Girder w/ Parabolic Haunch. What equation describes the haunch depth?
Girder w/ Parabolic Haunch. What equation describes the haunch depth?
(OP)
This has been driving me crazy. So I'm dealing with load rating continuous highway girders over bents that have parabolic haunches at the interior locations. The problem is, what equation do you used to describe the depth of the section?






RE: Girder w/ Parabolic Haunch. What equation describes the haunch depth?
Dx = Depth of beam at x from Left End
When x < a, Dx = d + [(x-a)/a]2*b
When x > (L-a), Dx = d + [(x-L+a)/a]2*b
When a < x < (L-a), Dx = d
For any x, Dx = d + (x<b)[(x-a)/a]2*b + (x>(L-a))[(x-L+a)/a]2*b
The Boolean expressions shown in red take the value 0 if false and 1 if true.
BA
RE: Girder w/ Parabolic Haunch. What equation describes the haunch depth?
When a > x > (L-a), Dx = d
BA
RE: Girder w/ Parabolic Haunch. What equation describes the haunch depth?
BA
RE: Girder w/ Parabolic Haunch. What equation describes the haunch depth?
RE: Girder w/ Parabolic Haunch. What equation describes the haunch depth?
RE: Girder w/ Parabolic Haunch. What equation describes the haunch depth?
y-k = a(x-h)2
is a parabola with vertex at the point (h,k). The parabola opens upward if a>0 and downward if a<0. You want yours opening downward.
The vertex is the point where the curve meets the straight line representing the beam depth between haunches.
The equation
x-h = a(y-h)2
is a parabola which opens to the right or to the left, depending on the sign of a, but that is not what you want here.
BA
RE: Girder w/ Parabolic Haunch. What equation describes the haunch depth?
That equation should have read:
x-h = a(y-k)2 with vertex at point (h,k).
It could be used but the vertex would be at the support and the curve would meet the underside of beam at an angle rather than tangentially.
If the haunched beams are existing, I believe y=a.x2 is the more likely configuration for the haunches but this could be confirmed by visual examination.
BA