# D5.D.3.3 Clause 6.2.8 – Bending and shear

The D-NA requires the implementation of causes 11.3.1.1 and 11.3.1.3 of NEN 6770.

## Clause 11.3.1.1 (NEN 6770): Class 1 and Class 2 I-section profiles

Class 1 and class 2 I section profiles must satisfy the interaction formulae given in tables 10 & 11 of NEN 6770.

Table 10 Provides interaction checks for bending about the major axis (All necessary terms and formulae are described below):

1. If Vz;s;d ≤ 0.5·Vz;pl;d and Ns;d ≤ 0.5 · a1 · Npl;d , check equation 11.3.1
2. If Vz;s;d ≤ 0.5·Vz;pl;d and Ns;d > 0.5 · a1 · Npl;d , check equation 11.3.2
3. If Vz;s;d > 0.5·Vz;pl;d and Ns;d ≤ 0.5 · a2 · Nv;u;d , check equation 11.3-3
4. If Vz;s;d > 0.5·Vz;pl;d and Ns;d > 0.5 · a2 · Nv;u;d , check equation 11.3-4
where
Vz;s;d
=
Actual Shear force in the section along Z- axis
Vz;pl;d
=
Shear capacity of section  along Z - axis

= Aw · fy;d / √3

fy;d
=
yield stress
Aw
=
A - 2 (bf - tw - 2r) tf

### Definition of Aw

Ns;d
=
Axial force in the section
Npl;d
=
Axial capacity of section = A · fy;d
My;s;d
=
My;pl;d
=
Plastic moment capacity of section = fy;d · Wy;pl
Wy;pl
=
Plastic section modulus
a1
=
min( A-2bfx tf)/A , 0.5) - used in tables 10 & 11
a2
=
see eqn 11.3-10- used in tables 10 & 11
Mv;y;ud
=
see eqn 11.3.12
N;v;u;d
=
see eqn 11.3-13

Table 11: Provides interaction formulae for bending about the minor axis

1. If Vy;s;d ≤ 0.25 · Vy;pl;d and Ns;d ≤ 1.0 · a1 · Npl;d check equation 11.3-5
2. If Vy;s;d ≤ 0.25 · Vy;pl;d and Ns;d > 1.0 · a1 · Npl;d check equation 11.3-6
3. IfVy;s;d > 0.25 · Vy;pl;d and Ns;d ≤ 1.0 · a1 · Nv;u;d check equation 11.3-7
4. If Vy;s;d > 0.25 · Vy;pl;d and Ns;d > 1.0 · a1 · Nv;u;d check equation 11.3-8
where
 Vy;s;d = Actual Shear force in the section along Y-axis Vy;pl;d = Shear capacity of section along Y-axis $2 b t f f y ; d 3$ Mv;z;u;d = q · Mz;pld =  q · fy;d · Wpl;z;d Wpl;z;d = plastic section modulus about minor axis) & q as per eqn 11.3-14 Nv;u;d = Npl;d – 2·(1 - q)·bf · tf · fy;d

## Clause 11.3.1.3 ( NEN 6770) : Class 1 and Class 2 Square and rectangular hollow sections

This clause requires class 1 and class 2 square and rectangular tube profiles to satisfy the interaction equations in Table 13.

1. If Vz;s;d ≤ 0.25 · Vz;pl;d and Ns;d ≤ 0.5 · a3 · Npl;d check equation 11.3.22
2. If Vz;s;d ≤ 0.25 · Vz;pl;d and Ns;d > 0.5 · a3 · Npl;d check equation 11.3.23
3. If Vz;s;d > 0.25 · Vz;pl;d and Ns;d ≤ 0.5 · a4 · Nv;u;d check equation 11.3-24
4. If Vz;s;d > 0.25 · Vz;pl;d and Ns;d > 0.5 · a4 · Nv;u;d check equation 11.3-25
where
 Vz;s;d = Actual Shear force in the section along Z-axis Vz;pl;d = Shear capacity of section along Z-axis b = breadth of section h = height of section A = area of section Vz;pl;d = $V z ; c l ; d = h b + h A f y ; d 3$ a3 = min{ (A - 2 · b · t)/A or 0.5} a4 = from equation 11.3.27

• =
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