Designing Local Transverse Forces According to EN 199313
Technical Article
The design of coldrolled steel products is defined in EN 199313. Typical crosssection shapes are channel, C, Z, top hat, and sigma sections. These are coldrolled steel products made of thinwalled sheet metal that has been coldformed by rollforming or bending methods. When designing the ultimate limit states, it is also necessary to ensure that local transverse forces do not lead to compression, crippling of the web, or local buckling in the web of the sections. These effects can be caused by local transverse forces by the flange into the web, as well as by support forces at the supported points. Section 6.1.7 of EN 199313 specifies in detail how to determine the resistance of the web R_{w,Rd} under local transverse forces.
In the RF/STEEL EC 3 addon module, you can use the RF/STEEL ColdFormed Sections extension to perform an analysis of local transverse forces for nonstiffened webs according to [1], 6.1.7 (the module extension requires a separate license). This article shows the corresponding design methods using the example of a bending beam made of a coldformed Csection and subjected to a single load.
System and Loading
A beam with a length of two meters consists of a C 2020 coldformed section made of S 235 steel. It is loaded with a single load of 10 kN at a distance of 50 cm from the support. The load acts at the shear center. The selfweight is not taken into account.
When selecting the crosssection from the library, please note that the crosssection shape of the Csection corresponds to the "ColdFormed CSections" category. This condition can be set using the filter function. The RF/STEEL ColdFormed Sections module extension is made for the design of coldformed sections: A rolled Csection or channel section would not be designed according to [1].
Entering Data in RF/STEEL ColdFormed Sections
In the RF/STEEL EC 3 addon module, the specifications for a design according to EN 199313 [1] must be made in the "ColdFormed Sections" tab of the "Details" dialog box.
Image 02  Activating the Design of Local Transverse Forces
The "Design of local transverse forces according to 6.1.7 if possible" check box controls whether the program checks local failure modes in the web. If this option is activated, it is possible to define the boundary conditions such as the length of the stiff bearing in Window "1.14 Local Transverse Forces".
Image 03  Window "1.14 Local Transverse Forces"
The consideration of the transverse forces is activated by default. Thus, the shear force distribution is used for the design of the web loading for local load application. The program analyzes the locations of discontinuity resulting from the shear force distribution. The "Nominal length of stiff bearing" is preset to 0.10 m.
Results in RF/STEEL EC3
There are, at most, two steps to calculate the effective crosssection iteratively. Then, the design ratios due to local transverse forces are displayed in the designs. The details of each design can be viewed as "intermediate values".
Image 04  Local Transverse Forces Design
According to the shear force distribution, the local transverse force design is performed at both supports and the location of the local load application. Location x = 0.00 m has the maximum design ratio. The location design is as follows:
We have a support reaction on one crosssection that has only one web. The Csection with a plate thickness of t = 2.0 mm has stiffened belts because of its lips. The distance of the support from the free end is 0.00 m, which is less than 1.5 times the web height h_{w} = 198 mm. Thus, [1], Equation (6.15a) governs for determining the web resistance R_{w,Rd}.
${\mathrm{R}}_{\mathrm{w},\mathrm{Rd}}=\frac{{\mathrm{k}}_{1}\xb7{\mathrm{k}}_{2}\xb7{\mathrm{k}}_{3}\xb7\left(9.04\frac{{\displaystyle {\mathrm{}h}_{\mathrm{w}}/\mathrm{t}}}{60}\right)\xb7\left(10.001\xb7\frac{{\mathrm{s}}_{\mathrm{s}}}{\mathrm{t}}\right)\xb7{\mathrm{t}}^{2}\xb7{\mathrm{f}}_{\mathrm{yb}}}{{\mathrm{\gamma}}_{\mathrm{M}1}}$
You have to apply the following parameters:
${\mathrm{f}}_{\mathrm{yb}}=0.9\xb7235=211.50\mathrm{N}/{\mathrm{mm}}^{2}\left(\right[1]\mathrm{Table}3.1\mathrm{a},\mathrm{Note}1)\phantom{\rule{0ex}{0ex}}\mathrm{k}=\frac{{\mathrm{f}}_{\mathrm{yb}}}{228}=\frac{211.50}{228}=0.928\phantom{\rule{0ex}{0ex}}{\mathrm{k}}_{1}=1.330.33\xb7\mathrm{k}=1.330.33\xb70.928=1.024\phantom{\rule{0ex}{0ex}}{\mathrm{k}}_{2}=1.150.15\xb7\frac{\mathrm{r}}{\mathrm{t}}=1.150.15\xb7\frac{2.0}{2.0}=1.00\phantom{\rule{0ex}{0ex}}{\mathrm{k}}_{3}=0.70.3\xb7{\left(\frac{\mathrm{\varphi}}{90}\right)}^{2}=0.70.3\xb7{\left(\frac{90}{90}\right)}^{2}=1.00$
This results in the following web resistance:
${\mathrm{R}}_{\mathrm{w},\mathrm{Rd}}=\frac{1.024\xb71.00\xb71.00\xb7\left(9.04\frac{{\displaystyle 198.0/2.0}}{60}\right)\xb7\left(10.001\xb7\frac{100.0}{2.0}\right)\xb72.{0}^{2}\xb7211.50}{1.1}=8,730.0\mathrm{N}=8.73\mathrm{kN}$
The design condition according to [1], Equation (6.13) is fulfilled:
$\frac{{\mathrm{F}}_{\mathrm{Ed}}}{{\mathrm{R}}_{\mathrm{w},\mathrm{Rd}}}=\frac{7.50}{8.73}=0.86\le 1.0$
The design is the same for the remaining two design locations.
Option: Defining Forces Manually
If the shear force distribution does not represent the introduced load realistically, the locations of the load and the load magnitudes, including the nominal lengths of the stiff bearing, can be defined manually. You can see this in the attached RFEM model in design case 2.
In the case of a manually defined force, there is no automatic comparison of the shear force effect for the support points. You have to define these locations individually with the respective support forces. To do this, select the "Free End" check box as shown in Figure 05. Only then is the distance c ≤ 1.5 h_{w} taken into account, and [1], Equation (6.15a) is used for the design. Otherwise, [1] Equation (6.15d) would apply.
Image 05  Defining Local Transverse Forces Manually
Summary
With the RF/STEEL ColdFormed Sections module extension for RF/STEEL EC3, it is possible to perform, among other things, designs for local transverse forces according to [1], Section 6.1.7. The locations relevant for the design are determined automatically from the shear force distribution. Alternatively, you can specify the forces manually. The design for local transverse forces with RF/STEEL ColdFormed Sections is performed according to [1], 6.1.7.2 for crosssections with an unstiffened web or according to [1], 6.1.7.3 for crosssections with two or more webs without stiffening. Web crosssections with longitudinal stiffeners cannot be designed according to [1], 6.1.7.4.
Author
Dipl.Ing. (FH) Robert Vogl
Technical Editor, Product Engineering & Customer Support
Mr. Vogl creates and maintains the technical documentation. In addition, he is involved in the development of the SHAPETHIN program and provides customer support.
Keywords
Local transverse forces Coldformed section Stiffened chord Lip Concentrated load Web crippling Web resistance Web without stiffening Local load application Support reaction
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