A simple curve has a radius of 220 m and angle of intersection of 128°. The curve is to be shifted by rotating the forward tangent 24° counterclockwise about PT. If the back and forward tangents are originally having an azimuth (from south) of 222° and 348° respectively.Determine:Radius of the new curveCentral angle of the new curveStationing of new PC if the old PC is at 8+726.32Draw and plot the curve. Compute all of the necessary elements of the curve. Include the proper units/dimensions and round-off the answers to three decimal places. PIPTPCCBacktangentForwardtangentRPIIMI/2PCPTL/2L/2R- mBack TangentRForward Tangent20RI/2I• PC = Point of curvature. It is the beginning%3Dof curve.• PT = Point of tangency. It is the end ofcurve.• PI = Point of intersection of the tangents.%3DAlso called vertex• T = Length of tangent from PC to PI andfrom PI to PT. It is known as subtangent.• R = Radius of simple curve, or simplyradius.• L = Length of chord from PC to PT. Point Qas shown below is the midpoint of L.%3DLc = Length of curve from PC to PT. Point Min the the figure is the midpoint of Lc.• E = External distance, the nearest distance%3Dfrom PI to the curve.• m = Middle ordinate, the distance frommidpoint of curve to midpoint of chord.I = Deflection angle (also called angle ofintersection and central angle). It is the%3Dangle of intersection of the tangents. Theangle subtended by PC and PT at O is alsoequal to I, where O is the center of thecircular curve from the above figure.• x = offset distance from tangent to thecurve. Note: x is perpendicular to T.• 0 = offset angle subtended at PC betweenPI and any point in the curveD = Degree of curve. It is the central anglesubtended by a length of curve equal toone station. In English system, one stationis equal to 100 ft and in SI, one station is%3Dequal to 20 m.• Sub chord = chord distance between twoadjacent full stations.12UMATHalino.com

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Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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A simple curve has a radius of 220 m and angle of intersection of 128°. The curve is to be shifted by rotating the forward tangent 24° counterclockwise about PT. If the back and forward tangents are originally having an azimuth (from south) of 222° and 348° respectively.

Determine:

Radius of the new curve
Central angle of the new curve
Stationing of new PC if the old PC is at 8+726.32

Draw and plot the curve. Compute all of the necessary elements of the curve. Include the proper units/dimensions and round-off the answers to three decimal places.

PI
PT
PC
C
Back
tangent
Forward
tangent
R
PI
I
M
I/2
PC
PT
L/2
L/2
R- m
Back Tangent
R
Forward Tangent
20
R
I/2
I
• PC = Point of curvature. It is the beginning
%3D
of curve.
• PT = Point of tangency. It is the end of
curve.
• PI = Point of intersection of the tangents.
%3D
Also called vertex
• T = Length of tangent from PC to PI and
from PI to PT. It is known as subtangent.
• R = Radius of simple curve, or simply
radius.
• L = Length of chord from PC to PT. Point Q
as shown below is the midpoint of L.
%3D
Lc = Length of curve from PC to PT. Point M
in the the figure is the midpoint of Lc.
• E = External distance, the nearest distance
%3D
from PI to the curve.
• m = Middle ordinate, the distance from
midpoint of curve to midpoint of chord.
I = Deflection angle (also called angle of
intersection and central angle). It is the
%3D
angle of intersection of the tangents. The
angle subtended by PC and PT at O is also
equal to I, where O is the center of the
circular curve from the above figure.
• x = offset distance from tangent to the
curve. Note: x is perpendicular to T.
• 0 = offset angle subtended at PC between
PI and any point in the curve
D = Degree of curve. It is the central angle
subtended by a length of curve equal to
one station. In English system, one station
is equal to 100 ft and in SI, one station is
%3D
equal to 20 m.
• Sub chord = chord distance between two
adjacent full stations.
12
UMATHalino.com

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