FAQ 002542 EN

28 February 2019

# How is the rotational restraint stiffness calculated for a non-continuous rotational restraint (for example, purlins) in RF‑/STEEL EC3?

The total rotational spring comprises of several individual rotational springs, which are given in [1] as Equation 10.11.

In the case of a non-continuous rotational restraint by purlins, RF‑/STEEL EC3 takes into account the rotational stiffness due to the connection stiffness CD,A, the rotational stiffness CD,C due to the bending stiffness of the available purlins, and also the rotational stiffness CD,B due to the section deformation, if activated.

Since the execution of the connection is unknown, the infinite value is set by default. The spring stiffnesses are considered as a reciprocal value 1/C, thus giving 'infinitely' the result of spring stiffness = 0. If you know the rotational spring stiffness of the connection, you can specify this value manually.

The rotational stiffness CD,C due to the bending stiffness is determined according to the following formula:

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

where

E is the modulus of elasticity
k is the coefficient for position (inner span, outer span)
I is the moment of inertia Iy
s is the distance of the beams
e is the distance of the purlins

The rotational stiffness CD,B due to the bending stiffness is determined according to the following formula:

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

where

E is the modulus of elasticity
tw is the web thickness of the truss or the supported component
G is the G modulus
h is the height of the truss or the supported component
tf is the flange thickness of the truss
b is the truss width
e is the distance of the purlins

The attached example includes two design cases.

Case 1 was designed without taking into account the cross-section deformation. The total rotational spring stiffness is
CD = CD,C = 4,729 kNm/m

Case 2 was designed while taking into account the cross-section deformation. The total rotational spring stiffness is
CD = 72.02 kNm/m

Single spring CD,B = 73.14 kNm/m
Single spring CD,C = 4,729 kNm/m

Total spring:

$\begin{array}{l}\frac1{{\mathrm C}_{\mathrm D}}=\frac1{{\mathrm C}_{\mathrm D,\mathrm B}}+\frac1{{\mathrm C}_{\mathrm D,\mathrm C}}\;=\;\frac1{73.14}+\frac1{4,729}\\{\mathrm C}_{\mathrm D}\;=72.02\;\mathrm{kNm}/\mathrm m\end{array}$

#### Reference

 [1] Eurocode 3: Design of steel structures - Part 1‑1: General rules and rules for buildings; EN 1993‑1‑1:2010‑12 [2] Eurocode 3: Design of steel structures - Part 1‑3: General rules - Supplementary rules for cold-formed members and sheeting; EN 1993‑1‑3:2010‑12