The common tangent of a compound curve has a length of 70 m. This common tangent makes an angle of 14° and 20° to the tangents of the compound curve respectively. If T1 = 40 m, determine:a. The radius of the second curve.b. The radius of the first curve.c. The station of PT if PC is at 29+999.99Draw and plot the curve. Compute all of the necessary elements of the curve. Include the proper units/dimensions and round-off the answers to 3 decimal places. ヘーCOMPOUND CURVECOMMONTANGENTPCCPTPCLONGCHORD (LC)PILCPCPOINT OF TANGENCYKNOWN STA. PCSta PT- Sta PC+Le9tLezKNOWN STA PISta PT - Sta PI - x- TtLe+LezPII = I1 + I2yCommon tangentV1 I1РССIzV2LaT1T2L2L1MATH=I0mp.comHalin-PTLPCIzR2R1I1Compound CurvesElements of compound curve• PC = point of curvature%3D• PT = point of tangency%3D• PI = point of intersection• PCC = point of compound curve%3DT1 = length of tangent of the first curveT2 = length of tangent of the second curveV1 = vertex of the first curveV2 = vertex of the second curveI1 = central angle of the first curveI2 = central angle of the second curve• I = angle of intersection = I1 + I2%3D• L¢1 = length of first curveLc2 = length of second curveL1 = length of first chord%DL2 = length of second chord• L = length of long chord from PC to PT%3DT1 + T2 = length of common tangentmeasured from Vị to V2• 0 = 180° - Ix and y can be found from triangle V1-V2-PI.• L can be found from triangle PC-PCC-PTFinding the stationing of PTGiven the stationing of PCSta PT = Sta PC + Le1 + Le2Given the stationing of PISta PT = Sta PI – x – T1 + Lc1 + Lc2-T2 Y

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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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Question

The common tangent of a compound curve has a length of 70 m. This common tangent makes an angle of 14° and 20° to the tangents of the compound curve respectively. If T₁ = 40 m, determine:

a. The radius of the second curve.

b. The radius of the first curve.

c. The station of PT if PC is at 29+999.99

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 3 decimal places.

ヘー
COMPOUND CURVE
COMMON
TANGENT
PCC
PT
PC
LONG
CHORD (LC)
PI
LC
PC
POINT OF TANGENCY
KNOWN STA. PC
Sta PT- Sta PC+Le9tLez
KNOWN STA PI
Sta PT - Sta PI - x- TtLe+Lez
PI
I = I1 + I2
y
Common tangent
V1 I
1
РСС
Iz
V2
La
T1
T2
L2
L1
MATH=I0mp.com
Halin-
PT
L
PC
Iz
R2
R1
I1
Compound Curves
Elements of compound curve
• PC = point of curvature
%3D
• PT = point of tangency
%3D
• PI = point of intersection
• PCC = point of compound curve
%3D
T1 = length of tangent of the first curve
T2 = length of tangent of the second curve
V1 = vertex of the first curve
V2 = vertex of the second curve
I1 = central angle of the first curve
I2 = central angle of the second curve
• I = angle of intersection = I1 + I2
%3D
• L¢1 = length of first curve
Lc2 = length of second curve
L1 = length of first chord
%D
L2 = length of second chord
• L = length of long chord from PC to PT
%3D
T1 + T2 = length of common tangent
measured from Vị to V2
• 0 = 180° - I
x and y can be found from triangle V1-V2-
PI.
• L can be found from triangle PC-PCC-PT
Finding the stationing of PT
Given the stationing of PC
Sta PT = Sta PC + Le1 + Le2
Given the stationing of PI
Sta PT = Sta PI – x – T1 + Lc1 + Lc2
-
T2 Y

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