Cross-sectional shape equivalents for beam elements

rde

关于等效直径和形状因子的文章
Beam elements can be a variety of shapes. For these elements to be represented in a simpler fashion for analysis, they can be converted to an equivalent circular beam. Heat transfer also needs to be considered. A Shape Factor is applied which adjusts 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 that cross-sectional shape. The figure that follows illustrates the required dimensions graphically.
Shape        Required dimensions         
Circular        diameter (2r)        see A below
Annular        outer diameter (do), inner diameter (di)        see B below
Half-circular        diameter (2r), height (t)        see C below
Rectangular        width (a), height (b)        see D and E below
Trapezoidal        top width (b), bottom width (a), height (b)        see F below
U-shape        width (W), height (H), diameter (d)         see G and H below
Ellipse        long radii (a), short radii (b)        see I below
Other        Equivalent diameter, shape factor        user-defined
        Cross-sectional Geometry        Equivalent Diameter, Based on Equivalent Cross-sectional Area        Shape Factor
A         



B         



C         

where  

where  

D         



E         



F         



G         



H         

where


where


I         



Worked example
A rectangular shaped runner has a width(a) of 5mm, and a depth(b) of 3mm.
Using the formula above, this runner could be modeled by a circular beam element with a diameter of  or 5.64mm.
It would need a Shape Factor of  or 1.16.
When modelling this beam element, select the Properties (Edit  Properties). In the Cross-section is box select Other shape. Click Edit dimensions and enter the calculated values for Equivalent diameter(5.64) and Shape factor (1.16) in the Cross-Sectional Dimensions dialog that appears.

[ 本帖最后由 rde 于 2008-1-7 19:35 编辑 ]