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Twisting Moments

Twisting Moments

Twisting Moments

There seems to be different methods for combining the Mxy values with the Mx and My values; the "simple" method and then methods such as Wood & Armer? The simple method, best I can tell is:

Mxdesign = Mx +/- Mxy
Mydesign = My +/- Mxy

I am assuming the sign convention for the Mxy value is the same as for Mx and My, in that positive indicates tension on the top of the plate? If so, why the +/-? If Mx and Mxy are both positive, it would seem to indicate both were causing tension on the top side of the plate. If Mxy were negative but Mx were positive, it would seem the Mxy moment would reduce the tension on the top, unless of course Mxy was a greater magnitude than Mx.

If this isn't the case and you calculate two values for each principle direction; Mx + Mxy and Mx-Mxy, do you choose the greatest magnitude? In the case where Mx is originally positive and subtracting Mxy gives a Mxd that is negative, methods such as Wood & Armer say to use 0.

I am trying to analyze a circular concrete tank that has a notch. Being that the plates are not parallel to a global axis it is very difficult to use plate corner forces to determine the design bending moments, even if this is better method.

RE: Twisting Moments

Mxy would be a moment that acts on a plane perpendicular to the local x direction, but causes a stress in the positive y direction. Or, a Myx (since we're talking about isotropic materials) is a moment acting on a plane perpendicular to the local y direction causing a stress in the positive x direction.

Now look at an Mxx moment. It acts on a plane perpendicular to the local x direction and produces a stress parallel to the local x axis. At one end of the element, its stresses would add with the Myx moment and on the other side of the element the stresses would subtract from the Myx moment.

Hence, the simplest logical way to combine stresses is to +/- the Myx moment to the Mx to come up with a total design moment.

RE: Twisting Moments

Thanks Joshplum.

I see it now. I actually had to grab a piece of 2x4 and draw the stresses.

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