PRAGATI CONSULTANTS
CALCULATION OF PRESTRESS LOSSES
Grade of Concrete = M 40
Age of concrete at the time of 1st stage prestressing = 7 days
Age of girder at the time of 2nd stage prestressing = 14 days
Calculation of Creep and Shrinkage
Shrinkage Strain
Total Shrinkage strain ecs = ecd + eca
ecd = drying shrinkage strain
eca = Autogenous shrinkage strain
From Table 6.6 of IRC:112
Autogenous Shrinkage strain eca = 0.000055
The development of autogenous shrinkage with time can be taken as
eca (t) = bas (t) x eca (From eq. 6.12)
bas (t) = 1 - exp (-0.2*sqrt(t)) (From eq. 6.13)
bas (t) = 0.00 0 days
bas (t) = 0.41 7 days
bas (t) = 0.53 14 days
bas (t) = 0.65 28 days
bas (t) = 0.72 40 days
bas (t) = 0.76 50 days
bas (t) = 1 25550 days
Autogeneous shrinkage at time t
eca (t) 0 days = 0.00E+00
eca (t) 7 days = 2.26E-05
eca (t) 14 days = 2.90E-05
eca (t) 28 days = 3.59E-05
eca (t) 40 days = 3.95E-05
eca (t) 50 days = 4.16E-05
eca (t) 25550 days = 5.50E-05
Drying Shrinkage strain ecd
Relative Humidity = 50
From Table 6.8 of IRC:112
Drying Shrinkage strain ecd For M40 = 4.66E-04
The development of drying shrinkage with time can be taken as
ecd (t) = bds (t,ts) x kh x ecd
bds (t,ts) = (t-ts)/(t-ts)+0.04 x SQRT(ho^3)
ho = 2 x Ac/u
Ac = Concrete Cross sectional area = 7.174 m2
u = perimeter which is exposed to drying = 35.14 m
ho = 2 x Ac/u = 408.3 mm
From Table 6.7 of IRC:112
kh = 0.72
End of curing = 5 days
bds (t,ts) 7 days = 6.02E-03
bds (t,ts) 14 days = 2.65E-02
bds (t,ts) 28 days = 6.51E-02
bds (t,ts) 40 days = 9.59E-02
bds (t,ts) 50 days = 1.20E-01
1
PRAGATI CONSULTANTS
Drying shrinkage at time t
ecd (t) = bds (t,ts) x kh x ecd 7 days = 2.03E-06
ecd (t) = bds (t,ts) x kh x ecd 14 days = 8.94E-06
ecd (t) = bds (t,ts) x kh x ecd 28 days = 2.19E-05
ecd (t) = bds (t,ts) x kh x ecd 40 days = 3.23E-05
ecd (t) = bds (t,ts) x kh x ecd 50 days = 4.04E-05
ecd(infinty) = kh x ecd = 3.37E-04
Total Shrinkage strain ecs @ 0 days = 0
7 days = 2.46E-05
14 days = 3.79E-05
28 days = 5.79E-05
40 days = 7.18E-05
50 days = 8.21E-05
25550 days = 3.92E-04
Residual Shrinkage at 0 days (Shrinkage at infinity - Shrinkage at that time) = 3.92E-04
Residual Shrinkage at 7 days = 3.67E-04
Residual Shrinkage at 14 days = 3.54E-04
Residual Shrinkage at 28 days = 3.34E-04
Residual Shrinkage at 40 days = 3.20E-04
Residual Shrinkage at 50 days = 3.10E-04
Creep Strain
Creep strain of concrete = f x sc/Ec
where f = creep coefficient (calculated as per IRC-112)
sc = constant Compressive stress applied to the concrete at time t
Ec = Modulus of Elasticity of concrete
From Table 6.5 of IRC 112
Modulus of Elasticity of Concrete for M40 grade concrete = 33000 N/mm2
Calculation of Creep Coefficient
From IRC:112-2011,6.4.2.7(3)
The development of creep with time may be taken as
f (t,to) = b (t,to) x f (inf,to)
where
b (t,to) = ((t - to)/(bH+(t-to)))^0.3
t is the age of the concrete in days at the time considered
to is the age of the concrete in days at time of loading = 7 days
(t - to) is the actual duration of loading in days
bH is a coefficient depending on the relative humidity ( RH in percent) and the notional
member size (ho in mm).
bH = 1.5 x (1+(1.2 x RH/RHo)^18) x ho+250 <= 1500 for fcm <=45
bH = 1.5 x (1+(1.2 x RH/RHo)^18) x ho+250 a<= 1500a for fcm >=45
fcm = M 50
a3 = SQRT(43.75/fcm) = 0.935
Grade of concrete = M40
bH = 846
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PRAGATI CONSULTANTS
From IRC:112-2011,table 6.9
f (inf,to) = 2.82
b (t,to) = for 7 days = 0.000
7 to 14 days = 0.237
7 to 28 days = 0.327
7 to 40 days = 0.374
7 to 60 days = 0.428
7 to 25550 days = 0.990
f (t,to) = 7 days = 0.000
7 to 14 days = 0.668
7 to 28 days = 0.924
7 to 40 days = 1.054
7 to 60 days = 1.207
7 to 70 Y = 2.794
Creep Strain for a stress of 10 Mpa
Creep Strain at 7 days = 0
Creep Strain between 7 to 14 days = 2.02E-04
Creep Strain between 7 to 28 days = 2.80E-04
Creep Strain between 7 to 40 days = 3.19E-04
Creep Strain between 7 to 60 days = 3.66E-04
Creep Strain between 7 to 70 Y = 8.47E-04
For Loading on 7 days
Creep Strain between 7 to infinity = 8.47E-04
Creep Strain between 14 to infinity = 6.44E-04
Creep Strain between 28 to infinity = 5.67E-04
Creep Strain between 40 to infinity = 5.27E-04
Creep Strain between 60 to infinity = 4.81E-04
3
PRAGATI CONSULTANTS
Second stage Prestressing
to is the age of the concrete in days at time of loading = 14 days
fcm = 50
a3 = SQRT(43.75/fcm) = 0.935
Grade of concrete = M40
bH = 846.4
From IRC:112-2011,table 6.9
f (inf,to) = 2.48
b (t,to) = for 14 days = 0.000
14 to 40 days = 0.349
14 to 60 days = 0.411
14 to 25550 days = 0.990
f (t,to) = 14 days = 0.000
14 to 28 days = 0.720
14 to 40 days = 0.863
14 to 60 days = 1.017
14 to 25550 Y = 2.452
Creep Strain for a stress of 10 Mpa
Creep Strain at 14 days = 0
Creep Strain between 14 to 28 days = 2.18E-04
Creep Strain between 14 to 40 days = 2.62E-04
Creep Strain between 14 to 60 days = 3.08E-04
Creep Strain between 14 to 70 Years = 7.43E-04
For Loading on 14 days
Creep Strain between 14 to infinity = 7.43E-04
Creep Strain between 28 to infinity = 5.25E-04
Creep Strain between 40 to infinity = 4.82E-04
Creep Strain between 60 to infinity = 4.35E-04
