transverse loading of a curved beam?

[brashear]

Hi all,
I am trying to compute the stress and strain of a transversely loaded beam as pictured. I have seen analytical solutions for radial or tangential loading, but can't find anything for transverse loads. The boundary conditions are that the base is fixed and the slope at the end is zero. Thanks

 

[ishvaaag]

Transverse meaning this time..

1. Vertical loads
2. Horizontal loads
3. Perpendicular to the plane of the drawing.

Normally, for transverse in a case like this one would understand radial, I think. Yet please state your case.

If searching something like a closed form solution, it seems just something set for a problem to solve by energy methods, I think.

 

[brashear]

The load is perpendicular to the plane of the drawing.

 

[IDS]

See "Curved beams loaded normal to the plane of curvature" in Roarke's Formulas for Stress and Strain (Sec 9.5 in my edition).

You can check your results with a frame analysis using short straight elements (but note the comment in Roarke about possible secondary bending with flanged sections).

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[csd72]

Brashear, is this a homework question?

 

[rb1957]

looks a pretty simple problem (like you'd see in a textbook).

loading is out-of-plane, as shown, creating bending torsion and shear on a section. make your section (normal to the beam CL, ie along a radius of the arc), determine the beams internal reactions to balance the load, ...