Intelligent Life Cycle Cost-Based Framework for Seismic Design of Conventional Structures
Abstract
:1. Introduction
2. Methodology
subject to Cj(s) ≤ 0, j = 1, …, i
Multi-Objective Optimization Algorithm
- Initial population: Generate Pt parent vectors of the first generation (si, I = 1,2, …, Pt).
- Design and control stage: Perform structural analysis and review code constraints.
- Calculation of fitness indicators: Evaluate the objective functions CIC(si) and CLCC(si) for Pt parent vectors.
- Non-dominated sorting: Create a temporary Pareto front curve.
- Generation of offspring: Produce offspring vectors Qt by applying crossover and mutation processes to parent vectors.
- Design and control stage: Perform structural analysis and review code constraints.
- Calculation of fitness indicators: Evaluate the objective functions CIC(si) and CLCC(si) for Qt parent vectors.
- Non-dominated sorting: Sort Pt + Qt vectors based on dominance conditions.
- Selection stage: Calculate crowding distance and obtain new parents Pt+1 from Pt + Qt vectors.
- Sorting: Create a new temporary Pareto front curve.
- Convergence check: The algorithm stops if the stopping condition is met; otherwise, return to step 3.
3. Initial and LCC Objective Functions
3.1. Indirect Costs
3.1.1. Cost of Repair
3.1.2. Loss of Possessions
3.1.3. Relocation Cost
3.1.4. Economic Cost
3.1.5. Cost of Injuries
3.1.6. Cost of Human Fatality
4. Numerical Study
4.1. Basic Information
4.2. Optimization Procedure
5. Conclusions
- As structures increase in height, their LCC becomes more sensitive to changes in the initial cost. Even slight alterations in the initial cost can have significant long-term cost implications.
- Reducing the LCC of irregular structures requires a higher initial cost than regular structures. For instance, in the 13-story model, increasing the initial cost by 17% resulted in LCC reductions of approximately 48% and 40% for regular and setback irregular structures, respectively.
- The results showed that 7- and 10-story buildings had minimal differences, but the outcomes for 13-story buildings were markedly different. From economic and urban perspectives, this suggests that the number of floors has little impact on mid-rise buildings, beyond a certain limit, compared to high-rise buildings. Thus, the ideal number of floors should be determined based on each city’s economic and social considerations to achieve greater cost-effectiveness in construction.
- In mid-rise structures, the LCCs of regular buildings were more sensitive to changes in the initial costs compared to setback irregular structures. However, this relationship was reversed in high-rise buildings, and setback irregular structures displayed greater sensitivity to changes in initial costs despite having a lower floor area than regular buildings.
- Irregular high-rise structures exhibited a critical threshold where even a slight decrease in initial construction costs significantly increased LCCs. This is evident in the Pareto front curve, which displayed a noticeable break in those regions. It suggests that irregular high-rise structures are more susceptible to damage from seismic loads, leading to significantly higher financial and lifetime costs. Thus, optimizing structures exclusively based on minimizing initial weight may not be the most financially sound and safest approach.
- Compared to research using manual methods and limited models for optimization, utilizing a metaheuristic algorithm for optimizing LCCs not only identified the optimal LCCs but also reduced the structure’s weight due to its ability to explore more models. In other words, applying the bi-objective GA facilitated the simultaneous optimization of structure LCCs and weight reduction.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Story | Typical | Section |
---|---|---|
1–3 | C11 | BOX380X30, BOX400X25, BOX400X30, BOX420X25, BOX420X30, BOX440X30, BOX460X30, BOX440X25, BOX360X20, BOX340X20, BOX280X20, BOX300X20, BOX320X20, BOX480X25, BOX480X30, BOX500X25, BOX500X30, BOX520X25, BOX520X30, BOX540X25, BOX540X30, BOX560X25, BOX560X30, BOX580X25, BOX580X30, BOX600X25, BOX600X30 |
C21 | BOX400X20, BOX380X25, BOX400X25, BOX400X30, BOX420X25, BOX420X30, BOX380X20, BOX440X25, BOX440X30, BOX460X30, BOX360X20, BOX340X20, BOX320X20, BOX300X20, BOX480X25, BOX480X30, BOX500X25, BOX500X30, BOX520X25, BOX520X30, BOX540X25, BOX540X30 | |
C31 | BOX400X20, BOX380X25, BOX400X25, BOX400X30, BOX420X25, BOX420X30, BOX380X20, BOX440X25, BOX440X30, BOX460X30, BOX360X20, BOX340X20, BOX320X20, BOX300X20, BOX480X25, BOX480X30, BOX500X25, BOX500X30, BOX520X25, BOX520X30, BOX540X25, BOX540X30 | |
B11 | IPE600, IPE550, IPE500, IPE450, IPE400 | |
B21 | IPE600, IPE550, IPE500, IPE450, IPE400, IPE360 | |
4–5 | C12 | BOX340X20, BOX360X20, BOX360X25, BOX340X25, BOX420X30, BOX380X25, BOX380X30, BOX380X20, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX320X20, BOX260X20, BOX280X20, BOX300X20, BOX240X20, BOX420X25, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25 |
C22 | BOX320X20, BOX340X20, BOX360X20, BOX380X20, BOX400X20, BOX400X25, BOX400X30, BOX420X25, BOX340X25, BOX360X15, BOX360X25, BOX380X25, BOX380X30, BOX300X20, BOX240X20, BOX260X20, BOX280X20, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30, BOX480X25, BOX480X30 | |
C32 | BOX320X20, BOX280X20, BOX300X20, BOX340X20, BOX340X25, BOX260X20, BOX360X25, BOX300X15, BOX320X15, BOX220X20, BOX240X20, BOX220X15, BOX220X12, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30, BOX480X25, BOX480X30 | |
B12 | IPE550, IPE500, IPE450, IPE400, IPE360, IPE330 | |
B22 | IPE500, IPE450, IPE400, IPE360, IPE330 | |
6–7 | C13 | BOX240X20, BOX260X20, BOX280X20, BOX300X20, BOX320X20, BOX340X20, BOX240X15, BOX260X15, BOX280X15, BOX300X15, BOX320X15, BOX340X15, BOX200X12, BOX200X15, BOX200X20, BOX220X12, BOX220X15, BOX220X20, BOX340X25, BOX360X15, BOX360X20, BOX360X25 |
C23 | BOX220X20, BOX240X20, BOX260X20, BOX280X20, BOX300X20, BOX220X15, BOX240X15, BOX260X15, BOX280X15, BOX180X10, BOX180X12, BOX200X12, BOX200X15, BOX200X20, BOX320X15, BOX320X20, BOX340X15, BOX340X20, BOX340X25, BOX360X15 | |
C33 | BOX200X12, BOX220X15, BOX220X20, BOX180X12, BOX200X20, BOX200X15, BOX220X12, BOX180X10, BOX240X15, BOX240X20, BOX260X15, BOX260X20, BOX280X15, BOX280X20 | |
B13 | IPE500, IPE450, IPE400, IPE360, IPE330, IPE300, IPE270 | |
B23 | IPE450, IPE400, IPE360, IPE330, IPE300, IPE270, IPE240 |
Story | Typical | Section |
---|---|---|
1–3 | C11 | BOX300X20, BOX320X20, BOX340X20, BOX360X20, BOX380X20, BOX380X25, BOX400X20, BOX400X25, BOX400X30, BOX420X25, BOX420X30, BOX440X25, BOX440X30, BOX460X30, BOX480X25, BOX480X30, BOX500X25, BOX500X30, BOX520X25, BOX520X30, BOX540X25, BOX540X30, BOX560X25, BOX560X30, BOX580X25, BOX580X30, BOX600X25, BOX600X30 |
C21 | BOX300X20, BOX320X20, BOX340X20, BOX360X20, BOX380X20, BOX380X25, BOX400X20, BOX400X25, BOX400X30, BOX420X25, BOX420X30, BOX440X25, BOX440X30, BOX460X30, BOX480X25, BOX480X30, BOX500X25, BOX500X30, BOX520X25, BOX520X30, BOX540X25, BOX540X30 | |
C31 | BOX240X20, BOX260X20, BOX280X20, BOX300X15, BOX300X20, BOX320X15, BOX320X20, BOX340X20, BOX340X25, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30 | |
C41 | BOX240X20, BOX260X20, BOX280X20, BOX300X15, BOX300X20, BOX320X15, BOX320X20, BOX340X20, BOX340X25, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30 | |
B11 | IPE500, IPE450, IPE400, IPE360 | |
B21 | IPE500, IPE450, IPE400, IPE360, IPE330, IPE300 | |
B31 | IPE600, IPE550, IPE500, IPE450, IPE400, IPE360 | |
B41 | IPE450, IPE400, IPE360, IPE330, IPE300 | |
4–5 | C12 | BOX240X20, BOX260X20, BOX280X20, BOX300X20, BOX320X20, BOX340X20, BOX340X25, BOX360X15, BOX360X20, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30, BOX480X25, BOX480X30 |
C22 | BOX240X20, BOX260X20, BOX280X20, BOX300X20, BOX320X20, BOX340X20, BOX340X25, BOX360X15, BOX360X20, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25 | |
C32 | BOX180X10, BOX180X12, BOX200X12, BOX200X15, BOX200X20, BOX220X12, BOX220X15, BOX220X20, BOX240X15, BOX240X20, BOX260X15, BOX260X20, BOX280X15, BOX280X20, BOX300X15, BOX300X20, BOX320X15, BOX320X20 | |
C42 | BOX180X10, BOX180X12, BOX200X12, BOX200X15, BOX200X20, BOX220X12, BOX220X15, BOX220X20, BOX240X15, BOX240X20, BOX260X15, BOX260X20, BOX280X15, BOX280X20 | |
B12 | IPE450, IPE400, IPE360, IPE330, IPE300, IPE270 | |
B22 | IPE500, IPE450, IPE400, IPE360, IPE330 | |
B32 | IPE500, IPE450, IPE400, IPE360, IPE330, IPE300 | |
B42 | IPE400, IPE360, IPE330, IPE300, IPE270 | |
6–7 | C13 | BOX180X10, BOX180X12, BOX200X12, BOX200X15, BOX200X20, BOX220X12, BOX220X15, BOX220X20, BOX240X15, BOX240X20, BOX260X15, BOX260X20, BOX280X15, BOX280X20, BOX300X15, BOX300X20 |
C23 | BOX180X10, BOX180X12, BOX200X12, BOX200X15, BOX200X20, BOX220X12, BOX220X15, BOX220X20, BOX240X15, BOX240X20, BOX260X15, BOX260X20, BOX280X15, BOX280X20 | |
B13 | IPE450, IPE400, IPE360, IPE330, IPE300, IPE270 | |
B23 | IPE450, IPE400, IPE360, IPE330, IPE300, IPE270 | |
B33 | IPE400, IPE360, IPE330, IPE300, IPE270, IPE240 |
Story | Typical | Section |
---|---|---|
1–3 | C11 | BOX440X25, BOX440X30, BOX460X30, BOX480X25, BOX480X30, BOX500X25, BOX500X30, BOX520X25, BOX520X30, BOX540X25, BOX540X30, BOX560X25, BOX560X30, BOX580X25, BOX580X30, BOX600X25, BOX600X30 |
C21 | BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X25, BOX420X30, BOX440X25, BOX440X30, BOX460X30, BOX480X25, BOX480X30, BOX500X25, BOX500X30, BOX520X25, BOX520X30, BOX540X25, BOX540X30 | |
C31 | BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X25, BOX420X30, BOX440X25, BOX440X30, BOX460X30, BOX480X25, BOX480X30, BOX500X25, BOX500X30, BOX520X25, BOX520X30, BOX540X25, BOX540X30 | |
B11 | IPE450, IPE500, IPE550, IPE600 | |
B21 | IPE400, IPE450, IPE500, IPE550, IPE600 | |
4–6 | C12 | BOX360X20, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30, BOX480X25, BOX480X30 |
C22 | BOX360X20, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30 | |
C32 | BOX360X20, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30 | |
B12 | IPE400, IPE450, IPE500, IPE550, IPE600 | |
B22 | IPE360, IPE400, IPE450, IPE500 | |
7–8 | C13 | BOX260X20, BOX280X15, BOX280X20, BOX300X20, BOX320X20, BOX340X20, BOX340X25, BOX360X20, BOX360X25 BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20 |
C23 | BOX240X20, BOX260X15, BOX260X20, BOX280X15, BOX280X20, BOX300X15, BOX300X20, BOX320X15, BOX320X20, BOX340X20, BOX340X25, BOX360X15, BOX360X20 | |
C33 | BOX240X20, BOX260X15, BOX260X20, BOX280X15, BOX280X20, BOX300X15, BOX300X20, BOX320X15, BOX320X20, BOX340X20, BOX340X25, BOX360X15, BOX360X20 | |
B13 | IPE330, IPE360, IPE400, IPE450 | |
B23 | IPE300, IPE330, IPE360, IPE400 | |
9–10 | C14 | BOX200X12, BOX200X15, BOX200X20, BOX220X12, BOX220X15, BOX220X20, BOX240X15, BOX240X20, BOX260X15, BOX260X20, BOX280X15, BOX280X20, BOX300X15, BOX300X20, BOX320X15, BOX360X20, BOX360X25, BOX380X20 |
C24 | BOX180X10, BOX180X12, BOX200X12, BOX200X15, BOX200X20, BOX220X12, BOX220X15, BOX220X20, BOX240X15, BOX240X20, BOX260X15, BOX260X20, BOX280X15, BOX280X20 | |
C34 | BOX180X10, BOX180X12, BOX200X12, BOX200X15, BOX200X20, BOX220X12, BOX220X15, BOX220X20, BOX240X15, BOX240X20, BOX260X15, BOX260X20, BOX280X15, BOX280X20 | |
B14 | IPE270, IPE300, IPE330, IPE360 | |
B24 | IPE270, IPE300, IPE330 |
Story | Typical | Section |
---|---|---|
1–2 | C11 | BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30, BOX480X20, BOX480X25, BOX480X30, BOX500X25, BOX500X30 |
C21 | BOX340X20, BOX340X25, BOX360X15, BOX360X20, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30 | |
C31 | BOX320X20, BOX340X15, BOX340X20, BOX340X25, BOX360X15, BOX360X20, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20 | |
C41 | BOX320X20, BOX340X15, BOX340X20, BOX340X25, BOX360X15, BOX360X20, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20 | |
B11 | IPE330, IPE360, IPE400, IPE450, IPE500 | |
B21 | IPE330, IPE360, IPE400, IPE450, IPE500 | |
B31 | IPE400, IPE450, IPE500, IPE550, IPE600 | |
B41 | IPE300, IPE330, IPE360, IPE400, IPE450 | |
3–4 | C12 | BOX340X20, BOX340X25, BOX360X15, BOX360X20, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30, BOX480X20, BOX480X25, BOX480X30, BOX500X25, BOX500X30 |
C22 | BOX340X20, BOX340X25, BOX360X15, BOX360X20, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30, BOX480X20, BOX480X25, BOX480X30 | |
C32 | BOX280X15, BOX280X20, BOX300X15, BOX300X20, BOX320X15, BOX320X20, BOX340X15, BOX340X20, BOX340X25, BOX360X15, BOX360X20, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX440X20, BOX440X25, BOX440X30 | |
C42 | BOX320X15, BOX320X20, BOX340X15, BOX340X20, BOX340X25, BOX360X15, BOX360X20, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30 | |
B11 | IPE300, IPE330, IPE360, IPE400, IPE450, IPE500 | |
B21 | IPE300, IPE330, IPE360, IPE400, IPE450, IPE500 | |
B31 | IPE360, IPE400, IPE450, IPE500, IPE550, IPE600 | |
B41 | IPE300, IPE330, IPE360, IPE400, IPE450 | |
5–7 | C13 | BOX320X20, BOX340X15, BOX340X20, BOX340X25, BOX360X15, BOX360X20, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30 |
C23 | BOX340X20, BOX340X25, BOX360X15, BOX360X20, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30 | |
C33 | BOX280X20, BOX300X15, BOX300X20, BOX320X15, BOX320X20, BOX340X20, BOX340X25, BOX360X15, BOX360X20, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20 | |
C43 | BOX260X15, BOX260X20, BOX280X15, BOX280X20, BOX300X15, BOX300X20, BOX320X15, BOX320X20, BOX340X20, BOX340X25, BOX360X15, BOX360X20, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25 | |
B13 | IPE300, IPE330, IPE360, IPE400, IPE450, IPE500 | |
B23 | IPE300, IPE330, IPE360, IPE400, IPE450, IPE500 | |
B33 | IPE300, IPE330, IPE360, IPE400, IPE450, IPE500 | |
B43 | IPE270, IPE300, IPE330, IPE360, IPE400, IPE450 | |
8–10 | C14 | BOX180X10, BOX180X12, BOX200X12, BOX200X15, BOX200X20, BOX220X12, BOX220X15, BOX220X20, BOX240X15, BOX240X20, BOX260X15, BOX260X20, BOX280X15, BOX280X20, BOX300X15, BOX300X20, BOX320X15, BOX320X20, BOX340X20, BOX340X25, BOX360X15, BOX360X20, BOX360X25, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25 |
C24 | BOX180X10, BOX180X12, BOX200X12, BOX200X15, BOX200X20, BOX220X12, BOX220X15, BOX220X20, BOX240X15, BOX240X20, BOX260X15, BOX260X20, BOX280X15, BOX280X20, BOX300X15, BOX300X20, BOX320X15, BOX320X20, BOX340X20, BOX340X25, BOX360X15, BOX360X20, BOX360X25 | |
B14 | IPE270, IPE300, IPE330, IPE360, IPE400, IPE450 | |
B24 | IPE270, IPE300, IPE330, IPE360, IPE400, IPE450 | |
B34 | IPE240, IPE270, IPE300, IPE330, IPE360, IPE400 |
Story | Typical | Section |
---|---|---|
1–3 | C11 | BOX600X25, BOX600X30, BOX620X30, BOX640X30, BOX660X30, BOX660X35, BOX680X30, BOX680X35, BOX700X35, BOX700X40, BOX750X35, BOX750X40, BOX800X35, BOX800X40 |
C21 | BOX560X25, BOX560X30, BOX580X25, BOX580X30, BOX600X25, BOX600X30, BOX620X30, BOX640X30, BOX660X30, BOX660X35, BOX680X30, BOX680X35, BOX700X35, BOX700X40, BOX750X35 | |
C31 | BOX520X25, BOX520X30, BOX540X25, BOX540X30, BOX560X25, BOX560X30, BOX580X25, BOX580X30, BOX600X25, BOX600X30, BOX620X30, BOX640X30, BOX660X30, BOX660X35 | |
B11 | IPE500, IPE550, IPE600 | |
B21 | IPE500, IPE550, IPE600 | |
4–6 | C12 | BOX540X25, BOX540X30, BOX560X25, BOX560X30, BOX580X25, BOX580X30, BOX600X25, BOX600X30, BOX620X30, BOX640X30, BOX660X30, BOX660X35, BOX680X30, BOX680X35 |
C22 | BOX500X30, BOX520X25, BOX520X30, BOX540X25, BOX540X30, BOX560X25, BOX560X30, BOX580X25, BOX580X30, BOX600X25, BOX600X30, BOX620X30, BOX640X30 | |
C32 | BOX480X20, BOX480X25, BOX480X30, BOX500X20, BOX500X25, BOX500X30, BOX520X25, BOX520X30, BOX540X25, BOX540X30, BOX560X25, BOX560X30, BOX580X25, BOX580X30, BOX600X25 | |
B12 | IPE450, IPE500, IPE550 | |
B22 | IPE450, IPE500, IPE550 | |
7–9 | C13 | BOX460X20, BOX460X25, BOX460X30, BOX480X20, BOX480X25, BOX480X30, BOX500X20, BOX500X25, BOX500X30, BOX520X25, BOX520X30, BOX540X25, BOX540X30, BOX560X25, BOX560X30 |
C23 | BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30, BOX480X20, BOX480X25, BOX480X30, BOX500X20, BOX500X25BOX500X30 | |
C33 | BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30, BOX480X20 | |
B13 | IPE400, IPE450, IPE500 | |
B23 | IPE360, IPE400, IPE450 | |
10–11 | C14 | BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30, BOX480X20 |
C24 | BOX340X20, BOX360X20, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30 | |
C34 | BOX260X20, BOX280X20, BOX300X20, BOX320X20, BOX340X20, BOX360X20, BOX380X20, BOX380X25, BOX380X30 | |
B14 | IPE360, IPE400, IPE450 | |
B24 | IPE330, IPE360, IPE400 | |
12–13 | C15 | BOX200X20, BOX220X15, BOX220X20, BOX240X15, BOX240X20, BOX260X20, BOX280X20 |
C25 | BOX200X15, BOX200X20, BOX220X15, BOX220X20, BOX240X15, | |
C35 | BOX180X10, BOX180X12, BOX200X15, BOX200X20, BOX220X15, BOX220X20 | |
B15 | IPE300, IPE330, IPE360 | |
B25 | IPE270, IPE300, IPE330 |
Story | Typical | Section |
---|---|---|
1–3 | C11 | BOX700X35, BOX700X40, BOX750X35, BOX750X40, BOX800X35, BOX800X40 |
C21 | BOX660X35, BOX680X30, BOX680X35, BOX700X35, BOX700X40, BOX750X35, BOX750X40, BOX800X35, BOX800X40 | |
C31 | BOX540X25, BOX540X30, BOX560X25, BOX560X30, BOX580X25, BOX580X30, BOX600X25, BOX600X30, BOX620X30, BOX640X30, BOX660X30, BOX660X35, BOX680X30, BOX680X35, BOX700X35, BOX700X40, BOX750X35, BOX750X40 | |
C41 | BOX500X20, BOX500X25, BOX500X30, BOX520X25, BOX520X30, BOX540X25, BOX540X30, BOX560X25, BOX560X30, BOX580X25, BOX580X30, BOX600X25, BOX600X30, BOX620X30, BOX640X30, BOX660X30, BOX660X35, BOX680X30, BOX680X35, BOX700X35, BOX700X40 | |
B11 | IPE500, IPE550, IPE600 | |
B21 | IPE500, IPE550, IPE600 | |
B31 | IPE500, IPE550, IPE600 | |
B41 | IPE500, IPE550, IPE600 | |
4–6 | C12 | BOX600X30, BOX620X30, BOX640X30, BOX660X30, BOX660X35, BOX680X30, BOX680X35, BOX700X35, BOX700X40, BOX750X35, BOX750X40 |
C22 | BOX560X30, BOX580X25, BOX580X30, BOX600X25, BOX600X30, BOX620X30, BOX640X30, BOX660X30, BOX660X35, BOX680X30, BOX680X35, BOX700X35, BOX700X40 | |
C32 | BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30, BOX480X20, BOX480X25, BOX480X30, BOX500X20, BOX500X25, BOX500X30, BOX520X25, BOX520X30, BOX560X30, BOX580X25, BOX580X30, BOX600X25, BOX600X30, BOX620X30, BOX640X30, BOX660X30, BOX660X35 | |
C42 | BOX360X20, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30, BOX500X20, BOX500X25, BOX500X30, BOX520X25, BOX520X30, BOX540X25, BOX540X30, BOX560X25, BOX560X30, BOX580X25, BOX580X30, BOX600X25, BOX600X30, BOX620X30, BOX640X30 | |
B11 | IPE450, IPE500, IPE550 | |
B21 | IPE450, IPE500, IPE550 | |
B31 | IPE500, IPE550, IPE600 | |
B41 | IPE450, IPE500, IPE550 | |
7–9 | C13 | BOX500X30, BOX520X25, BOX520X30, BOX560X30, BOX580X25, BOX580X30, BOX600X25, BOX600X30, BOX620X30, BOX640X30, BOX660X30, BOX660X35 |
C23 | BOX480X25, BOX480X30, BOX500X20, BOX500X25, BOX500X30, BOX520X25, BOX520X30, BOX560X30, BOX580X25, BOX580X30, BOX600X25, BOX600X30 | |
C33 | BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30, BOX480X20, BOX480X25, BOX480X30, BOX500X20, BOX500X25, BOX500X30, BOX520X25, BOX520X30, BOX540X25, BOX540X30 | |
C43 | BOX360X20, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30 | |
B13 | IPE400, IPE450, IPE500 | |
B23 | IPE360, IPE400, IPE450 | |
B33 | IPE400, IPE450, IPE500 | |
B43 | IPE400, IPE450, IPE500 | |
10–11 | C14 | BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30, BOX480X20, BOX480X25, BOX480X30, BOX500X20, BOX500X25, BOX500X30, BOX520X25, BOX520X30 |
C24 | BOX360X20, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25, BOX440X30, BOX460X20, BOX460X25, BOX460X30 | |
B14 | IPE360, IPE400, IPE450 | |
B24 | IPE330, IPE360, IPE400 | |
B34 | IPE360, IPE400, IPE450 | |
12–13 | C15 | BOX300X20, BOX320X20, BOX340X20, BOX360X20, BOX380X20, BOX380X25, BOX380X30, BOX400X20, BOX400X25, BOX400X30, BOX420X20, BOX420X25, BOX420X30, BOX440X20, BOX440X25 |
C25 | BOX240X20, BOX260X15, BOX260X20, BOX280X15, BOX280X20, BOX300X20, BOX320X20, BOX340X20 | |
B15 | IPE300, IPE330, IPE360 | |
B25 | IPE270, IPE300, IPE330 | |
B35 | IPE300, IPE330, IPE360 |
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Performance Level | Damage State | Inter-Story Drift (%) |
---|---|---|
1 | None | ∆ < 0.2 |
2 | Slight | 0.2 < ∆ < 0.5 |
3 | Light | 0.5 < ∆ < 0.7 |
4 | Moderate | 0.7 < ∆ < 1.5 |
5 | Heavy | 1.5 < ∆ < 2.5 |
6 | Major | 2.5 < ∆ < 5.0 |
7 | Destroyed | 5.0 < ∆ |
Performance Level | Damage State | Repair Cost (Percentage of the Initial Cost) | Days of Downtime (Percentage of the Construction Time) |
---|---|---|---|
1 | None | 0 | 0 |
2 | Slight | 0.5 | 0.9 |
3 | Light | 5 | 3.33 |
4 | Moderate | 20 | 12.4 |
5 | Heavy | 45 | 34.8 |
6 | Major | 80 | 65.4 |
7 | Destroyed | 100 | 100 |
Performance Level | Damage State | Expected Minor Injury Incidence Rate | Expected Serious Injury Incidence Rate | Expected Fatality Incidence Rate |
---|---|---|---|---|
1 | None | 0 | 0 | 0 |
2 | Slight | 3.0 × 10−5 | 4.0 × 10−6 | 1.0 × 10−6 |
3 | Light | 3.0 × 10−4 | 4.0 × 10−5 | 1.0 × 10−5 |
4 | Moderate | 3.0 × 10−3 | 4.0 × 10−4 | 1.0 × 10−4 |
5 | Heavy | 3.0 × 10−2 | 4.0 × 10−3 | 1.0 × 10−3 |
6 | Major | 3.0 × 10−1 | 4.0 × 10−2 | 1.0 × 10−2 |
7 | Destroyed | 4.0 × 10−1 | 4.0 × 10−1 | 2.0 × 10−1 |
Variable | Cost | Equation | Basic Cost |
---|---|---|---|
Crek | Repair | Initial construction cost × building area × mean damage index | |
Cpk | Loss of content | Unit content cost × building area × mean damage index | Contents $212.5/m2 |
Crk | Relocation | Rental rate × gross leasable area × days of downtime | $0.3/daily/m2 |
Cek | Economic | Equivalent to rent | |
Cinjk | Injury | Injury cost per person × expected injury rate | $828/person (minor) $8725/person (serious) |
Cfk | Human fatality | Death cost per person × expected death rate | $510,000/person |
Limit State Level | Cre | Cp | Cr | Ce | Cinj | Cf | Sum (Ck) | |
---|---|---|---|---|---|---|---|---|
Minor | Serious | |||||||
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 4279 | 1673 | 2169 | 2169 | 2 | 2 | 32 | 10,326 |
3 | 42,793 | 16,734 | 8024 | 8024 | 16 | 22 | 321 | 75,936 |
4 | 171,174 | 66,938 | 29,881 | 29,881 | 156 | 220 | 3213 | 301,463 |
5 | 385,141 | 150,609 | 83,859 | 83,859 | 1565 | 2199 | 32,130 | 739,363 |
6 | 855,869 | 267,750 | 240,975 | 240,975 | 15,649 | 21,987 | 321,300 | 1,964,506 |
7 | 855,869 | 334,688 | 240,975 | 240,975 | 20,866 | 219,870 | 6,426,000 | 8,339,242 |
Damage State | Drift ∆k | Pk | Ck | Pk.Ck | |||
---|---|---|---|---|---|---|---|
1 | 0 | 0.100400 | −0.105805 | −0.065712 | 0.040093 | 0 | 0 |
2 | 0.002 | 0.063599 | −0.065712 | −0.032590 | 0.033122 | 10,326 | 342 |
3 | 0.005 | 0.032065 | −0.032590 | −0.020521 | 0.012069 | 75,936 | 916 |
4 | 0.007 | 0.020312 | −0.020521 | −0.003276 | 0.017245 | 301,463 | 5199 |
5 | 0.015 | 0.003271 | −0.003276 | −0.000334 | 0.002942 | 739,363 | 2175 |
6 | 0.025 | 0.000334 | −0.000334 | −1.11 × 10−6 | 0.000333 | 1,964,506 | 653 |
7 | 0.05 | 1.11 × 10−6 | −1.11 × 10−6 | 0 | 1.11 × 10−6 | 8,339,242 | 9 |
Sum | 9295 | ||||||
18.3583 | |||||||
Indirect Cost | 170,643 |
Model | Initial Structure Cost ($1000) | Indirect Cost ($1000) | LCC ($1000) | Column Sections | Beam Sections |
---|---|---|---|---|---|
A | 211.85 | 170.64 | 1028.24 | BOX180X12, BOX320X15, BOX380X20, BOX460X20, BOX500X30, BOX540X30 | IPE300, IPE330, IPE360, IPE400, IPE450, IPE500, IPE550 |
B | 181.88 | 567.17 | 1394.80 | BOX200X12, BOX200X15, BOX220X15, BOX280X20, BOX340X20, BOX380X20, BOX400X25 | IPE300, IPE330, IPE360, IPE400, IPE450 |
C | 288.23 | 68.22 | 1002.20 | BOX220X15, BOX260X20, BOX280X20, BOX320X20, BOX380X20, BOX400X20, BOX400X25, BOX420X25 | IPE300, IPE400, IPE450, IPE500, IPE550, IPE600 |
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© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
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Jebelli, S.T.; Behnam, B. Intelligent Life Cycle Cost-Based Framework for Seismic Design of Conventional Structures. Buildings 2024, 14, 2597. https://doi.org/10.3390/buildings14092597
Jebelli ST, Behnam B. Intelligent Life Cycle Cost-Based Framework for Seismic Design of Conventional Structures. Buildings. 2024; 14(9):2597. https://doi.org/10.3390/buildings14092597
Chicago/Turabian StyleJebelli, Sajad Taheri, and Behrouz Behnam. 2024. "Intelligent Life Cycle Cost-Based Framework for Seismic Design of Conventional Structures" Buildings 14, no. 9: 2597. https://doi.org/10.3390/buildings14092597