PRIMER 22.1

Cutting Through 1D (Beam) Elements

Cutting through 1D (beam) elements

In order to calculate the intersection PRIMER expands beams to their "true" 3-dimensional section shape, and then cuts through that using the same "90 degree" or "true" cut rules that are used for shells.

(Note that by default PRIMER does not show true beam sections in the main graphics window, but this can be turned on using the Display Options panel. However the cut-section properties display window will always show the true beam shape, as this is required in order to compute properties correctly.)

90 degree cut option

Calculates the section at exactly 90 degrees through the element, regardless of the actual angle of intersection between beam and plane.

This is a "safe" option when calculating section properties, and hence the default.

True cut option

Used the actual intersection between beam and plane, resulting in the section becoming taller as the cut angle gets shallower, as in this example.

This is useful if you need to visualise the true geometry of the cut plane, but it should not be used when calculating section properties as it will over-estimate the section capacity.

Special note on "true" sections used for circular beams

The "true" section shape used for solid circular and hollow tubular beams is an approximation that uses 12 facets, at 30 degree intervals around the circle, to represent the actual section. This is the same approximation as that used for "true" beam section graphics.

However to give approximately the correct Area and Inertia values in the cut-section property calculation the radii used to define the facets are approximately 2.3% greater than the actual radii in the true circular section.

This factor compensates for the fact that each facet is slightly smaller in area, and its centroid closer to the section centre, than the true section arc. It is based on the ratio of "true" area of a 30 degree arc vs that of the triangular slice subtended by 30 degrees. In the calculations to the right R = 1.0.

This solution is not precise, but it should be more than good enough for practical purposes.


The torsion constant (J) of circular and rectangular beam sections is calculated analytically from the true section dimensions, and used directly in the torsion calculations below.

Special note on beams with explicit Area, Iss and Itt values.

Some beam element formulations, notably elform = 2 and 12, do not provide section dimensions but rather the engineering properties: Area, Iss, Itt, J, SA and Ist . These get special treatment in the cut section calculations.

Section shape for beams with explicit section properties

PRIMER attempts to synthesise a symmetrical section shape based on A , Iss and Itt (ignoring any torsion constant J, shear area SA or cross inertia Ist ) and this shape is used both for " true " beam section graphics and for calculating derived cut-section properties.

The shape used will be one of:

A thin-walled rectangular hollow section (RHS)

Preferred shape, so long as the aspect ratio of width W to height H does not exceed 2 : 1 (or 1 : 2).

All sides have a constant wall thickness t.

An I beam

Alternative shape where the RHS shape would look stupid because of extreme W : H aspect ratios, generally because Irr and Itt are significantly different in magnitude.

The web has a wall thickness t, and the flanges 2t.

A solid rectangular section

Fall-back shape for cases where neither of the two sections above can be calculated from the properties supplied.

(Properties supplied for a composite beam may not give a "physical" result for a homogeneous beam as assumed here.)

There are no explicit solutions for calculating RHS or I beam shapes, so an iterative solution method is used. This usually gives a plausible shape, but it will not be an exact match for the original section shape from which the properties were derived. Also if a cross inertia term Ist is supplied this usually implies a cross section that is not symmetrical. This term is ignored in the section synthesis above since there is no way of knowing what shape to use, so if Ist is non-zero treat the derived shape with circumspection.

Elastic section calculations for beams with explicit section properties

Where these explicit properties are available and 90 degree cuts are in use then PRIMER uses the supplied Area, Iss, Itt and Ist for elastic properties directly in the Calculation of Elastic Section Properties, instead of calculating these values from the geometric shape.

If true cuts are in use then elastic properties are calculated from the geometric shape since it is assumed that the area-based properties of the skewed section are required.

Plastic section calculations for beams with explicit section properties

For the Calculation of Plastic Section Properties PRIMER always uses the geometric shape as synthesised above. This is necessary because these calculations require knowledge of actual shape and area, and you should be aware that such calculations - based on a synthesised shape - will only ever be approximate.

Torsion calculation for beams with explicit section properties.

If Calculating Torsion Properties for a section using these beams then the J value ( Irr in earlier Ansys LS-DYNA versions) supplied is used directly, and no attempt is made to derive a J value from the synthesised shape.

Not only is this much faster, but the J value is not considered when synthesising a shape; also there are no considerations of calculating plastic properties. This does mean that if J on the original *SECTION_BEAM card is zero then the beam will not contribute to the overall torsion constant - but then it would not contribute during an analysis either, so this is correct.


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