Moment-Rotation and Moment-Curvature
Moment-Rotation and Moment-Curvature
(OP)
What is the difference between moment-rotation relationship and moment-curvature relationship for a structural element (e.g. beam, column)?
Also, How to convert the moment-curvature which is calculated from the sectional analysis to moment-rotation relationship or the other way around?
Thank you in advance for your kind help and cooperation.
Also, How to convert the moment-curvature which is calculated from the sectional analysis to moment-rotation relationship or the other way around?
Thank you in advance for your kind help and cooperation.






RE: Moment-Rotation and Moment-Curvature
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Moment-Rotation and Moment-Curvature
RE: Moment-Rotation and Moment-Curvature
Dik
RE: Moment-Rotation and Moment-Curvature
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Moment-Rotation and Moment-Curvature
We must be thinking of two separate issues. Non-linear analysis considers the hinges in the plastic region so the load redistributes to elements that haven't yielded. I typically neglect the moment rotation of hinges in elastic analysis.
RE: Moment-Rotation and Moment-Curvature
RE: Moment-Rotation and Moment-Curvature
Curvature of a structural member is closely approximated by the expression M/EI. A dimensional analysis shows that the units turn out to be "#/(#/in2*in4) or in-1.
If you plot the M/EI diagram for a structural beam, you are plotting curvature from end to end of beam. In the case of a uniformly loaded beam, moment is a parabola. If EI is constant over the span, then M/EI is also a parabola. The rotation between any two points on the beam is the area under the M/EI curve between the two points.
A simple beam loaded with an equal and opposite moment at each end has a constant moment across the span, hence constant curvature. That is cylindrical bending. The change in rotation from one end to the other is the area under the M/EI curve, namely ML/EI where L is the span. By symmetry, the rotation is equal in magnitude at each support, so the rotation at each end is ML/2EI.
Rotations for other types of loading can be worked out in similar fashion. Sometimes the geometry gets a bit messy, but the concept is straight forward. The conjugate beam method is an easy way to determine slopes and deflections of simple span beams and I recommend you check that out using Google.
BA
RE: Moment-Rotation and Moment-Curvature
Rotation = Curvature x Hinge Length
If the hinge has zero length it's even simpler:
Curvature = 0 up to the yield moment, then infinite.
Rotation = 0 up to the yield moment, then rotational stiffness = 0, so you effectively have a pinned joint with a point moment.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Moment-Rotation and Moment-Curvature
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