To simplify calculations, beam elements with non-round cross-sectional shapes can be converted to equivalent circular beams.
Heat transfer of the original shape also needs to be considered. A shape factor, which is the ratio of the outer circumference of the actual cross-sectional shape to the circumference of the circular beam with equivalent cross-sectional area, makes adjustments for the additional surface area the converted beam should have.
Supported cross-sectional shapes for beam elements
The following table lists the available cross-sectional shapes and the required dimensions to define them.
| Shape | Required dimensions |
|---|---|
| Circular | Diameter (2r) |
| Annular | Outer diameter (do), inner diameter (di) |
| Semicircular | Diameter (2r), height (t) |
| Rectangular | Width (a), height (b) |
| Trapezoidal | Top width (b), bottom width (a), height (h) |
| U-shape (rounded trapezoidal), where H=d | Width (W), height (H) |
| U-shape (rounded trapezoidal), where H > d | Width (W), height (H), diameter (d) |
| Ellipse | Long radius (a), short radius (b) |
| Other | Equivalent diameter, shape factor |
Equivalent diameter and shape factor for non-round beam cross-sectional shapes
The following table illustrates the required dimensions to define non-round beam cross-sectional shapes and presents the calculations that define equivalent diameter and shape factor for each beam shape.
| Shape | Cross-sectional geometry | Equivalent diameter, based on equivalent cross-sectional area | Shape factor |
|---|---|---|---|
| Semicircular |
|
|
|
| Rectangular |
|
|
|
| Rectangular |
|
|
|
| Trapezoidal |
|
|
|
| U-shape (or rounded trapezoidal), where H=d |
|
|
|
| U-shape (or rounded trapezoidal), where H > d |
|
where
|
where
|
| Elliptical |
|
|
|
Worked example
A rectangular shaped runner has a cross-sectional width (a) of 5 mm and height (b) of 3 mm.
Using the formula above, this runner could be modeled by a circular beam element with a diameter of
or 4.37 mm.
The runner would need a shape factor of
or 1.16.
When modeling this beam element, select 
(). In the Cross-section is box, select Other shape. Click Edit dimensions and enter the calculated values for Equivalent diameter (4.37) and Shape factor (1.16) in the Cross-Sectional Dimensions dialog that appears.