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.

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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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
Transcribed Image Text: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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