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Beam resistance

It is also important to verify that the joint shear resistance of bolts, calculated above, is not limited by shear force resistance of a connected beam(s). The plastic resistance of the beam in general is calculated according to EN 1993-1-1 Article 6.2.6 (2) as:

with:

f_y	yield strength of beam material
γ_M0	partial factor for resistance of cross-sections
A_v	is the shear area of a connected beam calculated for different cross-sections as indicated by the table below distinguished for strong and weak-axis calculations:

with:

b	is the overall width
h	is the overall height
h_w	is the depth of the web
r	is the root radius
t_f	is the flange thickness
t_w	is the web thickness
η	national annex coefficient defined by EN 1993-1-5 Article 5.1.(2).
A	is the cross-sectional area always taken from the cross-section library in case a "real" haunch is not defined on a connected beam. If a real haunch is defined on a connected beam, the area of cross-section without haunch is calculated by formula below (distinction between top and bottom flange is used by the formula variables):

The final shear area A_v area also include the appropriate area of the defined haunch(es) if defined. The added area of a haunch is calculated as:

the area of the haunch web for strong-axis shear resistance V_z,Rd
the area of the haunch flange for weak-axis shear resistance V_y,Rd

The calculation of shear area takes into account the relative inclination of all cross-section parts and also includes haunches without flange.

According to the publication "Design example of a joint with extended end plate" by D.Grotmann, J.P.Jaspart, M.Steenhuis, K.Weynand, 1993, the reduction of the final V_Rd resistance needs to be done to take into account the fact, that the part of the connected beam is already used in tension. The part of a cross-section, recognized to be in tension, is determined in means of a vertical distance l₁ from the top of the steel section (assuming that the tension is on top of the section) to the point where the tensile yield line pattern from the last bolt row in tension may develop.

In general this means that distance l₁ is calculated as sum of distance between top of the beam and the last bolt-row in tension and the distance calculated as 2*m+0,625*e. If the value is negative, reduction coefficient l₁ is set to zero and no reduction needs to be done. On the other hand distance l₁ is limited by the height of the beam and in such case coefficient l₁ is set to 1. See picture below.

The last bolt-row in tension is recognized as such bolt row, which is the closest to the center of compression and is still contributing to the final bending moment resistance M_j,y,Rd. This means that the force F_t,r,Rdin the bolt-row is not zero in the "Determination of M_j,y,Rd" table.

The reduced shear force resistance is then calculated by the modified formula:

with:

l₁	coefficient calculated as l₁/h and representing relative part of a cross-section where the reduction is needed
l₂	coefficient calculated as 1-l₁ and representing relative part of a cross-section where the reduction is not needed

In case a bolt-row classified as "Outside of beam" is recognized as the last bolt-row in tension, the formula for calculation of the half of the additional yield line pattern, in the calculation of distance l₁, is modified to 2*m_x+0,625*e_x.

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