Age of concrete at the time time of loading,t 0 = 10 Age of concrete in days at the moment considered, considered, t = 28 Grade of concrete = M50 Mean com)ressive strength strength of concrete at age of 28 days,f cm = 60 Relative humidity,R = !0 "otional si#e of mem$er,h = 1000
( )
0 .7
43.75
*oefficient, *oefficient, +1 =
f cm
0%802
( ) 43.75
*oefficient, *oefficient, +2 =
0 .2
f cm
0%&'&
( ) 43.75
*oefficient, *oefficient, +' =
0 .5
f cm
0%85( *ree) coefficient ft,to- = ϕ o β c ( t,t o ) = 0.4642 fo = ϕ RH . β ( f cm ) . β ( t o )
= .actor to allo/ for the effect of R on notional cree) coeff, fR= =
1%6!6 1+
[
1 −RH/100 0 . 1 √ h o 3
1+
=
1− RH / 100 0. 1
3
√ ho
1%165
.actor to allo/ for the effect of concrete strength on notional cree) coeff,f cm-= 18%!8f cm = 2%(2( .actor to allo/ for the effect of concrete age at loading on notional cree) coeff,t o-= 10%13t o0%2 = 0%5&( coefficient to descri$e the develo)ment of cree) /ith time after loading, ct,to-= =
[
(t
−
t 0 )
β H + t −t 0
0%2!! 1%54130%0 *oefficient, *oefficient, = 1%54130%0 = 1280 1280%86& %86& 21'%(!81
]
0. 3
]
. α 1 α 2
Manual calculations ime ct,to- *ree) coe 1(%0! 0%1!!& 0%2&81(0 1&%81 0%2'1' 0%'8!6!0 2!%88 0%2!65 0%(6'2&! '&%2( 0%'1&6 0%5'5560 55%2' 0%'6'0 0%608222 !!%!' 0%(0!6 0%68'08! 10&%( 0%( 0%(5(2 0%!61086 15''%&! 15 %&! 0%50 0%5022! 0%8( %8(2(! (!88 216%! 0%5 0%55'2 0%&26&!0 '0((%&& '0 %&& 0%60 0%60((& 1%01 %01'66 66'' (2&&%26 (2 %26 0%65 0%65!!1 1%10 %10105 0511 60((%15 60 %15 0%!0 0%!088( 1%18 %18!06 06'' 8500%'1 85 %'1 0%!5 0%!5!!5 1%26 %26&'0 '0'' 11& 1&66%!5 %!5 0%80 %8028 1%'( %'(5'' ''!! 168 68((%'5 %'5 0%8( %8('' 1%(1 %(1'1' 1'55 2'! '!00%62 %62 0%8! %8!81 1%(! %(!1(0 (011 ''''6%5 0%& '' 0%&006& 1%51 %51&!' !''' (6& 6&55%&1 %&1 0%&' %&'01 1%55 %55855 5588 660 60&&%1& %1& 0%&( %&(82 1%58 %5888& 8&55 &'0 '022%02 %02 0%&6 %&620 1%61 %61206 0622 1'0& 0&22%01 %01 0%&! %&!2( 1%62 %62&(' ('(( 18(2 (266%1! %1! 0%&8 %&800 1%6( %6(22! 2!!!
day days Ma 7 mm
( ) 43.75
0 .7
f cm
( ) 43.75
0 .2
f cm
( ) 43.75
0 .5
f cm
ϕ o β c ( t,t o )
ϕ RH . β ( f cm ) . β ( t o )
1+
[
1 −RH/100
.or f cm = (5 Ma
0 . 1 √ h o 3
1+
[
25&' &'''%6! %6! 0%&8 %&856 '6500 0%&8&!
1− RH / 100
( t
3
0. 1
√
t 0 )
]
−
β H + t −t 0
ho
]
. α 1 α 2
.or f cm 9 (5
Ma
0. 3
2R-18:ho3250 = 1500, for fcm = (5 2R-18:ho3250+' = 1500+ ', for fcm 9 (5
1%65 %6516! 6!00 1%658(86
Manual cal Midas;
25&''%6! 1.667E+00 1.66E+00 '6500 1.674E+00
1.65E+00
otal hrin@age strain, εcs = Autogenous Autogenous hrin@age strain, strain, εca = Basic drying shrin@age strain,
εcd%0 =
εcd3εca
!%50;05 .or !%50;05 .or M50-
[
0.85 ( 220 +110. α ds1) .exp
= '%21 '%2115;0( 15;0( R = = f cm = f cmo = +ds1 = +ds2 = R> = Age of concrete at the $eginning $eginning of shrin@age,t s = h= @h = Manual *alculations t, days
ast-
1(%0! %0! 1&%81 %81 2!%88 %88 '&%2( %2( 55%2' %2' !!%!' %!' 10&%( 15'%&! %&! 216%! 6%! '0(%&& %&& (2&%26 %26 60(%15 %15 850%'1 %'1 11&6%! 6%!5 168( 8(%' %'55 2'!0 !0%6 %622 '''6%5 6%5 (6&5 &5%& %&11 660& 0&%1 %1&& &'02 02%0 %022 1'0& 1'0&2% 2%01 01 18( 8(226%1 6%1! 25& 5&'''%6 '%6! '65 65000
0%52 %52!! 0%58 %58&( 0%65 %6522 0%!1 %!1(' 0%!! %!!'8 0%82 %8285 0%8! %8!65 0%&1 %&16( 0%&( %&(!( 0%&6 %&6&6 0%&8 %&8(1 0%&& %&&2! 0%&& %&&!1 0%&& %&&&0 0%&& %&&&! 0%&& %&&&& 1%00 %0000 1%00 %0000 1%00 %0000 1%00 %0000 1%00 1%0000 00 1%00 %0000 1%00 %0000 1%00 %0000
εcat-
'%&6 %&6;05 ;05 (%(2 %(2;05 ;05 (%8&;05 5%'6 %'6;05 ;05 5%80 %80;05 ;05 6%21 %21;05 ;05 6%5!;05 6%8! %8!;05 ;05 !%1 !%11;0 1;055 !%2! %2!;05 ;05 !%'8 %'8;05 ;05 !%(5 %(5;05 ;05 !%(8 %(8;05 ;05 !%(& %(&;05 ;05 !%50 %50;05 ;05 !%50 %50;05 ;05 !%50 %50;05 ;05 !%50 %50;05 ;05 !%50 %50;05 ;05 !%50 %50;05 ;05 !%50 !%50; ;05 05 !%50 %50;05 ;05 !%50 %50;05 ;05 !%50 %50;05 ;05
dst,ts0%0 0%00086! 6!66 0%01 0%01''115 0%01 %01&2& 0%0 0%022!85 8522 0%0 0%0''&65 65(( 0%0 0%0555!8 !8(( 0%0! %0!!5& 0%100662 0%1 6266 0%1 0%1(((52 5288 0%1&&2!' 0%1 !'11 0%25 %2520 2055 0%'2221( 0%' 1(&& 0%(0111( 0%(0 1(66 0%(88552 0%( 5288 0%5!!06! 0%5 6!22 0%6551!8 0%6 !822 0%!22(&2 0%! &2(( 0%!88!68 0%! 68&& 0%8''&2& 0%8 2&!! 0%888026 0%8 2611 0%&1 0%&118 18!! !! 0%&''5!5 0%& !522 0%&55'(8 0%& (888 0%&66650 0%& 50''
εdst-
1%& 1%&5;0 5;066 2%& 2%&5;0 5;066 (%'(;06 6%2 6%26;0 6;066 8%& 8%&1;0 1;066 1%2 1%25;0 5;055 1%!(;05 2%( 2%(0;0 0;055 '%2 '%25;0 5;055 (%' (%'';0 ';055 5%6 5%6!;0 !;055 !%2 !%2(;0 (;055 &%0 &%02;0 2;055 1%0 1%0&;0 &;0(( 1%2 1%28;0 8;0(( 1%( 1%(!;0 !;0(( 1%6 1%6';0 ';0(( 1%! 1%!!;0 !;0(( 1%8 1%8&;0 &;0(( 1%& 1%&8;0 8;0(( 2%05 2%05; ;0( 0( 2%1 2%10;0 0;0(( 2%1 2%1(;0 (;0(( 2%1 2%1!;0 !;0((
1.55
[ ( )] RH 1− RHO
1%018 60 12%5 ( 0%12 100 ' 1000 0%! εcst-
(%15 %15;05 ;05 (%!2 %!2;05 ;05 5%'2 %'2;05 5%&8 %&8;05 ;05 6%6& %6&;05 ;05 !%(! %(!;05 ;05 8%'2 %'2;05 &%2! %2!;05 ;05 1%0( %0(;0( ;0( 1%16 %16;0( ;0( 1%'0 %'0;0( ;0( 1%(! %(!;0( ;0( 1%65 %65;0( ;0( 1%8( %8(;0( ;0( 2%0' %0';0( ;0( 2%22 %22;0( ;0( 2%'8 %'8;0( ;0( 2%52 %52;0( ;0( 2%6( %6(;0( ;0( 2%!' %!';0( ;0( 2%80 2%80; ;0( 0( 2%85 %85;0( ;0( 2%8& %8&;0( ;0( 2%&2 %&2;0( ;0(
3
Ma Ma .or .or "orm "orm .or .or "orm "orm 7 ?ays mm
(
α ds2
−
f cm f cmo
)]
. 10
−
0 . α ds1) .exp
(
α ds2
−
f cm f cmo
)]
. 10
6
−
. β RH
h
l cementl cement-
Manual cal shri@age strain
ime 1(%0! 1&%81 2!%88 '&%2( 55%2' !!%!' 10&%( 15'%&! 216%! '0(%&& (2&%26 60(%15 850%'1 11&6%!5 168(%'5 2'!0%62 '''6%5 (6&5%&1 660&%1& &'02%02 1'0&2%01 18(26%1! 25&''%6! '6500
@h 100 200 '00 500
1 0%85 0%!5 0%!
500 500
0%! 0%!
Midas;
shri@age strain
4.15E-05 1%(1301 -4.15E-05 4.72E-05 1%&8301 -4.72E-05 5.32E-05 2%!&301 -5.32E-05 5.98E-05 '%&2301 -5.98E-05
55%2' -6.69E-05 7.47E-05 !!%!' -7.47E-05 8.32E-05 10&%( -8.32E-05 9.27E-05 15'%&! -9.27E-05 1.04E-04 216%! -1.04E-04 1.16E-04 '0(%&& -1.16E-04 1.30E-04 (2&%26 -1.30E-04 1.47E-04 60(%15 -1.47E-04 1.65E-04 850%'1 -1.65E-04 1.84E-04 11&6%!5 -1.84E-04 2.03E-04 168(%'5 -2.03E-04 2.22E-04 2'!0%62 -2.22E-04 2.38E-04 '''6%5 -2.38E-04 2.52E-04 (6&5%&1 -2.52E-04 2.64E-04 660&%1& -2.64E-04 2.73E-04 &'02%02 -2.73E-04 2.80E-04 1'0&2%01 -2.80E-04 2.85E-04 18(26%1! -2.85E-04 2.89E-04 25&''%6! -2.89E-04 2.92E-04 '6500 -2.92E-04
6.69E-05
