E $405/505-$ Decision$-$Making for Sustainable and Resilient Civil Infrastructure Homework No$\mathrm{.}5$: Sustainability Due date: Tuesday, November $17,2020($at the beginning of the lecture period$)$ Problem $1(50$ points$)($a$)$ Discuss pros and cons of green building, $(6)$ List three buildings with different LEED rating levels $($i$.$c$.,$ LEED Platinum. LEED Gold, and LEED Silver buildings, respectively$)$ in Washington State. Discuss pros and cons of each building. Problem $2(30$ points$)$ The expected life$-$cycle cost of a building located in an earthquake$-$prone area can be expressed as follows: E$[$C$($t$,$ x$))=$ Co$+$GP $(1-$ e$-$dt$)$ where Co$=$ initial cost; G $=$ failure cost $($including reconstruction cost$),$ P$,=$ probability of failure; v $=$ annual rate of occurrence of an earthquake event; $2.=$ annual discount rate, and t $=$ the time of occurrence of an earthquake event. Based on the assumptions that $(1)$ hazard intensity is modeled by an exponential distribution with a mean value of $1\mathrm{.}0$; $($ii$)$ resistance is deterministic and a single limit state of design intensity being exceeded is considered; and $($iii$)$ initial cost is proportional to the design intensity X$,$ Eqn $(1)$ can be expressed as: E$[$C$($t$,$ x$))=$ ax $+($ax $+$ C$)*(1-$e$-$dt$)(2)$ where a$,$ C $=$ constants, and X $-$ design intensity of a building. Let's assume that a $=5($arbitrary unit$),$ C $=50($arbitrary unit$),$ v$=0\mathrm{.}2/$year$,$ and $1=0\mathrm{.}05/$year$.$ The optimal design intensity $($X$)$ is the design intensity with the minimum expected life$-$cycle cost. Draw a plot showing the optimal design intensities as a function of design life $($from $0$ to $50$ years$).$ Problem $3(20$ points$)$ The design life and all the relevant costs of a bridge are provided below. Draw an expenditure stream diagram and compute the life$-$cycle cost of the bridge. $$ Design life of the bridge: $80$ years Discount rate: $5\%$ per year Activities Year Expenditure in dollars Construction SSOM Regular maintenance Every $30$ years $$2$M Special maintenance and repair $40$ $$15$M Demolition $$3$M Salvage residual value $$12$M $08080$