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ChAPTER5: Final Design Challenge Engineering Mathematics
Introduction/Description Individually and/or in teams, you will • complete hand-drawn or CADD diagrams and drawings to scale, • build a scale model, and • present a 30-minute multimedia exhibition of your work.
Chapter 5: Outline Beams Supports Stress and Buckling Truss Analysis
Objectives and Results • Students will identify the different types of bridges and the strengths and weaknesses of each design. • Students will use critical thinking, problem solving, and team work to design, engineer, and troubleshoot a functional bridge truss design. • Students will develop public speaking and presentation planning skills.
Results Students will present a design, drawings, model, and other information about bridge truss design, using appropriate mathematical formulas, mathematical design analysis, and associated programs.
Vocabulary • Arch bridges • Beam • Bridge • Bracing • Catenary • Deck • Deck Truss • Forms, or Types of Bridges
Vocabulary, cont. • Materials • Model • Parabola • Pony truss
Vocabulary, cont. • Quadratic Equations • Span • Stringer • Strut • Suspension Bridges • Symmetry
Vocabulary, cont. • Technical drawing • Tie • Truss • Truss bridges
Engineering Problems and Solutions • Often, engineers encounter problems and must solve these problems using mathematical formulas and test data analysis. • You and your teammates will be solving similar issues by addressing the crucial elements of the engineering design process and using mathematical analysis and mathematical formulas for bridge truss design.
Mathematics in Construction • Obviously, architecture is geometric – a clear link to mathematics. • Consider blue prints, for example. A blue print is the paper layout, drafted by an architect, which illustrates the design of a building.
Mathematics in Construction, cont. • Math also provides architects with a solution to the question of possibility. • Think of yourself as an architect. • In your mind, dream up a beautiful buildingthat you can actually picture in your head. • How does that dream building become a blue print? Or become an actual structure?
Math in Everyday Construction • It is not only architects who design and build practical structures. • Every day people commonly do construction work to their houses and yards. • It would be very expensive to hire an architect if you just wanted to build a fence or a new deck.
Sample Problem • For example, imagine you are redecorating your living room. You want to hang three pictures on the wall in a triangular shape. • You realize that you must put the nails in the vertices of an equiangular triangle in order to create the shape you want. However, the studs in the wall are spaced 40 cm apart. • How do you figure out where to put the nails?
Solution to Sample Problem 60° x 60° 60° 40cm 40cm Solve for x: tan60 = x40
Bridges Overview A bridge is a structure built to span physical obstacles such as a body of water, valley, or road, for the purpose of providing passage over the obstacle.
Bridge Factors There are four main factors that are used in describing a bridge. • Span (simple, continuous, cantilever) • Material (stone, concrete, metal, etc.) • Placement of the travel surface in relation to the structure (deck, pony, through) • Form/type (beam, arch, truss, etc.) Bridge Identification Factors
Curves in Bridge Design There are two curves with very similar shapes that are important in bridge construction: • Catenary • Parabola
Symmetry • Symmetry is a way to describe shapes and design and to organize geometry. • Architecture encompasses basic line symmetry and other types, such as • rotational • spiral, • cylindrical, • chiral, • similarity, and • translational.
Forms (Types) of Bridges • While there are many different types of bridges, we will focus on truss bridge designs. • With over 30 different types of truss designs, we will cover 10 of them.
Types of Bridges Three main types of bridges are • arch, • truss, and • suspension. 1 2 3
Bridge Analysis Factors • Span • Load • Environmental influences • Budget • Soil characteristics • Building time frame
Analyzing Bridge Designs Analyze the bridge designs based on the following elements: • Length of span • Height • Materials to be used • Tools available • Weight to be held • Racking
Creating a Scale Drawing • A scale drawing is a drawing that shows a real object with accurate sizes. • Sizes are reduced or enlarged by a certain amount (the scale). • The example drawing below has a scale of "1:10."
Scale Drawing and Ratios • Scale of a drawing = drawing length : actual length • For example, a map cannot be of the same size as the area it represents. A ratio is used. • A scale is usually expressed in one of two ways: • using units or • 1 cm to 1 km • 1” = 1’ • without explicitly mentioning the measurement units. • 1:100,000 • 1:10
Scale Drawing Practice • Complete scale drawings for your project. • Follow your instructor’s directions to complete either hand-drawn or CAD drawings of your project, according to the scenario and team project outline and rubric.
Scale Models • A scale model is a physical model. It is a representation or copy of an object that is larger or smaller than the actual size of the object. • A scale model maintains the related proportions (or the scale) of the physical size of the original object. • Usually, the scale model is used as a guide to making the full-sized object. • You will be creating scale truss bridge models.
Scale Model Examples A model is a three-dimensional (3-D) alternative for a 2-D representation. An example of a scale 3-D model versus a scale drawing would be a globe, which is the 3-D alternative to a flat 2-D world map.
Scale Model Examples From Scale Model To Construction To Completed Building
Creating a Scale Model Much like creating a scale drawing, when creating a scale model, you have to decide on certain crucial design components, such as • measurement (length, height, width, depth, etc.), • real life applications, • design constraints, • design requirements, • materials, and • scale. Building a Scale Model
Four Forces and Bridge Design Several forces and formulas should be considered when designing: • Compression • Tension • Torsion • Shear
Formulas and Bridge Design • Compression and tension caused by a bridge’s load can cause racking. • Analyze and counteract racking in your design.
West Point Bridge Design (WPBD) • West Point Bridge Design Contest • The program is available for free download at http://bridgecontest.usma.edu/download.htm. • Visit the WPBD tutorials to learn how to use the software. • Visit the WPBD FAQs at http://bridgecontest.usma.edu/qcontest.htm. • WPBD YouTube video.
Bridge Truss Models • In teams, after analyzing the various designs and their strengths and weaknesses, design the strongest and lightest weight bridge to the specifications indicated in the student design brief. • In teams, create your bridge truss using 100 Popsicle sticks and glue only. • Get approval for using your design with your instructor. • Build your bridge.
Scale Drawings • Complete hand-drawn or CAD scale diagrams and drawings. • Your group should be prepared to present the following to your instructor and your class: • Problem statement and how you solved your problem using the engineering design process • Scenario • Original design of your system • Working model of your system
Racking and Geometric Figures • Explain how your design counteracts racking based on geometric and algebraic principles. • Which type of geometric figure is the best to counteract tension and compression? • Analyze which type of figure is the most efficient.