Bending resistance
The bending resistance is calculated for classes 1 and 2 using following formula
Where is: | Wpl,y, Wpl,z |
|
fy |
| |
γM0 |
|
The bending resistance for classes 3 and 4 is calculated in four points of the cross-section. These points are located in the corners of the cross-section. The following expression is used for the class 3
Where is: | iWy, iWz |
|
fy |
| |
γM0 |
|
The following expression is used for the class 4
Where is: | iWeff,y, iWeff,z |
|
fy |
| |
γM0 |
|
The bending resistance of perforated cross-section is calculated for classes 1 and 2 using following formula
Where is: | Wpl,y,osl,Wpl,z,osl |
|
fu |
| |
γM2 |
|
The following expression is used for the class 3
Where is: | iWy,osl, iWz,osl |
|
fu |
| |
γM2 |
|
The following expression is used for the class 4
Where is: | iWy,eff,osl, iWz,eff,osl |
|
fu |
| |
γM2 |
|
The minimum of the values Mc,Rd,y and Mc,Rd,y,osl or Mc,Rd,z and Mc,Rd,z,osl is used in the verification.
The design value of the resistance is reduced for "High shear" (described in the chapter "Low and high shear").
Where is: | iWpl,y,red, iWpl,z,red |
|
fy |
| |
γM0 |
|
The reduced plastic section moduli are calculated as plastic section moduli with reduced capacity in walls that are subjected to "high shear". The reduction is based on the factors ρz and ρy that are calculated in accordance with the chapter "Low and high shear". The minimum of the values Mc,Rd,y and Mc,Rd,y,red or Mc,Rd,z and Mc,Rd,z,red is used in the verification.
Bending resistance including the effect of lateral torsional buckling
ÚThe bending resistance is given by the formula
Where is: | χLT,y, χLT,z |
|
Mc,Rd,y, Mc,Rd,z |
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The reduction factors for lateral-torsional buckling χLT,y and χLT,z depends on the value of the elastic critical moment for lateral-torsional buckling Mcr, that is calculated according to the expression
where the factor μcr is the critical moment given by following expressions
The non dimensional torsion factor kwt is calculated using formula
ζg is the non dimensional parameter considereing the load position relatively to the shear centre
ζj is the non dimensional parameter considereing the unsymmetry of cross-sections
Where is: | C1, C2, C3 |
|
kz, ky, kw |
| |
E |
| |
G |
| |
Iz, Iy |
| |
L |
| |
Iω |
| |
It |
| |
zg, yg |
|
and zj and yj are given by expressions
Where is: | zs, ys |
|
The relative slenderness is calculated with the help of the critical moment Mcr:
Where is: | Wy, Wz |
|
The value of the imperfection factor αLT is set according to the buckling curves a, b, c, d. The factors χLT,y and χLT,z are given by expressions
however, following condition has to be fulfilled
where
The effect of lateral torsional buckling isn't considered for cross-sections resistant to LT buckling (e.g. RHS) and for cases, where the bending moment acts about the weak axis of the cross-section.