Abstract
For a structure, robustness is a high-level performance index since it takes account of the effects of impact, explosion, earthquake and other instantaneous dynamic actions on the structure safety. In this work, layer is taken as the tie between the column and the frame. Two concepts, namely, “layer importance coefficient” of the column and “layer vulnerability coefficient” of the frame, are introduced. Based on these, the method for calculating the seismic robustness is proposed and analyzes the seismic robustness of three FRP-reinforced frame models. The results show that: The robustness of the frame with the 1st layer column reinforced with two layer CFRP (carbon fiber reinforced polymer) (F20RC) and the 1st and 2nd layer column reinforced with one layer CFRP (F11RC), respectively are better than that of the 1st layer column reinforced with one layer CFRP (F10RC). As the intensity of earthquake action increases, the seismic robustness index decreases. When UBC97’s acceleration-related parameter Ca = 0.36 and velocity-related parameter Cv = 0.36, the robustness coefficient of the three models F20RC, F11RC, F10RC are 36.5, 37.2, 34.1, respectively. When Ca = 0.6, Cv = 0.6, that of F20RC, F11RC, F10RC are 24.2, 20.4, 19.5, respectively. Finally, the procedure for designing the FRP-reinforced frame based on the seismic robustness is presented and demonstrated.
Similar content being viewed by others
References
Baker, J. W., Schubert, M., and Faber, M. H. (2008). “On the assessment of robustness.” Structural Safety, Vol. 30, No. 3, pp. 253–267, DOI: https://doi.org/10.1016/j.strusafe.2006.11.004.
Bao, C., Du, Y. F., Liu, Y., Xu, T. N., and Wang, G. F. (2015). “Study on seismic robustness of structure.” China Earthquake Engineering Journal, Vol. 37, No. 3, pp. 660–666, DOI: https://doi.org/10.3969/j.issn.1000-0844.2015.03.0660 (in Chinese).
Bao, C., Du, Y. F., Xu, T. N., Qi, L., and Song, X. (2017). “Study of structural robustness analysis method based on seismic response.” Journal of Vibration, Measurement & Diagnosis, Vol. 37, No. 1, pp. 120–125, DOI: https://doi.org/10.16450/j.cnki.issn.1004-6801.2017.01.019 (in Chinese).
Du, Y. F., Bao, C., Zhang, S. R., and Tan, Z. P. (2014). “Robustness analysis of the vertical progressive collapse resistance of vertically irregular RC frames.” China Civil Engineering Journal, Vol. 47, No. Supp 2, pp. 101–107, DOI: https://doi.org/10.15951/j.tmgcxb.2014.s2.016 (in Chinese).
Ellingwood, B. R. (2006). “Mitigating risk from abnormal loads and progressive collapse.” Journal of Performance of Constructed Facilities, ASCE, Vol. 20, No. 4, pp. 315–323, DOI: https://doi.org/10.1061/(ASCE)0887-3828(2006)20:4(315).
Faber, M. H., Maes, M. A., Straub, D., and Baker, J. W. (2006). “On the quantification of robustness of structures.” Proc. 25th International Conference on Offshore Mechanics and Arctic Engineering, Hamburg, Germany, pp. 1–9, DOI: https://doi.org/10.1115/OMAE2006-92095.
FEMA 356 (2000). Prestandard and commentary for the seismic rehabilitation of building, FEMA 356, American Society of Civil Engineers, Reston, VA, USA.
Gao, Y. (2018). “Quantitative analysis of structural robustness and its application in underground frame structures” Journal of Building Structures, Vol. 39, No. 1, pp. 153–161, DOI: https://doi.org/10.14006/j.jzjgxb.2018.01.018 (in Chinese).
GB50011-2010 (2010). Code for seismic design of buildings, China National Standards GB50011-2010, Ministry of Housing and Urban-Rural Development of the People’s Republic of China, Beijing, China.
Hayes Jr, J. R., Woodson, S. C., Pekelnicky, R. G., Poland, C. D., Corley, W. G., and Sozen, M. (2005). “Can strengthening for earthquake improve blast and progressive collapse resistance?” Journal of Structural Engineering, Vol. 131, No. 8, pp. 1157–1177, DOI: https://doi.org/10.1061/(ASCE)0733-9445(2005)131:8(1157).
Huang, L. and Li, L. (2012). “A quantification method of structural robustness.” Engineering Mechanics, Vol. 29, No. 8, pp. 213–219, DOI: https://doi.org/10.6052/j.issn.1000-4750.2010.08.0588 (in Chinese).
Huang, J. Z. and Wang, Z. (2012). “An approach for evaluation of the structural robustness of steel frames.” China Civil Engineering Journal, Vol. 45, No. 9, pp. 46–54, DOI: https://doi.org/10.15951/j.tmgcxb.2012.09.020 (in Chinese).
Huang, L., Wang, Y., Chen, Y. L., and Li, D. (2013). “A quantification method of structural robustness.” Engineering Mechanics, Vol. 30, No. 10, pp. 46–53, DOI: https://doi.org/10.6052/j.issn.1000-4750.2012.05.0384 (in Chinese).
Husain, M. and Tsopelas, P. (2004). “Measures of structural redundancy in reinforced concrete buildings-I: Redundancy indices.” Journal of Structural Engineering, Vol. 130, No. 11, pp. 1651–1658, DOI: https://doi.org/10.1061/(ASCE)0733-9445(2004)130:11(1651).
Kanno, Y. and Ben-Haim, Y. (2011). “Redundancy and robustness, or when is redundancy redundant.” Journal of Structural Engineering, Vol. 137, No. 9, pp. 935–945, DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0000416.
Khandelwal, K. and El-Tawil, S. (2011). “Pushdown resistance as a measure of robustness in progressive collapse analysis.” Engineering Structures, Vol. 33, No. 9, pp. 2653–2661, DOI: https://doi.org/10.1016/j.engstruct.2011.05.013.
Kim, J. and Park, J. (2008). “Design of steel moment frames considering progressive collapse.” Steel and Composite Structures, Vol. 8, No. 1, pp. 85–98, DOI: https://doi.org/10.12989/scs.2008.8.1.085.
Lau, D. T. and Wibowo, H. (2010). “Seismic progressive collapse analysis of reinforced concrete bridges by applied element method.” Earth and Space 2010: Engineering, Science, Construction, and Operations in Challenging Environments, pp. 3019–3026, DOI: https://doi.org/10.1061/41096(366)287.
Li, L. L., Li, G. Q., Lu, Y., and Chen, S. W. (2015). “A review on the research of robustness of civil structures.” Progress in Steel Building Structures, Vol. 17, No. 5, pp. 5–17, DOI: https://doi.org/10.13969/j.cnki.cn31-1893.2015.05.002 (in Chinese).
Liu, C. M. and Liu, X. L. (2005). “Stiffness-based evaluation of component importance and its relationship with redundancy.” Journal of Shanghai Jiaotong University, Vol. 39, No. 5, pp. 746–750, DOI: https://doi.org/10.16183/j.cnki.jsjtu.2005.05.019 (in Chinese).
Lu, D. G., Cui, S. S., Li, Y. J., and Wang, G. Y. (2010). “Robustness analysis for progressive collapse of structures using an alternate load path based pushover analysis approach.” Journal of Building Structures, Vol. 31, No. 2, pp. 112–118, DOI: https://doi.org/10.14006/j.jzjgxb.2010.s2.003 (in Chinese).
Lu, D. G., Cui, S. S., Song, P. Y., and Chen, Z. H. (2012). “Robustness assessment for progressive collapse of framed structures using pushdown analysis methods.” International Journal of Reliability and Safety, Vol. 6, No. 1, pp. 15–37, DOI: https://doi.org/10.1504/IJRS.2012.044293.
Lu, D. G., Song, P. Y., Cui, S. S., and Wang, M. X. (2011). “Structural robustness and its assessment indicators.” Journal of Building Structures, Vol. 32, No. 11, pp. 44–54, DOI: https://doi.org/10.14006/j.jzjgxb.2011.11.016 (in Chinese).
Rezvani, F. H., Behnam, B., Ronagh, H. R., and Alam, M. S. (2017). “Failure progression resistance of a generic steel moment-resisting frame under beam-removal scenarios.” International Journal of Structural Integrity, Vol. 8, No. 3, pp. 308–325, DOI: https://doi.org/10.1108/IJSI-02-2016-0008.
Sheng, G. H., Yang, L., Bai, Q., and Han, J. J. (2016). “Critical drift statistics of RC column retrofitted with FRP and quantization of performance levels.” Earthquake Engineering and Engineering Dynamics, Vol. 36, No. 4, pp. 207–216, DOI: https://doi.org/10.13197/j.eeev.2016.04.207.shenggh.025 (in Chinese).
Sheng, G. H., Zhu, F. S., and Zhang, J. (2014). “Seismic performance evaluation for RC frames considering energy dissipation of component retrofitted with FRP composites.” Earthquake Engineering and Engineering Dynamics, Vol. 34, No. 5, pp. 247–253, DOI: https://doi.org/10.13197/j.eeev.2014.05.247.shenggh.031 (in Chinese).
Smith, J. W. (2006). “Structural robustness analysis and the fast fracture analogy.” Structural Engineering International, Vol. 16, No. 2, pp. 118–123, DOI: https://doi.org/10.2749/101686606777962521.
Starossek, U. and Haberland, M. (2008). “Approaches to measures of structural robustness.” Proc. 4th International Conference on Bridge Maintenance, Safety, and Management, Seoul, Korea, DOI: https://doi.org/10.1080/15732479.2010.501562.
Wibowo, H. and Lau, D. T. (2009). “Seismic progressive collapse: Qualitative point of view.” Engineering Dimension, Vol. 11, No. 1, pp. 8–14, DOI: https://doi.org/10.1001/jama.1914.02560320008003.
Ye, L. P., Cheng, G. Y., Lu, X. Z., and Feng, P. (2008a). “Introduction of robustness for seismic structures.” Building Structure, Vol. 38, No. 6, pp. 1–15, DOI: https://doi.org/10.19701/j.jzjg.2008.06.003 (in Chinese).
Ye, L. P., Qu, Z., Lu, X. Z., and Feng, P. (2008b). “Collapse prevention of building structures: A lesson from the Wenchuan Earthquake.” Journal of Building Structures, Vol. 29, No. 4, pp. 42–50, DOI: https://doi.org/10.14006/j.jzjgxb.2008.04.010 (in Chinese).
Yu, X. H. and Lu, D. G. (2012). “Seismic collapse fragility analysis considering structural uncertainties.” Journal of Building Structures, Vol. 33, No. 10, pp. 8–14, DOI: https://doi.org/10.14006/j.jzjgxb.2012.10.002 (in Chinese).
Yu, X. H., Lu, D. G., and Zheng, H. Q. (2014). “Seismic sideway collapse fragility analysis based on structural typical failure modes.” Journal of Building Structures, Vol. 35, No. 8, pp. 8–14, DOI: https://doi.org/10.14006/j.jzjgxb.2014.08.023 (in Chinese).
Zheng, S. S., Tian, J., Han, Y Z., Xu, Q., and Sung, L. B. (2014). “Seismic fragility analysis of steel structure considering steel corrosion.” China Earthquake Engineering Journal, Vol. 36, No. 1, pp. 1–6, DOI: https://doi.org/10.3969/j.issn.1000-0844.2014.01.0001 (in Chinese).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sheng, G., Bai, Q., Jin, S. et al. Analysis and Design of Seismic Robustness of FRP-Reinforced Frame based on Interlayer Displacement. KSCE J Civ Eng 23, 2573–2583 (2019). https://doi.org/10.1007/s12205-019-0999-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-019-0999-9