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Figure 6.7. Hierarchy of material strengths and resistance when factors are applied to material properties only

Figure 6.8 does likewise for the second format, applying resistance factors (yr) instead of material factors. The arrow denotes the insertion of design material strengths into the calculation model. The resultant design resistance Rd will invariably differ from that shown in Figure 6.7.

Resistance

Material strength

Resistance

Material strength

Figure 6.8. Hierarchy of material strengths and resistance when factors are applied to resistance only tan (J)

Figure 6.8. Hierarchy of material strengths and resistance when factors are applied to resistance only

6.2.3 Geometry

The calculation of geometrical parameters follows the route shown in the central channel of Figure 6.4:

Nominal dimensions ^ Design dimensions

Design geometrical parameters ad are obtained from nominal geometrical parameters anom by adding or subtracting a tolerance Aa: a = a ± Aa d nom —

Because it would be impractical to apply tolerances to all the dimensions that affect a design, EN 1990 allows nominal dimensions to be used as design dimensions, i.e. adopting Aa = 0. The uncertainty in the dimensions is catered for by the values of the partial factors on actions (yf) and on material properties (ym). The use of Aa > 0 is reserved for design situations where it is known that small deviations in geometrical parameters have a large impact on the resulting action effects or resistance. See Chapters 11 and 12 for examples where it is normal to assume Aa > 0.

6.2.4 Verification

Substituting the expressions for effects of actions (Section 6.1.1) and resistance (Section 6.1.2) into that for verification of strength (Section 6.1) gives:

Expanding the terms Fd, Xd, and ad results in:

which is mathematically equivalent to the process illustrated in Figure 6.4. 6.2.5 Partial factors

Partial factors for verification of strength in persistent and transient design situations are specified in EN 1997-1 in Tables A.3 (for actions and effects), A.4 (for soil parameters), and A.5-8 and A.12-14 (for resistance). Some values are amended in the UK National Annexes to ENs 1990 and 1997-1.

The following table lists the partial factors given in EN 1997-1 for general foundations (e.g. slopes, footings, and walls); factors for pile foundations and anchorages are given in Chapters 13 and 14, respectively. The code presents the factors in 'Sets': A1 and A2 apply to actions; Ml and M2 to material properties; and R1 to R3 to resistance. (Values for set R4 are presented in Chapter 13.)

Parameter

Actions Material Resistance or effects properties

Parameter

Actions Material Resistance or effects properties

0 0

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