1 Introduction
2 Literature Review
2.1 Experimental Tests
2.2 Theoretical Investigations
3 Dynamic Behaviour of PRC Beams
3.1 Compression Softening
3.2 Concrete Softening
3.3 Confinement
3.4 Early-Age Cracking
-
Main cracks that affect large areas of concrete section;
-
Local secondary cracks (micro-cracking) that affect the concrete around a single steel rebar.
4 Flexural Stiffness of PRC Beams
5 Numerical Modeling of the Dynamics of PRC Beams
6 Identification of the Unknown Parameters
6.1 Comparison with Tests by Saiidi et al.
Prestressing force | 1\(\mathrm{st}\) frequency | 2\(\mathrm{nd}\) frequency |
---|---|---|
(kN) | (Hz) | (Hz) |
0 | 11.41 | 43.99 |
26.7 | 13.47 | 44.89 |
56.6 | 14.15 | 45.71 |
80.9 | 14.49 | 45.57 |
120.1 | 14.72 | 45.86 |
131.3 | 15.07 | 45.87 |
6.2 Comparison with Tests by Kim et al.
Prestressing force | 1\(\mathrm{st}\) frequency | 2\(\mathrm{nd}\) frequency |
---|---|---|
(kN) | (Hz) | (Hz) |
0 | 22.73 | 98.42 |
39.2 | 23.08 | 98.73 |
58.8 | 23.23 | 101.39 |
78.4 | 23.39 | 101.65 |
98.0 | 23.60 | 101.70 |
117.6 | 23.72 | 102.54 |
6.3 Comparison with Tests by Zhang and Li
Prestressing force | 1\(\mathrm{st}\) frequency | 2\(\mathrm{nd}\) frequency |
---|---|---|
(kN) | (Hz) | (Hz) |
0 | 28.36 | 100.71 |
20 | 28.36 | 102.67 |
40 | 28.83 | 103.09 |
60 | 29.32 | 104.07 |
80 | 29.48 | 105.05 |
100 | 29.69 | 105.50 |
120 | 29.80 | 105.53 |
6.4 Comparison with Tests by Jang et al.
Prestressing force | 1\(\mathrm{st}\) frequency | 2\(\mathrm{nd}\) frequency |
---|---|---|
(kN) | (Hz) | (Hz) |
0 | 7.51 | 28.18 |
146 | 8.22 | 29.40 |
264 | 8.54 | 30.98 |
356 | 8.72 | 30.00 |
465 | 8.70 | 30.13 |
523 | 8.79 | 29.85 |
7 Comments to the Results of the Identification Procedure
Experimental tests |
\(f_{c,28}\)
|
\(f_{c,iden}\)
|
\(\varepsilon _{sh}\)
|
a
|
---|---|---|---|---|
(MPa) | (MPa) | (\(\permil \)) | ||
Saiidi et al. (1994) | 20.3 | 27.8 | 0.0911 | 7716 |
Kim et al. (2010) | 23.6 | 24.3 | 0.0551 | 5015 |
Zhang and Li (2007) | 37.5\(^\mathrm{a}\) | 43.1 | 0.0698 | 5925 |
Jang et al. (2010) | 35.0 | 35.2 | 0.0692 | 6774 |
Experimental tests |
\(\sigma _{c,mean}\)
|
\(f_{c,iden}\)
|
\({\sigma _{c,mean}}/{f_{c,iden}}\)
| Compression softening |
---|---|---|---|---|
(MPa) | (MPa) | |||
Saiidi et al. (1994) | 10.1 | 27.8 | 0.364 | Relevant |
Kim et al. (2010) | 1.0 | 24.3 | 0.039 | Absent |
Zhang and Li (2007) | 4.17 | 43.1 | 0.097 | Moderate |
Jang et al. (2010) | 5.81 | 35.2 | 0.165 | Moderate |