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
	*V_fi,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 M_y, M_z 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	*N_fi,θ,Rd*	The tensile resistance N_t,fi,θ,Rd or resistance in plain compression N_c,fi,θ,Rd
	*M_c,fi,θ,Rd,y*	The bending resistance about the axis y
	*M_c,fi,θ,Rd,z*	The bending resistance about the axis z
	*B_fi,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:	*N_b,fi,θ,Rd*	The buckling resistance
	k_y, *k_z*	The interaction factors

The factors k_y, k_z are given by the expression

but

Where is:

χ_y, χ_z

The reduction factors for flexural buckling

and factors μ_y, μ_z are given by equations

but

Where is:	,	The relative slenderness
	β_My, *β_Mz*	The equivalent uniform moment factors

The formula for the class 3:

Where is:	*N_b,fi,θ,Rd*	The buckling resistance
	k_y, *k_z*	The interaction factors

The factors k_y, k_z are given by the expressions

but

Where is:

χ_y, χ_z

The reduction factors for flexural buckling

and factors μ_y, μ_z are given by equations

but

Where is:	,	The relative slenderness
	β_My, *β_Mz*	The equivalent uniform moment factors

The formula for the class 4:

Where is:	*N_b,fi,θ,Rd*	The buckling resistance
	k_y, *k_z*	The interaction factors

The factors k_y, k_z are given by the expressions

but

Where is:

χ_y, χ_z

The reduction factors for flexural buckling

and factors μ_y, μ_z are given by equations

but

Where is:	,	The relative slenderness
	β_My, *β_Mz*	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:	*N_fi,θ,Rd,z*	The buckling resistance for buckling perpendicular to the axis z
	*N_fi,θ,Rd,y*	The buckling resistance for buckling perpendicular to the axis y
	*M_c,fi,θ,Rd,y*	The bending resistance about the axis y
	*M_c,fi,θ,Rd,z*	The bending resistance about the axis z
	*M_b,fi,θ,Rd,y*	The bending resistance about the axis y including the consideration of lateral torsional buckling
	*M_b,fi,θ,Rd,z*	The bending resistance about the axis z including the consideration of lateral torsional buckling
	*B_fi,θ,Rd*	The resistance for stresses due to the bimoment

The factor k_LT is given by the expression

but

Where is:

χ_y, χ_z

The reduction factors for flexural buckling

and the factor μ_LT is given by the expression

but

Where is:	,	The relative slenderness
	*β_M,LT*	The equivalent uniform moment factor

The formula for the class 4:

and

Where is:	*N_fi,θ,Rd,z*	The buckling resistance for buckling perpendicular to the axis z
	*N_fi,θ,Rd,y*	The buckling resistance for buckling perpendicular to the axis y
	*M_c,fi,θ,Rd,y*	The bending resistance about the axis y
	*M_c,fi,θ,Rd,z*	The bending resistance about the axis z
	*M_b,fi,θ,Rd,y*	The bending resistance about the axis y including the consideration of lateral torsional buckling
	*M_b,fi,θ,Rd,z*	The bending resistance about the axis z including the consideration of lateral torsional buckling
	*B_fi,θ,Rd*	The resistance for stresses due to the bimoment

The factor k_LT is given by the expression

but

Where is:

χ_y, χ_z

The reduction factors for flexural buckling

and the factor μ_LT is given by the expression

but

Where is:	,	The relative slenderness
	*β_M,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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