Fcme

Jy where p2 =As2/bd is the compression reinforcement ratio. Both p1 and p2 are normalized to the width b of the compression flange, not of the web. The expression adopted in Section 5 for the upper limit value of the beam tension reinforcement ratio, pv involves the design values,/cd =/ck/7C and/yd =fyk/%, of the concrete and steel strengths and the corresponding value eyd =fyJEs of ey =fy/Es:

J yd

As noted in Section 5.6.3.2 (see p. 104), for the value of 0.3 of the ratio Lpl/Ls representative of typical beams in buildings, application of equation (D5.10) gives a safety factor of about 1.35 with respect to the more realistic values provided by inverting equation

(D5.5) - or of 1.9 if it is recognized that only <7/1.5 produces inelastic deformation and ductility demands. With the value of 0.0018 of the coefficient in the second term on the right-hand side of equation (D5.24), the safety factor on /.i0 becomes 1.35 x 0.0019 x 1.5/(1.15)70.0018 = 1.6 when the values 7c = 1.5 and 7s = 1.15 recommended in Eurocode 2 for the persistent and transient design situation are used, or 1.35 x 0.0019/0.0018 = 1.4 If the values 7C = 1.0 and 7S = 1.0 recommended in Eurocode 2 for the accidental design situation are used instead. The ratio between these implicit safety factors is: 1.6/1.4 = 1.15, i.e. equal to the partial factor of steel in the persistent and transient design situation, consistent with adopting, or not, this safety factor in the seismic design situation. This 'theoretical' safety factor can be compared with the ratio of (1) the real value of (pl - p2) in beams cyclically tested to flexural failure to (2) the value obtained from equations (D5.24) and (D5.10) for the value of /.i„ at beam ultimate deflection. The median value of the ratio in 52 beam tests is 0.725 for 7C = land7s= I,or0.825if7c= 1.5and7s = 1.15 is used. Being less than 1.0, these values suggest that equation (D5.24) is unconservative. However, if the value of f.ig is determined not as the ratio of beam ultimate deflection to the experimental yield deflection but to the value MyL s/3(0.5£7) that corresponds to the assumed effective elastic stiffness of 0.5EI in Eurocode 8, the median ratio in the 52 tests becomes 2.5 for 7C = 1 and 7S = 1, or 2.85 for 7C = 1.5 and % = 1.15, i.e. above the 'theoretical' safety factors of 1.4 or 1.6 above.

Equation (D5.24) is quite restrictive for the top reinforcement ratio at beam supports, especially if the value of is high, as in, for example, DCH buildings with high basic values of the q factor. To accommodate the area of top reinforcement required to satisfy the ULS in bending at beam supports for the seismic design situation without an undue increase in the beam cross-section, the bottom reinforcement ratio p2 may be increased beyond the value pmin from equation (D5.22), and the prescriptive minimum of 0.5pl specified by Section 5 for the bottom reinforcement in beam critical regions.

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