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Cross-sections

The program contains a pre-defined database of cross-sections, which contains a wide range of rolled cross-sections and 11 shapes with arbitrary dimensions. Nine of these cross-sections are walled shapes (cross-section segments have thickness much smaller than the length), two of them are solid shapes. These pre-defined shapes are automatically considered as welded ones. The hot-rolled cross-section, that isn't included in the database, may be entered with the help of these shapes. However, the correct analysis parameters (plastic or elastic resistance, buckling curve) have to be specified manually in these cases.

The cross-sections are defined in dextrorotary coordinate system, the positive direction of the axis y is oriented to the left and the positive direction of the axis z is oriented downward. The origin is in the centre of gravity

Following cross-sectional characteristics are used in the analysis:

b, h, t1, t2 ...

  • The dimensions [mm]

A

  • The cross-sectional area [mm2]

Iy, Iz

  • The moments of inertia about axes y and z [mm4]

iy, iz

  • The radius of gyration for axes y and z [m]

Dyz

  • The mixed moment of inertia [mm4] (only L-shapes)

Iη, Iζ

  • The moments of inertia about main axes η and ζ [mm4] (only L-shapes)

iη, iζ

  • The radius of gyration for main axes η and ζ [m] (only L-shapes)

It

  • The rigidity moment in simple torsion [mm4]

Iω

  • The sectional moment of inertia [mm6]

yt, zt

  • The coordinates of the centre of gravity [mm]

ay, az

  • The coordinates of shear centre [mm]

yp, zp

  • The coordinates of load position [mm]

hpl, bpl

  • The levels of horizntal and vertical neutral axes for plastic resistance [mm]

Wpl,y, Wpl,z

  • The plastic cross-sectional moduli [mm3]

The cross-sectional moduli are calculated including the effect of unsymmetry with the help of the mixed moment of inertia Dyz. Following expressions are used:

The rigidity moment in simple torsion is calculated using following expression for walled cross-sections:

The simplified theory de Saint Venant is applied for solid cross-sections:

The sectional moment of inertia is defined by expression:

Where is:

F

  • The cross-sectional area

ω

  • The sectional ordinate

Coordinate systems

Two coordinate systems are defined in the cross-section: the local coordinate system of member (axes 2,3) and the coordinate system of cross-section (axes y,z). Input (except of buckling and LTB) is done usually in the local coordinate system of member (2, 3). Buckling and LTB are assigned in coordinate system of cross-section (y,z). The rotation of the cross-section is the rotation relatively to the local axes 2,3. Forces are also defined in the local coordinate system. The analysis is performed in the coordinate system of cross-section. Load is automatically recalculated from the local coordinate system to the coordinate system of the cross-section.

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