ENGI3703- Surveying and Geomatics Fall Lab 6: Horizontal Curve Layout

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Gilbert Moody
7 years ago
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1 Lab 6: Horizontal Curve Layout Objective: To gain familiarity with the theory, design and layout of Horizontal curves for most types of transportation routes, such as highways, railroads, pipelines, etc,. Preparation: Read chapter 24 in the Elementary Surveying, 11 th ed. Textbook. Overview: When a highway changes horizontal direction, making the point where it changes direction at a point of intersection between two straight lines is not feasible. The change in direction would be too abrupt for the safety of modem, high-speed vehicles. It is therefore necessary to interpose a curve between the straight lines. The straight lines of a road are called tangents because the lines are tangent to the curves used to change direction. In circular curve layout, the curve staking notes and calculations are prepared prior to the actual field layout. Here we use similar data of the sample metric circular curve calculation discussed during your lecture. Equations and necessary calculations, the description of the field procedure, and the figures of circular curve terminology and of geometry are given below. Instruments to be used: Check out the following equipments: 1. Total Station/theodolites 2. Tripod 3. Reflector/leveling rod 4. Pegs 5. Tape Curve parameters calculation Give: The station of PI is Point of intersection I = Intersection angle R = 400 m Radius of the curve Stake the curve at 20 m increments. Solution: # L = RI = * & % ( = m Length of the curve $ ' T = R * tan$ I % % ' = 400 *tan$ 0 ' = m Tangent # 2& # 2 & 1

2 Station calculation for PC (Point of the curvature or the beginning of the curve (BC)) and PT (Point of tangency or the end of the curve (EC)): PI Station = T = PC Station = L = PT Station = LC = 2 * R * sin I /2 $ # ( ) = 2 * 400 * sin 0 2 % ' = m & E = T *tan I % % $ ' = *tan$ 0 ' = m # 4& # 4 & M = E * cos$ I % % ' = * cos$ 0 ' = m # 2& # 2 & Arc Distances: Long Cord External Distance Mid-ordinate The arc distance from the PC to station is ( ) = m The arc distance for the final stationing is ( ) = m. All other stations have 20 m stationing interval. Deflection angles: = I 2L * Arc a = 2 * *5.044 = 00 21'40 = 2* *20 =10 25'57 b = 2 * * = 00 20'03 Cords from station to station: C = 2* R *sin() First cord between PC and 0+060: c a = 2 * R *sin( a ) = 2 * 400*sin(0 o 21'40) = m Consecutive chords (20 m arc): c = 2* R *sin() = 2 * 400*sin(1 o 25'57) = m 2

3 Last cord between and PT: c b = 2 * R *sin( b ) = 2* 400*sin(0 o 20'03) = m Long cord from the PC can be calculated using the deflection angle measured from the tangent (T). LC T = 2 * R * sin ( T ) where T is the deflection angle from PC. Table 6.1 depicts the curve data necessary to stake the curve. Station Table 6.1 Deflection angle, Incremental cord and Long cord data for the curve Incremental Cord (m) Deflection Increment Deflection Angle Long Cord from PC (m) (PC) o 21'40 0 o 21'40 0 o 22' o 25'57 1 o 47'37 1 o 48' o 25'57 3 o 13'34 3 o 14' o 25'57 4 o 39'31 4 o 40' o 25'57 6 o 05'28 6 o 06' (PT) o 20'03' 6 o 25'31 6 o 26' Figure 6.1 Circular curve elements (Figure 24.4 from textbook). 3

4 Figure 6.2 Sample circular curve layout by deflection angles (Figure 24.5 from textbook). Figure 6.2 Sample field notes (Figure 24.7 from textbook). 4

5 Field procedure for curve layout: The normal way of staking out a circular curve is to layout the intersection angle (I) and tangent length at and from the PI, then lay out the curve from the PC to the PT using a series of appropriate deflection angles and chords. Use increment cord method to layout the curve by deflection angles. The normal field layout procedure may be described stepwise as follows: 1. Set up the instrument at the point of intersection (PI). Use the end of your reference line that you used for profile leveling (Lab 4) as PI. 2. Establish the PC and PT by measuring tangent distance T from the PI along both the back and forward tangents. To stake PC and PT, sight along the back tangent with telescope in reverse position (plunge), set the horizontal angle to zero and measure the tangent distance and stake PC. Plunge telescope to direct position, lay off intersection (I) angle with upper motion and sight along the forward tangent. Measure the tangent distance and stake PT. 3. Establish directions of the external distance (E) and mid-ordinate (M), then stake out these points. This can be set by bisecting the angle (180 o -I) at the PI and laying off the external distances from there. A check of the deflection angle from the PC to the midpoint should yield I/4. 4. Set up and level the instrument over PC, backsighting on the PI and set the horizontal angel reading as 0 o Stake intermediate curve points by lay off the consecutive appropriate deflection angles and measuring the incremental cord between points using tape. 5. Check the positions of M and PT by laying out and measuring half of the long cord and the full long cord (LC). The first point should coincide with the stake of the M and the second with the PT stake. 5

HORIZONTAL CURVES. What They Are And How To Deal With Them

HORIZONTAL CURVES. What They Are And How To Deal With Them HORIZONTAL CURVES What They Are And How To Deal With Them 2 HORIZONTAL CURVE TERMINOLOGY Symbol Terminology Equation LC Long Chord 2R sin 2 R Radius OA = OB = OC L Length of Curve L = 0.0174533 R T Tangent