Revision as of 16:58, 8 May 2016

Notes

Civil engineering applications of Simpson's Rule
Building a highway going through a town
Cross-sectional design of highway - arc length, volume of materials
Design of highway: top X rectangle is asphalt, bottom X rectangle plus cut-out half-circle is concrete, coord system has split down middle
Curve design is a piecewise curve. Given a set of formulas.
Use Simpson's Rule to compute the arc length of the road, and report the total length in ft.
Highway standards require a minimum lane width of 15 feet, 10 feet for side shoulder, 5 feet for inner shoulder, 3 lanes both directions. Total width of X.
Use Simpson's Rule to find the total volume of asphalt, volume of concrete required (use Pappus' Theorem to obtain the volume via V = A * length traveled)

Back Story

You are a civil engineer working for a design firm. Another engineer has designed the layout of the curves to go through the town, and you are tasked with ordering the materials for the construction site.

Route Layout

You are given a map of the curve through the town, along with a coordinate system and piecewise mathematical functions that represent the curves. Given this information, you will determine the length of the road, and the amount of material required for construction.

Road Design

You are also given a cross-sectional diagram of the highway road bed. This diagram shows several features of the road design - for example, sloped surfaces to prevent water buildup and geometry that allows for expansion and contraction due to heating and cooling.

Calc II Questions

Use Simpson's Rule, and the spreadsheet template you used for the prior worksheet, to complete the following exercises. Submit a report that answers each of the following questions with complete sentences.

1) Compute the total length of the road, in feet, using Simpson's Rule and the arc length formula. Justify your choices of N. Why is the centerline of the road used to find the length?

2) Determine the total volume of asphalt and concrete that will be used using Simpson's Rule together with Pappus' Theorem (Volume = Area * Distance Traveled By Centroid)

3) On the morning of the construction project, the engineer who gave you the original map of the site runs up to you, breathlessly, and apologizes, explaining that her map did not show that the road was sloped at a 3% grade the entire length of the road. You don't have your spreadsheets or calculations in front of you - all you have is a pencil, and the back of an envelope. The pressure's on: if you want more material in time for the construction job, you'll have to order it before the dump trucks leave in 15 minutes. How much more concrete and asphalt do you need to order?