tension side. This causes resistance when the c
initially not a problem, however too much curvature can cause not acceptable deflections and cracks. The effects of shrinkage in reinforced and unreinforced structures are shown in
12 Service
tension side. This causes resistance when the cinitially not a problem, however too much curvature can cause not acceptable deflections and cracks. The effects of shrinkage in reinforced and unreinforced structures are shown in
Fig. tension side. This causes resistance when the c
initially not a problem, however too much curvature can cause not acceptable deflections and cracks. The effects of shrinkage in reinforced and unreinforced structures are shown in
Fig. 106: Effects of shrinkage on unre
Ability Aspects of t
commonly defined by SLS properties.
In a homogenous unreinforced concrete structure, shrinkage is usually not a problem since it causes the concrete to shrink evenly. As long as the concrete structure
directions with no resistance, shrinkage will not cause any stresses or curvature to the
However, concrete structures are usually reinforced with most of the reinforcement on the tension side. This causes resistance when the c
initially not a problem, however too much curvature can cause not acceptable deflections and cracks. The effects of shrinkage in reinforced and unreinforced structures are shown in
: Effects of shrinkage on unre
Ability Aspects of t
tension side. This causes resistance when the concrete shrinks which leads to curvature. This is initially not a problem, however too much curvature can cause not acceptable deflections and cracks. The effects of shrinkage in reinforced and unreinforced structures are shown in: Effects of shrinkage on unreinforced versus reinforced beam
Ability Aspects of t
oncrete shrinks which leads to curvature. This is initially not a problem, however too much curvature can cause not acceptable deflections and cracks. The effects of shrinkage in reinforced and unreinforced structures are shown ininforced versus reinforced beam oncrete shrinks which leads to curvature. This is initially not a problem, however too much curvature can cause not acceptable deflections and cracks. The effects of shrinkage in reinforced and unreinforced structures are shown in
inforced versus reinforced beam oncrete shrinks which leads to curvature. This is initially not a problem, however too much curvature can cause not acceptable deflections and cracks. The effects of shrinkage in reinforced and unreinforced structures are shown in Fig.
inforced versus reinforced beam [45].
131 oncrete shrinks which leads to curvature. This is initially not a problem, however too much curvature can cause not acceptable deflections and Fig. 106.
12. Service Ability Aspects for the CSS Concept
132
Total shrinkage εcs can be separated into two parts, drying shrinkage εcd and autogenous shrinkage εcs. Total shrinkage is described of the following relation (12.1):
εcs = εcd + εcs
(12.1)
The curvature can then be calculated easily by the following simplified expression (12.2):
κ ε
d (12.2)
Drying shrinkage starts as soon as the relative humidity of the concrete structure becomes less than 100%. The autogenous shrinkage starts as soon as the curing process of the concrete starts. The drying shrinkage can be reduced by not letting the concrete dry to quick.
Like LWAC in general, the W1150 concrete suffers more from shrinkage than normal concrete.
SINTEF Byggforsk has an ongoing shrinkage study in progress [46] for this specific kind of concrete, but with some small modifications regarding the recipe compared to the W1150 concrete used in this report. The results from the first 365 days on this study are plotted in Fig.
107. In the figure, the W1150 shrinkage is compared with theoretical shrinkage of a B30 concrete calculated with Eurocode 2 [2]. As one can see, the shrinkage on the W1150 concrete is approximately twice as large as for the B30.
Fig. 107: Results from SINTEF shrinkage study on the W1150 concrete compared to theoretical shrinkage of B30 concrete calculated with Eurocode 2 [2].
1 10 100 1000
Age [days]
0 0.2 0.4 0.6 0.8 1
ChangeinLength[‰]
W1150 B30
133
12.1.1 Shrinkage of the CSS
A composite structure is very sensitive to shrinkage if the composite materials have different shrinkage properties. With its three layers, the CSS can be compared with a laminate compounded by two different concrete materials with different shrinkage properties.
A general laminate with thickness h and laminate stiffness Qki,j is shown in Fig. 108. The general expression relating forces and moments to strains and curvatures are shown in Fig. 109.
Fig. 108: General multidirectional laminate with coordinate notation of individual plies [47].
Fig. 109: General expression to relate in-plane forces and moments to reference plane strains and curvatures [47].
If the CSS is considered, it can be simplified to a symmetric laminate after the top is cast. This means that the coupling matrix, Bi,j will have all its elements equal to zero, Bi,j = 0 because of the symmetry. From Fig. 109 it can be seen how the expression for Bi,j only will return zero values for symmetric laminates and that in plane strains, as for example shrinkage strains, will not cause any moment and consequently no curvature.
However, the prefabricated part of the CSS is asymmetric and suffers therefore of severe curvature problems due to changes in plane strains. In this case, the coupling matrix Bi,j ≠ 0
12. Service Ability Aspects for the CSS Concept
134
which means correlation between strains and curvature. Since the stiffer material is located in the bottom, the curvature induced by shrinkage will have the same direction as the curvature from later loading. This is not a desired behavior. In addition to this, the reinforcement will increase the curvature effects.
The shrinkage induced curvature on the prefabricated part of the CSS can be evened out by casting it with an initial curvature in the opposite direction. However, this can only be done if the crack widths can be held on a reasonable level. Another solution to the problem could be if the prefabricated part of the CSS could be stored with a relative humidity close to 100% until the top layer is to be cast. Then the drying shrinkage would not start before the top is in place and the structure would have the behavior of a symmetric laminate. The autogenous shrinkage will still cause some curvature, but this part is small compared to the drying part.