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Verification of axial resistance for built-up cross-sections

The resistance of the partial member in tension or in plain compression is calculated using the expression

or

Where is:

A

  • The cross-sectional area

fy

  • The yield strength

γM0

  • The partial safety factor

The bending resistance for bending moment My is calculated for the classes 1 and 2 according to the following formula:

The formula for the class 3:

The formula for the class 4:

Where is:

Wpl,y

  • The plastic section modulus of partial cross-section about the axis y

Wy

  • The elastic section modulus of partial cross-section about the axis y

Wy,eff

  • The effective section modulus of partial cross-section about the axis y

The bending moment Mz is recalculated into the increment of axial force in partial cross-section dN. The recalculation uses following expression

The formula for members with battens:

Where is:

h0

  • The distance of points of inertia of partial cross-sections

A

  • The area

Iz

  • The second moment of inertia of partial cross-section

The similar recalculation is used for the shear force Vy in the direction of the strong axis. The shear force will be transferred into bending moment Mz for partial cross-section. Following expression is used:

Where is:

l1

  • The distance of battens

The bending resistance of partial cross-section for bending moment Mz is calculated for the classes 1 and 2 according to the following formula:

The formula for the class 3:

The formula for the class 3:

Where is:

Wpl,z

  • The plastic section modulus of partial cross-section about the axis z

Wz

  • The elastic section modulus of partial cross-section about the axis z

Wz,eff

  • The effective section modulus of partial cross-section about the axis z

The verification of the combination of axial force and bending moments is done according to the rules similar to the verification of solid cross-sections. This expression is used:

Where is:

n

  • The number of partial cross-sections

dN

  • The increment of axial force due to bending moment Mz

Mz,Sd

  • The bending moment in partial cross-section due to shear force Vy

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