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:

Design value of the plastic tensile strength of the gross cross -section

$$Npl,Rd = A · fyγM0$$

 Npl, Rd Design value of the plastic tension resistance of the gross cross -section A gross cross-sectional area fy Yield strength γM0 Partial safety factor for cross -section resistance

$$Nu,Rd = 0,9 · Anet · fuγM2$$

 Nu, Rd Design value of the tension resistance of the net cross -section Anet Net cross -section area along the critical crack line fU Tensile strength γM2 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.

Design value of the tension resistance of the net cross -section

$$Nu,Rd = Anet,eff · fuγM2$$

 Nu, Rd Design value of the tension resistance of the net cross -section fU Tensile strength γM2 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

Equivalent net cross-section area for input in RF-/STEEL EC 3

$$Nu,Rd = 0,9 · Anet* · fuγM2 ⇒ Anet* = Anet,eff0,9$$

 Nu, Rd Design value of the tension resistance of the net cross -section Anet * Equivalent net cross-section area for input in RF-/STEEL EC3 fU Tensile strength γM2 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

$$Anet = A - d0 · t$$

 A gross cross-sectional area

Anet = 4.8 cm 2 - 2.2 cm 0.8 cm = 3.04 cm 2

The following design resistances result for the material S235:

Npl, Rd = (4.8 cm² ⋅ 23.5 kN/cm²)/1.0 = 112.8 kN

Nu, 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:

e1 = 40 mm

p1 = 60 mm

e2 = 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

Anet, eff = β2 ⋅ Anet = 0.44 ⋅ (11.4 cm² - 2.2 cm ⋅ 0.8 cm) = 4.21 cm²

The following design resistances result for the material S355:

Npl, Rd = (11.4 cm² 35.5 kN/cm²)/1.0 = 404.7 kN

Nu, 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:

Anet * = 4.21 cm²/0.9 = 4.67 cm²

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