Global Moments in Plates

Applies To
Environment: ALL
Area: Postprocessing workflow
Subarea: N/A
Original Author:Kris Sathia, Bentley Technical Support Group

Can you explain whether the Global Moments for plates include the contribution from MXY or not?

Yes, the Global Moments are calculated considering the contribution from plate local moments MX, MY and MXY.

The rules for computing the global moments are the same as the rules for computing the moments along any 2 orthogonal axes in the plane of the element. So, the information below is provided for any two general axes "g1" and "g2" in which we wish to transform the plate local moments into. Further, let "g3" be the axis formed by the cross product of g1 and g2. Thus, "g3" is normal to the plane formed by "g1" and "g2" and its positive direction is determined by the Right hand thumb rule. We wish to transform Mx and My into Mg1 and Mg2.

Theta in the above figure is measured

a) from the local X to the axis g1, and its magnitude is determined by the rule in step b
b) the normal vector formed by rotation from local x to the axis g1 is in the same direction as the local Z of the element as per the right handle thumb rule

The sign of the transformed moment is determined as follows.

Take a unit vector along local Z. Call it u1.

Take a unit vector along the axis g3. Call it u2.

Find the dot product of u1 and u2. This is a scalar quantity. If it is positive, the computed M_g1 and M_g2 are unchanged. If it is negative, the computed M_g1 and M_g2 are to be multiplied by -1.0.

Positive values for Mg1 and Mg2 produce tension on the surface of the element that is on the positive side of the axis "g3", and, negative values for Mg1 and Mg2 produce tension on the surface that is on the negative side of the axis "g3".

Note that the above equations are meant to be used only when the axes in which the results are desired are in the same plane as that of the element.

The calculation for global moment for element 89 for the attached model, is provided below

The STAAD.Pro model used for the above calculations is attached below

For your reference, the definition of Mx, My and Mxy in STAAD's element is as shown below.

Though the elements shown in the above figures are quadrilateral, the procedure is the same for triangular elements too.