AISC ruddy1986Q3.pdf
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1、Ponding of Concrete Deck Floors JOHN L. RUDDY This paper was presented at the AISC National Engineering Conference in Nashville, TN, in June 1986. Floor construction consisting of concrete over metal decking and supported by steel beams and girders is a frequently employed structural system. When te
2、mporary shoring is not used, the steel framing and decking deflects during placement of the concrete floor slab. If the concrete were placed to the specified uniform thickness, the result would be a floor surface defined by the deflected shape of the supporting members. To create an acceptable level
3、 surface, one of the following options is normally employed: 1.The floor system is shored during concrete placement; 2.The floor beams are cambered to compensate for anticipated concrete placement deflections; 3.The concrete volume is increased resulting in a varying slab thickness to compensate for
4、 placement deflections. The third option, placing a varying slab thickness, is probably the most commonly employed alternative. The success of the approach is often left to the control of the contractor, and seldom is considered in the design process. The purpose of this paper is to present an inter
5、im report concerning studies toward an ultimate objective of predicting concrete volumes required to produce an acceptably level slab which is placed over a flexible substrate. As concrete is placed, the supporting system deflects. As more concrete is placed to compensate for the deflection, additio
6、nal displacements occur. The situation may be considered analogous to the rainwater ponding phenomenon of roof systems. However, there are notable differences between the rainwater ponding phenomenon and the concrete placement operation. Concrete is plastic, not liquid, consequently it does not seek
7、 a constant level. Also, the concrete placement process is controlled by man and rainwater deposition is not. John L. Ruddy is vice president and director of engineering, Fletcher-Thompson, Inc. a Bridgeport, Connecticut architectural/engineering firm. ANALYSIS Despite the shortcomings, a ponding an
8、alogy offers a convenient analytic approach to predicting a maximum concrete volume as a function of beam and girder stiffnesses. Several investigators have reported on the cyclic load- deflection phenomenon caused by rainwater accumulations on flat roofs.1,2,3 The objective of the rainwater ponding
9、 investigations has been to assure that the equilibrium position of the system is reached before the elastic limit of the structural elements is exceeded. The structural element stresses occurring during concrete placement are normally well below the elastic limit of the materials and attainment of
10、the equilibrium position within the elastic material limitations is not normally a concern. The objective here is to develop a procedure for determining the volume of concrete required to reach the equilibrium position. The structural system under investigation is shown in Fig. 1. It represents an i
11、nterior bay of a floor system and con- Figure 1 THIRD QUARTER / 1986107 2003 by American Institute of Steel Construction, Inc. All rights reserved. This publication or any part thereof must not be reproduced in any form without the written permission of the publisher. sists of equally spaced beams s
12、upported by girders. The perimeter members of the bay are supported by columns and identical framing systems are assumed to occur on all sides of the bay being investigated. The work of Marino3 regarding ponding of two-way roof systems is used as the basis of this study. The investigation will be ma
13、de assuming the deck contribution to the system deflection is negligible, and therefore the inertia of the members may be considered distributed uniformly over the bay. It is also assumed concrete placement will occur over a sufficiently large area so the load contributed to the perimeter members by
14、 placement of concrete within the bay being considered is equaled by placement of concrete in adjacent bays. The load transfer from the floor beams to the girders is assumed to be distributed, rather than as load concentrations. The equilibrium position deflections are determined by considering the
15、deflected position of both the beams and girders to vary as the ordinates of a half sine wave as illustrated in Fig. 2. If beam and girder flexibility constants are defined as, Beam C Ln L E I b gb b = (/ ) 4 4 (1) Girder C L L E I g bg g = 4 4 (1a) and associated flexibility parameters are defined
16、as, Beamb b b C C = 1 (2) Girderg g g C C = 1 (2a) then it has been demonstrated3 that mid-span girder deflection caused by the compensating concrete can be expressed as, c ggb gb = + + + 0000 44 1 4 () (3) Figure 2 Also, the mid-bay mid-span deflection of the beam which is caused by the compensatin
17、g concrete can be expressed as: c= bbgbg gb 0 2 0 2 000 8844 2 1 4 4 + + ( ) In these expressions, o represents the mid-bay, mid-span deflection which exists at the outset of compensating concrete placement and similarly o represents the mid-span girder deflection which exists at the outset of compe
18、nsating concrete placement. Both the flexibility constants Cb and Cg and the deflections 0 and 0 are directly proportional to L4/EI and the following substitution is applicable: = 0 0 = C C b g (5) Note that the substitution is valid as long as no operation is performed to unbalance the ratio. Conse
19、quently, if the deflections due to the self weight of the framing members are considered, the load influencing the deflection should be calculated using the unit steel framing weight within the bay (psf) multiplied by the contributing load width (ft) for the member rather than independently consider
20、ing the actual foot weight of the member. Substituting Formula 5 into Formulas 3 and 4 yields: () c gbb bg 0 1 44 1 4 = + 1+ (6) () 32 + 1 32 c bggbg bg 0 1 8 11835 4 = + . (7) Formulas 6 and 7 present the ratio of compensating concrete induced deflection to the deflection present at the outset of c
21、ompensating concrete placement for both the floor beam and girder. The formulas are a function of the flexibility constants Cb and Cg of the floor system. The graphic representation of Formula 6 is presented in Fig. 3 and the graphic representation of Formula 7 is in Fig. 4. The total volume of addi
22、tional concrete required to compensate for the initial deflected position, as well as the deflection induced by the placement of the additional concrete, can be determined by using the deflection magnitude at three locations over the surface of the bay. If the deflection magnitude at the mid-span of
23、 the girder is designated A, where, 108ENGINEERING JOURNAL/AMERICAN INSTITUTE OF STEEL CONSTRUCTION 2003 by American Institute of Steel Construction, Inc. All rights reserved. This publication or any part thereof must not be reproduced in any form without the written permission of the publisher. Fig
24、ure 3 A c =+ 0 (8) and the mid-bay deflection is designated B, where, B cc =+ 00 (9) and finally the mid-span deflection of the perimeter beam is designated C, where, C b =+ 00* (10) The equation of the surface can be written as: z x yA x L CBC x L A x L y L x xxy ( , )sin() sinsinsin =+ (11) The vo
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