Reza Mahallati Chapter 6 Problem 60

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Can someone please explain what distance exactly the "Offset From Entering Grade"  (r*x^2/2) represents in this problem? 

Posting a simple and sketch may help me.

Thank you in advance.

 
I have an old version of the book and there is no problem 60 for chapter 6. It ends at problem no. 54. If you can scan in and post the problem, I can try to help. 

Thank you.

 
Thank you Maji.

Attached are the question and solution.  I have no problem understanding how to solve the question, my problem what understanding what dimension the solution of -17.93 feet represents in the vertical curve ( It is a distance from where to where?)

Thank you again,

FLPEG

6-60 sln.JPG

Reza 6-60.JPG

 
Last edited by a moderator:
So it is the offset from the projection of the entering grade/tangent to the POC. 

Got it now thanks, kind of a silly question, no practical use.

Thanks again.

FLPEG

 
I don't care for the question too much.  To me, the term "offset" in the problem statement should be "Tangent Offset", or "Vertical Curve Tangent Offset".  y' is typically used to represent the VC Tangent Offset.  I also think when they give the benchmark station and elevation, it should be clear that the elevation is on the curve.  What's with mixing "existing" curve (meaning actual/as-built) with "designed" entering grade (not necessarily actual/as-built)?  The solution does not include units.  And everyone knows x should be a little x, not a big X!  Moving on....

There are two formulas to calc the VC Offset that I know of:

y' = (r/2)(x^2);  r being (well, you know what r is) and x being the distance to the point on the curve measured from the BVC, in stations.  y' is in feet and I believe always from the incoming tangent (g1) to the curve. 

- or -

y' = (4 M x^2) / L^2;  M being the Middle Ordinate Distance. M = |g1 - g2| L / r  - or -  M = (1/2)[(ELbvc + ELevc)/2 - ELpvi]

r = [(-4.7 - 3.6) / 7] x^2 = -1.1857 %/sta

M = |3.6 - (-4.7)| 7 / -1.1857 = 7.26 ft

x = 18+50 - 23+00 = 550 ft = 5.5 sta

y' = (r/2)x^2 = (-1.1857/2)(5.5)^2 = -17.93 ft

y' = 4 M x^2 / L^2 = (4)(7.26)(7^2) / 5.5^2 = 17.93 ft (or, -17.93 ft since g1 is above the curve)

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

 
I agree that as written, the question is not clearly articulated.  The use of the term 'offset' threw me in this case and had me thinking an offset form a position as in construction staking.  It is a good concept to test on.  Good example for how a question can be written to unintentionally lead the examinee in an unintended direction.  Also, not very psychometrically sound in terms of distinguishing or measuring competence.

 
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