Question $5[20$ Marks$]$

You are tasked with designing the trusses for a bridge to allow golf carts to cross a stream. So as not to interfere with golf balls, a deck truss is required. Figure $4$ shows the general elevation of the location, the required span is $6\mathrm{.}0$ m $.$ The truss will be constructed with lumber available in the dimensions and at the costs indicated in Table $1.$ Other pertinent design information is summarized below.

Specified live load of $P=20kN,$ which should be considered as being potentially applied to any joint along the top chord.

For lumber, assume $E=14,000$MPa,$f_c=27$MPa,$f{y}_y=100$MPa.

A load factor of $1\mathrm{.}5$ should be applied to live loads at ULS. A resistance factor of $0\mathrm{.}9$ should be used for both tensile and compressive capacities.

Assume that all connections can be made safely and do not need to be considered in your solution.

Please follow these steps in preparing your design:

$[2]$ a$)$ Sketch two possible alternative designs.

$2$ b$)$ Select a preferred alternative and provide a brief justification

$[12]$ c$)$ For your chosen preliminary design, determine the factored axial forces in all members and specify the required proportions of all members to meet ultimate limit states requirements. Show all supporting calculations.

$[4]$ d$)$ Write a brief paragraph describing the steps you would take to iterate and improve your design if you had more time to work on it$.$

Table $1-$ Lumber Availability

$\backslash$table$[[$Nominal$,$X$-$section $(mm),$Cost $(\frac{8^{\text{'}}}{{12}^{\text{'}}}\frac{?}{{16}^{\text{'}}})$