Tied Arch - Roark's Formula
Tied Arch - Roark's Formula
(OP)
I'd like someone to double check my calcs on a tied arch. I'm using Roark, Table 9.3.1.h. The arch has the following:
Span = 100'
Radius = 97.7'
Theta = 31 degrees = 0.54 rad
w = 625 plf
The top chord of the arch is 2-L5x3-1/2x1/2 angles, so this would be a thin arch.
I assumed k1 and k2 to be 1.
I assumed Rg = R.
I get LPh = 611 lbs and Ahh = 0.019
Therefore, Ha = 32,158#.
Span = 100'
Radius = 97.7'
Theta = 31 degrees = 0.54 rad
w = 625 plf
The top chord of the arch is 2-L5x3-1/2x1/2 angles, so this would be a thin arch.
I assumed k1 and k2 to be 1.
I assumed Rg = R.
I get LPh = 611 lbs and Ahh = 0.019
Therefore, Ha = 32,158#.






RE: Tied Arch - Roark's Formula
if down, then the vertical component of the reactions is 31250 lbs, and the lateral componentis tan(0.54)* (yes?) which is 18615 lbs.
another day in paradise, or is paradise one day closer ?
RE: Tied Arch - Roark's Formula
This is snow+dead. Are you using Roark's equation?
RE: Tied Arch - Roark's Formula
No, I'm assuming the reaction is inclined, along the tangent.
another day in paradise, or is paradise one day closer ?
RE: Tied Arch - Roark's Formula
BA
RE: Tied Arch - Roark's Formula
That's what I thought too. That's why I want someone to check the Roark formula.
I used (wL^2)/(8f) to check it and got 55,804# (f=14', which is the distance from the bottom chord to the top chord at mid-span). Something doesn't seem right.
RE: Tied Arch - Roark's Formula
BA
RE: Tied Arch - Roark's Formula
take 1/2 the arch, horizontal reaction at the top CL, inclined reaction at the ground.
vertical load on 1/2 arch is 32,500 lbs, horizontal off-set between load and reaction is 25'
if height 14', then horizontal reaction is 32500*25/14 = 58305 ...
dumba$$, took tan of the wrong angle !
i get the 1/2 angle as asin(50/97.7) = 0.537rad (about 30deg, about right ... the span is close to the radius, total angle about 60deg)
so the horizontal reaction is tan(pi/2-0.537)*32500 = 52460
another day in paradise, or is paradise one day closer ?
RE: Tied Arch - Roark's Formula
Your answer is close, but no cigar. There is no reason why the reaction should be tangential because the arch is a circular curve and the moment diagram is parabolic.
BA
RE: Tied Arch - Roark's Formula
I think your reasoning is right. The difference between answers is probably rounding error.
RE: Tied Arch - Roark's Formula
BA
RE: Tied Arch - Roark's Formula
Using Theta = ASin(50/97.7) = 0.537245 radians I get:
Lph = -651.496
Ahh = 0.011295
Ha = -57682
Or for Theta = 31 degrees (0.541052 radians):
Lph = -673.814
Ahh = 0.011691
Ha = -57634
So they are reasonably consistent with the other estimates.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Tied Arch - Roark's Formula
By the way, it looks like a very slender section for a 100 foot span!
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Tied Arch - Roark's Formula
if this is a ring (a section that doesn't support bending) then the 1/2 arch is a three force body and the reactions are tangential.
another day in paradise, or is paradise one day closer ?
RE: Tied Arch - Roark's Formula
The arch, hinged at both ends and under uniform load, is not in pure axial compression, so it must be capable of resisting bending moment.
The reactions are not tangential to a circular arch. They would be tangential if the arch was parabolic.
BA
RE: Tied Arch - Roark's Formula
The greatest trick that bond stress ever pulled was convincing the world it didn't exist.
RE: Tied Arch - Roark's Formula
BA
RE: Tied Arch - Roark's Formula
As Robert Hooke wrote, "as hangs the flexible line, so but inverted stands the rigid arch".
Well actually he wrote "abcccddeeeeefggiiiiiiiillmmmmnnnnnooprrsssttttttuuuuuuuvx", but that's what he meant.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Tied Arch - Roark's Formula
The greatest trick that bond stress ever pulled was convincing the world it didn't exist.
RE: Tied Arch - Roark's Formula
RE: Tied Arch - Roark's Formula
RE: Tied Arch - Roark's Formula
BA