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# Intro to Civil Envir Eng CE 271

MSU

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This 10 page Class Notes was uploaded by Jolie Shields on Saturday September 19, 2015. The Class Notes belongs to CE 271 at Michigan State University taught by Richard Lyles in Fall. Since its upload, it has received 51 views. For similar materials see /class/207374/ce-271-michigan-state-university in Civil Engineering at Michigan State University.

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Date Created: 09/19/15

CE 271 Spring 2009 Introduction to Civil Engineering Horizontal Curves Muhammad Abrar Siddiqui siddiq16msuedu Outline IIII Introduction Degree of circular curve Curve geometry Circular curve stationing Laying out horizontal curves Examples Reference Wolf and Ghilani Elementary Surveying 10th ed Chapter 24 Introduction I Curves in horizontal and vertical planes connect straight tangent sections of transportation routes I A horizontal curves connects two straight tangent sections in horizontal plane I Types of horizontal curves circular arcs and spirals Introduction Simple curve circular arc connecting two tangents Compound curve two or more circular arcs of different radii tangent to each other centers on the same side Brokenback curve short tangent lt 100ft connecting two circular arcs centers on the same side Reverse curve two circular arcs tangent to each other centers on opposite sides Tangent I l r I Brokenback curve Reverse curve Simple curve Compound curve a b C id Degree of circular curve I Rate of curvature of circular curves designated by 100 radius or degree of curve I Two different designations for degree of curve arc definition and chord definition both defined R D R D 100 using English units 350 27 xquot H 572958 I Arc definition central angle subtended by a D circular arc of 100ft preferred for highway work Aquot dam I Chord de nition angle at the center of a circular arc subtended by a chord of 100ft i sway2i Ax 1 Ixquot w Chord definition bl Curve geometry I Pl point of intersection of two tangents also called vertex Pi I I Back tangent and forward dam tangent Lu I PC point of curvature tangent to curve Q0 I PT point of tangency curve to l tangent i 6 6 I R radius radii at PC and PT 5 ex 2 1 ltx are perpendicular to tangents I T tangent distance l I LC long chord I E external distance I POT any point on tangent I L length of curve For arc definition measured along I M middle ordinate I l intersection angle equal the curve from PC to PT For to the central angle chord definition L measured I POC any point on curve subtended by the curve in 100ft chords from PC to PT Curve geometry IIII 1 1 100 ft PI DD 3 2 L Sta L i R fin radians 572958 R 2 re D n Jylhq TIRtan I LC 2R quot 5m 2 Circular curve stationing III I Example Handout 10A Horizontal Curves page 8 Dr Wolff Laying out horizontal curves I Curve radii are generally too large to swing an arc from the curve center I Practical methods of laying out curves include deflection angles coordinates tangent offsets chord offsets middle ordinates and ordinates from the long chord A table of curve properties arc de nition Degree of Radius R True Chord True Chord Curve D ft Full station Half station 1 572958 10000 5000 2 286479 9999 5000 3 190986 9999 5000 4 143239 9998 5000 5 114592 9997 5000 6 95493 9995 5000 7 81851 9994 5000 8 71620 9992 4999 9 63662 9990 4999 10 57296 9988 4998 Laying out horizontal curves Layout by deflection angles incremental chord method and total chord method Set up the instrument at PC Sight to the Pl Turn DI2 in the direction of curvature Hold a tape at PC and swing the other end until the calculated chord length is in the line of sight Stake that point Turn another DI2 Hold one end of the tape at the pointjust staked and again swing the other end until the calculated chord length is in the line of sight Stake the next point AL 39 66 3708 Continue until the entire curve is laid out If vision is obstructed the instrument can be moved to another stake

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