9+4 +9$%$4 * $4'$4 2! 4'! V4*! %# 0! 0! 0!5[ 0!5[ 2! 4' 1,2K 4' 1,2K4' J 12K J 2 12KJ K! m / s 12700! P#
E+6;4 T'+%&' ' * C#* E+! T'+%&'
12700.8 Pa
(
)
3.1416 x 0.5 pulg ²
1010!K P#96*
K! (%'%$# * '6#* *# '4# 86 %' #* $#+4)! T'%'4 ' $6'# *4+ +6%4+ @ '+#@4+ 9%''+ *# '4# NSR-10 + +#*$ * &6*4 *#+%$%#, E$, 9## * $4'$4 86 96 1.5 4#+ $44 w c 0.043 √ f ' c (' MP#), 9## #*4+ $ $49'%4+
' 10 @ 250 J! P## $4'$4 '+%# '4#*, Ec 96 4#+ $44
4700
√ f ' c
E$ 21M9# 4 210 J$ 1.5
wc
0.043
√ f ' c
1.5
wc
0.043 √ 21 Mpa
=0.1970
10! C#*$6*# * +6;4 # #$$%&' @ * +6;4 # $49+%&' *# %# ' * $'4 *# *6; ' #94@4+, ' * 96'4 (%) =+ #*#4 * '64, +% *# %# %' 6'# +$$%&' $6### 0!200!0
RBy
RDy
a. Su%a!ria *e fuerzas e" e+ e5e ,
\F BD0 \F RB@ ] RD@ - 20 - 0 0 6. Su%a!ria *e %%e"!s
\M -20 2!5 ] 0 RD@ 5 0 S$$%&' *# %# 0.2m 0.4m
0.2m 0.2m
0.2m
I'$%#
Y 0!2
I =
b∗h ³
I =
12
I'$%# ' * ;
Iz =
b∗h ³ 12
∗0.4³
0.2 m
12
=0.0010 m
I =
∗
0.4 0.2³ 12
c. Su%a!ria *e fuerzas e" e+ e5e 0
\F@ 0 20 ] 0 R R 0 \M 0
*. Ca+cu+a%s e+ 7a+r *e R* *e +a si8uie"!e %a"era.
4
=0.00026 m
R (-20') (2!5) ] (0') () (R) (5) 0 -50 ] 120 R 5 70 R 5 R* 9 2 ; / 9 1) <"
e. Ca+cu+a%s e+ 7a+r *e R6.
20 ] 0 R R 0 R 0 R 1 0 R6 9 = >1) 9 ) <"
14
46
! C4' *4+ #4+ 4'%4+ * $=*$6*4 *#+ $##+ 94+%4' + 94$ # #*%;# *4+ %###+ $4#' @ 4'4 #+:
-ara
*ia8ra%a
*e
-ara *ia8ra%a *e %%e"!
cr!a"!e.
F6;# *4'%6
20 ' ' 2'
20' 2!5 50'
2 ' 0' 1'
2' 2!5 5' 2' 7' 1' 2 2'
Grafica 1. Dia8ra%a *e cr!a"!e 0 %%e"!
C6#'4 + %' $##+ 96'6#*+ ' * %### $4#' *#+ =%$#+ + 9+'#' ' $='6*4+! Y $6#'4 *#+ $##+ +4' %+%6%#+ *#+ =%$#+ ' * %### 4# %='6*4+ E%+' #%4+ 44+ 9## '$4'# *4+ #*4+ *#+ $##+ 9## #%$# * %### 4'4H * #'%4 4 94 * +%6%' 86 + 94 %4 *# +!
3m 78 Kn
=
2.5 m
y
→ Y =
78 Kn x 2.5 m 3m
=65 Kn∗m
! C#*$6*4 * +6;4 (%''4) =%4 $49+%&'!
P## +
9#=4 + %' ' $6'# *# +$$%&' *# %#! σ max
∗
65 0.2
Kn∗m 0.2m =13000 C 0.001 0.4m EN 0.2m T 0.2m
E* +6;4 %''4 $49+%&' + 1000' .! C#*$6*4 *# %'$%# 3
Iy =
bh
12
=
∗h
0.20 m 12
3
= 0.0010 m
4
˃
C#*$6*4 *# %'$%# 3
Iz=
bh
12
=
3
∗h
0.20 m 12
=0.00026 m
4
˂
S #'+4# *#+ 6'%#+ # M9#! 13000
Kn 13000 Kn / m ² = =13 Mpa → Mpa ² 1000 m
CONCLUCIONES
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