What is a Curved Beam ?
Many Machine Parts such as Crane Hook, C-Clamp, Mechanical Punch Press Frame (C shaped side view), Chain Links, Pipe Bends, Curved portion of machine frames are the practical examples of the Curved Beams. The major difference compared to straight Beam is that curved beams have initial curvature before applying load whereas straight beams get deflection or curvature after applying the load.
Design of a Curved Beam (online calculator)
The Basic Design of the curved beam is basically calculating the area of cross-section so as to keep bending stress within permissible limits (assuming beam material, overall dimensions, application conditions, etc. are already known to the designer)
Now for straight beams, we assume that amount of bending or radius of curvature is very small when the load is applied, which means, Neutral axis and centroidal axis will coincide and no additional calculation is required to find the position of the neutral axis. But in the case of curved beams where the initial radius of curvature is significantly high then the Neutral axis and centroidal axis will not coincide so we need to perform additional calculations to find the location of the neutral axis.
Below is the analysis of a small portion of a curved beam, where the position of the centroidal axis, neutral axis, radius of curvature, etc are represented.
Another difference in curved beams is that the stress distribution across the cross-section is not linear but hyperbolic. And stress is greatest on the inner surface being close to the neutral axis. The inner surface of the curved beam is under tensile load and the outer surface is under compression load. By convention, the positive moment is defined as the one that tends to straighten the beam.
In the case of pure moment applied to the curved beam only bending stresses are generated. However, a more common cause is the applied force. This force generated bending stress as well as direct axial stress on the midsection of the beam.
Following is the Calculator for Shift of Neutral Axis of a Curved Beam
Keywords: Curved Beam, Centroidal Axis, Shifting of neutral axis, application conditions, applied force, applied moment, design of curved beam, neutral axis, online calculator, hyperbolic, permissible stress, tensile load