Mathematical Problems in Engineering

Research Article

Performance-Based Multiobjective Optimal Seismic Retrofit Method for a Steel Moment-Resisting Frame Considering the Life-Cycle Cost

Optimal retrofit scheme of the nine-story SMRF for performance objective .


	Before	Scheme 1	Scheme 2	Scheme 3	Scheme 4	Scheme 5	Scheme 6	Scheme 7

Number of retrofit connections	0	23	30	40	47	50	58	79
Retrofit location	—	X1, X8-9 X23, X25 X28–29 X41, X45 X48, X51 X55, X62 X64, X67 X71, X73 X76-77 X81, X83 X86-87	X2-3, X14 X18-19 X21, X24 X32, X34 X37, X40 X46, X47 X52 X55–59 X62, X67 X69 X70–72 X74, X78 X81 X86-87	X3, X7, X11 X19–21 X23-24 X28 X30–34 X36–38 X44, X48 X51-X52 X54 X56-57 X64–66 X68, X71 X75 X77–80 X82–86 X90	X2–4, X7 X11, X13 X17 X21-22 X25–27 X29–32 X34, X36 X38–40 X42-43 X47–51 X54–X56 X58, X60 X62, X65 X69 X71–73 X75-76 X78, X80 X83-84 X86–88	X1, X4 X8–12 X14, X16 X20 X23-24 X26, X29 X32–37 X39, X42 X45–49 X53, X55 X57 X60-61 X63–65 X67, X69 X71-72 X74-75 X78 X80–82 X86–90	X1, X3–6 X8–X10 X15, X18 X20, X22 X24–28 X31–X35X41– X44X46-47 X49– X52X54– X57X59- X60X63– X66X68–70 X72 X75– X77X79–84 X86 X88-89	X1 X3–13 X15–21 X24–33 X35–37 X39–46 X49–62 X65–79 X81–90
Initial retrofit cost (thousand dollars)	0	460	600	800	940	1,000	1,160	1,580
Lifetime seismic damage cost (thousand dollars)	1,839	1,505	1,327	1,164	1,147	1,093	1,077	1,041
Maximum interstory drift ratio (%)	5.71	4.82	4.48	4.12	4.26	4.06	4.01	4.23
Dissipated energy (kN·m)	3,522.71	4,304.61	4,424.63	4,814.29	4,931.91	5,022.90	5,125.60	5,716.21