Task $1($Linear systems $-$ Truss Analysis$)-15$ PointsTask $2($Broadly$-$defined problem$)-70$ Points

Choose a type of bridge and develop a preliminary design based on given specifications, such

as span length, load requirements, and material constraints. Document the design parameters

and constraints. Perform a comprehensive structural analysis of the preliminary bridge design.

Utilize matrix algebra to model the structural system, considering factors like forces, moments,

and boundary conditions. Employ numerical techniques to calculate the stress and deformation

distribution across the bridge.

Explore different materials commonly used in bridge construction. Use numerical methods to

optimize material selection based on factors such as cost$,$ strength, and durability. Consider the

environmental impact of materials in the optimization process. Implement iterative design

optimization techniques to refine the initial bridge design. Utilize numerical methods for

algebraic equations to optimize critical design parameters, such as beam dimensions, cable

tensions, or support locations. Consider constraints related to budget, safety codes, and

aesthetic aspects.

Present the final optimized bridge design, incorporating all the refined parameters and

constraints. Provide a comprehensive analysis report detailing the numerical methods

employed, design rationale, and the implications of the optimization on the structural

performance and cost$-$effectiveness.

Assignment Instructions:

Detailed report documenting the entire design and optimization process, including

methodology, assumptions, and results.

Computer$-$aided analysis model implemented in a programming language $($e$.$g$.,R,$

Python, ete.$)[$Remember to comment code!$]$

A presentation summarizing the design optimization process, key findings, and the

practical implications of the optimized bridge design.

Deliverables:

Detailed report documenting the design parameters, formulation of the design

problem, and the system of linear equations.

R code $($or other programming tool$)$ for the numerical solution of the system of

equations, including comments explaining the logic.

Cost and performance evaluation results for each reinforcement scenario.

Presentation summarizing the findings and optimization recommendations.

Appraisal of the analysis using manual calculations or any other analysis tool that is

available as Open Electronic Resource $($OER$).$

Discussion of the obtained results.

Consider the truss below. Members $AB$ and $BC$ are assumed to be in tension, and members BD

and $BE$ are in compression.

Members $AB,BC,BD,$ and $BE$ represent the truss members.

Supports at points A and $C$ are pin joints.

Support at point $E$ is a roller joint.

A downward force of $10kN$ is applied at joint $B$

From the truss above, form a system of linear equations. Hint: Use equilibrium

equations for all the joints.

Write the equations in matrix form $(Ax=B)$

Given alpha $(),$ solve the linear equations and find the forces in each truss member.

Write your answers in terms of alpha and $L$ of each member $($e$.$g$.L_{AB}).$

$(5$ points$)$