# Geometric Properties of an Equilateral Triangle

Aim: To check the accuracy of the geometric properties calculation for a rod cross-section in the form of an equilateral triangle.

Name of a file with the initial data: Triangle.cns

Formulation: Check the accuracy of the torsional geometric properties calculation for a rod cross-section in the form of an equilateral triangle.

References:     Young W.C., Budynas R.G., Roark's Formulas for Stress and Strain, New York , McGraw-Hill,  New York, 2002.

Initial data:

 ν = 0.3 - Poisson’s ratio; a = 40 cm - side length of an equilateral triangle.

Design model: The design model is created by triangulation (the number of triangles ≈ 3000) on the basis of a model of the external contour. The external contour is an equilateral triangle. The number of vertices of the contour in a model is 3.

## Results Obtained in Consul

Design model, coordinate and principal axes, center of mass, ellipse of inertia, core of the section

Comparison of results:

Parameter

Theory

CONSUL

Deviation, %

Torsional moment of inertia, It cm4

55425,625

54477,143

1.71

Y-coordinate of the shear center, yb cm

20

19,999

0,005

Z-coordinate of the shear center, zb cm

11,547

11,589

0,36

Notes: Geometric properties can be determined analytically by the following formulas:

$I_{t} =\frac{\sqrt 3 }{80}a^{4};$ $y_{b} =a/2;$ $z_{b} =\frac{a}{2\sqrt 3 }.$