UNIVERSIDAD CENTRAL DE VENEZUELA FACULTAD DE INGENIERÍA ESCUELA DE INGENIERÍA CIVIL DEPARTAMENTO DE INGENIERÍA ESTRUCTURAL INSTITUTO DE MATERIALES Y MODELOS ESTRUCTURALES (IMME) TECNOLOGÍA DEL CONCRETO (1162)
PRACTICA N°8: CONCRETO ENDURECIDO
Prof.: I!. N"#$o C%&%'o
C%r%'%$ 2*1+
RESUMEN L% $,!-,"" /r0','% ,"" 'o&o /ro/$,o "# " 'o&/ro3%r #% r"$,$"',% " '%% -% " #%$ /ro3"%$ " 'o'r"o /or &",o " "$%4o$ % 'o&/r"$, 4 f#"5, /%r% %$ 'o&/%r%r#%$ 'o #%$ r"$,$"',%$ %"r,or&"" '%#'-#%%$ " &%"r% %%#,'%. A"&0$ ,"" "# f, " 'oo'"r "# &-#o " ro-r% 7-" -8o '%% /ro3"% 4 "&o$r%r % #o$ "$-,%"$ '&o $" r"%#,9% '%% "$%4o. L%$ &"9'#%$ " #%$ /ro3"%$ " 'o'r"o f-"ro #%$ "5r%%$ " #% /r0','% %"r,or " o" $" "$-, "# 'o&/or%&,"o "# 'o'r"o fr"$'o. T","o " #% &"9'#% : '-%ro ',#,ro$ " 6; o$ ',#,ro$ " <; 4 -% 8,!% " *51*51*= " #% &"9'#% >: '-%ro ',#,ro$ " 6; 4 o$ 8,!%$ " ,!-%# &%!,- 7-" #% %"r,or. S" r"%#,9%ro "$%4o$ % 'o&/r"$, % #%$ $,!-,""$ /ro3"%$: ?
Do$ ',# ',#, ,r ro$ o$ " " 6; ," ," ,f ,f,' ,'% %o$ o$ 'o&o 'o&o M 1 M 4 M>< M>> #o$ o$ ',#, ',#, ro ro$$ " <; " #% &"9' &"9'#% #% "$"$-8, 8,"r "ro o "5/"5/-"$ "$o o$$ % "$% "$%4o 4o$$ % 'o&/r"$, ,",f,'%o$ 'o&o M 1 4 M2 r"$/"',8%&"".
S" r"%#,9%ro "$%4o$ % r%'', ,,r"'% ("$%4o 3r%$,#"@o) % #%$ $,!-,""$ /ro3"%$: ?
A# ',#, ',#, ro ro r"$ r"$% %" " " 6; " %&3% %&3%$$ &"9'# &"9'#%$ %$ $" #" r"%# r"%#,9 ,9o o - "$%4 "$%4o o% r%'', ,,r"'% ("$%4o r%$,#"ro).
S" r"%#,9%ro "$%4o$ /or f#"5, % #%$ 8,!%$ " *51*51* " %&3%$ &"9'#%$. R"%#,9%o -% 'o&/%r%', " !""r%# "r" #o$ "$%4o$ $" /-o 'o'#-,r 7-" #%$ /ro3" /ro3"%$ %$ 7-" $o/or $o/or%ro %ro -% &%4or &%4or r"$,$ r"$,$"' "',% ,% f-"ro f-"ro #%$ 7-" $" "'o "'or%3 r%3% % 'ofor&%%$ /or #% &"9'#% 4% 7-" "$%$ $o #%$ 7-" "% -% r"#%', %!-%B'"&"o &"or " $"&"%9% % #% " #% &"9'#% >.
ÍNDICE INTRODUCCIN............................................................................................................................... < OETIVOS....................................................................................................................................... > O3",8o$ G""r%#"$....................................................................................................................... > O3",8o$ E$/"'f,'o$..................................................................................................................... > MARCO TERICO............................................................................................................................. 6 Fr%!-%o "# 'o'r"o....................................................................................................................6 E$%o "-r"',o......................................................................................................................... 6 R"$,$"',% 4 -r%3,#,%................................................................................................................ 6 L% r"$,$"',% 4 #% -r%3,#,% $o %f"'%%$ /or:..........................................................................+ Pro/,"%"$ f$,'%$ 4 7-&,'%$...................................................................................................... + D"$,%.................................................................................................................................... + R"$,$"',%................................................................................................................................. + V%r,%',o"$ " 8o#-&" 4 " #%$ f,$-r%$..................................................................................... D-r%3,#,%................................................................................................................................. I&/"r&"%3,#,%......................................................................................................................... Pr-"3%$ " '%#,% '#%$,f,'%', $"! $- %-r%#"9%................................................................... D"$r-',8%$:............................................................................................................................... H No "$r-',8%$:.......................................................................................................................... H Pro'",&,"o " &-"$r"o............................................................................................................ H Pr-"3% " 'o&/r"$,............................................................................................................... H Pr-"3% " f#"5,......................................................................................................................1* T,/o$ " f%##% 7-" $" /-"" /r"$"%r #-"!o " #o$ "$%4o$.....................................................11 METODOLOGÍA...............................................................................................................................12 Moo /%r% #% "#%3or%', '-r%o 4 "$%4o % 'o&/r"$, " ',#,ro$ " 'o'r"o.................12 Moo " "$%4o /%r% ""r&,%r "# &o-#o " "#%$,',% ($"'%") " /ro3"%$ ',#r,'%$ " 'o'r"o........................................................................................................................................ 1 Moo " "$%4o /%r% ""r&,%r #% r"$,$"',% % #% r%'', ,,r"'% "# 'o'r"o -$%o /ro3"%$ ',#r,'%$:......................................................................................................................1< Moo " "$%4o /%r% ""r&,%r r"$,$"',% % #% f#"5, " #%$ 8,!%$ $,&/#"&"" %/o4%%$ 1> Moo " "$%4o /%r% ""r&,%r #% r"$,$"',% % #% 'o&/r"$, "# 'o'r"o -$%o /or',o"$ " 8,!%$ ro%$ /or f#"5,..............................................................................................................16 DATOS CJLCULOS Y RESULTADOS............................................................................................ 1+ D%o$:........................................................................................................................................... 1+ T%3#% NK 1................................................................................................................................. 1+ T%3#% NK 2................................................................................................................................. 1 C0#'-#o$ 4 R"$-#%o$:................................................................................................................. 1 1. P"$o /or -,% "# 8o#-&" "# 'o'r"o "$%4%o......................................................1 T%3#% NK ................................................................................................................................. 1H
T%3#% NK <................................................................................................................................. 2* 2. E$%4o " r"$,$"',% % #% 'o&/r"$, "# 'o'r"o.......................................................2* T%3#% NK >................................................................................................................................. 21 . E$%4o " /ro3"%$ ',#r,'%$ " 6; % r%'', ,,r"'% (RASILEO) $"! Nor&% COVENIN <1?1H+H................................................................................................................. 21 T%3#% NK6.................................................................................................................................. 22 <. E$%4o " r%'', /or f#"5, " 8,!%$ $"! #% Nor&% COVENIN <?1H+H................22 T%3#% NK+.................................................................................................................................. 22 >. E$%4o " 'o&/r"$, " 'o'r"o -$%o /or',o"$ " 8,!%$ ro%$/or f#"5, $"! #% Nor&% COVENIN >*?+H......................................................................................................... 2 T%3#% NK.................................................................................................................................. 2 6. Co&/%r%', "# /"$o -,%r,o 4 #% r"$,$"',% " #%$ &"9'#%$ 4 >...........................2 T%3#% NKH ................................................................................................................................. 2< ANJLISIS DE RESULTADOS.......................................................................................................... 2< CONCLUSIONES............................................................................................................................. 2> ILIOGRAFÍA................................................................................................................................ 26
INTRODUCCIÓN E# Co'r"o "-r"',o "$ %7-"# 7-" r%$ "# /ro'"$o " ,r%%', % /%$%o "# "$%o /#0$,'o %# "$%o r!,o "$o 7-,"r" "',r 7-" '-4o ,"&/o " "#%3or%', % $o3r"/%$%o "# ,"&/o " fr%!-%o 4 " 'o$"'-"',% $" "'-"r% " "$%o r!,o. E# 'o'r"o "-r"',o "3" /o$""r #% r"$,$"',% 4 -r%3,#,% "$"%%= 4 "# 'o$o "# /ro-'o r"$-#%" "3" $"r "# &,&o 'o&/%,3#" 'o '%#,% "$"%%. E# 'o'r"o 'o&o &%"r,%# "$r-'-r%# $" ,$"@% /%r% 7-" "!% -% ""r&,%% r"$,$"',%. L% r"$,$"',% % #% 'o&/r"$, $,&/#" "$ #% '%r%'"r$,'% &"'0,'% &0$ ,&/or%" " - 'o'r"o 4 $" -,#,9% or&%#&"" /%r% -9!%r $- '%#,%. S" % "$%3#"',o -% 'orr"#%', "r" #% r"$,$"',% % #% 'o&/r"$, 4 #% r"$,$"',% % #% f#"5, " - ""r&,%o 'o'r"o. E #% /r"$"" /r0','% $" "$-,%r0 "$% "%/% f,%# "# 'o'r"o 'o "# f, " '-&/#,r 'o #o$ o3",8o$ /%-%o$ /%r% "$% %',8,% &",%" /r-"3%$ "5/"r,&"%#"$ -$%o ,$,%$ /ro3"%$ /r"8,%&"" "#%3or%%$ " #%$ 7-" $" !""r" #o$ ,/o$ &0$ 'o&-"$ " $o#,',%',o"$ ('o&/r"$, f#"5o?r%'', 4 r%'', ,,r"'%) $"! #o$ &oo$ "$/"',f,'%o$ " #%$ or&%$ COVENIN338, COVENIN 1468, COVENIN 341 y COVENIN 342 .
OBJETIVOS
Objetivos Gee!"#es •
V"r,f,'%r #% r"$,$"',% % 'o&/r"$, " #%$ /ro3"%$ ',#r,'%$ " #%$ &"9'#%$ N 4 N > "# 'o'r"o "#%3or%o " #% /r0','% " 'o'r"o fr"$'o 4 ""r&,%r #% r%'', 4 "# &-#o " "#%$,',% "# 'o'r"o.
Objetivos Es$e%&'i%os •
D""r&,%r "# /"$o /or -,% " 8o#-&" "# 'o'r"o " #%$ /ro3"%$ " #%$ &"9'#%$ N Y N > 'o %0#,$,$ "$%$,'o.
•
Co&/%r%r #o$ r"$-#%o$ " #%$ r"$,$"',%$ (%o % r%'', 'o&o % 'o&/r"$,) o3",o$ " #o$ "$%4o$ (%0#,$,$ "$%$,'o) 'o #%$ '%#'-#%%$ "r,'%&"".
•
E#%3or%r -% !r%f,'% "$f-"r9o ? "for&%', -,%r,% "# 'o'r"o %/#,'%o #% or&% COVENIN 1<6.
MARCO TEÓRICO (!")*"+o +e# %o%!eto U% 8"9 7-" "# '"&"o 4 "# %!-% "r% " 'o%'o $" ,,',% -% r"%'', 7-&,'% 7-" ""r&,% "# /%-#%,o "-r"',&,"o " #% &"9'#%= &,"r%$ "5,$% %!-% " 'o%'o 'o "# '"&"o /ro!r"$% "# "-r"',&,"o "# 'o'r"o. A"$ " $- o%# "-r"',&,"o #% &"9'#% "5/"r,&"% o$ "%/%$ "ro " $- /ro'"$o !""r%# 7-" $o: "# fr%!-%o ,,',%# 4 "# fr%!-%o f,%#. E# /r,&"ro 'orr"$/o" '-%o #% &"9'#% /,"r" $/#%$,',% 8o#8,o$" ,f',#&"" r%3%%3#". Cofor&" #% &"9'#% 'o,-% "-r"',"o "$% ##"!%r0 % $- $"!-% "%/% %#'%9%o -% -r"9% % %/r"',%3#" 7-" #% &"9'#% "r% 4% " $- fr%!-%o f,%#. Co'r"o "-r"',o: "$ %7-"# 7-" r%$ "# /ro'"$o " ,r%%', % /%$%o "# "$%o /#0$,'o %# "$%o r!,o.
Est"+o e+*!e%i+o D"$/-$ " 7-" "# 'o'r"o % fr%!-%o "&/,"9% % !%%r r"$,$"',% 4 "-r"'". L%$ /ro/,"%"$ "# 'o'r"o "-r"',o $o r"$,$"',% 4 -r%3,#,% "# 'o'r"o "-r"',o o "r0 -"##%$ " /,$%%$ $, $" '%&,% $o3r" #.
Resiste%i" , +*!"bi#i+"+ E# 'o'r"o 3," "'o "$ - &%"r,%# %-r%#&"" r"$,$"" 4 -r%3#". E$ "$o r%9o%3#"&"" ,&/"r&"%3#" %# %!-% '%/%9 " r"$,$,r '%&3,o$ " "&/"r%-r% %$ 'o&o %&3, r"$,$,r "$!%$" /or #% ,"&/"r,". L% r"$,$"',% 4 #% -r%3,#,% $o %f"'%%$ /or #% "$,% "# 'o'r"o 4% 7-" '-%o "# 'o'r"o "$ &0$ "$o "$ &0$ ,&/"r&"%3#" %# %!-%. L% -r%3,#,% "# 'o'r"o $" ,'r"&"% 'o #% r"$,$"',% $,"o &",% "$% " "# "$%o "-r"',o 7-" !""r%#&"" 8,"" %o /or #% r"$,$"',% % #% 'o&/r"$, -$%o #% /r-"3% " r"$,$"',% % #% 'o&/r"$,.
-" !esiste%i" , #" +*!"bi#i+"+ so "'e%t"+"s $o!: •
L% 'o&/%'%',. S,!,f,'% r"&o8"r "# %,r" "# 'o'r"o. L% 'o&/%'%', %/ro/,%% % 'o&o r"$-#%o - 'o'r"o 'o -% "$,% ,'r"&"%% 7-" "$ &0$ r"$,$"" 4 &0$ -r%3#".
•
C-r%o. C-r%r "# 'o'r"o $,!,f,'% &%""r &"o "# 'o'r"o /or - /"r,oo " ,"&/o /%r% /"r&,,r 7-" %#'%'" #% r"$,$"',% &05,&%. U &%4or ,"&/o " '-r%o %r0 - 'o'r"o &0$ -r%3#".
•
C#,&%. U '#,&% &0$ '%#-ro$o %r0 7-" "# 'o'r"o "!% - &%4or r"$,$"',% "&/r%%.
P!o$ie+"+es '&si%"s , .*&/i%"s Densidad
L% "$,% "# 'o'r"o $" "f," 'o&o "# /"$o /or -,% " 8o#-&". D"/"" " #% "$,% r"%# 4 " #% /ro/or', " 7-" /%r,',/% '%% -o " #o$ ,f"r""$ &%"r,%#"$ 'o$,-4""$ "# 'o'r"o. P%r% #o$ 'o'r"o$ 'o8"',o%#"$ for&%o$ /or &%"r,%#"$ !r%-#%r"$ /ro8",""$ " ro'%$ o &,"r%#,9%%$ " #% 'or"9% "rr"$r" $8%#or o$',#% "r" 2.> 4 2.>> !.B&. Resistencia
L% r"$,$"',% "$ -% " #%$ /ro/,"%"$ &0$ ,&/or%"$ "# 'o'r"o /r,',/%#&"" '-%o $" #" -,#,9% 'o f,"$ "$r-'-r%#"$. E# 'o'r"o " $- '%#,% " 'o$,-4"" " - "#"&"o "$r-'-r%# 7-"% $o&",o % #%$ "$,o"$ "r,8%%$ " #%$ $o#,',%',o"$ 7-" %'% $o3r" $". Variaciones de volumen y de las fisuras
E# 'o'r"o "5/"r,&"% 8%r,%',o"$ " 8o#-&" ,#%%',o"$ o 'or%'',o"$ -r%" o% $- 8,% ,# /or '%-$%$ f$,'o?7-&,'%$. E# ,/o 4 &%!,- " "$%$ 8%r,%',o"$ "$0 %f"'%o$ " for&% ,&/or%" /or #%$ 'o,',o"$ %&3,"%#"$ "5,$""$ " -&"% 4 "&/"r%-r% 4 %&3, /or #o$ 'o&/o""$ /r"$""$ " #% %&$f"r%.
Durabilidad
Co&o 4% $" % ,,'%o - 'o'r"o $"r0 3-"o $, "$ -r%3#". L% -r%3,#,% "5/r"$% #% r"$,$"',% %# &",o%&3,"". L% ,&/"r&"%3,#,% #% '-%# "$0 ,r"'%&"" r"#%',o%% 'o #% -r%3,#,% $" 'o$,!-" 'o #% 'o$o#,%', r"#%', %!-%?'"&"o %"'-%% 4 '-r%o 'o8","" $"! "# #-!%r o" $" "'-"r" #% o3r%. E# "$%4o " r"$,$"',% "$ "# &0$ 'o& " #o$ %/#,'%o$ %# 'o'r"o 4 'o$,-4" - ,'" " $'%#,%. L% r"$,$"',% f,%# "# 'o'r"o "$ f-', " #% r"#%', %!-%?'"&"o "# /ro'"$o " ,r%%', "# '"&"o "# '-r%o " #%$ 'o,',o"$ %&3,"%#"$ 4 " #% "% "# 'o'r"o. L% -r%3,#,% "5/r"$% "# 'o&/or%&,"o "# &%"r,%# /%r% o/o"r$" % #% %'', %!r"$,8% "# &",o %&3,"" - oro$ f%'or"$ 'o&o "# "$!%$" %$"!-r%o $- ,"!r,% 4 #% " #%$ %r&%-r%$ " r"f-"r9o -r%" "# /"roo " 'o$r-'', 4 "$/-$ % #o #%r!o " o% #% 8,% " $"r8,',o " #% "$r-'-r%. Impermeabilidad
E$ -% '%r%'"r$,'% "$r"'%&"" #,!%% % #% -r%3,#,% 4 #% 7-" &0$ 'o#%3or% 'o $%. L% ,&/"r&"%3,#,% "$ "# r"$-#%o " ,$/o"r " - 'o'r"o 'o&/%'o 4 -,for&" 'o #% $-f,',"" '%,% " '"&"o %!r"!%o$ " 3-"% '%#,% 4 !r%-#o&"r% 'o,-% o$,f,'%', r%',o%# r"#%', %!-%B'"&"o #o &0$ 3%% /o$,3#" "ro " #%$ 'o,',o"$ " o3r% /%r% /"r&,,r - "5'"#"" ##"%o " "'ofr%o$ 4 r"'-3r,&,"o " %r&%-r% "#,&,%o o% /o$,3,#,% " 7-" 7-"" " #% &%$% 3o#$o"$ " %,r" % f, " ,&/",r 7-" ,!r"$" % #% &%$% "# 'o'r"o #o$ "#"&"o$ %!r"$,8o$.
P!*eb"s +e %"#i+"+ %#"si'i%"%i0 se)1 s* "t*!"#e2" Destructivas: ""r&,% #% r"$,$"',% &",%" #% ro-r% " /ro3"%$ o /,"9%$ "
'o'r"o. L%$ /r-"3%$ "$r-',8%$ 7-" 'o&&"" $" -,#,9% $o: Pr-"3% % #% 'o&/r"$, $,&/#" /r-"3% " f#"5, /r-"3% " "$,. No destructivas: ""r&,% #% '%#,% $, "$r-,r #% "$r-'-r%. L%$ /r-"3%$ o
"$r-',8%$ &0$ 'o&-"$ ""&o$= /r-"3% "# &%r,##o " r"3o" ("$'#"r&"ro) /r-"3% " r"$,$"',% % #% /""r%', (/,$o#% " ,$or) /r-"3% " /-#$o-#r%$,'o /r-"3%$
,0&,'%$ o " 8,3r%', 4 /r-"3% " "5r%'', " 'or%9o"$ "$% #,&% %#!-o$ %-or"$ #% 'o$,"r% 'o&o /r-"3% $"&,"$r-',8%.
P!o%e+i/ieto +e /*est!eo Prueba de compresión
P%r% -% /r-"3% " r"$,$"',% $" "'"$,% /r"/%r%r 'o&o &,&o o$ ',#,ro$ "$0%r " -% &-"$r% " 'o'r"o.
M*est!eo P%r% 7-" "# &-"$r"o $"% r"/r"$"%,8o "3"r"&o$ o&%r /or',o"$ " ,f"r""$ /-o$ " #% &"9'#% % &-"$r"%r. L% &-"$r% "3"r0 $"r r%$/or%% %# #-!%r o" $" 8% % /r"/%r%r #o$ ',#,ro$ 4 #-"!o $" 8o#8"r0 % &"9'#%r 'o -% /%#% /%r% %$"!-r%r $-,for&,%.
Mo#+es Lo$ &o#"$ /%r% /o"r 'o#%r #o$ "$/"'&""$ ',#r,'o$ /%r% /r-"3%$ " r"$,$"',% % #% 'o&/r"$, "3"r0 "$%r 'o$r-,o$ % 3%$" " &%"r,%#"$ o %3$or3""$ 4 $"r #o $-f,',""&"" r!,o$ /%r% o "for&%r$". A"&0$ "3"r0 $"r ,&/"r&"%3#"$.
E#"bo!"%i0 +e #"s $!obet"s Lo$ &o#"$ "3"r0 'o#o'%r$" $o3r" -% 3%$" #,$% 4 r!,% &"0#,'% " /r"f"r"',% /%r% #o!r%r 7-" #% 3%$" "# ',#,ro " 'o'r"o $"% "r$% 4 "8,%r 7-" $" o3"!% -% $-/"rf,'," '-r8%. E# 'o'r"o $" "3"r0 'o&/%'%r /"rf"'%&"" "ro "# &o#" ',#r,'o. L% &"or for&% /%r% #o!r%r "$o "$ 'o#o'%o #% &-"$r% " 'o'r"o " "# &o#" " r"$ '%/%$ "# &,$&o 8o#-&" %/ro5,&%%&"". E$o "3" %'"r$" 'o - '-'%r " %# &%"r% 7-" $" #o!r" -% ,$r,3-', -,for&". C%% '%/% "3"r0 8%r,##%r$" 'o 2> !o#/"$ 'o -% 8%r,##% " >B; 4 /-% " for&% " 3%#%. Lo$ !o#/"$ $" "3"r0 ,$r,3-,r -,for&"&"" " o% #% $"'', r%$8"r$%# "# &o#" " ,ro-',r #% 8%r,##% %$% %/"%$ /""r%r #% '%/% ,f"r,or 2 '&. E# 8%r,##%o o "3"r0 %3o##%r , "for&%r #% /#%'% &"0#,'% "# foo
C*!"+o +e #"s $!obet"s +e $!*eb" S" "3"r0 '-r%r % -% "&/"r%-r% " 16 % 1+ C -r%" 2< or%$ " "# $,,o " #% o3r%. Po$"r,or&"" $" r%$/or%r0 %# #%3or%or,o $" "5r%"r0 " #o$ &o#"$ 4 $" %#&%'"%r0 " 'o,',o"$ 'oro#%%$ " #%3or%or,o % -% "&/"r%-r% " 2 Q 2C 4 -&"% r"#%,8% " &,&o "# H>
Prueba de flexión
E$% /r-"3% $" -$% /%r% ""r&,%r #% r"$,$"',% % #% f#"5, "# 'o'r"o "&/#"%o -% 8,!% $,&/#"&"" %/o4%% 'o '%r!% " #o$ "r',o$ "# '#%ro.
P!o%e+i/ieto L% /ro3"% " "$%4o $"r0 !,r%o $o3r" -o " $-$ #%o$ r"$/"'o % #% /o$,', " 7-" f-" 'o#%o 4 '"r%o $o3r" #o$ %/o4o$. Lo$ ,$/o$,,8o$ " %/#,'%', " '%r!% $" /or0 " 'o%'o 'o #% $-/"rf,'," " #% /ro3"% " #o$ "r',o$ "# '#%ro "r" #o$ %/o4o$. S, o $" #o!r% - 'o%'o 'o&/#"o "r" #% /ro3"% #o$ ,$/o$,,8o$ " %/#,'%', " #% '%r!% 4 #o$ %/o4o$ #%$ $-/"rf,',"$ " 'o%'o $"r0 '%3"'"%%$ /-#,%$ o '%#9%%$ 'o ,r%$ " /,"# " oo "# %'o " #% /ro3"%. L% '%r!% $" %/#,'%r0 r0/,%&"" %$% %#'%9%r "# >* %/ro5,&%%&"" "# 8%#or " r-/-r%. D"$/-$ #% 8"#o',% " %/#,'%', $"r0 -,for&" " %# &%"r% 7-" #o$ ,'r"&"o$ "# "$f-"r9o " #%$ f,3r%$ "5r"&%$ " #% /ro3"% o "5'"% " 1*!B'&2 /or &,-o. D"$/-$ "# "$%4o $" &",r0 " #% $"'', " f%##% "# %'o 4 "# /"r%#" /ro&",o " #% /ro3"% %/ro5,&%o #%$ #"'-r%$ %# &,#&"ro.
M3to+o +e# es%#e!0/et!o4 E# "$'#"r&"ro o &%r,##o " S'&, "$ " "$"',% - &",or " #% -r"9% " #% $-/"rf,'," 7-" 'o$,-4" - &",o r0/,o 4 $,&/#" /%r% r"8,$%r #% -,for&,% "# 'o'r"o. M," "# r"3o" " - &3o#o '%r!%o 'o - r"$or" "$/-$ " %3"r !o#/"%o -% $-/"rf,'," /#%% " 'o'r"o. L% #"'-r% "# &"ro " r"3o" % -% ,,'%', " #% r"$,$"',% % 'o&/r"$, "# 'o'r"o. Lo$ r"$-#%o$ " #% /r-"3% 'o "$'#"r&"ro $" 8" %f"'%o$ /or #% #,$-r% " #% $-/"rf,'," "# %&%@o for&% 4 r,!,"9 "# "$/',&"= #% "% 4 'o,', " -&"% "# 'o'r"o= "# ,/o " %!r"!%o !r-"$o= 4 #% '%r3o%%', " #% $-/"rf,'," "# 'o'r"o. C-%o $" r"'oo'" "$%$ #,&,%',o"$ 4 "# "$'#"r&"ro $" '%#,3r% /%r% #o$ &%"r,%#"$ /%r,'-#%r"$ 7-" $" -,#,'" " "# 'o'r"o "o'"$ "$" ,$r-&"o /-"" $"r ,# /%r% ""r&,%r #% r"$,$"',% % #% 'o&/r"$, r"#%,8% 4 #% -,for&,% "# 'o'r"o " #% "$r-'-r%.
M3to+o +e $eet!"%i04 Co&o "# "$'#"r&"ro "$ 30$,'%&"" - /ro3%or " -r"9% 7-" 3r,% - &",o r0/,o /%r% ""r&,%r #% r"$,$"',% r"#%,8% "# 'o'r"o. E# "7-,/o 'o$,$" "
-% /,$o#% %'',o%% 'o /#8or% 7-" '#%8% -% $o% " %#"%', %'"r%% (%!-%) "ro "# 'o'r"o. S" &," #% #o!,- "5/-"$% " #% $o% 4 $" r"#%',o% 'o #% r"$,$"',% % 'o&/r"$, "# 'o'r"o /or &",o " -% %3#% " '%#,3r%',. T%o "# "$'#"r&"ro 'o&o "# $o"o " /""r%', %@% #% $-/"rf,'," "# 'o'r"o " ',"ro !r%o. E# "$'#"r&"ro /ro-'" -% /"7-"@% &-"$'% $o3r" #% $-/"rf,',"= 4 "# $o"o " /""r%', "% - %!-"ro /"7-"@o 4 /-"" '%-$%r %!r,"%&,"o$ #"8"$.
P!*eb"s +i5/i%"s o +e vib!"%i04 U% /r-"3% ,0&,'% o " 8,3r%', (8"#o',% " /-#$o) $" 3%$% " "# /r,',/,o " 7-" #% 8"#o',% "# $o,o " - $#,o $" /-"" &",r: 1) ""r&,%o #% fr"'-"',% r"$o%" " - "$/',&" 2) r"!,$r%o "# ,"&/o " r"'orr,o " /-#$o$ 'oro$ " 8,3r%', % r%8$ " -% &-"$r%. L%$ 8"#o',%"$ "#"8%%$ ,,'% 7-" "# 'o'r"o "$ " 3-"% '%#,% 4 #%$ 8"#o',%"$ 3%%$ ,,'% #o 'or%r,o.
Ti$os +e '"##" .*e se $*e+e $!eset"! #*e)o +e #os es",os
(i)*!"4 6 D,%!r%&% "$7-"&0,'o " #o$ /%ro"$ /,'o$ " fr%'-r%
METODO-OGÍA M3to+o $"!" #" e#"bo!"%i07 %*!"+o , es",o " %o/$!esi0 +e %i#i+!os +e %o%!eto Co&o #o ,'" #% or&% COVENIN "# &oo " "$%4o 7-" -% 8"9 /r"/%r%% #% &-"$r% 'o -% "% /r"8,$% /%r% "# "$%4o $" ##"8% % '%3o "# /ro'",&,"o: •
Lo$ ',#,ro$ $" 'o#o'% " #% &07-,% " "$%4o (/r"$% ,r0-#,'%) $" '"r% '-,%o$%&"" 4 $" 'o&/r,&". T%o #%$ $-/"rf,',"$ r"&%%%$ " #o$ ',#,ro$ 4 #o$ /#%o$ " #% &07-,% "3" "$%r "5"o$ " /o#8o !r%$% 4 " '-%#7-,"r oro
•
&%"r,%# "5r%@o 4 "3" "$%r ,8"#%o. E "# '%$o " #%$ &07-,%$ " ,/o &"'0,'o "# "$/#%9%&,"o "# '%3"9%# "3" $"r %/ro5,&%%&"" " 1 && /or &,-o= " #%$ &07-,%$ o/"r%%$ ,r0-#,'%&"" $" %/#,'%r0 -% /r"$, > % -% %$% 'o$%" "ro "# r%!o " 1< !B'&2B$"! % > !B'&2B$"!. D-r%" #% %/#,'%', " #% /r,&"r% &,% "
•
#% /r"$, $" /"r&," ,'r"&"%r ,'% %$%. L% r"$,$"',% % 'o&/r"$, " '%% ',#,ro $" '%#'-#% /or #% $,!-,"" fr&-#%:
R% P9A Do+e: R' R"$,$"',% % 'o&/r"$, !fB'&2 P C%r!% &05,&% %/#,'%% !f A Jr"% " #% $"'', r%$8"r$%# "# ',#,ro '&2 L% r"$,$"',% % 'o&/r"$, " '%% ',#,ro "$ "# 'o',"" "r" #% '%r!% &05,&% 4 "# 0r"% " #% $"'', &",% "# ',#,ro. E# r"$-#%o "# "$%4o "$ "# /ro&",o " #%$ r"$,$"',%$ " #o$ ',#,ro$ /or '%% 'o,', " "$%4o. •
L% "$8,%', "$0%r &05,&% " #o$ "$%4o$ " r"$,$"',% " -% &-"$r% "3" $"r !B'&2 /%r% 'o$,"r%r #% /r"',$, #% ,$/"r$, &05,&% "r" o$ #%3or%or,o$ "3" $"r " 16 !B'&2 (o$ 8"'"$ #% "$8,%', "$0%r) . E$o "$ #% "5/r"$, " #% "5%',-.
M3to+o +e es",o $"!" +ete!/i"! e# /o+*#o +e e#"sti%i+"+ se%"te; e $!obet"s %i#&+!i%"s +e %o%!eto Y% 'o /r"/%r%', " #%$ /ro3"%$ 4 $- '-r%o 'o&o #o ,'" " #% or&% COVENIN 4 <> $" ##"8% % '%3o #% /r"/%r%', "# "$%4o &",%" #% or&% COVENINA 1<6 /%r% ""r&,%r " &o-#o " "#%$,',%. S" o&% #% "&/"r%-r% 4 #% -&"% r"#%,8% " "# &o&"o "# "$%4o. Y% 'o #%$ r"$,$"',%$ o3",%$ "# "$%4o % 'o&/r"$, $"! #% or&% " #% '-%# $" o&% "# <* 7-" $" "o&,% '%r!% /ro&",o " r-/-r% C. Eo'"$ $": •
Co#o'% #%$ /ro3"%$ 'o #o$ ,$r-&"o$ " &",', 4% f,%o$ " #% /#%%for&% ,f"ro$ " '%r!% o "# /#%'% " %/o4o " #% &07-,% " "$%4o 4 $"
•
'"r% 'o r"$/"'o % #% ro-r% " #% /#%'% " '%r!% $-/"r,or. S" 3%% #"%&"" #% /#%'% /%r% 7-" 7-"" " 'o%'o 'o #% /ro3"% $" !,r%
•
$-%8"&"" 'o #% &%o #% /%r" &8,# /%r% o3""r "# %$,"o -,for&". Pr"'%r!%: $" %/#,'% #% '%r!% % 8"#o',% " ,&/%'o " 2> B? *> !B'&2B$"! %$% %#'%9%r "# 8%#or C. $" &%,"" #% '%r!% /or - &,-o 4 $" &%,"" !r%-%#&"" %$% ##"!%r % '"ro. S" %o% #%$ #"'-r%$ " #o$ "5"$&"ro$.
•
E$" /ro'",&,"o $" %'" -% 8"9 &0$ E$" /ro'",&,"o $" %'" %$% 7-" #%$ "for&%',o"$ o3",% " #% -#,&% '%r!% $" 'o&/r%r% 'o #% "# ','#o %"r,or o" #% ,f"r"',% "r" "##%$ "3" $"r &"or 7-" "# > $, o $" $,!-" 'o "# ','#o %$% 7-" $" '-&/#%.
M3to+o +e es",o $"!" +ete!/i"! #" !esiste%i" " #" t!"%%i0 i+i!e%t" +e# %o%!eto *s"+o $!obet"s %i#&+!i%"s: Co #%$ /ro3"%$ ',#r,'%$ 4% "#%3or%%$ 'o %&%@o '%r%'"r$,'%$ 4 /ro'"$o " '-r%o $"! ,,'%o " #%$ or&%$ COVENIN <> 4 $" ##"8% % '%3o "# /ro'",&,"o: •
S" &%r'% #%$ #"%$ ,%&"r%#"$ " '%% "5r"&o " #% /ro3"% -$%o "#
•
%/%r%o " &%r'%o /%r% !%r%,9%r 7-" "$0 " "# &,$&o /#%o %5,%#. S" ""r&,% "# ,0&"ro " #% /ro3"% " "$%4o 'o -% %/ro5,&%', " 1* && /ro&",%o r"$ ,0&"ro$ &",o$ '"r'% " #o$ "5r"&o$ 4 % #% &,% " #%
/ro3"% 4 $" ""r&,% #% #o!,- " #% /ro3"% 'o -% %/ro5,&%', " 1* && •
%&3,. L%$ ,r%$ " 'o%'o $" 'o#o'% "r" #% /ro3"% 4 #%$ /#%'%$ " %/o4o$ $-/"r,or
•
" #%$ &%7-,%$ " "$%4o S" 'o#o'% #% $"!-% ,r% #o!,-,%#&"" $o3r" "# ',#,ro '"r%% $o3r" #%$ #"%$ /r"8,%&"" &%r'%%$ " #o$ "5r"&o$ "# &,$&o. L% /ro4"'', "# /#%o 7-" %'" #%$ o$ ,r%$ $" "3"r0 ,"r$"'%r "# '"ro " #% /#%'% $-/"r,or "
•
%/o4o. L% /#%'% $-/#"&"%r,% $, $" -$% 4 "# '"ro " #% /ro3"% "3" " "$%r
•
,r"'%&"" /or "3%o "# '"ro " '%r!% " #% /#%'% " %/o4o "$fr,'o. S" %/#,'% #% '%r!% % 8"#o',% $, ,&/%'o " for&% 'o,-% % -% 8"#o',% 'o$%" " for&% %# 7-" #o$ "$f-"r9o$ " "# /#%o ,%&"r%# " r-/-r% $"
•
,'r"&"% % *> B? *2 !B'&2B$"! %$% 7-" f%##" #% /ro3"%. L% fr&-#% /%r% '%#'-#%r #% r%'', " #% /ro3"% "$: 2 xP
πxLxD
P '%r!% &05,&% %/#,'%% /or #% &07-,% " "$%4o L #o!,- D ,0&"ro
M3to+o +e es",o $"!" +ete!/i"! !esiste%i" " #" '#e
" 8%',%o 4 $" '"r% r"$/"'o % #%$ /#%'%$ " %/o4o. L% /#%'% " %/#,'%', " '%r!% $" /o" " 'o%'o 'o #% /ro3"% $o3r" #o$
•
/-o$ "5r"&o$ "# "r',o '"r%# " #% #-9 #,3r". S" %/#,'% #% '%r!% $, ,&/%'o 4 % -% %$% -,for&" %$% %/ro5,&%%&"" - >* " #% '%r!% " ro-r%= "$/-$ $" "3" %/#,'%r$" -% r%/,"9 %# 7-" "#
•
%-&"o " #% f,3r% "5r"&% "$" 'o&/r",% "r" 4 12 !B'&2B&,. S" &," #% /ro3"% 'o -% /r"',$, " 1&& 'o "# f, " ""r&,%r "# %'o 4
•
#% %#-r% /ro&",o " #% $"'', " f%##%. L% fr&-#% 7-" $" -$% /%r% '%#'-#%r "# &o-#o " ro-r%: f r=
P x L b xh
2
f r &o-#o " ro-r%
P '%r!% &05,&% %/#,'%% /or #% &07-,% " "$%4o L#-9 "r" %/o4o$ 3 %'o /ro&",o " #% /ro3"% %#-r% /ro&",o " #% /ro3"%
M3to+o +e es",o $"!" +ete!/i"! #" !esiste%i" " #" %o/$!esi0 +e# %o%!eto *s"+o $o!%ioes +e vi)"s !ot"s $o! '#e
S" 8"r,f,'% $, #%$ $-/"rf,',"$ " %/o4o " #% /ro3"% o ,f,"r" " - /#%o " &0$ " **>* && $, #%$ $-/"rf,',"$ " %/o4o o $o /#%%$ "o'"$ "3" r"'-3r,r$" %$% o3""r #% o#"r%',% ,,'%% %"r,or&"". E# r"'-3r,&,"o $" %'" " %'-"ro % #o f,%o " #% or&% COVENIN . Lo$ r"'-3r,&,"o$ "3" %3%r'%r oo "# %'o " #% 8,!% 4 "3" ""r -% #o!,- %# 7-" $"% /o$,3#" "# %-$" " #%$ /#%'%$ " '%r!% /%r% "# "$%4o " &oo 7-" #% /#%'% " '%r!% $-/"r,or /-"% 'o#o'%r$" ,r"'%&"" $o3r" #% /#%'% " '%r!% ,f"r,or.
•
S" "3" &%""r #%$ /ro3"%$ " #%$ &,$&%$ 'o,',o"$ /r""$'r,%$ " "# &oo /%r% #% "#%3or%', " /ro3"%$ /%r% "$%4o$ " f#"5, $"! "# '-%# $" o3-8,"ro #%$ /ro3"%$ /%r% "$" "$%4o -r%" "# ,"r8%#o 'o&/r",o "r" "# "$%4o % f#"5, " #%$ /ro3"%$ 4 "# r"'-3r,&,"o " #%$ '%r%$ /%r% "# "$%4o " 'o&/r"$, " #%$ /or',o"$ ro%$.
•
S" or,"% #% /ro3"% " for&% %# 7-" "# %'o 3 $"% ,!-%# o &"or % #% %#-r% . S, #% 8,!% ,"" -% $"'', '-%r%% #%$ $-/"rf,',"$ " '%r!% /-"" $"r #o$ #%o$ " #% 8,!% 'o$,"r%% $% " $- /o$,', or,!,%# " 8%',%o.
•
S" '"r% #%$ /#%'%$ " '%r!%$ " #%$ &%7-,%$ " "$%4o " &oo 7-" #% $-/"rf,'," " /r"$, " #% r-#% " #% &07-,% " "$%4o 7-"" %#,"%% " "# '"ro " #%$ /#%'%$ " '%r!%. L% '%r!% $" %/#,'% % #%$ /#%'%$ /or &",o " - '%3"9%# %-$%3#".
•
S" %/#,'% #% '%r!% " for&% 'o,-% 4 $, ,&/%'o. E# '%3"9%# &8,# "3" "$/#%9%r$" % -% 8"#o',% %/ro5,&%% " 1&&B&, '-%o "$ "$'%r!%%. E #%$ &07-,%$ ,r0-#,'%$ #% '%r!% "3" %-$%r$" % -% 8"#o',% 'o$%" "r" 2> 4 1* !B'&2B$"!.
•
L% fr&-#% $" /-"" ,"r/r"%r 'o&o:
Ru=
P b´ xb
R-: R"$,$"',% -,%r,% % #% 'o&/r"$, P: '%r!% &05,&% %/#,'%% /or #% &07-,% " "$%4o 3: %'o /ro&",o " #% /ro3"% 3: %'o /ro&",o " #% /#%'%
DATOS7 C=-CU-OS > RESU-TADOS D"tos:
P%r% "$" ,for&" $" -,#,9%ro #%$ &"9'#%$ NK 4 NK > ,$"@%%$ " #% /r0','% " 'o'r"o fr"$'o r"%#,9%% 'o %"r,or,%. L%$ '-%#"$ ,"" #%$ $,!-,""$ /ro/,"%"$. P!o$ie+"+es Ce/eto ); A)*" -; (ios ); G!*esos ); Tabla N° 1 Pro3"%$
Me2%#" ?
Me2%#" @
2 16 >6 >6
2 1 6 >6
',#r,'%$ " 'o'r"o "$%4%%$ % 'o&/r"$, 4 r%'',
,,r"'%. Me2%#"
P!obet"
D6 %/;
D %/;
D? %/;
6 %/;
%/;
? %/;
Peso );
P /5<4 )';
1< ** 2H+* *1* 12*16 1>.1> * * 1>* *< M2?6; 1>1* 1>** *1* *2* 1222* .1>* * * M?6 ; 1<H+ 1>* 1>* *<* * *1 122* 1>.+HH * * M1?6;
1<H 1>*6
>
M6;
1>*< 1>*
M1?<;
HH6
M2?<;
1** 1**1
M>1?6;
1>*+ 1<H+
M>2?6;
1>** 1<H*
M>?<;
1<HH 1>**
M><;
1<H 1>**
M>>?6;
1<H6 1<H+
1**<
1>* *2 *2H *2* * * 2*1 HH+ 2**6 2*12 H 2*1 HHH 2*2* 2*16 H 1>1 ** ** ** + 6 1>* * *6 *1 H < 1>* *2 *21 *2 * H 1>* *1 *1H *16 * > 1<H *< *<1 *<* * 2
122H +.1>* 6>H
.>
61H
+.262
11H2*
WX
11H6
+.>>*
11H+*
6.2**
11H6> 1.6H6 11HH 1.H
F-"": I$,-o " M%"r,%#"$ 4 Mo"#o$ E$r-'-r%#"$ (IMME) UCV. Tabla N° ! Pro3"%$ ,/o 8,!% " 'o'r"o "$%4%%$ % f#"5,.
Me2%#"
Vi)"
A#t*!" %/;
A%o %/;
-"!)o %/;
Peso );
P /5<4 )';
> >
M M>1 M>2
1*.2 1*.2< 1*.>>
1*.2 1*.> 1*.
2H.H> 2H.H1 *.+
+.*+2 6.H6< +.26
6>* >+> 62>
F-"": I$,-o " M%"r,%#"$ 4 Mo"#o$ E$r-'-r%#"$ (IMME) UCV.
C5#%*#os , Res*#t"+os: 1 Peso por unidad del volumen del concreto ensayado
S" $%3" 7-" /"$o -,%r,o ( γ) 8,"" %o /or #% "5/r"$,: γ =
Peso Volumen
(1)
A$ 'oo',"o "# /"$o " #%$ /ro3"%$ 4 #%$ &",%$ !"o&r,'%$ " #%$ &,$&%$ $" /-"" o3""r "# /"$o /or -,% " 8o#-&". E# 8o#-&" $" '%#'-#% " #% $,!-,"" &%"r% /%r% #%$ /ro3"%$ ',#r,'%$: 2 Π ∗ D V = ∗ H (2) 4 D": D D,0&"ro. A#-r%.
A$ &,$&o /%r% #%$ /ro3"%$ ,/o 8,!% $" '%#'-#% 'o&o: V = A ∗ H ∗ L () D": A A'o " #% 8,!%. A#o " #% 8,!%. L Lo!,- " #% 8,!%. •
C0#'-#o ,/o: S" o&%r0 #o$ 8%#or"$ " #% /ro3"% 1 " #% &"9'#% NK /%r% "# '0#'-#o
,/o. =
V
∗(14,92)2
Π
4
∗30.00 =5231,046 cm3
S-$,-4"o " #% "'-%', -o (1) "# /"$o " #% /ro3"% 4 "# 8o#-&" o3",o 'o #% "'-%', o$ (2) $" o3,"" "# /"$o -,%r,o: γ =
12,016 Kg 3
5231,031 cm
=0,0229
Kg cm
3
= 2,297
Ton 3
m
Tabla N° " P"$o$ U,%r,o$ " #%$ /ro3"%$ " 'o'r"o "$%4%%$ " #%3or%or,o.
Me2%#"
?
@
P!obet" Peso Uit"!io To9/F?; 2,297 M1?6; 2,277 M2?6; 2,277 M?6 ; 2,293 M6; 2,320 M1?<; 2,278 M2?<; 2,211 M>1?6; 2,237 M>2?6; 2,239 M>?<; 2,246 M><; 2,250 M>>?6; F-"": E#%3or%', Pro/,%.
NOTA: #o$ 8%#or"$ () 'orr"$/o" % #o$ %$o',%o$ % #%$ 8,!%$ 4 $-$ 8o#&""$
f-"ro '%#'-#%o$ &",%" #% "'-%', r"$ ().
6464
A5#isis est"+&sti%o +e #os $esos *it"!ios:
E'-%',o"$ %$o',%%$ %# %0#,$,$ "$%$,'o " #o$ /"$o$ -,%r,o$ o3",o$ /%r% #%$ o$ &"9'#%$ Pro&",o " #o$ /"$o$ "$/"'f,'o$ /or '%% &"9'#%:
X
=
1
n
∑ X
(<)
i
n i =1
V%r,%9% " '%% &"9'#%: S
2
=
n
1
∑ ( X − X ) n =
2
(>)
i
1
i
D"$8,%', E$0%r " '%% &"9'#%: S = √ S = 2
√
1
n
∑ ( X − X ) n =
2
i
i 1
(6)
Co"f,',"" " V%r,%',: C V = Tabla N° # V%#or"$
S X
(+)
"$%$,'o$ "# r"$-#%o " #o$ /"$o$ -,%r,o$ " #%$ /ro3"%$
" 'o'r"o.
P!o/e+io ; V"!i"2" SF; Desvi"%i0 Est5+"! S; Coe'i%iete +e V"!i"%i0 C4V4;
Me2%#" ?
Me2%#" @
22H*
22+
**** **16 ***+
****2 **1>1 ***6+
F-"": E#%3or%', Pro/,%.
! $nsayo de resistencia a la compresión del concreto
464
E$%4o " r"$,$"',% % #% 'o&/r"$, $"! #% Nor&% COVENIN ? 2**2
S" $%3" 7-" #% r"$,$"',% % #% 'o&/r"$, "o%% 'o&o R' " #% or&% COVENIN ?2**2 8,"" %% /or #% "5/r"$,: Pm!x ( Kgf ) Rc= 2 () A ( cm ) D": R' R"$,$"',% % #% 'o&/r"$, ([!fB'&\2) P&%5 L% '%r!% % #% '-%# o'-rr" #% ro-r% " #% /ro3"% ([!f) A Jr"% r%$8"r$%# " #% /ro3"% " 'o'r"o ('&\2) D" ,!-%# &%"r% $" '%#'-#% "# 0r"% " #% /ro3"% ',#r,'% " #% $,!-,"" &%"r%:
=
A
∗
Π D
2
4
(H)
D": D D,0&"ro " #% /ro3"% " 'o'r"o. C0#'-#o T,/o:
•
S" "&/#"%r0 -"8%&"" #% /ro3"% 1 " #% &"9'#% NK /%r% "# '0#'-#o ,/o " #% r"$,$"',% % #% 'o&/r"$,: D 1 + D 2+ D 3 14,89 + 15,06 + 14,80 = D,0&"ro 1<H2 '& 3 3 D" #% "'-%', -"8" (H) $" ,"" 7-" "# 0r"% r%$8"r$%# " #% /ro3"% "$: 2
A =
Π ∗14,92 4
=
174,757 cm
2
D" ,!-%# &%"r% -,#,9%o "# 8%#or " '%r!% &05,&% " #% %3#% 1 /%r% #% /ro3"% 1 " #% &"9'#% NK 4 "# 8%#or " 0r"% o3",o $" ,"" 7-" #% r"$,$"',% % #% 'o&/r"$, " #% /ro3"% "$: Rc=
15.158 174,757
=
86,74
Kgf cm
2
Tabla N° %: R"$,$"',% % 'o&/r"$, " #%$ /ro3"%$ " 'o'r"o.
DPROM %/;
PROM %/;
=REA %/;
P MA )';
ES(UERHO A -A COMPRESIÓN )'9%/
M1?6;
1<H2
2HH
1+<+6
1>.1>
6+<
M?6 ;
1>**
*<
1+6+1
1>.+HH
H<*
M6;
1>*2
*2
1++26
+.1>*
<*<
M1?<;
HHH
2*12
+
.>
1*6>+
M2?<;
1**1
2*1
++*
+.262
H22
M>6;
1<HH
*1+
1+6>6
1.6H6
++>+
M>>?6;
1<H<
*<1
1+>
1.H
+66
Me2%#" P!obet"
3
5
" $nsayo de probetas cil&ndricas de '( a tracción indirecta )*R+,I-$./0 se2n Norma 3/V$NIN "#141565
D" %'-"ro 'o #% Nor&% COVENIN <1?1H+H "# "$f-"r9o " r%'', " #% /ro3"% $" '%#'-#% 'o&o $,!-": 2∗ P " br = Π ∗ L∗ D (1<)
D": ]3r E$f-"r9o " r%'', " !fB'&\2 P C%r!% &05,&% %/#,'%% " [!f L Lo!,- " '&. D D,0&"ro " '&. •
C0#'-#o T,/o: To&%o #o$ 8%#or"$ " #% /ro3"% > " #% &"9'#% NK $" ,"" 7-": C%r!% &05,&% %/#,'%% 122** [!f H 1 + H 2+ H 3 30,10 + 30,40 + 30,20 = =¿ *2'& Lo!,- 3
D,0&"ro
3
D 1 + D 2+ D 3 3
=
15,10 + 15,00 + 15,00 3
=¿
1>* '&
A/#,'%o #% "'-%', '%or'" (1<) $" ,"" 7-" "# "$f-"r9o " r%'', " #% /ro3"% "$: Kgf 2∗8.150 =11,42 " br = 2 Π ∗30,23∗15,03 cm
Tabla 7': E$f-"r9o
" Tr%'', " #%$ /ro3"%$ " #%$ &"9'#%$ NK 4 NK> " %'-"ro % #% or&% COVENIN <1?1H+H. Me2%# " >
M2?6;
DPROM %/; 1>*
PROM %/; *2
P MA )'; .1>*
ES(UERHO A TRACCIÓN INDIRECTA )'9%/ 11<2
M6;
1>*2
*2
+.1>*
1**2
M>2?6;
1>**
*<
+.>>*
1*>6
M>?6;
1>**
*26
6.2**
+*
P!obet"
# $nsayo de tracción por flexión en vias se2n la Norma 3/V$NIN "#"41565
D" %'-"ro % #% or&% COVENIN <?1H+H "# &-#o " ro-r% " -% /ro3"% ,/o 8,!% " 'o'r"o $,&/#"&"" $o&",% % r%'', /or f#"5, 'o '%r!% " "# '"ro "# r%&o 8,"" %o /or #% "'-%', $,!-,"": #r=
3∗ P∗ L 2
2∗$∗ H
D": Mr M-#o " Ro-r% "5/r"$%o " [!fB'&\2
(1>)
P C%r!% &05,&% %/#,'%% ,,'%% " #% &07-,% " "$%4o "5/r"$%% " [!. L L-9 "5/r"$%% " '&. A'o /ro&",o " #% /ro3"% "5/r"$%o " '&. A#-r% /ro&",o " #% /ro3"% "5/r"$%% " '&. C0#'-#o T,/o: S" "&/#"%r% #% 8,!% 1 " #% &"9'#% NK /%r% "# '0#'-#o ,/o. Kgf 3∗650∗27 #r= =24,14 2 2 2∗10,32∗( 10,28 ) cm •
Tabla 76: M-#o " Ro-r% " #%$ 8,!%$ " #%$ &"9'#%$ NK 4 NK> " %'-"ro 'o
#% or&% COVENIN <?1H+H '& 2 Me2%# "
Vi)"
A#t*!" %/;
A%o %/;
-"!)o %/;
P )';
M0+*#o +e Rot*!" M!; )'9%/;
?
M
1*2
1*2
2HH>
6>*
2<1<
M>1
1*2<
1*>
2HH1
>+>
2*HH
M>2
1*>>
1*
*+
62>
22*
@
NOTA: L% #-9 #,3r" (L) 'orr"$/o" % #% #o!,- " #% 8,!% &"o$ 2 '& 7-" $" r"$%ro (1 '& %
'%% #%o) "3,o %# /o$,',o%&,"o " #o$ %/o4o$ " #% 8,!%.
% $nsayo de compresión de concreto usando porciones de vias rotaspor flexión se2n la Norma 3/V$NIN "%8465
D" %'-"ro % #% or&% COVENIN >*?1H+H #% r"$,$"',% -,%r,% " -% /ro3"% ,/o 8,!% " 'o'r"o $,&/#"&"" $o&",% % 'o&/r"$, 'o '%r!% %/#,'%% " -% /#%'% 8,"" %o /or #% "'-%', $,!-,"": Ru=
P b´ xb
R-: R"$,$"',% -,%r,% % #% 'o&/r"$, P: '%r!% &05,&% %/#,'%% /or #% &07-,% " "$%4o 3: %'o /ro&",o " #% /ro3"% 3: %'o /ro&",o " #% /#%'%
Tabla 79: R"$,$"',% -,%r,% " #%$ 8,!%$ " #%$ &"9'#%$ NK 4 NK> " %'-"ro
'o #% or&% COVENIN >*?1H+H '& 2
Me2%#"
Vi)" Tro9o 1 Tro9o 2 Tro9o 1 Tro9o 2
M M>
Avi)" %/; 1*> 1*> 1*> 1*>
A$#"%" %/; 1*1H 1*1H 1*1H 1*1H
P MA )'; 1.>** 12.>** 1*.1>* 11.>*
RESISTENCIA UNITARIA COMPRESIÓN )'9%/ 12** 11>2 H62< 1*+62
' 3omparación del peso unitario y la resistencia de las meclas 7" y 7%
A"r,or&"" $" %3% '%#'-#%o - /"$o -,%r,o "# 'o'r"o " "$%o fr"$'o 4 $" %3% "$,&%o #% r"$,$"',% 7-" o3"r% % #o$ + %$ /%r% #%$ ,f"r""$ &"9'#%$ ,$"@%%$. D" "$% for&% $" ,"" 7-": Tabla N°5 P"$o$
-,%r,o$ 4 r"$,$"',%$ % #% 'o&/r"$, " "$%o fr"$'o 4 % #% " "% " + %$ " #%$ &"9'#%$ " 'o'r"o 4 >. Me2%#"
? @
Est"+o (!es%o Peso Uit"!io Resiste%i" )9#; )'9%/;
21+ 21+
+&"s +e E+"+ Peso Uit"!io Resiste%i" )'9%/; )9#;
211H* 1211
AN=-ISIS DE RESU-TADOS
22H 22<
*6 +6H+
E "# ,for&" $" 'o&/%r%ro o$ &"9'#%$ " 'o'r"o 7-" ,f"r% " '%,% " %!r"!%o$ f,o$ #% r"#%', %!-% '"&"o #% r"$,$"',% " 'o'r"o "/"" /r0','%&"" " "$% #,&% $,"o % #% or% " ,$"@o "# f%'or % o&%r " '-"% %# '%#'-#%r #% r"$,$"',% % 'o&/r"$, "$/"r%% /%r% ""r&,%o ,"&/o. E# /"$o -,%r,o "# 'o'r"o "-r"',o f-" &%4or %# " #% &"9'#% f#-,% "&o$r%o 7-" "3,o % #% r"%'', " fr%!-%o " 'o'r"o ,"" % r"r%"r$" 4 %$ %'"r &0$ "$o "r" #%$ o$ &"9'#%$ o 8%r, " &%"r% 'o$,"r%3#". L% r"$,$"',% "$/"r%% f-" &-4 %#% 7-" #% r"$,$"',% r"%# " #% &-"$r% "$o $" "3" % 7-" #% &"9'#% $" r"%#,9 % for&% " %/r",9%" /or #o 7-" /-o %3"r /ro3#"&%$ " #% 'o&/%'%', " #% &"9'#% %o 'o&o "# ,"&/o "# /ro'"$o " &"9'#%o "$o "&-"$r% #o "#,'%o "# /ro'"$o 4 oo$ #o$ '-,%o$ 7-" $" "3" ""r.
CONC-USIONES
S" r"%#,9%ro #o$ "$%4o$ " r"$,$"',% % 'o&/r"$, r%'', 4 f#"5, " o$ &-"$r%$ " 'o'r"o 8,"o '&o $" r"%#,9% oo$ "$o$ /ro'"$o$ " "# #%3or%or,o $"! $-$ r"$/"',8%$ or&%$ COVENIN. S" ""r&,%ro #o$ /"$o$ -,%r,o$ #o$ '-%#"$ o f-"ro &-4 ,f"r""$ "r" #%$ &-"$r%$ 4 $" #" r"%#,9o $- r"$/"',8o %0#,$,$ "$%$,'o $"! or&%. L% &-"$r% 'o &"or r"#%', %!-% '"&"o /r"$"o &%4or r"$,$"',% $, "&3%r!o %&3%$ &"9'#%$ /r"$"%ro &"or"$ r"$,$"',%$ 7-" #%$ '%#'-#%%$ /or - &%# /ro'"$o " &"9'#%o 4 'o&/%'%',. L% ""r&,%', " #% r"$,$"',% " o%$ #%$ /ro3"%$ " '%% -% " #o$ "$%4o$ %$ 'o&o "# 'or%$" " "$o$ r"$-#%o$ 'o r"$/"'o % #o$ "$/"r%o$ % /%r,r " #o$ '0#'-#o$ "r,'o$ '$oo$ " #% &%4or% " #o$ '%$o$ % /," % 'o$,"r%r 'o&o '-&/#,o$ #o$ o3",8o$ /ro/-"$o$ %# /r,',/,o " "$% /r0','%. L% '-#&,%', " "$% /r0','% %&3, r"$-#o " !r% %4-% " #% f%&,#,%r,9%', "# "$-,%%o 'o #%$ or&%$ 7-" r,!" '%% -o " #o$ "$%4o$ %7- ##"8%o$ % '%3o $,"o "'"$%r,o $- "$-,o /%r% "# '0#'-#o " #% r"$,$"',% % /%r,r " #% '%r!% &05,&% o3",% " "$o$.
BIB-IOGRA(ÍA
•
A%& C. (2**+). Control de calidad del concreto. R"'-/"r%o "# 21 " -#,o " 2*16
"
/:BB.%o'"&.or!B'%/%',%',o?4?/-3#,'%',o"$B3o#",?
"','oB12H?'oro#?"?'%#,%?"#?'"&"o. •
"r%# . (2**H). Fragado del ce!ento. R"'-/"r%o "# 21 " -#,o " 2*16 " /:BB"#'o'r"o.3#o!$/o.'o&B2**HB*1Bfr%!-%o?"#?'"&"o.
•
or&,!. ^,,/",% L% "','#o/",% #,3r". F"'% " 'o$-#%: -#,o 1> 2*16 S,,o
•
^"3: /$:BB"$.,,/",%.or!B,,Bor&,!C Mor"ro " '"&"o. ^,,/",% L% "','#o/",% #,3r". F"'% " 'o$-#% -#,o 1>
• •
2*16 S,,o "3: /$:BB"$.,,/",%.or!B,,BMor"ro_"_'"&"o Porr"ro . R%&o$ C. Gr%$"$ . 4 V"#%9'o G. (2**H). M%-%# "# 'o'r"o E$r-'-r%#. V""9-"#%?C%r%'%$: SIDETUR