vertical curve question

[ketanco]

Find: Which of the following is NOT true for symmetrical vertical curves:
(A) The elevation of the mid-chord point is the average of the elevations of the
BVC and EVC
(B) The vertical curve lies midway between the PVI and the midpoint of the
chord
© The low point on a sag vertical curve is always at the PVI station
(D) All of the above

The answer is C

I didnt understand why B is true and what does this mean?

and again what is exactly a symmetrical vertical curve? in the AM section all we have is symmetrical curves ?

 

[ptatohed]

Hmmm, I've never heard of the term chord used for VCs. I guess the chord of a VC is a straight line from the BVC to the EVC.

If that is true, then we know A is true.

I had no idea B was true but I just checked a few plans I had lying around and it does jive. What they mean is the elevation difference from PVI to midpoint on curve (Also known as M) is the same elevation difference from midpoint on curve to the midpoint of the chord.

C is definitely not true.

D can't be true if C is not true.

I answered in another thread but a symmetrical VC is one that has the PVI at 1/2 L. All complete VCs are symetrical by definition. I suspect you'll only be tested on full/symmetrical VCs.

 

[civilized_naah]

As far as B is concerned:

R = (G2 - G1)/L

Elevation of curve at x = L is y = yPVC + G1L + 1/2 R L2 = yPVC + G1L + (G2 - G1)L/2 = yPVC + G1 L/2 + G2 L/2

Elevation of curve at x = L/2 is y = yPVC + G1 L/2 + 1/2 R (L/2)2 = yPVC + G1 L/2 + (G2 - G1)L/8 = yPVC + G1 3L/8 + G2 L/8

Elevation of mid-chord (below/above PVI) = average of elev at x = 0 and x = L: yPVC + G1 L/4 + G2 L/4

Elevation of PVI = yPVC + G1 L/2

Average of elevation of mid-chord and PVI = yPVC + G1 3L/8 + G2 L/8 (identical to elevation of curve at midpoint of curve)

 

[ptatohed]

Very nice Dr. G. Good job. And thanks.

I have been doing street plan and profile plans for years and I have never once seen any mention of a "vertical curve cord".

I learned something new today.

 

[John QPE]

I am missing something, how is C not true in a symmetrical curve?

 

[John QPE]

Disregard...I just saw the other thread. Terminology will kill you.