Design of Curved Beams 2

[abusementpark]

For the design of beams that are curved in the plane of the loading, how do you account for the effect the curvature has on the strain distribution?

Both steel and concrete beam design provisions are based on ultimate strength methodologies using a linear strain assumption. Since, curved beams do not have a linear strain relationship, how do you check the beams for flexure? Is there a significant difference?

For steel, I was thinking that since flexural strength is based on a plastic stress distribution the effect of the curvature would only make a difference at lower stress levels, prior to ultimate, but enough redistribution can occur to bring it to a plastic stress distribution.

For reinforced concrete, I am less sure since all of the ductility checks are based linear strain.

 

[IDS]

Regarding the effect of the non-linear strain distribution on the ultimate strength of reinforced concrete, the effect will be very small, but it would be quite straightforward to calculate it:

- Get the strain distribution for the particular radius/thickness ratio, from the link posted earlier.

- Apply the ultimate strain specified in the applicable code (usually 0.003 or 0.0035) at the compressive face.

- Assume a neutral axis position and calculate strains and stresses across the section using published stress/strain curves for steel and concrete (linear/ perfectly plastic for the steel, and parabolic/ plastic with no tensile strength for the concrete makes it easy and is perfectly adequate for design purposes, but you can use something more precise if you want to).

- Integrate the stresses to find the nett force.

- Adjust theneutral axis position and repeat until the nett force is equal to the applied axial force at the section.

- Take moments about the section centroid. That's the section ultimate moment capacity.

- Apply the capacity reduction factor in accordance with the code, and compare with the applied (factored up) design bending moment.

- Compare with a conventional analysis and let us know if the difference is more than a few percent.

Because the steel is likely to be well past yield, and most of the concrete in compression will also be past yield, the effect of the non-linear strain is likely to be very small, but for a sufficiently thick section (or small radius) it may become significant.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[abusementpark]

Here is crude sketch. I realize that I have drawn the wall a good bit shorter than it actually is. I realize that there is the cantilever shell action that dhengr discussed and that a finite element model is suitable approach. I was thinking about the horizontal beam strip action and that piqued my interest about ultimate design of curved beams in general, hence, the generic original post.

 

[csd72]

abusementpark,

There is one fundamental issue that has been missed due to the fact that things went off in the wrong direction ( a better description at the beggining would have given much more appropriate comments from the start).

If this is precast cladding then then needs to be provision for thermal movent and if so then arching action will be out of the question. You will then have to treat it as a beam.

Wind suction plus eccentric dead load will give your maximum support reaction at the top.

Even if it is fully restrained at the ends then wind suction will induce tension in the member.