The CSS beams are also analyzed with Abaqus as the test specimens from phase performed
described earlier in Chapter
10.1
The numerical model used for the analyses of the CSS is shown in analyze
was performed, the same model was used but the analysis are listed in
Fig.
Table
*Abaqus default value
10.2
The material input data for the analyses are based on the phase 1
10 Test Phase 2:
CSS
The CSS beams are also analyzed with Abaqus as the test specimens from phase performed 2-dimensional analyses of the CSS.
described earlier in Chapter
10.1 Numerical
The numerical model used for the analyses of the CSS is shown in analyze half the beam
was performed, the same model was used but the analysis are listed in
Fig. 94: Numerical model used in analyses of CSS beams. In the analyses of
Table 32: Summary of
The material input data for the analyses are based on the phase 1 (phase 2 for compression), Eurocode rules
Test Phase 2:
CSS Beam
The CSS beams are also analyzed with Abaqus as the test specimens from phase dimensional analyses of the CSS.
described earlier in Chapter
Numerical Model
The numerical model used for the analyses of the CSS is shown in half the beam due to symmetry.
was performed, the same model was used but the analysis are listed in Table
: Numerical model used in analyses of CSS beams. In the analyses of cast, the same mode
: Summary of plasticity parameters and element properties used in analyses of CSS beams.
Parameter
The material input data for the analyses are based on the (phase 2 for compression), Eurocode rules
Test Phase 2:
Beams
The CSS beams are also analyzed with Abaqus as the test specimens from phase dimensional analyses of the CSS.
described earlier in Chapter 7.
Model
The numerical model used for the analyses of the CSS is shown in due to symmetry.
was performed, the same model was used but Table 32.
: Numerical model used in analyses of CSS beams. In the analyses of , the same mode
plasticity parameters and element properties used in analyses of CSS beams.
Material Input
The material input data for the analyses are based on the (phase 2 for compression), Eurocode rules
Test Phase 2: Analys
The CSS beams are also analyzed with Abaqus as the test specimens from phase
dimensional analyses of the CSS. All analyses were run as implicit analyses as
The numerical model used for the analyses of the CSS is shown in
due to symmetry. When the analyses of the beams without the top cast was performed, the same model was used but without the top
: Numerical model used in analyses of CSS beams. In the analyses of , the same model is used but without the top layer.
plasticity parameters and element properties used in analyses of CSS beams.
10
The material input data for the analyses are based on the (phase 2 for compression), Eurocode rules
Analysis
The CSS beams are also analyzed with Abaqus as the test specimens from phase
All analyses were run as implicit analyses as
The numerical model used for the analyses of the CSS is shown in
When the analyses of the beams without the top cast without the top
: Numerical model used in analyses of CSS beams. In the analyses of l is used but without the top layer.
plasticity parameters and element properties used in analyses of CSS beams.
Value
The material input data for the analyses are based on the results from the laboratory
(phase 2 for compression), Eurocode rules [2] and experience from the parameter
of Concept
The CSS beams are also analyzed with Abaqus as the test specimens from phase
All analyses were run as implicit analyses as
The numerical model used for the analyses of the CSS is shown in Fig. 94
When the analyses of the beams without the top cast without the top layer. The parameters used in
: Numerical model used in analyses of CSS beams. In the analyses of the beams without the top l is used but without the top layer.
plasticity parameters and element properties used in analyses of CSS beams.
Value
The CSS beams are also analyzed with Abaqus as the test specimens from phase 1. It was only All analyses were run as implicit analyses as
94. It was chosen to When the analyses of the beams without the top cast layer. The parameters used in
the beams without the top
plasticity parameters and element properties used in analyses of CSS beams.
10.2 When the analyses of the beams without the top cast layer. The parameters used in
the beams without the top
plasticity parameters and element properties used in analyses of CSS beams.
testing in and experience from the parameter
10. Test Phase 2: Analysis of Concept CSS Beams
118
study in Chapter 7. All material data are given to Abaqus as tabular values. The material data defining the plastic behavior of the concretes are shown in Fig. 95. The elastic behavior of the LWAC and the “NC30” are described by the material values summarized in Table 33 and Table 34 respectively.
Compressive Input Data
“NC30”
Tensile Input Data
“NC30”
Compressive Input Data W1150 (22 days old)
Tensile Input Data W1150 (22days old)
Fig. 95: Tension and compression data for the W1150 and “NC30” concrete, used in analyses of concept CSS beams.
0 0.001 0.002 0.003
Inelastic Strain [epl]
0 5 10 15 20 25 30
YieldStress[MPa]
"NC30", 22 days old
"NC30", 15 days old
0 0.02 0.04 0.06
Inelastic Strain [epl]
0 1 2 3
YieldStress[MPa]
"NC30", 22 days old
"NC30", 15 days old
0 0.0005 0.001 0.0015 0.002 0.0025
Inelastic Strain [epl]
0 4 8 12
YieldStress[MPa]
0 4 8 12
Displacement [mm]
0 0.4 0.8 1.2
YieldStress[MPa]
119
10.2.1 W1150 Concrete
The material parameters which constitutes the basis for the numerical analysis for the W1150 concrete is summarized in Table 33.
Table 33: Summary of W1150 material parameters.
Parameter Value Note
Ecm,22 11700 Mpa Adjusted according to fcm,22*
fcm,22 11.6 Mpa Mean measured cylinder strength Phase 2, see Appendix C.2.
fctm,22 1.26 Mpa Adjusted according to fcm,22**
V% 0.0033 Adjusted for LWAC***
u 0.2
*Ecm,22 = (fcm,22/fcm)0.3 x Ecm Ecm= 13000 Mpa from test phase 1
** fctm,22= (fcm,22/fcm) x fctm fcm= Mean measured cylinder strength W1150 phase 1, fctm = measured tensile strength W1150 specimen B3-1 phase 1
*** According to Table 11.3.1 in Eurocode 2 [2]
10.2.1.1 Tensile Data
The tensile data is based on tension specimen B3-1 in test phase 1 which was concluded to represent the W1150 concrete with 1% fiber in an appropriate way. The tensile data is in this case defined in Abaqus in terms of stress-displacement for chosen values from first yield to failure of the tension specimen.
10.2.1.2 Compression Data
In the previous analyses in Chapter 7, the simplified stress-strain relationship in Eurocode 2 [2], have been used to define the compressive path. Based on recommendations from supervisors it is here instead chosen to use the stress-strain relation that is suggested for non-linear analyses in Eurocode 2. This should in theory be a more correct way of describing the compressive behavior of concrete. The schematic representation of the stress-strain relation from Eurocode 2 is shown in Fig. 96.
10. Test Phase 2: Analysis of Concept CSS Beams
120
Fig. 96: Schematic representation of the stress-strain relation for structural analysis (the use of 0,4fcm for the definition of Ecm is approximate) [2].
The compression data in the analyses of the concept CSS beams is based on the measured compressive strength from the test cylinders that were sampled during the production of the CSS beams. The compression data is given to Abaqus in terms of yield stress and inelastic strain from first yield to ultimate strain εcu1 according to the recommendations in Eurocode 2 [2]. The compressive data given to Abaqus is shown as plotted values in the top left diagram in Fig. 95 and is based on equation (10.1) [2] together with the values in Table 33:
5% '%6,77 >3 − 3"
1 + > − 2 3 (10.1)
where:
3 = V%/V%
> = 1.05k%6,77× |V%|/'%6,77
121
10.2.2 “NC30” Concrete
The material parameters which constitutes the basis for the numerical analysis for the
“NC30”concrete is summarized in Table 34.
Table 34: Summary of “NC30” material parameters.
Parameter Value Note
Ecm,22 29570 MPa Calculated on basis of fcm,i [2] *
Ecm,15 29130 MPa Calculated on basis of fcm,i [2] *
fcm,22 26.8 MPa Mean measured cylinder compressive strength
fcm,15 25.5 MPa Mean measured cylinder compressive strength
fctm,22 2.1 MPa Calculated on basis of fcm,i **
fctm,15 2.0 MPa Calculated on basis of fcm,i **
Gf,22 67.2 N/m From Abaqus manual [34]
Gf,15 62 N/m From Abaqus manual [34]
V% 0.0035 Table 3.1 Eurocode 2 [2]
u 0.2
*Ecm,I = 22[(fcm,i)/10]0.3 (Based on mean measured cylinder compressive strength in phase 2)
**Linearly interpolated according to Table 3.1 in Eurocode 2 [2] on basis of fcm,i.
10.2.2.1 Tensile Data
The tensile data for the “NC30” concrete is based on fracture energy values, Gf,recommended in the Abaqus manual [34] for normal concrete, together with values for tensile strength fctm from Eurocode 2[2]. The values are adjusted for curing time of 15 and 22 days respectively.
Fig. 97: Schematic representation of postfailure stress-fracture energy curve [34].
The tensile data is given to Abaqus in terms of stress and displacement with values from Table 33 together with the relationship expressed in (10.2) [34]. Fig. 97 explains the content of expression (10.2).
10. Test Phase 2: Analysis of Concept CSS Beams
122
l 2 g(,77
'%)6,77
(10.2)
10.2.2.2 Compression Data
The compressive data is given as described in Section 10.2.1.2 but based on values from Table 34.
10.2.2.3 Reinforcement and Bond Between Concrete Layers
The yield stress for the reinforcement is given as 500MPa on basis of Eurocode 2 [2]. Only longitudinal reinforcement is included in the numerical model. The vertical reinforcement is excluded, instead perfect bond is assumed between the different concrete layers. Perfect bond is also assumed between the reinforcement and the concrete. The longitudinal reinforcement is added as embedded objects and placed in equivalent amount on correct center distances matching Fig. 80.