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Verification of solid cross-sections

Verification of shear resistance

The verification of the shear resistance is done in two directions (y and z). Following expression is used:

Where is:

Q

  • The entered shear force

Vfi,θ,Rd

  • The shear resistance of the cross-section

Verification of axial stress in cross-section

The axial stress in the cross-section may be caused by axial force N, bending moments My, Mz and bimoment B. The combination of these forces and moments is verified.

The verification without consideration of buckling and lateral torsional buckling is done according to the following expression:

Where is

Nfi,θ,Rd

  • The tensile resistance Nt,fi,θ,Rd or resistance in plain compression Nc,fi,θ,Rd

Mc,fi,θ,Rd,y

  • The bending resistance about the axis y

Mc,fi,θ,Rd,z

  • The bending resistance about the axis z

Bfi,θ,Rd

  • The resistance for stresses due to the bimoment

The verification including the consideration of buckling is done according to the following expression:

The formula for classes 1 and 2:

Where is:

Nb,fi,θ,Rd

  • The buckling resistance

ky, kz

  • The interaction factors

The factors ky, kz are given by the expression

but

Where is:

χy, χz

  • The reduction factors for flexural buckling

and factors μy, μz are given by equations

but

Where is:

,

  • The relative slenderness

βMy, βMz

  • The equivalent uniform moment factors

The formula for the class 3:

Where is:

Nb,fi,θ,Rd

  • The buckling resistance

ky, kz

  • The interaction factors

The factors ky, kz are given by the expressions

but

Where is:

χy, χz

  • The reduction factors for flexural buckling

and factors μy, μz are given by equations

but

Where is:

,

  • The relative slenderness

βMy, βMz

  • The equivalent uniform moment factors

The formula for the class 4:

Where is:

Nb,fi,θ,Rd

  • The buckling resistance

ky, kz

  • The interaction factors

The factors ky, kz are given by the expressions

but

Where is:

χy, χz

  • The reduction factors for flexural buckling

and factors μy, μz are given by equations

but

Where is:

,

  • The relative slenderness

βMy, βMz

  • The equivalent uniform moment factors

The verification including the consideration of buckling and lateral torsional buckling is done according to the following expression:

The formula for classes 1 and 2:

and

The formula for the class 3:

and

Where is:

Nfi,θ,Rd,z

  • The buckling resistance for buckling perpendicular to the axis z

Nfi,θ,Rd,y

  • The buckling resistance for buckling perpendicular to the axis y

Mc,fi,θ,Rd,y

  • The bending resistance about the axis y

Mc,fi,θ,Rd,z

  • The bending resistance about the axis z

Mb,fi,θ,Rd,y

  • The bending resistance about the axis y including the consideration of lateral torsional buckling

Mb,fi,θ,Rd,z

  • The bending resistance about the axis z including the consideration of lateral torsional buckling

Bfi,θ,Rd

  • The resistance for stresses due to the bimoment

The factor kLT is given by the expression

but

Where is:

χy, χz

  • The reduction factors for flexural buckling

and the factor μLT is given by the expression

but

Where is:

,

  • The relative slenderness

βM,LT

  • The equivalent uniform moment factor

The formula for the class 4:

and

Where is:

Nfi,θ,Rd,z

  • The buckling resistance for buckling perpendicular to the axis z

Nfi,θ,Rd,y

  • The buckling resistance for buckling perpendicular to the axis y

Mc,fi,θ,Rd,y

  • The bending resistance about the axis y

Mc,fi,θ,Rd,z

  • The bending resistance about the axis z

Mb,fi,θ,Rd,y

  • The bending resistance about the axis y including the consideration of lateral torsional buckling

Mb,fi,θ,Rd,z

  • The bending resistance about the axis z including the consideration of lateral torsional buckling

Bfi,θ,Rd

  • The resistance for stresses due to the bimoment

The factor kLT is given by the expression

but

Where is:

χy, χz

  • The reduction factors for flexural buckling

and the factor μLT is given by the expression

but

Where is:

,

  • The relative slenderness

βM,LT

  • The equivalent uniform moment factor

If the shear verification fails for particular directions y and z, the value 1.0 is used for corresponding direction in equations described above.

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