Consideration of the net cross-section for tensile stress according to EN 1993-1-1
Technical Article
When connecting tension -loaded components with bolted connections, the cross -section weakening due to the bolt holes must be considered in the ultimate limit state design. The following article describes how the design of the tension resistance according to DIN EN 1993-1-1 can be performed with the net cross-section area of the tension member in the RF-/STEEL EC3 add-on module.
Design of tension resistance according to EN 1993-1-1
According to DIN EN 1993-1-1, Chapter 6.2.3 (2), the tension resistance of a cross-section weakened by holes results from the minimum of the following design values:
${\mathrm{N}}_{\mathrm{pl},\mathrm{Rd}}=\frac{\mathrm{A}\xb7{\mathrm{f}}_{\mathrm{y}}}{{\mathrm{\gamma}}_{\mathrm{M}0}}$
N_{pl, Rd} | Design value of the plastic tension resistance of the gross cross -section |
A | gross cross-sectional area |
f_{y} | Yield strength |
γ_{M0} | Partial safety factor for cross -section resistance |
${\mathrm{N}}_{\mathrm{u},\mathrm{Rd}}=\frac{0,9\xb7{\mathrm{A}}_{\mathrm{net}}\xb7{\mathrm{f}}_{\mathrm{u}}}{{\mathrm{\gamma}}_{\mathrm{M}2}}$
N_{u, Rd} | Design value of the tension resistance of the net cross -section |
A_{net} | Net cross -section area along the critical crack line |
f_{U} | Tensile strength |
γ_{M2} | Partial safety factor for cross -section resistance in the event of failure due to tension |
The net cross -section area is to be determined from the gross cross -section area minus all openings and holes for fasteners. Depending on the arrangement of the bolt holes, the hole deduction area to be applied is adjusted to the critical crack line.
Input in RF-/STEEL EC3
By default, the design of the tension resistance in the add -on module is only performed considering the plastic tension resistance of the gross cross -section ( Formula 1 ). The design according to Formula 2 can be activated by selecting the 'Net Cross -Sectional Area' option in the 'Parameters of Members' input window. It is possible to enter a net cross_{-section area A net} for member start (x = 0) and member end (x = l). To enter the same net cross -section area for several members at the same time, it is recommended to use the 'Set input for member no.'
Then, both design values of the tension resistance are calculated and the design is performed according to DIN EN 1993-1-1 with the minimum value.
Modification for the design of angle sections connected on one side
For asymmetrically connected components, such as angle sections connected on one side to a leg, the DIEN EN 1993-1-8 provides additional regulations. Accordingly, the angle connected on one side for tensile loading may be designed like a centrally loaded angle if the load -bearing capacity is determined with an effective net cross -section.
${\mathrm{N}}_{\mathrm{u},\mathrm{Rd}}=\frac{{\mathrm{A}}_{\mathrm{net},\mathrm{eff}}\xb7{\mathrm{f}}_{\mathrm{u}}}{{\mathrm{\gamma}}_{\mathrm{M}2}}$
N_{u, Rd} | Design value of the tension resistance of the net cross -section |
f_{U} | Tensile strength |
γ_{M2} | Partial safety factor for cross -section resistance in the event of failure due to tension |
The effective net cross -section can be determined by means of modification factors depending on the number of bolts and the hole spacings. An additional reduction factor of 0.9 as in Equation 1 is no longer required for the design with the net cross -section. The input window in RF-/STEEL EC3 does not allow you to enter the effective net cross-section directly, but the net cross-section area to be entered can be adjusted to the design in the add-on module by means of a simple conversion.
Design with effective net cross -section in the module
${\mathrm{N}}_{\mathrm{u},\mathrm{Rd}}=\frac{0,9\xb7{\mathrm{A}}_{\mathrm{net}}*\xb7{\mathrm{f}}_{\mathrm{u}}}{{\mathrm{\gamma}}_{\mathrm{M}2}}\Rightarrow {\mathrm{A}}_{\mathrm{net}}*=\frac{{\mathrm{A}}_{\mathrm{net},\mathrm{eff}}}{0,9}\phantom{\rule{0ex}{0ex}}$
N_{u, Rd} | Design value of the tension resistance of the net cross -section |
A_{net} * | Equivalent net cross-section area for input in RF-/STEEL EC3 |
f_{U} | Tensile strength |
γ_{M2} | Partial safety factor for cross -section resistance in the event of failure due to tension |
Example
Flat bars 60 x 8 mm were selected as crossings in Y-direction. The net area results for the fastening with an M20 screw in the critical crack line
${\mathrm{A}}_{\mathrm{net}}=\mathrm{A}-{\mathrm{d}}_{0}\xb7\mathrm{t}$
A | gross cross-sectional area |
A_{net} = 4.8 cm ^{2} - 2.2 cm 0.8 cm = 3.04 cm ^{2}
The following design resistances result for the material S235:
N_{pl, Rd} = (4.8 cm² ⋅ 23.5 kN/cm²)/1.0 = 112.8 kN
N_{u, Rd} = (0.9 3.04 cm² 36 kN/cm²)/1.25 = 78.8 kN
For the crossing in the X-direction, isosceles angle sections L 75 x 8 were selected in S355. The connection is to be realized on an angle leg with 2 screws M20 one behind the other. The dimensions are selected as follows:
e_{1} = 40 mm
p_{1} = 60 mm
e_{2} = 30 mm
The effective net cross-section area for this connection situation results from the factor β2 according to EN 1993-1-8
β2 = 0.44
A_{net, eff} = β2 ⋅ A_{net} = 0.44 ⋅ (11.4 cm² - 2.2 cm ⋅ 0.8 cm) = 4.21 cm²
The following design resistances result for the material S355:
N_{pl, Rd} = (11.4 cm² 35.5 kN/cm²)/1.0 = 404.7 kN
N_{u, Rd} = (4.21 cm² ⋅ 49 kN/cm²)/1.25 = 164.9 kN
The input in RF-STEEL EC3 is carried out with the equivalent net cross-section area:
A_{net} * = 4.21 cm²/0.9 = 4.67 cm²
Keywords
tension design Net cross -section Outcrossing Hole weakening
Links
Write Comment...
Write Comment...
Contact us
Do you have questions or need advice?
Contact our free e-mail, chat, or forum support or find various suggested solutions and useful tips on our FAQ page.
Recommended Events
Videos
Models to Download
Knowledge Base Articles
New
Reinforcement of Existing Column in RFEM per AISC Design Guide 15
Sometimes a structure needs reinforcement in cases where a new floor being added, or when an existing member is found to be under design due to hard-to-predict loading assumption.
Screenshots
Product Features Articles
SHAPE-THIN | Cold-Formed Sections
SHAPE-THIN determines the effective cross-sections according to EN 1993-1-3 and EN 1993-1-5 for cold-formed sections. You can optionally check the geometric conditions for the applicability of the standard specified in EN 1993‑1‑3, Section 5.2.
The effects of local plate buckling are considered according to the method of reduced widths and the possible buckling of stiffeners (instability) is considered for stiffened sections according to EN 1993-1-3, Section 5.5.
As an option, you can perform an iterative calculation to optimize the effective cross-section.
You can display the effective cross-sections graphically.
Read more about designing cold-formed sections with SHAPE-THIN and RF-/STEEL Cold-Formed Sections in this technical article: Design of a Thin-Walled, Cold-Formed C-Section According to EN 1993-1-3.
Frequently Asked Questions (FAQ)
- I would like to calculate and design "Temporary Structures". What do I need for this?
- How can I create a twisted beam in RFEM?
- How can I perform the design of the tension resistance of a smooth column in a smooth bucket column base, i.e. the design against pulling out of the column?
- For which programs is the STEEL Warping Torsion add-on module available?
- In the RF‑/STEEL EC3 add-on module, I obtain an extremely high design ratio for a member in the case of "Biaxial bending, shear and axial force." Although the axial force is relatively high, the design ratio seems to be unrealistic. What is the reason?
- I have just noticed that the STEEL EC3 add-on module also calculates with γ_{M0} = 1.0 when designing a tension member, although it should actually be γ_{M2} = 1.25. How can I perform the design correctly?
- Is it possible to design intermittent welds in the CRANEWAY add-on module?
- I design a cross-section created in the SHAPE‑THIN program by using the RF‑STEEL EC3 add-on module, but the program shows the error message "ER006 Invalid type of c/t-part for cross-section of type General." What can I do?
- For a buckling analysis, FE‑BUCKLING determines the governing shear stress of τ = 7.45 kN/cm², while RF‑/STEEL gives the result of the maximum shear stress of τ = 8.20 kN/cm². Where does this difference come from?
- Why do I get a design ratio for the stability analysis according to 6.2.9.1 in the STEEL EC3 add-on module? Why is a * added to Equation (6.36)?