The Problem

You are a civil designer working for the state department of transportation. You have been assigned responsibility for the design of a truss bridge to carry a two$-$lane highway across the river valley shown below.

Design Objective

Satisfy all of the specifications listed below, while keeping the total cost of the project as low as possible.

Bridge Configuration

The bridge may cross the valley at any elevation from the high water level to $24$ meters above the high water level.

If the elevation of the bridge is below $24$ meters, excavation of the river banks will be required to achieve the correct highway elevation.

To provide clearance for overhead power lines $($shown above$),$ the highest point on the bridge may not exceed an elevation $32\mathrm{.}5$ meters above the high water level $(8\mathrm{.}5$ meters above the top of the river banks$).$

The bridge may consist of either standard $($simple supports$)$ or $($arch supports$).$ If necessary, the bridge may also use one intermediate $,$ located near the centre of the valley. If necessary, the bridge may also use cable $,$ located $8$ meters behind one or both abutments.

Each main truss can have no more than $100$ and no more than $200.$

The bridge will have a flat, reinforced deck. Two types of concrete are available:

Medium$-$strength concrete requires a deck thickness of $23$ centimetres $(0\mathrm{.}23$ metres$).$

High$-$strength concrete requires a deck thickness of $15$ centimetres $(0\mathrm{.}15$ meter$).$

In either case, the deck will be supported by transverse spaced at $4$ metre intervals. To accommodate these floor beams, your must have a row of joints spaced $4$ meters apart at the level of the deck. These joints are created automatically when you begin a new design.

The bridge deck will be $10$ meters wide, such that it can accommodate two lanes of traffic.

Member Properties

Materials. Each member of the truss will be made of either carbon steel, high$-$strength low$-$alloy steel, or quenched and tempered steel.

$.$ The members of the truss can be either solid bars or hollow tubes. Both types of cross$-$sections are square.

Member Size. Both cross$-$sections are available in a variety of standard sizes.

Loads

The bridge must be capable of safely carrying the following loads:

Weight of the deck.

Weight of a $5-$cm thick $,$ which might be applied at some time in the future.

Weight of the steel floor beams and supplemental bracing members $($assumed to be

$12\mathrm{.}0$ applied at each deck$-$level joint$).$

Weight of the main trusses.

Either of two possible truck loadings:

Weight of one standard H$25$ truck loading per lane, including appropriate allowance for the dynamic effects of the moving load. $($Since the bridge carries two lanes of traffic, each main truss must safely carry one H$25$ vehicle, placed anywhere along the length of the deck.$)$

Weight of a single $480$ kN Permit Loading, including appropriate allowance for the dynamic effects of the moving load. $($Since the Permit Loading is assumed to be cantered laterally, each main truss must safely carry one$-$half of the total vehicle weight, placed anywhere along the length of the deck.$)$

Structural Safety

The bridge will comply with the structural provisions of the state specified standards, to include:

Material densities

Load combinations

Tensile strength of members

Compressive strength of members

Cost

The cost of the design will be calculated using the following cost factors:

Material Cost:

Carbon steel bars $-$ $$4\mathrm{.}50$ per kilogram

Carbon steel tubes $-$ $$6\mathrm{.}30$ per kilogram

High$-$strength steel bars $-$ $$5\mathrm{.}00$ per kilogram

High$-$strength steel tubes $-$ $$7\mathrm{.}00$ per kilogram

Quenched and tempered steel bars $-$ $$5\mathrm{.}55$ per kilogram

Quenched and tempered steel tubes $-$ $$7\mathrm{.}75$ per kilogram

Connection Cost: $$500\mathrm{.}00$ per joint

Product Cost: $$1000\mathrm{.}00$ per product

Site Cost:

Reinforced concrete deck $($medium strength$)-$ $$5,150$ per $4-$meter panel

Reinforced concrete deck $($high strength$)-$ $$5,300$ per $4-$meter panel

Excavation $-$ $$1\mathrm{.}00$ per cubic meter $($See the Site Design Wizard for excavation volume$)$

Supports $($abutments and pier$)-$ Cost varies $($See the Site Design Wizard for specific values$)$

o $$6,000$ per anchorage

Required:

Make a detailed list of all constraints and requirements to the bridge design.

Prepare functional specifications

Present at least $2$ designs to meet the design specifications. The designs are to include, as relevant:

calculations, which may include:

loads

sheer forces

bending moments

stresses

construction materials and services quantities

construction cost estimates

recommended sizing of components

recommended materials

recommended reinforcement sizing and location

drawings

risk assessment of:

the existing conditions

the application of the design

maintainability of the works

health, safety and environmental requirements

contribution to ancillary documentation, which may include:

design notes

construction notes

supplementary drawings

input to the specifications

Note: The designs, and their development, should comply with rel