3 / 14
Calculation of Shear Areas and Torsional Constant using the Boundary Element Method with Scada Pro
3
1. Introduction
In a bar with arbitrary cross-section, the coordinates of the center of gravity as well as
the bending moments of inertia can be calculated analytically, i.e. using closed-form
relationships. However, shear areas as well as torsional constant can be calculated
analytically only for bars with simple geometry cross-sections, while in all other cases the
calculation is accomplished only numerically, since solution of boundary value problems are
required. Boundary value problems can be solved using numerical methods such as the
Finite Element Method (FEM) or the Boundary Element Method (BEM) [1.1].
In order to solve the above boundary value problems and to calculate the shear areas
and torsional constant, the Boundary Element Method with Scada Pro is implemented. It is
worth here noting that in the Boundary Element Method only the boundary of the cross-
section (with boundary elements) is discretized (Img.1.1a), unlike the Finite Element
Method in which the entire interior area of the cross-section is discretized (using surface
elements) (Img.1.1b). This results in Boundary Element Method, a more simple process of
discretization and significantly reduce the number of unknowns. It is also stressed that the
Boundary Element Method has a rigorous mathematical approach, which means that the
method is so accurate that the results can be considered to be practically precise.
(a)
(b)
Img. 1.1. Box shaped cross-section discretization with the Boundary Element Method (a)
& with the Finite Element Method (b).
BIBLIOGRAPHY
[1.1]. Katsikadelis, J.T (2002)
Boundary Elements: Theory and Application
, Elsevier,
Amsterdam-London.