Fachthemen DOI: 10.1002/stab.201710517 736 © Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Stahlbau 86 (2017), Heft 8 If structural regularity is not given acc. to EC8-1, a modal ap- proach including modal superposition is required instead of the lateral force method. The number of modes to be included is – according to a ‘deemed to be satisfied rule’ – depending on the total amount of the modal masses, or the individual percentage of modal mass. A clear definition for ‘modal mass’ is not given within EC8-1. In the technical literature similar, but different quantities are denoted with similar terms. In the present study, a simple two storey sway frame example is investigated. From the results conclusions are drawn, which can help the designer to avoid the inclusion of higher modes as well as torque modes. Modale Überlagerung nach EC8. Nach EC8-1 ist modale Über- lagerung anzuwenden, wenn die Kriterien für Regelmäßigkeit nicht eingehalten sind. Die Ersatzkraftmethode darf dann nicht mehr angewendet werden. Nach einer „gilt als erfüllt Regel“ hängt die Anzahl der zu berücksichtigenden Moden von der Summe der modalen Masse und von der individuellen modalen Masse einer Mode ab. Dabei ist „modale Masse“ innerhalb des EC8-1 nicht klar definiert. In der Fachliteratur werden ähnliche, aber unterschiedliche Größen mit ähnlichen Begriffen bezeich- net. Im vorliegenden Artikel wird ein einfacher, zweigeschossiger, unausgesteifter Rahmen untersucht. Die Ergebnisse erlauben Schlussfolgerungen, die dem Tragwerksplaner dabei helfen kön- nen, höhere Moden sowie Torsionsmoden außer Acht zu lassen. 1 Introduction EC8-1 4.3.3.3.1 (2)P [1] requires to consider all mode shapes which contribute significantly to the global response of the structure. This condition may be deemed to be satisfied, if either – the sum of the modal masses considered represent at least 90 % of the total mass (see definition of CEMPF in chapter 2) – or all modes are considered with an individual modal mass greater than 5 % of the total mass Remark: it seems, that these rules were proposed in [2] (among others), see also [3]. Note, that the modal mass cannot be interpreted di- rectly in terms of the total mass, as given below by the definitions in chapter 2. Additional steps are required, which lead to the required EMPF. EC8-1 lacks a proper definition on what is meant with modal mass in that con- text. In this paper a study on a simple 2-DOF-oscillator is presented. Conclusions are drawn and hints on the practi- cal application of the EC8-1 rules are given. This article is an extended version of [4]. 2 Terms and definitions CEMPF cumulated EMPF eigenvector Φ see mode shape EMPF effective mass participation factor; dimen- sionless quantity of the mass of mode j, which is contributing to the oscillation of the structure, in relation to the total mass of the structure; weighting is done by the displacements of the eigenvector Φ (compare the notation given in [5]); i is a pointer to the individual masses in the system, e. g. number of storey (see Eq. (1)) EMPF m m 1 m j j i i i,j 2 i i i,j 2 i i ∑ ∑ ∑ ( ) =α = Φ Φ ⋅ (1) K stiffness matrix of the system (see Eq. (4)) K G geometric stiffness matrix, accounting for the modification of K due to the presence of normal forces; compressive forces cause negative matrix elements, due to the ‘weakening’ of the structure (see Eq. (4)) l load factor to be applied to the given load configuration, needed to satisfy Eq. (4); a negative l indicates that the signs of the applied loads need to be switched in order to get a bifurcation of equilibrium MDOF multi degree of freedom (oscillator); multi storey buildings are often modelled as cantilevers with discrete masses, where each storey is represented by one lump mass (see e. g. [6]) modal mass M j [kg∙m 2 ] for each of the j mode shapes there is a modal mass, which contributes to the energy activated within this mode (see also a more rigorous notation in [8]); when the term is expressed as sum, the pointer i denotes the individual (discon- tinuous) masses; as can be seen from the definition of mode shape in Eqs. (4)/(5) Modal superposition according to EC8 Frau Univ.-Prof. Dr.-Ing. Ulrike Kuhlmann zur Vollendung ihres 60. Lebensjahres gewidmet Thomas Ummenhofer Peter Knoedel