8.5. Explanation cross sectional properties#
Castellated beams IPE/HEA/HEB#
Fig. 8.11 Castellated beams.#
The carthesian coordinate system#
In this coordinate system the axes are defined as follows:
x-axis: length axis of the element
y-axis: cross product of x and z axis
z-axis: downward axis
Name |
Structural Mechanics |
NEN-EN 1993 |
|---|---|---|
Moment of inertia around y-axis (Resistance against moments in x-z plane) |
\(I_{zz}\) |
\(I_{y}\) |
Moment of inertia around z-axis (Resistance against moments in x-y plane ) |
\(I_{yy}\) |
\(I_{z}\) |
Section modulus around y-axis (Resistance against moments in x-z plane) |
\(W_{zz}\) |
\(W_{y}\) |
Section modulus around z-axis (Resistance against moments in x-y plane) |
\(W_{yy}\) |
\(W_{z}\) |
Top hat beams#
Fig. 8.12 Radius of gyration.#
The radius of gyration is needed to determine the slenderness of a structure. When the radius of gyration and the buckling curve are known, the buckling force can be determined.
Radius of gyration around strong axis (y-axis)
\( i_y = \sqrt{\frac{I_y}{A}} \)
Radius of gyration around weak axis (z-axis)
\( i_z = \sqrt{\frac{I_z}{A}} \)