Homework Help is Here – Start Your Trial Now!
Engineering
Civil Engineering
a 600 ft equal tangent sag vertical curve has the PVC at Station 170+00 and elevation 1000 ft. The initial grade is -3.5% and the final grade is +0.5%. Determine the stationing And elevation of the PVI, the PVT, and the lowest point on the curve.

a 600 ft equal tangent sag vertical curve has the PVC at Station 170+00 and elevation 1000 ft. The initial grade is -3.5% and the final grade is +0.5%. Determine the stationing And elevation of the PVI, the PVT, and the lowest point on the curve.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
In this question I got everything correct up to where I have to find elevation of PVT. (Not sure how the textbook got 991.0 ft) and I also don’t understand why the textbook found “a” by not putting G1 and G2 in percentages? Handwritten work only please
essages File Edit View Conversations Window Help K Transportation engineering textbook.pdf 88 ♫ curve will occur when the first derivative of the parabolic function (Eq. 3.1) is zero because the initial and final grades are opposite in sign. When initial and final grades are no opposite in sign, the low (or high) point on the curve will not be where the first derivative is zero because the slope along the curve will never be zero. For example, a sag curve with an initial grade of -2.0% and a final grade of -2.0% will have its lowest elevation at the PVT and the first derivative of Eq. 3.1 will not be zero at any point along the curve. However, in our example problem the derivative will be equal to zero at some point, so the low point will occur when From Eq. 3.3 we have Substituting for a and b gives b=G₁ = -3.5 with G₁ in percent. From Eq. 3.6 (with L in stations and G₁ and G₂ in percent), 0.5-(-3.5) 2(6) IOB RADIO a= 1.K dy dx 7.281 = 2ax+b=0 This gives the stationing of the low point at 175 + 25 (5 + 25 stations from the PVC). For the elevation of the lowest point on the vertical curve, the values of a, b, c (elevation of the PVC), and x are substituted into Eq. 3.1, giving dy -= 2(0.33333)x+ (-3.5) = 0 dx x = 5.25 stations Note that the preceding equations can also be solved with grades expressed as the decimal equivalent of percent (for example, 0.02 ft/ft for 2%) if x is expressed in feet instead of stations Care must be taken not to mix unite A dimensional analysis of Ea 31 must ensure -= 0.33333 y = 0.33333(5.25)²+(-3.5) (5.25)+1000 = 990.81 ft 125 Subscribed ✓ MAR 25 Like C tv G
Transcribed Image Text:essages File Edit View Conversations Window Help K Transportation engineering textbook.pdf 88 ♫ curve will occur when the first derivative of the parabolic function (Eq. 3.1) is zero because the initial and final grades are opposite in sign. When initial and final grades are no opposite in sign, the low (or high) point on the curve will not be where the first derivative is zero because the slope along the curve will never be zero. For example, a sag curve with an initial grade of -2.0% and a final grade of -2.0% will have its lowest elevation at the PVT and the first derivative of Eq. 3.1 will not be zero at any point along the curve. However, in our example problem the derivative will be equal to zero at some point, so the low point will occur when From Eq. 3.3 we have Substituting for a and b gives b=G₁ = -3.5 with G₁ in percent. From Eq. 3.6 (with L in stations and G₁ and G₂ in percent), 0.5-(-3.5) 2(6) IOB RADIO a= 1.K dy dx 7.281 = 2ax+b=0 This gives the stationing of the low point at 175 + 25 (5 + 25 stations from the PVC). For the elevation of the lowest point on the vertical curve, the values of a, b, c (elevation of the PVC), and x are substituted into Eq. 3.1, giving dy -= 2(0.33333)x+ (-3.5) = 0 dx x = 5.25 stations Note that the preceding equations can also be solved with grades expressed as the decimal equivalent of percent (for example, 0.02 ft/ft for 2%) if x is expressed in feet instead of stations Care must be taken not to mix unite A dimensional analysis of Ea 31 must ensure -= 0.33333 y = 0.33333(5.25)²+(-3.5) (5.25)+1000 = 990.81 ft 125 Subscribed ✓ MAR 25 Like C tv G
a 600 ft equal tangent sag vertical curve has the PVC at Station 170+00 and elevation 1000 ft. The initial grade is -3.5% and the final grade is +0.5%. Determine the stationing And elevation of the PVI, the PVT, and the lowest point on the curve. L=600 ft T=300 ft Options -3.5% PVC = PVT-L 17000 = PVT -600 17600 = PVT 176 +00= PVT PVC 170+00 PUI = PVC + T 54°F Cloudy Elevation 1000 = 17,000 + 300 - 17300 PVI = 173+00 - y = 2ax + b O Search PVI 173+00 Elevation = a 989.5' Elevation PUI = E pvc + 9²/12 = 1000 + (-0.035) (600) = 989.5' G₂+0.5% PVT 1776+00 elevation = 974.5¹ Elevation PVT = EPI-9²/2/2 b= = 989.5 - (+0.05)(b) = 974.5' a= = G₂-G₁₂₁ = 0.05-(-0.035) 2L 2(600) = 7.0833•10-5 0.035 4:54 PM
Transcribed Image Text:a 600 ft equal tangent sag vertical curve has the PVC at Station 170+00 and elevation 1000 ft. The initial grade is -3.5% and the final grade is +0.5%. Determine the stationing And elevation of the PVI, the PVT, and the lowest point on the curve. L=600 ft T=300 ft Options -3.5% PVC = PVT-L 17000 = PVT -600 17600 = PVT 176 +00= PVT PVC 170+00 PUI = PVC + T 54°F Cloudy Elevation 1000 = 17,000 + 300 - 17300 PVI = 173+00 - y = 2ax + b O Search PVI 173+00 Elevation = a 989.5' Elevation PUI = E pvc + 9²/12 = 1000 + (-0.035) (600) = 989.5' G₂+0.5% PVT 1776+00 elevation = 974.5¹ Elevation PVT = EPI-9²/2/2 b= = 989.5 - (+0.05)(b) = 974.5' a= = G₂-G₁₂₁ = 0.05-(-0.035) 2L 2(600) = 7.0833•10-5 0.035 4:54 PM
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Methods of Surveying
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Structural Analysis
Structural Analysis
Civil Engineering
ISBN:
9781337630931
Author:
KASSIMALI, Aslam.
Publisher:
Cengage,
Structural Analysis (10th Edition)
Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Principles of Foundation Engineering (MindTap Cou…
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Fundamentals of Structural Analysis
Fundamentals of Structural Analysis
Civil Engineering
ISBN:
9780073398006
Author:
Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:
McGraw-Hill Education
Sustainable Energy
Sustainable Energy
Civil Engineering
ISBN:
9781337551663
Author:
DUNLAP, Richard A.
Publisher:
Cengage,
Traffic and Highway Engineering
Traffic and Highway Engineering
Civil Engineering
ISBN:
9781305156241
Author:
Garber, Nicholas J.
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS