To compute or not to compute?
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摘要
In a previous paper "to retrofit or not to retrofit?"(Nuti and Vanzi, 2003) a straightforward procedure able to forecast the economic return of seismic structural upgrading was presented. More recently, the authors realized that the final mathematical results can be much simplified so as to allow back-of-an-envelope computation. The title of this paper tries to highlight precisely this aspect, namely that for many a regular seismic structural upgrading cases, nearly no computation is needed(apart from one subtraction and one multiplication) to assess their economic convenience. These findings are presented and discussed in this paper, together with a state of the art on the cost-studies available in literature and technical codes. The mathematical formulation leading to the proposed approximation is suitably explained, underlining its applicability field and comparing it with the rigorous solution. Also a table and a formula are furnished that alternatively allows to calculate the maximum estimation errors, in order to obtain an upper and lower bound for the maximum amount of money which should be allocated for seismic structural upgrading.
In a previous paper "to retrofit or not to retrofit?"(Nuti and Vanzi, 2003) a straightforward procedure able to forecast the economic return of seismic structural upgrading was presented. More recently, the authors realized that the final mathematical results can be much simplified so as to allow back-of-an-envelope computation. The title of this paper tries to highlight precisely this aspect, namely that for many a regular seismic structural upgrading cases, nearly no computation is needed(apart from one subtraction and one multiplication) to assess their economic convenience. These findings are presented and discussed in this paper, together with a state of the art on the cost-studies available in literature and technical codes. The mathematical formulation leading to the proposed approximation is suitably explained, underlining its applicability field and comparing it with the rigorous solution. Also a table and a formula are furnished that alternatively allows to calculate the maximum estimation errors, in order to obtain an upper and lower bound for the maximum amount of money which should be allocated for seismic structural upgrading.
In a previous paper "to retrofit or not to retrofit?"(Nuti and Vanzi, 2003) a straightforward procedure able to forecast the economic return of seismic structural upgrading was presented. More recently, the authors realized that the final mathematical results can be much simplified so as to allow back-of-an-envelope computation. The title of this paper tries to highlight precisely this aspect, namely that for many a regular seismic structural upgrading cases, nearly no computation is needed(apart from one subtraction and one multiplication) to assess their economic convenience. These findings are presented and discussed in this paper, together with a state of the art on the cost-studies available in literature and technical codes. The mathematical formulation leading to the proposed approximation is suitably explained, underlining its applicability field and comparing it with the rigorous solution. Also a table and a formula are furnished that alternatively allows to calculate the maximum estimation errors, in order to obtain an upper and lower bound for the maximum amount of money which should be allocated for seismic structural upgrading.
引文
Aon Benfield, 2013. Annual Global Climate and Catastrophe Report, 2012. Impact Forecasting, Chicago.
Applied Technology Council(ATC), 1996. Seismic Evaluation and Retrofit of Concrete Buildings. ATC-40. ATC, Redwood City.
Braga, F.,Gigliotti, R.,Monti, G., et al., 2014. Speedup of post earthquake community recovery:the case of precast industrial buildings after the Emilia 2012 earthquake.Bulletin of Earthquake Engineering 12(5), 2405-2418.
Demartino, C., Vanzi, I., Monti, G., 2017a. Probabilistic estimation of economic losses of portal-like precast industrial buildings.Earthquakes and Structures 13(3), 323-335.
Demartino, C., Monti, G., Vanzi, I., 2017b. Seismic loss-of-support conditions of frictional beam-to-column connections.Structural Engineering and Mechanics 61(4), 527-538.
Demartino, C., Vanzi, I., Monti, G., et al., 2018. Precast industrial buildings in southern Europe:loss of support at frictional beam-to-column connections under seismic actions. Bulletin of Earthquake Engineering 16(1), 259-294.
Federal Emergency Management Agency(FEMA), 1988. Typical Costs for Seismic Rehabilitation of Existing Buildings. FEMA156-157. FEMA, Washington DC.
Federal Highway Administration(FHWA), 2006. Seismic Retrofitting Manual for Highway Structures:Part 1-Bridges.FHWA, Washington DC.
Fiore, A., Marano, G.C., 2017. Serviceability performance analysis of concrete box girder bridges under traffic-induced vibrations by structural health monitoring:a case study. International Journal of Civil Engineering 16(5), 553-565.
Fiore, A., Monaco, P., Raffaele, D., 2012. Viscoelastic behaviour of non-homogeneous variable-section beams with post-poned restraints. Computers and Concrete 9(5), 375-392.
Fiore, A., Sulpizio, C., Demartino, C., et al., 2018a. Seismic vulnerability assessment of historical centres at urban scale.International Journal of Architectural Heritage 12(2), 257-269.
Fiore, A., Demartino, C., Greco, R., et al., 2018b. Seismic performance of spherical liquid storage tanks:a case study.International Journal of Advanced Structural Engineering 10(2), 121-130.
Fiorentino, G., Forte, A., Pagano, E., et al., 2018. Damage patterns in the town of Amatrice after August 24th 2016 Central Italy earthquakes. Bulletin of Earthquake Engineering 16(3),1399-1423.
Greco, R., Fiore, A., Marano, G.C., 2014. The role of modulation function in nonstationary stochastic earthquake model.Journal of Earthquake and Tsunami 8(5), 1450015.
Grossi, P., Kunreuther, H., 2005. Catastrophe Modeling:a New Approach to Managing Risk. Springer Science&Business Media, Cham.
Imperatore, S., Lavorato, D., Nuti, C., et al., 2012. Shear performance of existing reinforced concrete T-beams strengthened with FRP. In:6th International Conference on FRP Composites in Civil Engineering, Roma, 2012.
Institutul de Cercetari in Constructii si Economia Constructiilor(INCERC), 2000. Probleme de Economia Constructiilor,Bucharest, Romania. INCERC, Bucuresti.
Kappos, A.J., Dimitrakopoulos, E.G., 2008. Feasibility of preearthquake strengthening of buildings based on cost-benefitand life-cycle cost analysis, with the aid of fragility curves.Natural Hazards 45, 33-54.
Kappos, A., Lekidis, V., Panagopoulos, G., et al., 2007. Analytical estimation of economic loss for buildings in the area struck by the 1999 Athens earthquake and comparison with statistical repair costs. Earthquake Spectra 23, 333-355.
Lavorato, D., Nuti, C., 2010. Seismic response of repaired bridges by pseudodynamic tests. In:5th International Conference on Bridge Maintenance, Safety and Management, Philadelphia,2010.
Lavorato, D., Nuti, C., 2015. Pseudo-dynamic tests on reinforced concrete bridges repaired and retrofitted after seismic damage. Engineering Structures 94, 96-112.
Lavorato, D., Nuti, C., Santini, S., et al., 2015. A repair and retrofitting intervention to improve plastic dissipation and shear strength of Chinese RC bridges. In:IABSE Conference,Geneva, 2015.
Lavorato, D., Vanzi, I., Nuti, C., et al., 2017. Generation of nonsynchronous earthquake signals. In:Gardoni, P.(Ed.), Risk and Reliability Analysis:Theory and Applications. Springer Series in Reliability Engineering, Cham, pp. 169-198.
Marano, G.C., Acciani, G.,Fiore, A.,et al.,2015. Integration algorithm for covariance non-stationary dynamic analysis of SDOF systems using equivalent stochastic linearization.International Journal of Structural Stability and Dynamics 15(2), 1450044.
Neddermann, R., 2007. Kostenermittlung im Altbau. Aktuelle Baupreise-Rechtliche Grundlagen-Technische Beurteilung-Kostenermittlungsmethoden, fourth ed.Werner, Neuwied.
Nuti, C., Vanzi, I., 2003. To retrofit or not to retrofit? Engineering Structures 25(9), 701-711.
Nuti, C., Santini, S., Vanzi, I., 2004. Damage, vulnerability and retrofitting strategies for the Molise hospital system following the 2002 Molise, Italy, earthquake. Earthquake Spectra 20(S1), 285-299.
Nuti, C., Rasulo, A., Vanzi, I., 2009. Seismic assessment of utility systems:application to water, electric power and transportation networks-safety, reliability and risk analysis:theory, methods and applications. In:ESREL Conference,Prague, 2009.
Paudel, Y., Botzen, W.J.W., Aerts,J.C.J.H., et al., 2015. Risk allocation in a public-private catastrophe insurance system:an actuarial analysis of deductibles, stop-loss,and premiums. Journal of Flood Risk Management 8(2),116-134.
Quaranta, G., Fiore, A., Marano, G.C., 2014. Optimum design of prestressed concrete beams using constrained differential evolution algorithm. Structural and Multidisciplinary Optimization 49(3), 441-453.
Rose, A., 2004. Economic principles, issues, and research priorities in hazard loss estimation. In:Okuyama, Y.,Chang, S.E.(Eds.), Modeling Spatial and Economic Impacts of Disasters. Springer, Berlin, pp. 13-36.
Smyth, A.W., Altay, G., Deodatis, G., et al., 2004. Probabilistic benefit-cost analysis for earthquake damage mitigation:evaluating measures for apartment houses in Turkey.Earthquake Spectra 20(1), 171-203.
Vanzi, I., Marano, G.C., Monti, G., et al., 2015. A synthetic formulation for the Italian seismic hazard and code implications for the seismic risk. Soil Dynamics and Earthquake Engineering 77,111-122.
Yang, T.Y, Moehle, J.,Stojadinovic, B.,et al., 2009. Seismic performance evaluation of facilities:methodology and implementation. Journal of Structural Engineering 135(10),1146-1154.
Zhou, Z., Lavorato, D., Nuti, C., et al., 2015. A model for carbon and stainless steel reinforcing bars including inelastic buckling forevaluation of capacity of existing structures. In:5th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Crete Island, 2015.
Applied Technology Council(ATC), 1996. Seismic Evaluation and Retrofit of Concrete Buildings. ATC-40. ATC, Redwood City.
Braga, F.,Gigliotti, R.,Monti, G., et al., 2014. Speedup of post earthquake community recovery:the case of precast industrial buildings after the Emilia 2012 earthquake.Bulletin of Earthquake Engineering 12(5), 2405-2418.
Demartino, C., Vanzi, I., Monti, G., 2017a. Probabilistic estimation of economic losses of portal-like precast industrial buildings.Earthquakes and Structures 13(3), 323-335.
Demartino, C., Monti, G., Vanzi, I., 2017b. Seismic loss-of-support conditions of frictional beam-to-column connections.Structural Engineering and Mechanics 61(4), 527-538.
Demartino, C., Vanzi, I., Monti, G., et al., 2018. Precast industrial buildings in southern Europe:loss of support at frictional beam-to-column connections under seismic actions. Bulletin of Earthquake Engineering 16(1), 259-294.
Federal Emergency Management Agency(FEMA), 1988. Typical Costs for Seismic Rehabilitation of Existing Buildings. FEMA156-157. FEMA, Washington DC.
Federal Highway Administration(FHWA), 2006. Seismic Retrofitting Manual for Highway Structures:Part 1-Bridges.FHWA, Washington DC.
Fiore, A., Marano, G.C., 2017. Serviceability performance analysis of concrete box girder bridges under traffic-induced vibrations by structural health monitoring:a case study. International Journal of Civil Engineering 16(5), 553-565.
Fiore, A., Monaco, P., Raffaele, D., 2012. Viscoelastic behaviour of non-homogeneous variable-section beams with post-poned restraints. Computers and Concrete 9(5), 375-392.
Fiore, A., Sulpizio, C., Demartino, C., et al., 2018a. Seismic vulnerability assessment of historical centres at urban scale.International Journal of Architectural Heritage 12(2), 257-269.
Fiore, A., Demartino, C., Greco, R., et al., 2018b. Seismic performance of spherical liquid storage tanks:a case study.International Journal of Advanced Structural Engineering 10(2), 121-130.
Fiorentino, G., Forte, A., Pagano, E., et al., 2018. Damage patterns in the town of Amatrice after August 24th 2016 Central Italy earthquakes. Bulletin of Earthquake Engineering 16(3),1399-1423.
Greco, R., Fiore, A., Marano, G.C., 2014. The role of modulation function in nonstationary stochastic earthquake model.Journal of Earthquake and Tsunami 8(5), 1450015.
Grossi, P., Kunreuther, H., 2005. Catastrophe Modeling:a New Approach to Managing Risk. Springer Science&Business Media, Cham.
Imperatore, S., Lavorato, D., Nuti, C., et al., 2012. Shear performance of existing reinforced concrete T-beams strengthened with FRP. In:6th International Conference on FRP Composites in Civil Engineering, Roma, 2012.
Institutul de Cercetari in Constructii si Economia Constructiilor(INCERC), 2000. Probleme de Economia Constructiilor,Bucharest, Romania. INCERC, Bucuresti.
Kappos, A.J., Dimitrakopoulos, E.G., 2008. Feasibility of preearthquake strengthening of buildings based on cost-benefitand life-cycle cost analysis, with the aid of fragility curves.Natural Hazards 45, 33-54.
Kappos, A., Lekidis, V., Panagopoulos, G., et al., 2007. Analytical estimation of economic loss for buildings in the area struck by the 1999 Athens earthquake and comparison with statistical repair costs. Earthquake Spectra 23, 333-355.
Lavorato, D., Nuti, C., 2010. Seismic response of repaired bridges by pseudodynamic tests. In:5th International Conference on Bridge Maintenance, Safety and Management, Philadelphia,2010.
Lavorato, D., Nuti, C., 2015. Pseudo-dynamic tests on reinforced concrete bridges repaired and retrofitted after seismic damage. Engineering Structures 94, 96-112.
Lavorato, D., Nuti, C., Santini, S., et al., 2015. A repair and retrofitting intervention to improve plastic dissipation and shear strength of Chinese RC bridges. In:IABSE Conference,Geneva, 2015.
Lavorato, D., Vanzi, I., Nuti, C., et al., 2017. Generation of nonsynchronous earthquake signals. In:Gardoni, P.(Ed.), Risk and Reliability Analysis:Theory and Applications. Springer Series in Reliability Engineering, Cham, pp. 169-198.
Marano, G.C., Acciani, G.,Fiore, A.,et al.,2015. Integration algorithm for covariance non-stationary dynamic analysis of SDOF systems using equivalent stochastic linearization.International Journal of Structural Stability and Dynamics 15(2), 1450044.
Neddermann, R., 2007. Kostenermittlung im Altbau. Aktuelle Baupreise-Rechtliche Grundlagen-Technische Beurteilung-Kostenermittlungsmethoden, fourth ed.Werner, Neuwied.
Nuti, C., Vanzi, I., 2003. To retrofit or not to retrofit? Engineering Structures 25(9), 701-711.
Nuti, C., Santini, S., Vanzi, I., 2004. Damage, vulnerability and retrofitting strategies for the Molise hospital system following the 2002 Molise, Italy, earthquake. Earthquake Spectra 20(S1), 285-299.
Nuti, C., Rasulo, A., Vanzi, I., 2009. Seismic assessment of utility systems:application to water, electric power and transportation networks-safety, reliability and risk analysis:theory, methods and applications. In:ESREL Conference,Prague, 2009.
Paudel, Y., Botzen, W.J.W., Aerts,J.C.J.H., et al., 2015. Risk allocation in a public-private catastrophe insurance system:an actuarial analysis of deductibles, stop-loss,and premiums. Journal of Flood Risk Management 8(2),116-134.
Quaranta, G., Fiore, A., Marano, G.C., 2014. Optimum design of prestressed concrete beams using constrained differential evolution algorithm. Structural and Multidisciplinary Optimization 49(3), 441-453.
Rose, A., 2004. Economic principles, issues, and research priorities in hazard loss estimation. In:Okuyama, Y.,Chang, S.E.(Eds.), Modeling Spatial and Economic Impacts of Disasters. Springer, Berlin, pp. 13-36.
Smyth, A.W., Altay, G., Deodatis, G., et al., 2004. Probabilistic benefit-cost analysis for earthquake damage mitigation:evaluating measures for apartment houses in Turkey.Earthquake Spectra 20(1), 171-203.
Vanzi, I., Marano, G.C., Monti, G., et al., 2015. A synthetic formulation for the Italian seismic hazard and code implications for the seismic risk. Soil Dynamics and Earthquake Engineering 77,111-122.
Yang, T.Y, Moehle, J.,Stojadinovic, B.,et al., 2009. Seismic performance evaluation of facilities:methodology and implementation. Journal of Structural Engineering 135(10),1146-1154.
Zhou, Z., Lavorato, D., Nuti, C., et al., 2015. A model for carbon and stainless steel reinforcing bars including inelastic buckling forevaluation of capacity of existing structures. In:5th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Crete Island, 2015.