## Global to Local for plates (and three node beams)

The Glob_to_Loc function (see Converting from global to local coordinates (and vice versa) ) converts forces and deflections of a beam from the global coordinate system to the local system, defined by the longitudinal axis of the beam and a rotation angle from the horizontal plane.  The rotation angle is required because a beam defined by its two end nodes has no defined rotation, but an alternative is to define the beam orientation with three nodes; i.e. the two end nodes and a third node lying on the local x-y plane.  This approach is also used for plate-shell elements, where the plane of the element is defined by the coordinates of the corner nodes.

To work with elements defined by 3 nodes I have added two new user defined functions (UDFs) to the IP2 spreadsheet:  Glob_to_Loc3 and Loc_to_Glob3.  The new version of the spreadsheet may be downloaded from: IP2.ZIP – including full open source code.  The download zip file also includes a Python version of these functions.  Use of the Python versions requires the PyXll add-in.  See Installing Python, Scipy and Pyxll for more details. Details of usage are shown in the screen-shot below (also included in the download file).:

Glob_to_Loc3 and Loc_to_Glob3 functions

The example below shows input for a trapezoidal plate element, followed by results from the FEA program Strand7:

For a 3 Node beam element, using the Strand7 definition of the beam principal axes, use the Axtype = 3 option as shown below.  In this case the beam orientation is defined by the 3 node coordinates, with an additional rotation of 30 degrees.

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### 3 Responses to Global to Local for plates (and three node beams)

1. Bill Harvey says:

Doug,

I think what you need in Numpy is here:

Bill

Bill’s award winning paper from ICE available here: http://www.icevirtuallibrary.com/content/article/10.1680/bren.11.00032

Sutherland History Lecture 2012 at http://bit.ly/J4gblz Includes the viaduct demolition video

Bill Harvey, bill@obvis.com, Ph +447879425884 Software House, OBVIS Ltd Consultancy, Bill Harvey Associates Ltd Gairloch, Hensleigh Drive, Exeter, EX2 4NZ http://www.billharveyassociates.co.uk http://www.obvis.com http://www.moiretelltales.com http://billharvey.typepad.com

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2. PRABU says:

Dear Sir,

I am having a plate model with irregular quadrilateral plates which was created using STAAD Pro V8i software, from which I can got Mx & My (for both Local & global moment). But in that STAAD program there is no possibilities to get global Out-of-plane shear, the program is giving only local Out-of-plane shear.
So I tried to use this excel to convert Local to Global Shear force. Initially I tried to verify the comparision of Global Vs local Bending moment arrived from the STAAD Pro program with this excel sheet. But it is not matching!
In the excel sheet, while input the Bending moment we need to give local direction MX, MY, MXY (or) MX, MY, MZ.
But in my STAAD program there is not MZ result output. How to overcome this issue.