In the analysis of the structure, the designer should consider the effects of the realistic combinations of permanent and variable actions. Within each set of combinations (e.g. dead and imposed loads) a number of different arrangements of loads (load cases) throughout the structure (e.g. alternate spans loaded and adjacent spans loaded) will need consideration to identify an envelope of action effects (e.g. bending moment and shear envelopes) to be used in the design of sections.
Fig. 3.1. Definition of structural elements for analysis. (a) Beam. (b) Deep beam. (c) Slab. (d, e) One- way spanning slab (subject predominantly to ultimate design load)
Fig. 3.1. (Contd.) (f) Ribbed and waffle slabs (conditions to be met to allow analysis as solid slabs). (g) Column. (h) Wall
As stated in Chapter 2, EN 1990 provides the magnitude of the design loads to be used when loads are combined. Account is taken of the probability of loads acting together, and values are specifed accordingly.
The EN code for actions (Eurocode 1) specifies the densities of materials (to enable the calculation of permanent actions and surcharges), and values of variable action (such as imposed gravity, wind and snow loads). It also provides information for estimating fire loads in buildings, to enable fire engineering calculations to be carried out.
Although EN 1992-1-1 forms part of a suite of codes including those which specify loads, there is no reason why the Eurocode cannot be used in conjunction with other loading codes. It has been assumed in the Eurocode system that the loads specified in Eurocode 1 are characteristic values with only 5% of values likely to fall above them. Note that for wind loads it is 2%. The definition of the characteristic value will affect the overall reliability.
While the general requirement is that all relevant load cases should be investigated to arrive at the critical conditions for the design of all sections, EN 1992-1-1 permits simplified load arrangements for the design of continuous beams and slabs. The arrangements to be considered are:
Clause 5.1.3 (1) alternate spans loaded with the design variable and permanent loads (1.35Gk+ 1.5Qk)
and other spans carrying only the design permanent load (1.35Gk)
(2) any two adjacent spans carrying the design variable and permanent loads (1.35Gk+ 1.5Qk),
with all other spans carrying only the design permanent load (1.35Gk).
Although not stated, the above arrangements are intended for braced non-sway structures. They may also be used in the case of sway structures, but the following additional load cases involving the total frame will also need to be considered:
(1) all spans loaded with the design permanent loads (1.35Gk) and the frame subjected to
the design wind load (1.5Wk), when Wkis the characteristic wind load
(2) all spans at all floor levels loaded with (1.35Gk+ 1.5Qk) and the frame subjected to the
design wind load of 1.05Wk
(3) in sensitive structures (sensitivity to lateral deformation), it may be necessary to consider the effects of wind loading in conjunction with patterned imposed loading through out the frame.
Clause 5.1.3 of EN 1992-1-1 also allows the National Annexes to specify simplification of
load arrangements, and the UK National Annex permits the following additional choices.
• For frames:
– all spans loaded with the maximum design ultimate load (1.35Gk+ 1.5Qk)
– alternate spans loaded with the maximum ultimate load noted above and all other
spans loaded with 1.35Gk.
• For slabs only: a single load case of maximum design load on all spans or panels provided
the following conditions are met:
– in a one-way spanning slab the area of each bay exceeds 30 m2(here a bay means a
strip across the full width of a structure bounded on the other two sides by lines of supports)
– the ratio of the characteristic variable load to the characteristic permanent load
does not exceed 1.25
– the characteristic variable load does not exceed 5 kN/m2.
The resulting support moments (except those at the supports of cantilevers) should be reduced by 20%, and the span moments adjusted upwards accordingly. No further redistribution should be carried out.
Clause 5.1.1(8) Clause 5.1.1(8) of EN 1992-1-1 states that in linear elements and slabs subject predominantly
to bending, the effects of shear and axial forces on deformation may be neglected, if these are likely to be less than 10%. In practice, the designer need not actually calculate these additional deformations to carry out this check.
Deflections are generally of concern only in members with reasonably long spans. In such members, the contribution of shear to the deflections is never significant for members with normal (span/depth) ratios. When the spans are short, EN 1992-1-1 provides alternative design models (e.g. truss or strut and tie) in which deflections are rarely, if ever, a consideration.
The contribution of axial loads to deflections may be neglected if the axial stresses do not
exceed 0.08fck.
3.3. Imperfections
3.3.1. General
Perfection in buildings exists only in theory; in practice, some degree of imperfection is unavoidable, and designs should recognize this, and ensure that buildings are sufficiently robust to withstand the consequences of such inaccuracies. For example, load-bearing elements may be out of plumb or the dimensional inaccuracies may cause eccentric application of loads. Most codes allow for these by prescribing a notional check for lateral stability. The exact approach adopted to achieve this differs between codes.
EN 1992-1-1 has a number of provisions in this regard, affecting the design of (1) the structure as a whole, (2) some slender elements and (3) elements which transfer forces to bracing members.
3.3.2. Global analysis
For the analysis of the structure as a whole, an arbitrary inclination of the structureθ0= 1/200
is prescribed as a basic value. This is then modified for height and for the number of members involved.
The design value will be
θi=θ0αnαm
where
αn= 2/÷l
where l is the total height of the structure in metres (0.67 £αn£ 1.0), and
αm= ÷[0.5(1 + 1/m)]
where m is the number of vertically continuous elements in the storeys contributing to the total horizontal force on the floor. This factor recognizes that the degree of imperfection is statistically unlikely to be the same in all the members.
As a result of the inclination, a horizontal component of the vertical loads could be thought of being applied at each floor level, as shown in Figs 3.2 and 3.3. These horizontal Fig. 3.2. Application of the effective geometrical imperfections: braced structure (number of vertically continuous members = 2)
forces should be taken into account in the stability calculation. This is in addition to other design horizontal actions, such as wind.
3.3.3. Design of slender elements
In the design of slender elements, which are prone to fail by buckling (e.g. slender columns), EN 1992-1-1 requires geometrical imperfection to be added to other eccentricities. For
example, in the design of the columns, an eccentricity ofθil0/2 is assumed for geometrical
imperfection (where l0is the effective length of the column).
3.3.4. Members transferring forces to bracing elements
In the design of these elements (such as a floor diagram), a force to account for the possible imperfection should be taken into account in addition to other design actions. This additional force is illustrated in Fig. 3.4. This force need not be taken into account in the design of the bracing element itself.