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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
25、lume of concrete is determined by the integration of equation 11 over the limits of the bay: *Ponding induced deflections of simply supported members are applicable to the perimeter beams and the validity of Formula 10 was demonstrated by Chinn.1 Figure 4 Vz x y dxdy LxLy = ( , ) 00 (12) the integra
26、tion yields: VL LABC xy = + 2 1 242 1 2 2 (13) substituting Lg for Lx and Lb for Ly and simplifying: VL LABC bg =+( .)023104050231(14) Formula 14 predicts the volume of concrete required to fully compensate for initial and placement induced deflections if a true horizontal plane surface were created
27、. EXAMPLE 1 4-in. slab Normal wt. conc. (145 pcf) 0.084 lbs./in.3 2 20 ga. Composite floor deck THIRD QUARTER / 1986109 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 o
28、f the publisher. Live load50 psf Dead load Partitions20 psf Flr. fin.1 psf Slab & deck44 psf Framing5 psf Sprinklers3 psf Mech. & elec.5 psf Ceiling2 psf 80 psf 130 psf Assume deflections induced by slab, deck and framing exist at the outset of compensating concrete placement. Slab & deck= 44 psf Fr
29、aming= 5 psf 49 psf Initial beam deflection: (W14 22) 0 4 6 5 384 749 281728 29 10198 0826= = ()() () . Initial girder deflection: (W18 60) 0 3 6 74928 28 1728 48 29 10986 = + ()() () () () () ()(). 74928 7 1728 24 2910986 3 284 70630 6 22 = Beam flexibility constant: C Ln L E I b gb b = = ( 44 / )
30、.() () . 4 4 6 0084 84 336 29 10 199 0160 Girder flexibility constant: C L L E I g bg g = = 44 4 4 6 0084 336 336 29 10986 0129 .() () . Beam flexibility parameter: b b b C C = = = 1 0160 1 0160 0190 . . . From Figs. 3 and 4 with Cb = 0.160 and Cg = 0.129 cc /./. 00 045035= Deflection A: Initial gir
31、der deflection0 = 0.630 Concrete induced girder deflection c=035 06300221.( .). 0851. = A Deflection B: Initial beam deflection0 = 0.826 Concrete induced beam deflectionc = 0.45(0.826) = 0.372 Initial girder deflection0 = 0.630 Concrete induced girder deflectionc=035 06300221.( .). 2049. = B Deflect
32、ion C: Initial beam deflection0 = 0.826 Concrete induced beam deflection b0 0190 08260157=.( .). 0983. = C Added concrete volume: VL LABC bg =+ =+ = = = ( .) ().( .).( .).( .) ,. . 023104050231 336 336 0231 08510405 20490231 0983 141515 8190 303 3 3 in ft cy Note: Concrete volume added is equivalent
33、 to 1- in. of concrete over the entire bay. CONSTRUCTION PROCEDURES A concrete placement operation involves a repeated sequence of deposition, screed, darby float and final finish. The quantity of concrete placed in a continuous operation is determined as that quantity which can be placed, leveled a
34、nd finished in a normal working day. Generally, 200 to 275 cu. yds. of concrete are scheduled for a single crew for each day of placement. That quantity would require finishing of 10,000 to 15,000 sq. ft of slab surface for a nominal 6-in. slab thickness. The number of repetitions of the placement s
35、equence (i.e. deposit, screed, float and finish) is determined by the length of the screed board, which is typically a 16-ft long 2 6. Consequently, once concrete is deposited over an area of approximately 200 sq. ft ( 14 14) the concrete is struck to a plane surface with the screed board and the fl
36、oating operation started. The levelness of the slab is monitored for each placement sequence. Consider the four 28-ft 28-ft bays in Fig. 5. This partial plan represents the northwest corner of an elevated floor system. The sequence: place, screed, float and finish occurs in a rotation over 200-sq. f
37、t areas within a bay and subsequently, in a sequence over the floor. The contractor responsible for concrete placement is normally free to select a sequence. It will become apparent from the description of a specific sequence that both the final surface profile and the volume of concrete required is
38、 affected by this selection. 110ENGINEERING 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. Figure 5 O
39、ne placement sequence typically used is shown graphically in Fig. 5 and is described in the following: Top of finished slab elevations are marked on columns as control points prior to concrete placement. Concrete is deposited over quadrant until completely covered. A control point is set at mid-bay
40、(Location e) by mounding the concrete to the desired surface elevation. This control point is set to the finished slab elevation referencing a remote fixed point using an optic level or laser. A wet screed is formed by striking off the concrete in a straight line between the control point (Location
41、e) and the top of the north slab edge angle (Location b). The concrete in the quadrant is then screeded using wet screed line (Location b to Location e) and the west slab edge angle (Location a to Location d). Immediately following the screed operation, the concrete is float finished. Concrete is de
42、posited over quadrant as the floating operation is accomplished over quadrant . A control point is set by mounding concrete at Location h referencing a remote fixed point. The concrete is struck in a straight line between Locations h and e and this wet screed is used in conjunction with the west edg
43、e angle to screed the concrete in quadrant . The concrete placement operation continues and follows a similar process in quadrants and . However, the concrete surface of quadrant is used as the screed edge line for quadrant and the floated concrete surface of quadrant is used as the screed edge line
44、 for quadrant in lieu of the slab edge angle. The placement operation proceeds from quadrant to quadrant in the sequence indicated by the quadrant numbers shown on Fig. 5. The area of concrete placement to be accomplished in a single operation is determined prior to starting. The boundary of the pla
45、cement area is usually defined by the floor edge angle on two or three sides. The remaining boundary edges are established by affixing a screed board of a thickness equivalent to the slab thickness to the floor deck. THIRD QUARTER / 1986111 2003 by American Institute of Steel Construction, Inc. All
46、rights reserved. This publication or any part thereof must not be reproduced in any form without the written permission of the publisher. REFLECTIONS ON CONSTRUCTION PROCESS Concrete is placed to match the top of the edge angle at the building perimeter. The elevation of this angle is not constant s
47、ince the concrete weight deflects the substrate to which the angle is attached. Control points which are monitored from a fixed reference are set at only three positions during concrete placement within a bay. These points are set prior to superimposing the full concrete weight and displace vertical
48、ly immediately following their establishment. Concrete is worked to screed boards at interior placement boundaries. These bulkheads are used as surface screed lines and, since they are attached to the decking, they dictate that the surface conform to the deflected deck shape. Since concrete is screeded to the top of the edge angle at the building perimeter, the slab thickness is maintained at a constant thickness at these locations. As concrete placement progresses away from the perimeter, previ