curved beam analysis

huangyhg

curved beam analysis
a project i am working on requires a horizontally curved lintel beam with a radius = 9'-7".  it will support a metal stud & gypsum bd. decorative wall that is 3'-0" wide & 4'-0" tall.  in plan view the lintel will form a quarter circle.  where can i find analysis/design procedure for this lintel beam?  to design this as a straight beam with a 2'-0" eccentric load seems overly conservative but appears to be the only way to apply aisc #9 guidelines.

what do you come up with if you calculate the true length along the beam centerline and then design as a simple beam with an increased span?
arc= 15'-0 5/8
let arch length be your span for a simple beam with uniform load along the centerline.  
how are you planning to fix the ends so that it just doesn't roll off its bearings (i assume that this is a single span)?
you can find lots of information relative to curved beam analysis in formulas for stress and strain, by roark and young.  but just plugging the numbers into the formulas can become a pretty good chore.
the big issue is that after all is done and said and you've calculated the stresses to 8 decimal places, there's not any design code to give an allowable stress- you're on your own there.  it will simplify matters if you use a square tube so you don't have lateral buckling issues.
restraining the ends is very important to stability.  depending on the magnitude of the load, you may need to use a box shape, such as an hss tube.  in my opinion, if you satisfy equilibrium of the applicable free-body diagram, then you got it done.  but make sure you account for warping and torsional stresses.  good luck.
a horizontally curved beam will experience significant torsion.  be sure to account for that in both the beam design and the connection to the supports.  depending on how you detail, the torsion in the beam will likely be transmitted to its support, if a column or wall, as bending moment.  
blodgett's design of welded structures has formulas for calculating the torque for a beam on a horizontal curve under uniform load.  it's way at the end of the book under "torsion member diagrams and formulas."
each end of the beam will bear on a 2'-0" dia. reinforced concrete column, so there is plenty of bearing area available & the translation of the moment to the column shouldn't be a problem.  my initial approach was to treat the arc length as a simple span length & then apply the wall weight as an eccentric load, just to be conservative.  the combined stresses were handled by a w12x26 but i was concerned with my overall approach.  i have a copy of blodgett's book but didn't get all the way to the last page before - i stopped after the section on torsional loading turned up no useful advice.  i am also looking into purchasing roark's book for additional analysis info.  thanks.