mathcad - fc age.mcd

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FcEHE t () Fc2 t () Sets 1 = if Fc1 t () otherwise := Fc2 t () linterp ages fc2s , t , ( ) := Fc1 t () linterp ages fc1s , t , ( ) := EHE table 30.4.b fc2s 0.55 0.75 1 1.15 1.2 f c28 := fc1s 0.4 0.65 1 1.2 1.35 f c28 := ages 3 7 28 90 360 day := not wholly coherent, see fc 28 day ( ) 352.52 kgf cm 2 = according to Branson fc t () t day α β t day + f c28 := month, year (singular) also permitted units for time End_chart 1 year := Sets 1 := 1 for quick setting of concrete (42.5R, 52.5 and 52.5R with w/c less than 0.60, 32.5R and 42.5 with w/c less than 0.50) 0 for normal or slow setting of concrete strength at 28 days β 0.85 := α 4 := f c28 350 kgf cm 2 := β β β =0.85 for cement Type I and moist curing β β β =0.92 for cement Type III and moist curing β β β =0.95 for cement Type I and steam curing β β β =0.98 for cement Type III and steam curing α α α=4.00 for cement Type I and moist curing α α α=2.30 for cement Type III and moist curing α α α=1.00 for cement Type I and steam curing α α α=0.70 for cement Type III and steam curing fc_age expected strength of a concrete as a function of age and strength at 28 days of age

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Mathcad - Fc Age.mcd

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Page 1: Mathcad - Fc Age.mcd

FcEHE t( ) Fc2 t( ) Sets 1=if

Fc1 t( ) otherwise

:=

Fc2 t( ) linterp ages fc2s, t,( ):=Fc1 t( ) linterp ages fc1s, t,( ):=

EHE table 30.4.bfc2s

0.55

0.75

1

1.15

1.2

fc28⋅:=fc1s

0.4

0.65

1

1.2

1.35

fc28⋅:=ages

3

7

28

90

360

day⋅:=

not wholly coherent, see

fc 28 day⋅( ) 352.52kgf

cm2

=according to Bransonfc t( )

t

day

α βt

day⋅+

fc28⋅:=

month, year (singular) also permitted units for timeEnd_chart 1 year⋅:=

Sets 1:= 1 for quick setting of concrete (42.5R, 52.5 and 52.5R with w/c less than 0.60, 32.5R and 42.5 with w/c less than 0.50)0 for normal or slow setting of concrete

strength at 28 days

β 0.85:=α 4:=fc28 350

kgf

cm2

⋅:= ββββ=0.85 for cement Type I and moist curingββββ=0.92 for cement Type III and moist curingββββ=0.95 for cement Type I and steam curingββββ=0.98 for cement Type III and steam curing

αααα=4.00 for cement Type I and moist curingαααα=2.30 for cement Type III and moist curingαααα=1.00 for cement Type I and steam curingαααα=0.70 for cement Type III and steam curing

fc_age expected strength of a concrete as a function of age and strength at 28 days of age

Page 2: Mathcad - Fc Age.mcd

FcEP_93 t( ) fc28

t

day

0.75

t

day

0.75

5.5+

280.75

280.75 5.5+

⋅:= commentary to art. 35.9

Parts 200:=

j 1 Parts 1+..:= Fc j fcEnd_chart

Partsj 1−( )⋅

:= Time jEnd_chart

Partsj 1−( )⋅:=

FcQj Fc2 Time j( ):= FcS j Fc1 Time j( ):= FcEP j FcEP_93 Time j( ):=

Compressive strength as a function of age, Branson's

Page 3: Mathcad - Fc Age.mcd

0 50 100 150 200 250 300 3500

100

200

300

400

500

Fc j

kgf

cm2

Time j

day

1 10 100 1 .1030

100

200

300

400

500

Fc j

kgf

cm2

Time j

day

Compressive strength as a function of age, EHE Table 30.4.bConcrete that sets quickly

Page 4: Mathcad - Fc Age.mcd

0 50 100 150 200 250 300 3500

100

200

300

400

500

FcQj

kgf

cm2

Time j

day

Compressive strength as a function of age, EHE Table 30.4.b

Page 5: Mathcad - Fc Age.mcd

Concrete that sets slowly

0 50 100 150 200 250 300 3500

100

200

300

400

500

FcSj

kgf

cm2

Time j

day

Compressive strength as a function of age, EP-93 comm. to 35.9

Page 6: Mathcad - Fc Age.mcd

0 50 100 150 200 250 300 3500

1 .107

2 .107

3 .107

4 .107

5 .107

FcEP j

Time j

day

1 10 100 1 .1030

1 .107

2 .107

3 .107

4 .107

5 .107

FcEP j

Time j

day

Compressive strength as a function of age, comparative chart

Page 7: Mathcad - Fc Age.mcd

EP-93 commentary to 35.9 more consistent with quick settings as proper of prestressed concrete

FcEP_93 t( ) 4.57ksi=FcEP_93 t( ) 31.51MPa=FcEP_93 t( ) 321.3kgf

cm2

=

EHE code (linear interpolation between given points,pertaining to the line representing setting time)

FcEHE t( ) 4.5ksi=FcEHE t( ) 31.05MPa=FcEHE t( ) 316.67kgf

cm2

=

fc t( ) 4.74ksi=fc t( ) 32.69MPa= Branson's, in redfc t( ) 333.33kgf

cm2

=t 20 day⋅:=

Prediction of compressive strength at given age

fc28 350kgf

cm2

=

1 10 100 1 .1030

100

200

300

400

500

Fc j

kgf

cm2

FcEP j

kgf

cm2

Time j

day

0 50 100 150 200 250 300 3500

100

200

300

400

500

Fc j

kgf

cm2

FcQj

kgf

cm2

FcSj

kgf

cm2

FcEP j

kgf

cm2

Time j

day