Engineering analysis + design software

User Area > Advice

What are stress resultants?

These are defined as "force per unit width" and are denoted by the following symbol types :-

Nx, Ny, Nxy, Mx, My, Mxy

A stress resultant can be changed into an average continuum stress measure simply by dividing by the thickness of the plate or shell at the point of interest. Alternatively, it may be converted to an approximate force by multiplying by the width over which the resultant acts.

Stress resultant output is obtained at a Gauss point by integrating the layer continuum stresses at that Gauss point.


More information on "force per unit width"

The example illustrated below shows a comparison of the different results obtained between a beam model, a shell model and a volume meshed model:

For the beam the cross-section properties are defined in a geometric attribute. The force obtained at a node represents the resulting force for the cross-section.

In the Volume meshed model, the width and depth of the cross-section are modelled in the elements and stresses are obtained at each node. The stress at a node is a force per unit area at that discrete location. To obtain a force comparable with the beam model, the stresses would have to be integrated with respect to the width and depth of the cross-section.

When looking at resultant forces, the shell model is part way between the two with the width modelled by shell elements, but the thickness is defined by a geometric attribute. Now Nx can be obtained as a force per unit width at each node across the width (width is in the local y direction in the example above). If Nx is divided by the element thickness, an average stress will be obtained. In LUSAS direct stresses due to both membrane and flexural deformation are also available for shell elements at Top, Middle and Bottom locations through the thickness.

The resulting force in the x direction for a shell element model is the integral of Nx with respect to the width. This can be obtained using by selecting the menu item: Utilities > Slice Resultants Beams/Shells

A line is drawn across the model to define a path to slice normal to, and through, the model.  With this tool, the equivalent axial force in the x direction is determined by integrating the stresses.

For further information please see: Modeller Reference Manual > Chapter 8 - Viewing the Results > Manipulating the Results Model > Beam Stress Resultants from Beams and Shells  

Please also see the worked example: Section Slicing of a 3D Shell Structure

innovative | flexible | trusted

LUSAS is a trademark and trading name of Finite Element Analysis Ltd. Copyright 1982 - 2022. Last modified: March 09, 2023 . Privacy policy. 
Any modelling, design and analysis capabilities described are dependent upon the LUSAS software product, version and option in use.