Geometric Properties of an Arbitrary Plane Domain

This program will compute the following properties of an arbitrary plane domain:

* Area

* Position of the centroid with respect to the given axis

* First moments with respect to the given axis

* Inertia moments and inertia product with respect to the given axis

* Position of the principal axes of inertia

* Principal moments of inertia

The given domain is defined by its exterior contour and any arbitrary number of interior contours (i.e., no restriction is placed on the degree of connectivity of the domain). In turn, each contour is defined by any arbitrary number of points. Finally, each point is defined by its coordinates with respect to an arbitrary system of Cartesian coordinates. The only restrictions are as follows:

*The points for each contour must be numbered consecutively, either clockwise or counter-
clockwise.

*The program always assumes that each consecutive point is connected to its neighbors by a
straight segment.

The following diagram illustrates the convention chosen to define the principal axes::

Exterior Contour         Contour 1            Contour 2              Contour 3

1(7.5,3)                         1(8,4)                     1(11,13)                  1(20,13)
2(18.5,3)                        2(10,4)                   2(15,13)                  2(16,13)
3(21,13)                         3(10,13)                3(15,4)                    3(16,4)
4(23,13)                         4(6,13)                   4(11,4)                     4(18,4)
5(23,15)

6(3,15)
7(5,13)

Downloads:

Basic program - liberty basic- lbgpapd.bas

Test Case:

GEOMETRIC PROPERTIES OF AN
ARBITRARY PLANE DOMAIN

(R)EAD FROM DATA OR (I)NPUT DATA? R



GEOMETRIC PROPERTIES
WITH RESPECT TO GIVEN AXES

AREA=85

COORDINATES OF CENTROID
XG=13
YG=10.4666667

MOMENTS OF INERTIA
IXX =10716
IYY =16600.9583
IXY=11565.6667

STATIC MOMENTS
MXX=889.666667
MYY =1105

PRESS RETURN TO CONTINUE
?


INERTIA TENSOR WITH RESPECT
TO PARALLEL AXES THRU CENTROID

IXXG =1404.15556
IYYG=2235.95833
IXYG=0.36379788e-11


PRINCIPAL AXES AND MOMENTS OF INERTIA

ANGLE =0.25058925e-12
IMAX = 2235.95833
IMIN =1404.15556