## 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

idealisedareas of plastic hinges, rotation continues without additional restraint once Mp has been obtained.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

^{-1}where L represents length. In the imperial system, curvature would be measured in ft^{-1}or in^{-1}.Curvature of a structural member is closely approximated by the expression M/EI. A dimensional analysis shows that the units turn out to be "#/(#/in

^{2}*in^{4}) 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

Jason McKee

proudR&D Manager ofCross Section Analysis & Design

Software for the structural design of cross sections

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