The common radius of a reverse curve is 1650 ft. The central angle of the first curve is 10°. a. What is the distance of the parallel tangents? b. What is the shortest distance from PC to PT?  c. What is the station of PT if PI1 is at 10+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
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Chapter2: Loads On Structures
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The common radius of a reverse curve is 1650 ft. The central angle of the first curve is 10°.

a. What is the distance of the parallel tangents?

b. What is the shortest distance from PC to PT? 

c. What is the station of PT if PI1 is at 10+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.

PC
T1
V1
Le1
T1
R2
Iz
R1
R2
T2
R1
Lcz
I1
PRC
V2
T2
Common tangent
PT
Reversed Curves
PC
V1
back tangent
R2
forward tangent
PRC
PT
I2
V2
R1
R1
Reversed Curves for Nonparallel Tangents
PC
V1
back tangent
R2
R2
PRC
forward tangent
V2
PT
R1
I
R1
Reversed Curves for Parallel Tangents
Elements of Reversed Curve
• PC = point of curvature
%3D
• PT = point of tangency
• PRC = point of reversed curvature
T1 = length of tangent of the first curve
T2 = length of tangent of the second curve
%3D
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
Lc1 = length of first curve
Lc2 = length of second curve
L1 = length of first chord
%D
L2 = length of second chord
T1 + T2 = length of common tangent
measured from Vị to V2
%3D
Finding the stationing of PT
Given the stationing of PC
Sta PT = Sta PC + Le1 + L2
|
Given the stationing of V1
Sta PT = Sta Vị – Tị + Lcl + Le2
-
Transcribed Image Text:PC T1 V1 Le1 T1 R2 Iz R1 R2 T2 R1 Lcz I1 PRC V2 T2 Common tangent PT Reversed Curves PC V1 back tangent R2 forward tangent PRC PT I2 V2 R1 R1 Reversed Curves for Nonparallel Tangents PC V1 back tangent R2 R2 PRC forward tangent V2 PT R1 I R1 Reversed Curves for Parallel Tangents Elements of Reversed Curve • PC = point of curvature %3D • PT = point of tangency • PRC = point of reversed curvature T1 = length of tangent of the first curve T2 = length of tangent of the second curve %3D 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 Lc1 = length of first curve Lc2 = length of second curve L1 = length of first chord %D L2 = length of second chord T1 + T2 = length of common tangent measured from Vị to V2 %3D Finding the stationing of PT Given the stationing of PC Sta PT = Sta PC + Le1 + L2 | Given the stationing of V1 Sta PT = Sta Vị – Tị + Lcl + Le2 -
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