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Weak axis calculation

Stiffness model for weak-axis bending showing weak-axis bolt-line components given by the general weak-axis reference. For further info on weak-axis calculation see chapter: "Weak-axis calculation".

As given by the reference, the weak-axis stiffness should be calculated in a similar way as in-plane stiffness. We do not recognize any difference in the stiffness between component 4a and 4b in SCIA Engineer. Stiffness coefficients k₄, k₅,k₁₀ for all bolt-rows are calculated according EN 1993-1-8 Article 6.3.2 Table 6.11 as for the strong-axis calculation. The final value is however divided by 2 for usage in weak-axis calculation. In weak-axis calculation all bolt-rows are used compared to the strong-axis stiffness calculation, where only bolt-rows above center of compression are used.

The additional stiffness bolt-line coefficients for components Column flange in twisting k₁₇ and for Column web in bending k₁₈ are defined by the reference as:

Column flange in twisting:

with:

b_c	is the width of the column
t_fc	is the thickness of the column flange
ν	Poisson's ratio of a column material
∑p₁	is the spacing between the first and last bolt-row
y	is the design distance from the bolt-line in tension to the centre of compression for weak-axis bending
l_eff,fct	effective length of column in twisting calculated assuming a maximum spread at 60° from the bolts across the width of the column flange, given as:

Column web in bending:

with:

t_wc	is the web thickness of the column web
p₂	is the spacing between the two bolt-lines
h_c	is the height of the column
b_eff,wbc	is the effective length of the web in bending, considered simply supported in both ends, given as:

Based on the different bending stiffness model several modification, to the strong-axis calculation, are introduced both for:

Beam-column connections:

the k_eff_,r stiffness given by EN 1993-1-8 Article 6.3.3.1 (1) is not required, since only one bolt-line needs to be calculated. The stiffness for each of the components in the bolt-line is calculated as a sum of the component stiffness coefficients of all bolts in the bolt-line
the k_eq stiffness given by EN 1993-1-8 Article 6.3.3.1 (2) is not required to be used, since it is not used by the stiffness model
the leverage arm z_eq given by EN 1993-1-8 Article 6.3.3.1 (3) is set equal to "y"
rotational stiffness S_j formula given by EN 1993-1-8 Article 6.3.1 (4) is changed to the formula below, while coefficient k₄, k₅,k₁₀ are taken as: k_i = ∑(k_i_,r), where "r" represent the number of all bolt-rows. Coefficient k₇ is taken as infinity.

Splice connections:

the k_eff,r stiffness given by EN 1993-1-8 Article 6.3.3.1 (1) is not required, since only one bolt-line needs to be calculated. The stiffness for each of the components in the bolt-line is calculated as a sum of the component stiffness coefficients of all bolts in the bolt-line
the k_eq stiffness given by EN 1993-1-8 Article 6.3.3.1 (2) is not required to be used, since it is not used by the stiffness model
the leverage arm z_eq given by EN 1993-1-8 Article 6.3.3.1 (3) is set equal to "y"
rotational stiffness S_j formula given by EN 1993-1-8 Article 6.3.1 (4) is changed to the formula below, while coefficient k_5,l, k₅_,r,k₁₀ are taken as: k_i = ∑(k_i_,r), where "r" represent the number of all bolt-rows. Coefficient k₇ is taken as infinity.

The stiffness classification and check are not done for the weak-axis stiffness calculation, since the classification and check limits are not available.

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