Class #27.1
1

Time-Dependent Volume Changes
(MacGregor, 5 th ed., pp. 70-83)

 Negative volume change due to curing, drying,
- shrinkage is less in a structure than in a cylinder,
- rebars restrain shrinkage,
- less exposed surface area per volume,
- structure is built in stages, shrinkage not simultaneous throughout structure.
- in a parking garage, concrete absorbs CO
2
,
- shrinkage due to carbonation = shrinkage due to drying.

 Volume change due to load over time,

 Volume change due to change in temperature of mass.
2

Time-Dependent Volume Changes

(MacGregor, 5 th ed., pp. 70-83)
Negative volume change, shortening, under constant temperature due to;
 Drying & hardening: causes water to evaporate from cement paste, causing shrinkage to occur;
- aggregate does not evaporate, does NOT shrink;
Shrinkage;
 Increases with decreasing humidity,
 Increases with increasing cement-to-aggregate ratio,
(Fig. 3.22a,
MacGregor, 5 th ed.)
 Cement paste shrinks, aggregate does not shrink.
 Increases with increasing water-to-cement ratio,
 More water, less aggregate,
 water evaporates, paste shrinks, aggregate does not shrink.
 Increases with increasing fineness of cement,
 Finer cement absorbs more water, water evaporates, more shrinkage.
 Decreases with increasing member size,
 More mass per exposed surface area, less shrinkage.
3

Time-Dependent Volume Changes

(MacGregor, 5 th ed., pp. 70-83)

Equation for Axial Shrinkage Strain between days t s t , t s
 cs
  s
  cso
 s
  s
& t in plain concrete:
 cso
 
= basic shrinkage strain, for a specific concrete & relative humidity,
= coefficient, a function of time and member effective thickness, s
(Fig. 3.24,
MacGregor, 5 th ed.)
 s
  s



 350
 h e
 t h
0
 t s

  t
1 t
 t s
 t
1



0 .
5 h e t = age of the concrete, days, t
1
= 1 day

2 A u c t s
= age of concrete at end of moist curing, days,
A c
= concrete cross sectional area, in 2 .
h
0
= 4 in.

Time-Dependent Volume Changes
Equation for Axial Shrinkage Strain between days t s
 cs
  s
  cso
 s
  s
& t in plain concrete:
(MacGregor, 5 th ed., pp. 70-83)
 cso
= basic shrinkage strain, for a specific concrete & relative humidity,
 cso
  s f cmo
= 1450 psi,
  cm

RH
 s
  cm

1 .
2

 160

  sc

 9
 f f cm cmo






10

6 f cm f cm
= mean compressive strength, at 28 days, psi,
 f
' cr
 '  ' from ACI 318, Sect. 5.3.2.1, or assuming a standard deviation of s

0 .
15 f f f
' cr
' cr

 f c
'
1 .
2
 f c
'
1 .
34

0 .
15 f c
'
 f cr
' f cr
'

 f f c c
'
' 

2 .
33



1247
 c
'
0 .
15 f
 f
' cr c
'

 f c
' 
2 .
33 s
5000
 


500
500
2
'
Use = smaller of or
 sc f c
' 
1200 psi
= coefficient accounting for type of cement
 sc

5

Time-Dependent Volume Changes

(MacGregor, 5 th ed., pp. 70-83)
Equation for Axial Shrinkage Strain between days t s
 cs
  s
  cso
 s
  s
& t in plain concrete:
 cso
= basic shrinkage strain, for a specific concrete & relative humidity,
  cso
 s
  cm

RH

RH
= coefficient accounting for relative humidity,

RH
= +0.25, for Relative Humidity ≥99%
(Fig. 3.23,
MacGregor, 5 th ed.)
For Relative Humidity 40% < RH < 99%

RH
 
1 .
55



1



RH
RH
0


3



RH = Relative Humidity of ambient atmosphere, %
RH
0
= 100%
6

Time-Dependent Volume Changes


(MacGregor, 5 th ed., pp. 74-76)
 Underground parking garage,
 Floor slab, 6 in. thick, lightly reinforced,
 Floor restrained on outside edge by 16 in. thick basement wall,
 Walls 26 months old, moist cured, 5 days, cast against ground,
 Slab 24 months old, moist cured, 5 days, not on ground,


Relative humidity, roughly constant over period, 50%,
Concrete; Type I cement, f c
' 
3000 psi

Shrinkage for reinforced concrete ≈ 0.75 shrinkage plain concrete
 Cracks developed in slab, perpendicular to wall, at roughly every 6 ft.
 Assume cracks resulted from restraint by wall of slab shrinkage parallel to wall.
 Calculate crack width.
7

Time-Dependent Volume Changes

plus

(MacGregor, 5 th ed., pp. 79-81)

Concrete pedestal, plain (unreinforced), 24”x24”x10’
 Moist cured, not on ground,
 Applied load 1 month after casting,
 Load causes average stress = 1000 psi.,
 Temperature, roughly constant over period, 68 ˚F,
 Relative humidity, roughly constant over period, 50%,
 Concrete; cement content = 675 Lb/yd 3 , slump = 3 in.
 Compute total shortening in 5 years.
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