【正文】
culated from elastic theory using the elastic modulus of concrete Ec and an effective moment of inertia, Ie. The value of Ie for the member is the value calculated using Eq. [1] at midspan for a simply supported member and a weighted average value calculated in the positive and negative moment regions of a continuous span 33( ) 1 c r c re g c r gaa???? ??? ? ? ? ? ? ????????? ( 1) where Icr=moment of inertia of the cracked transformed section。 Ma=maximum moment in the member at the stage deflection is puted。 fr=modulus of rupture of concrete (= fc in psi and fc in Mpa)。 2= for a single, shortterm load and for repeated or sustained loading。 s is reinforcement stress at loading under consideration (., when the inservice moment Ms is acting), calculated while ignoring concrete in tension。 and uncr=curvature on the uncracked transformed section. For slabs in pure flexure, if the pressive concrete and the reinforcement are both linear and elastic, the ratio sr /s in Eq.(3) is equal to the ratio Mcr /Ms. Using the notation of Eq.( 1) , Eq.(2) can be reexpressed as ? ?1M s M s M sEc I e Ec I c r Ec I unc r??? ? ? ?? ? ?? ? ? ?? ? ? ? ( 4) For a flexural member containing deformed bars under shortterm loading, Eq. (3) bees =1?( Mcr /Ms) 2 and Eq.( 4) can be rearranged to give the following alternative expression for Ie for shortterm deflection calculations [recently proposed by Bischoff (2021)]: 2/1 I c r M c rI e I c r I un c r M s??? ? ? ??? ? ? ? ???? ? ? ??? (5) BS 81101985 This approach, which has now been superseded in the . by the Eurocode 2 approach, also involves the calculation of the curvature at particular cross sections and then integrating to obtain the deflection. The curvature of a section after cracking is calculated by assuming that (1) plane sections remain plane。 and( 3) the stress distribution for concrete in tension is triangular, having a value of zero at the neutral axis and a value at the centroid of the tensile steel of MPa instantaneously, reducing to MPa in the long term. Comparison with Experimental Data To test the applicability of the ACI 318, Eurocode 2, and BS 8110 approaches for lightly reinforced concrete members, the measured moment versus deflection response for 11 simply supported, singly reinforced oneway slabs containing tensile steel quantities in the range ? are pared with the calculated responses. The slabs (designated S1 to S3, S8, SS2 to SS4, and Z1 to Z4) were all prismatic, of rectangular section, 850 mm wide, and contained a single layer of longitudinal tensile steel reinforcement at an effective depth d (with Es=200,000 MPa and the nominal yield stress fsy=500 Mpa). Details of each slab are given in Table 1, including relevant geometric and material properties. The predicted and measured deflections at midspan for each slab when the moment at midspan equals , , and Mcr are presented in Table 2. The measured moment versus instantaneousdeflection response at midspan of two of the slabs (SS2 and Z3) are pared with the calculated responses obtained using the three code approaches in Fig. 2. Also shown are the responses if cracking did not occur and if tension stiffening was ignored. Discussion of Results It is evident that for these lightly reinforced slabs, tension stiffening is very significant, providing a large proportion of the postcracking stiffness. From Table 2, the ratio of the midspan deflection obtained by ignoring tension stiffening to the measured midspan deflection (over the moment range Mcr to Mcr )is in the range – with a mean value of . That is, on average, tension stiffening contributes more than 50% of the instantaneous stiffness of a lightly reinforced slab after cracking at service load. For every slab, the ACI 318 approach underestimates the instantaneous deflection after cracking, particularly so for lightly reinforced slabs. In addition, ACI 318 does not model the abrupt change in direction of the momentdeflection response at first cracking, nor does it predict the correct shape of the postcracking momentdeflection curve. The underestimation of shortterm deflection using the ACI318 model is conside