EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

In this section, Eurocode load combinations for multi-storeybuildings are set out. General guidance for both simple andmoment resisting frames is given in Section 4.1, since, in principle,load combinations are the same for both types of structure.However, differences in treatment often arise due to differences insway stiffness, member interaction etc. and hence, specificguidance and examples for simple and moment resisting frames isprovided in Sections 4.2 and 4.3, respectively.

4.1 General

4.1.1 Classification of framesStructural frames may be classified with regards to their lateralload resisting system and sway stiffness. Concerning the lateralload resisting system, a frame may be regarded as either bracedor unbraced. As a guide, for a frame to be classified as ‘braced’,it should contain a bracing system with lateral stiffness of at leastfive times that of the unbraced frame [8], which will be the case inbraced simple construction. Bracing systems using wire ties (asopposed to open or hollow sections) may result in the frame beingclassified as ‘unbraced’.

Sway stiffness is commonly achieved through the provision of asuitable bracing system or by utilising the inherent bendingresistance of a rigid frame. Adequate sway stiffness is importantbecause it limits the lateral deflections of the frame and hencecontrols second order (P-Δ) effects. Sway stiffness is assessed inEN 1993-1-1 in a similar way as it is in BS 5950, through the αcrparameter (equivalent to λcr in BS 5950), which represents thefactor by which the vertical design loading would have to beincreased to cause overall elastic buckling of the frame (Clause5.2.1(3) of EN 1993-1-1). A simplified means of determining αcr forregular frames is also given in Equation 5.2 of EN 1993-1-1.Regardless of the frame type, if αcr is greater than 10, the swaystiffness is deemed sufficiently large for second order effects to beignored. Conversely, if αcr is less than 10, second order effectsmay no longer be ignored. Second order effects are discussedfurther in Section 4.1.3.

4.1.2 Frame imperfections and equivalent horizontalforces (EHF)

Frame imperfections may be incorporated directly into thestructural analysis by defining an initial sway for the frame.However, the more general approach is to replace this geometricimperfection with a system of equivalent horizontal forces (EHF),referred to as notional horizontal loads in BS 5950. Whereas in BS5950, equivalent horizontal forces were only required in thevertical load case, in the Eurocodes it is deemed that since frameimperfections are inherently present, they should be included in allULS load combinations. This appears entirely rational. EHF arenot required in SLS load combinations. The EHF should bedetermined separately for each load combination since theydepend on the level of design vertical loads. For each storey, theEHF may be calculated as the design vertical load for that storey(not the cumulative vertical load) multiplied by 1/200 (i.e. 0.5%).Depending on the height of the structure and the number ofcolumns in a row, reductions to this basic value of 1/200 arepossible, as detailed in Clause 5.3.2(3) of EN 1993-1-1. Ifhorizontal loads (HEd) exceed 15% of vertical loads (VEd) these

sway imperfections may be disregarded, and EHF ignored – thiswould more oftern apply to low rise buildings.

4.1.3 Second order (P-Δ) effectsSecond order effects relate to the increase in member forces andmoments that occur as a result of deformation of the structureunder load. As outlined in Section 4.1.1, second order (P-Δ)effects need not be considered provided the frame is sufficientlystiff (i.e. sway deformation under the design loading is relativelysmall) – this is deemed to be the case for elastic analysis when αcr> 10, and similarly, according to the UK National Annex, for plasticanalysis of clad frames when the additional stiffening effect of thecladding has been neglected. In cases where αcr is less than 10,the designer is presented with a number of options. These includeenhancement of the stability system such that αcr is raised above10 and hence second order effects may be ignored, makingallowance for second order effects by approximate means(amplified sway method or effective length method, both of whichwere allowed in BS 5950), or making allowance for second ordereffects by performing a second order structural analysis enablingand accounting for deformation of the structure under load. Itshould be noted that if αcr is less than 3, then an accurate secondorder analysis must be performed (Clause 5.2.2(5) of EN 1993-1-1). The aforementioned is summarised in Table 4.1.

Table 4.1: Summary of analysis methods and treatment ofsecond order effects

Limits on αcr Analysis method Result

αcr > 10 First order analysis Second order effects ignored

10 > αcr > 3 First order analysis plus Second order effects amplified sway method or allowed for byeffective length method approximate means

αcr < 3 Second order analysis Second order effects allowed for moreaccurately

The most common approximate treatment of second order effectsin multi-storey buildings, which may be applied provided that αcr>3, is the so called ‘amplified sway method’. In this method,account for second order effects is made by amplifying all lateralloading on the structure (typically wind loads and EHF) by a factor,referred to in the UK National Annex to EN 1993-1-1 as kr, whichis related to the sway stiffness of the structure through EquationD4.1 (Equation 5.4 of EN 1993-1-1).

kr = 1 (D4.1)1-1/αcr

4.1.4 Reduction factors for number of storeys (αn) andfloor area (αA)

As the number of storeys in a building increase, the likelihood thatall floors will be loaded to the full design level decreases. Similarly,large floor areas will seldom be subjected to the full design loadinguniformly. To reflect this, reduction factors for imposed loads maybe applied for the design of floors, beams and roofs and for thedesign of columns and walls. For the design of individual floors,

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