Verification According to EN 1993-5
1. Check for bending (without axial force):
The design resistance for bending of U-type sheet piles:
where: | βB | - | factor accounting for the possible reduction of the section modulus of U-piles due to insufficient shear force transmission in the interlocks |
Wel | - | is the elastic section modulus determined for a continuous wall |
fy | - | steel yield stress |
γM0 | - | partial factor for resistance of a cross-section |
The design moment resistance for other cross-sections:
The utilization ratio is determined according to:
where: | MEd | - | design bending moment |
2. Check for the combination of bending and axial force:
Sheet pile
- the reduced design moment resistance allowing for the axial force:
where: | NEd | - | design axial force |
Npl,Rd | - | design plastic resistance to normal forces of the cross-section |
Where design plastic resistance to normal forces:
where: | A | - | area of cross-section |
The utilization ratio:
Other cross-sections:
The utilization ratio:
where: | σX,Ed | - | is the maximum normal stress on the cross-section due to the moment and axial force |
3. Check for shear:
The elastic shear stress at the center of gravity of the cross-section is calculated:
where: | VEd | - | is the design value of the shear force |
S | - | the first moment of area about the centroidal axis |
I | - | second moment of area of the whole cross section |
t | - | section thickness at the center of gravity |
The shear utilization ratio is determined according to:
4. Check for shear buckling:
Shear buckling is calculated if the following condition is met:
where: | c | - | slant height of the web of steel sheet piles |
tW | - | nominal web thickness of steel sheet piles |
Sheet pile:
The resistance of shear buckling shall be determined from the relationship:
where: | h | - | total height of sheet pile wall |
fbv | - | is the shear buckling strength determined for a web without stiffeners and for the relative slenderness of the web, which is determined from the relationship: |
where: | λ | - | relative web slenderness |
E | - | modulus of elasticity of steel |
Other cross-sections:
The resistance of shear buckling is determined according to:
where: | χw | - | factor for the contribution of the web to the shear buckling resistance |
fyw | - | yield strength of the web |
hw | - | depth of the web |
where: factor χw
Value λW | χW |
λW <0,83/η | η |
0,83/η ≤ λW <1,08 | 0,83/λW |
λW ≥ 1,08 | 0,83/λW |
The slenderness parameter λw is to be determined according to the relation:
The utilization ratio for shear buckling is determined by:
where: | Q | - | design shear force |
5. Check for the combination of bending, shear and axial force:
Sections with defined shear area Av:
The check for the combination of bending, shear and axial force is carried out if there is a big shear, i.e. if:
where: | Vpl,Rd | - | plastic shear resistance |
Where the plastic shear resistance:
where: | AV | - | shear area |
The reduced yield strength due to shear is determined:
Where the reduction factor ρ:
Utilization ratio:
Other cross-sections:
Utilization ratio:
where: | σx,Ed | is the largest normal stress on the cross-section due to the moment and axial force |
τEd | average shear stress across the cross-section |
Recommended values for reduction factors due to the insufficient shear transmission and corrosion rates can be found in the standard, which are entered in the dialog box for entering the cross-section of the sheet pile.
Literature: EN 1993-5