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FAQ 002542 EN 28 February 2019

René Flori Results STEEL EC3 RF-STEEL EC3

# According to which formula or calculation method, in the program module Steel EC3, the rotational bed rigidity in the case of a non-continuous rotary bedding (eg. B. Purlins)?

The total torsion spring consists of several individual torsion springs, which are given in equation [1] as equation 10.11.

In a non-continuous bedding by purlins in STAHL EC3 the rotary bedding from the connection stiffness C D, A , the rotary bedding C D, C from the bending stiffness of the resting purlins, as well as when activating the bedding C D, B from profile deformation are considered.
Since the execution of the connection is unknown, an infinite value is set here by default. The spring stiffnesses are taken into account as reciprocal 1 / C, thus giving "infinite" a spring stiffness = 0. If the user knows the torsional stiffness of the connection, he can enter this value manually.

The determination of the rotary bedding C D, C from the bending stiffness is carried out according to the following formula:

$\ begin {array} {l} {\ mathrm c} _ {\ mathrm D, \ mathrm C} \; = \; {\ mathrm C} _ {\ mathrm D, \ mathrm C} \; / \; \ mathrm e \\ {\ mathrm C} _ {\ mathrm D, \ mathrm C} \; = \ frac {\ mathrm k \; \ cdot \; \ mathrm E \; \ cdot \; \ mathrm I} {\ mathrm s} \ end {array}$

In it are:
E = Emodul
k = coefficient for position (infield, outfield)
I = moment of inertia I y
s = distance of the bars
e = distance of the purlins

The determination of the rotary bedding C D, B from profile deformation takes place according to the following formula:

$\ begin {array} {l} {\ mathrm c} _ {\ mathrm D, \ mathrm B} \; = \; {\ mathrm C} _ {\ mathrm D, \ mathrm B} \; / \; \ mathrm e \\ {\ mathrm C} _ {\ mathrm D, \ mathrm B} \; = \ sqrt {\ mathrm E \; \ cdot \; \ mathrm t _ {\ mathrm w} ^ 3 \; \ cdot \; \ mathrm G \; \ cdot \; {\ mathrm I} _ {\ mathrm T, \ mathrm G} \; / \; (\ mathrm h - {\ mathrm t} _ {\ mathrm f})} \\ { \ mathrm I} _ {\ mathrm T, \ mathrm G} \; = \ mathrm b \; \ cdot \; \ mathrm t _ {\ mathrm f} ^ 3 \; / \; 3 \ end {array}$

In it are:
E = Emodul
t w = web thickness binder or supported component
G = G module
h = height of the binder or supported component
t f = flange thickness of the binder
b = width binder
e = distance of the purlins

In the attached example there are two STEEL EC3 cases.
Case 1 was measured without taking into account the profile deformation. The total torsion spring results
to C D = C D, C = 4729 kNm / m

Case 2 was measured taking into account the profile deformation. The total spring results
to C D = 72.02 kNm / m
Single spring C D, B = 73.14 kNm / m
Single spring C D, C = 4729 kNm / m

Total spring:

$\ begin {array} {l} \ frac1 {{\ mathrm C} _ {\ mathrm D}} = \ frac1 {{\ mathrm C} _ {\ mathrm D, \ mathrm B}} + \ frac1 {{\ mathrm C} _ {\ mathrm D, \ mathrm C}} \; = \; \ frac1 {73,14} + \ frac1 {4729} \\ {\ mathrm C} _ {\ mathrm D} \; = 72, 02 \; \ mathrm {kNm} / \ mathrm m \ end {array}$

#### Reference

 [1] Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings; EN 1993-1-1:2010-12 [2] EN 1993-1-3 (2006): Eurocode 3: Design of steel structures - Part 1-3: General rules - Supplementary rules for cold-formed members and sheeting [Authority: The European Union Per Regulation 305/2011, Directive 98/34/EC, Directive 2004/18/EC]