## Mohr’s Circle and Plate Stresses and Actions

The functions described in this post can be found in the download file PlateStress.zip, including examples and full open source code.

PlateStress Functions, click for full size view

The function MCircle returns the plane stress components (XX, YY and XY stress) for any specified stress field, when rotated through a specified angle.  If no angle is specified the function returns the principal stresses, and the principal stress angle to the X axis of the original stresses.

MCircle is used in the function PlateStress4, which returns the in-plane forces and moments on a finite element analysis plate element, given the stresses at 4 Gauss Points.  The stresses may either be specified in the element local axis system, or the global XY system, in which case the angle between the X axis and the element longitudinal axis at each section must be specified.  Examples are included in the spreadsheet and illustrated below.

The first example looks at an inclined simply supported beam, modelled with 8 noded plate elements in the finite element package Strand7:

Strand7 results for inclined beam

The spreadsheet analysis of the stresses extracted from Strand7 is shown below, including:

• Global stresses from the FE analysis
• Stresses converted to the element local axes with the MCircle function
• Beam actions found using the global stresses with a rotation angle
• Beam actions from the local stresses with no rotation angle (identical results).

Plate stresses and beam actions in an inclined beam

The second example is a circular arc subject to vertical point loads, and modelled using 8-noded plate elements and with short straight beam elements:

Strand7 analysis of a circular arc modelled with plate elements and beam elements

The analysis results are shown below, with Strand7 global plate stresses, plate actions found with the PlateStress function, and for comparison beam actions from the analysis using short beam elements:

PlateStress results from Strand7 analysis of a circular arc

Plate results compared with Strand7 beam results for bending and shear force