11,151 1101

(2) These values are assumed to take account of differences between the strength of test specimens of the structural materials and their strength in situ.

(3) The values given above are valid when the quality control procedures given in chapter 7 are followed. They apply to characteristic values defined in chapter 3 and for design data as described in chapter 4.2.

(4) Higher or lower values of Yc may be used if these are justified by adequate control procedures.

(5) These values do not apply for fatigue verification.

(6) Where structural properties are determined by testing, see the relevant Part of this Code. 2.3.4 Serviceability limit states

P(1) It shall be verified that

Ed r Cd or Ed r Rd where

Cd is a nominal value or a function of certain design properties of materials related to the design effects of actions considered, and

Ed is the design effect of actions, determined on the basis of one of the combinations defined below.

The required combination is identified in the particular clause for serviceability verification (see 4.4). P(2) Three combinations of actions for serviceability limit states are defined by the following expressions: Rare combination

Frequent combination

Quasi-permanent combination

where the notation is defined in 2.3.2.2(2).

Imposed deformations should be considered when relevant.

(3) Upper limits of compressive stresses in the concrete in the presence of rare and quasi permanent combinations may be fixed to avoid damage to the concrete and excessive creep deformations

(4) An upper limit of the tensile stress in the steel may be fixed to reduce the risk of inelastic deformation and permanently open cracks (see chapter 4.4.1).

P(5) Where simplified compliance rules are given in the relevant clauses dealing with serviceability limit states, detailed calculations using combinations of actions are not required.

Z Gk j <+P) + ^ J Qk1 + Z M>2 f i Qk.i i > 1

P(6) Where the design considers the compliance of serviceability limit states by detailed calculations, simplified expressions may be used for building structures.

(7) For building structures the rare combination may be simplified to the following expressions, which may also be used as a substitute for the frequent combination.

— design situations with only one variable action, Qk.1

— design situations with two or more variable actions, Qk.i whichever gives the larger value. P(8) Values of Ym shall be taken as 1.0, except where stated otherwise in particular clauses.

2.4 Durability

P(1) To ensure an adequately durable structure, the following inter-related factors shall be considered:

— the required performance criteria;

— the expected environmental conditions;

— the composition, properties and performance of the materials;

— the shape of members and the structural detailing;

— the quality of workmanship, and level of control;

— the particular protective measures;

— the likely maintenance during the intended life.

P(2) The environmental conditions shall be estimated at the design stage to assess their significance in relation to durability and to enable adequate provisions to be made for protection of the materials.

2.5 Analysis

2.5.1 General provisions

Hfd Additional horizontal force to be considered in the design of horizontal structural elements, when taking account of imperfections

AHj Increase in the horizontal force acting on the floor of a frame structure, due to imperfections

Nba} Design axial forces on columns or walls adjacent to a horizontal load transferring element, when

Nbc} considering imperfections c}

1 Total height of a structure in metres n Number of vertical continuous members acting together an Reduction coefficient in calculating v (Equation 2.11)

V Angle of inclination of a structure, assumed in assessing the effects of imperfections

P(1) The purpose of analysis is the establishment of the distribution of either internal forces and moments, or stresses strains and displacements, over the whole or part of a structure. Additional local analysis shall be carried out where necessary.

(2) In most normal cases analysis will be used to establish the distribution of internal forces and moments; however, for certain complex elements, the methods of analysis used (e.g. finite element analysis) give stresses, strains and displacements rather than internal forces and moments. Special methods are required to use these results to obtain appropriate reinforcement areas.

P(3) Analyses are carried out using idealisations of both the geometry and the behaviour of the structure. The idealisations selected shall be appropriate to the problem being considered.

(4) The geometry is commonly idealised by considering the structure to be made up of linear elements, two dimensional elements and, occasionally, shells. Geometrical idealisations are considered in 2.5.2.

(5) Common behavioural idealisations used for analysis are:

— elastic behaviour with limited redistribution (see 2.5.3.4.2)

— plastic behaviour (see 2.5.3.5.5), including strut and tie models (see 2.5.3.7)

— non-linear behaviour (see Appendix 2)

(6) Additional local analyses may be necessary where the assumption of linear strain distribution does not apply, e.g.

— under concentrated loads

— beam and beam-column intersections

— anchorage zones

2.5.1.2 Load cases and combinations

P(1) For the relevant combinations of actions, sufficient load cases shall be considered to enable the critical design conditions to be established at all sections within the structure or part of the structure considered.

(2) Depending on the type of structure, its function or the method of construction, design may be carried out primarily for either the ultimate limit state or the serviceability limit. In many cases, provided that checks for one of these limit states have been carried out, checks for the other may be dispensed with as compliance can be seen by experience.

(3) Simplified combinations of actions and load cases may be used, if based on a reasonable interpretation of the structural response.

(4) For continuous beams and slabs in buildings without cantilevers subjected to dominantly uniformly distributed loads, it will generally be sufficient to consider only the following load cases (see 2.3.2.2).

a) alternate spans carrying the design variable and permanent load (Yq Qk + Yg Gk), other spans carrying only the design permanent load, Yg Gk, b) any two adjacent spans carrying the design variable and permanent loads (Yq Qk + Yg Gk). All other spans carrying only the design permanent load, Yg Gk.

(5) For linear elements and slabs in buildings, the effects of shear and longitudinal forces on the deformations may be ignored where these are likely to be less than 10 % of those due to bending.

P(1) In the ultimate limit state, consideration shall be given to the effects of possible imperfections in the geometry of the unloaded structure. Where significant, any possible unfavourable effect of such imperfections shall be taken into account.

P(2) Individual sections shall be designed for the internal forces and moments arising from global analysis, combining effects of actions and imperfections of the structure as a whole.

(3) In the absence of other provisions, the influence of structural imperfections may be assessed by representing them as an effective geometrical imperfection using a procedure such as that given in (4) to (8) below.

(4) Where a structure is being analysed as a whole, the possible effects of imperfections may be assessed by assuming that the structure is inclined at an angle V to the vertical where:

where 1 is the total height of the structure in metres. V should not be taken as less than | 1/400 | for cases where second order effects are insignificant or | 1/200 | where they have to be taken into account (e.g. 4.3.5.4). [see Figure 2.1 a), Figure 2.1 b) and Figure 2.1 c)].

a) imperfections for the calculation of the horizontal forces on the bracing element b) imperfections for the calculation of the horizontal forces in the floors transferring stabilising forces from the braced sub-assembly to the bracing elements.

c) equivalent horizontal forces AH acting on an unbraced frame

(5) For cases where n vertical elements act together, V, given by (4) above may be reduced by the factor an given by Equation (2.11)

In Figure 2.1 a), n is n = 2; in Figure 2.1 c), n is n = 3.

(6) If more convenient, the deviations from the vertical given by (4) above may be replaced by equivalent horizontal forces which should be taken into account in the overall analysis of the structure, bracing elements, supports and ties (see Figure 2.1 a), Figure 2.1 b) and Figure 2.1 c).

(7) Structural elements which are assumed to transfer stabilising forces from the elements of a structure to be braced to the bracing elements should be designed to carry an additional horizontal force Hfd

where:

Nbc and Nba denote the design axial forces on the adjacent columns or walls, acting on the load transferring element being considered

Hfd should not be taken into account in the design of the bracing elements.

(8) Where the effects of imperfections are smaller than the effects of design horizontal actions, their influence may be ignored. Imperfections need not be considered in accidental combinations of actions.

P(1) Second order effects shall be taken into account where they may significantly affect the overall stability of a structure or the attainment of the ultimate limit state at critical sections.

(2) For normal buildings, second order effects may be neglected where they increase the moments, calculated ignoring displacements, by not more than 10 %.

2.5.1.5 Time dependent effects

P(1) Time dependent effects shall be taken into account where significant.

(2) Creep and shrinkage normally need only be considered for the serviceability limit state except where their influence in the ultimate limit state are likely to be significant.

2.5.1.6 Design by testing

P(1) The design of structures or structural elements may be based on testing.

(2) In this case, a specification for the test programme and interpretation of the results should be approved nationally.

2.5.2 Idealisation of the structure

ai,a2,ai |
Coefficients used in calculating values for effective spans (Equation 2.15 and Figure 2.4) |

beff |
Effective flange width of a T or L beam |

hf |
Overall depth of a flange in T or L beams |

Wf |
Effective span of beams and slabs |

ln |
Clear distance between the faces of the supports |

lo |
Length of span(s) between points of zero moment |

t |
Thickness of a supporting element |

2.5.2.1 Structural models for overall analysis

P(1) The elements of a structure are normally classified, by consideration of their nature and function, as beams, columns, slabs, walls, plates, arches, shells etc. Rules are provided for the analysis of the commoner of these elements and of structures consisting of combinations of these elements.

(2) To be considered as a beam or column, the span or length of the member should not be less than twice the overall section depth. A beam whose span is less than twice its depth is considered as a deep beam.

(3) To be considered as a slab, the minimum span should not be less than four times the overall slab thickness.

(4) A slab subjected to dominantly uniformly distributed loads may be considered to be one-way spanning if either:

a) it possesss two free (unsupported) and sensibly parallel edges or b) if it is the central part of a sensibly rectangular slab supported on four edges with a ratio of the longer to shorter span greater than 2.

(5) Ribbed or waffle slabs may be treated as solid slabs for the purposes of analysis, provided that the flange or structural topping and transverse ribs have sufficient torsional stiffness. This may be assumed provided that:

— the rib spacing does not exceed 1 500 mm

— the depth of the rib below the flange does not exceed four times its width

— the depth of the flange is at least 1/10 of the clear distance between ribs or 50 mm, whichever is the greater.

— transverse ribs are provided at a clear spacing not exceeding | 10 | times the overall depth of the slab.

The minimum flange thickness of 50 mm may be reduced to 40 mm where permanent blocks are incorporated between the ribs.

(6) A wall should have a horizontal length of at least four times its thickness. Otherwise it should be treated as a column.

2.5.2.2 Geometrical data

2.5.2.2.1 Effective width of flanges (all limit states)

P(1) In T beams the effective flange width depends on the web and flange dimensions, the type of loading, the span, the support conditions and the transverse reinforcement.

(2) For analysis, when a great accuracy is not required (e.g. continuous beams in buildings), a constant width may be assumed over the whole span.

(3) The effective width for a symmetrical T beam may be taken as:

and, for an edge beam (i.e. with flange on one side only)

(for the notations see Figure 2.2 and Figure 2.3 below).

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