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1、 2 ACI Committee 435 INTRODUCTION Temperature changes can significantly affect deflections of reinforced concrete building structures. Deflections occur in unrestrained flexural members when a temperature gradient is set up between opposite faces of the member. In cases where deformations due to tem
2、perature change are restrained, tensile stresses induced in the member can result in cracking and consequent reduction in flexural stiffness. Because temperature effects do not often affect the ultimate limit state of the structure, effects of temperature on deflection are sometimes not considered i
3、n design. However, it has been standard practice to compute thermal stresses and displacements in structures for tall building design. Also, elongation and shortening of bridge superstructures and precast concrete structures are normally computed for support and expansion joint designs. De Serio (1)
4、 states that“Designing for thermal and shrinkage stresses is the most neglected part of todays design practice.“ With the use of higher strength materials and more refined methods of analysis the need to consider temperature effects is becoming increasingly important. Most general purpose computer p
5、rograms have the capability to include temperature changes in the analysis for certain types of members. However, in many cases,particularly those involving relatively simple structures,where computer analysis is not required, or where the computer program does not include the capability for analysi
6、s of flexural members subjected to temperature gradient,calculations may be required to investigate the effect of temperature change on serviceability. The objective of this report is to indicate some of the problems that can result from differential thermal movement and to outline procedures for ca
7、lculating deflections that result from temperature change. The scope of the report is restricted to performance of structures in service. Temperature effects due to heat of hydration are not considered. SERVICEABILITY PROBLEMS RELATED TO DIFFERENTIAL THERMAL MOVEMENT The following examples illustrat
8、e potential problems that can result from differential thermal movement in building structures. Office building - cantilever roof and floor slabs. Daily temperature changes caused deflections of about one inch at the cantilever ends of roof slabs in a four-story building constructed of cast-in-place
9、 concrete. The post-tensioned floors and roof were 80 feet by 80 feet in plan. Only four columns were provided and these were 48 feet apart in each direction which resulted in the columns being 16 feet from the edges of the floor and roof slabs in each direction. During construction it was noted tha
10、t diurnal solar heating caused the roof slab to deflect up and down. The change in elevation was about one inch at the extreme overhanging Temperature-Induced Deflections ends. Fortunately the detail for the connection of the windows, which were located in the perimeter of the floors and roof, provi
11、ded for sufficient movement that the windows remain attached to the roof when it is its highest position and does not result in the window becoming loaded when the roof is in its lowest position. Industrial building - cantilever roof slab. Similar temperature- induced movements caused damage at the
12、joint between a cantilever roof slab and exterior wall in a one-storey building that was erected using the lift-slab technique. The post-tensioned waffle roof slabs had significant overhangs at all four exterior walls. The exterior walls were constructed using the tilt-up method. Because of the cons
13、truction techniques used, the roof was not supported vertically by the exterior walls and the connection of the exterior walls (for horizontal loads) was made when the edges of the roof were in a low position due to the effects of diurnal solar heating. During service the effect of solar heating has
14、 been to apply vertical loads to the exterior walls. This has resulted in the vertical cast-in-place concrete closure pours between the wall panels, particularly at the corners of the building, to crack and disintegrate near their bottoms with the passage of time. Reconstructing the destroyed concre
15、te does not solve the problem; it simply disintegrates again. Eventually, attempts to reconstruct the disintegrated concrete were abandoned and steel plates, painted to match the color of concrete, were placed on the affected joints to cover the damage and improve the appearance of the building. Par
16、king structure - deflection of double tee beams. In a precast parking structure, rotation at bearing ends of beams resulting from deflections caused by diurnal solar heating produced cracking near the ends of the beams. The precast prestressed double-tee beams span about 55 feet. A concrete topping
17、was placed over the top of the double-tee beams. Reinforcing steel was placed in the topping at interior joints in a configuration similar to that used with negative moment reinforcement in cast-in-place construction. At some locations elastomeric bearing pads were placed between the stems of the do
18、uble-tee beams and their supports; at others, elastomeric bearing pads were not provided under the stems. Measurements showed the deflection caused by diurnal solar heating to be of the order of 0.75 inches at midspan of the double-tee beams. The deflection due to solar heating caused rotations at t
19、he ends of the double-tee beams and many of the double-tee beam stems, not provided with elastomeric bearing pads, cracked as a result of the rotation. Office building - vertical wall panels. Exterior precast wall panels two stories high were supported at the bottom and supported laterally at the to
20、p of the second storey. In some locations the panels were placed adjacent to wall construction supported laterally at the top and bottom of the second storey. Seasonal temperature changes caused bowing of the two storey panels resulting in mid panel deflections up to 3/4 in. Relative deflection betw
21、een the two-storey panels and adjacent walls supported at the bottom of the second storey caused damage to the 4 ACI Committee 435 caulking material in the vertical joint. These examples illustrate the need to consider differential thermal movements in design. The following sections outline calculat
22、ion procedures that can be used to estimate stiffness changes and deflections resulting from temperature change in structural members. DESIGN TEMPERATURES Before performing an analysis for temperature effects it is necessary to select design temperatures and temperature gradients for use in the anal
23、ysis. Martin (2) summarizes design temperatures that are provided in various national and foreign codes. Design information is given in terms of temperature rise ranging from 27 to 40F and temperature drop ranging from 27 to 45oF. Martin also provides extreme values of normal daily maximum and minim
24、um temperatures as reported by the Environmental Data Service for various locations in the United States. He suggests that design should be based on 2/3 of the difference between extreme values of normal daily maximum and minimum temperatures for each location. Based on this criterion average propos
25、ed design thermal differential is 41F with a minimum of 10 and a maximum of 62oF. Fintel and Khan (3) suggest contacting the local weather bureau to obtain mean temperatures for specific localities. They also point out that surface temperatures can be affected by direct radiation. This may be signif
26、icant, particularly for thin members. Fintel and Khan provide a method to determine isotherms and temperature gradients for irregular configurations and boundary conditions. They show that nonlinear thermal gradient can induce internal stresses in the member even if the member is free to deform at t
27、he ends. A design thermal gradient used in New Zealand for concrete bridge superstructures is shown in Fig. 1. A fifth power temperature profile is used between the top surface and a point at depth 1200 mm for webs and cantilever decks. For decks above enclosed air-cells, a linear gradient is used.
28、A linear thermal gradient is also used for the bottom 200 mm of a section. For superstructures less than 1400 mm in depth, the top and bottom thermal gradients are superimposed. Charts showing temperature gradients in slabs of different thickness exposed to sunlight on a summer day in Melbourne, Aus
29、tralia are given in Ref. 4. These charts show approximately linear temperature gradients and a temperature difference of about 40F over the depth of an 8-in. slab. Fintel and Khan (3) provide a graphical method for determining temperature gradients for given steady state temperatures. Temperature gr
30、adients can also be determined by the finite element method (5), or the finite difference method (6). Temperature-Induced Deflections 5 TEMPERATURE GRADIENT ON UNRESTRAINED CROSS SECTION Consider a temperature distribution t(y) on the cross section shown in Fig. 2(a). Thermal strain at distance y fr
31、om the bottom of the section is given by: Et(Y)= NY(1) To restrain movement due to temperature t(y), apply a stress in the opposite direction to Et(y): a(Y)= WY)(2) The net restraining axial force and moment are obtained by integrating over the depth: h P = I odA = ( aEt(y)b(y)dy A 0 h (3) M = IA4Y-
32、n)dA = J bt(Y)b(Y)(Y-n)dy(4) 0 To obtain total strains on the unrestrained cross section, as shown in Fig.2(d), apply P and M in the opposite direction to the restraining force and moment. Assuming plane sections remain plane, axial strain (Ed) and curvature (4) are given by: P h a = _AE: =; J t(Y)b
33、(Y)dY(5) 0 h = h = ; I t(YMY)(Y-WY (6) 0 The net stress distribution on the cross section is given by: (7) For a temperature gradient varying linearly from 0 to At, the curvature obtained by Eq. (6) is given by ($ , t(y)b(y)(y-n)dy 0 36 “i, 40 x 96(y - 26.86)dy 33 88,013 x 0.0000055 69319 0.00000698
34、 : = 4000 psi % = 60,000 psi cr = 59 in.4/ft. Mcr= 2.85 ft.kips/ft. (a) D+L Maximum Negative Moment = (wD + wL)L2 8 Maximum Moment = 5.60 ft.kips/ft. Ie = (%j31g + l - (,$+j3 I, 3 = (GG) (216) + l - (gG)3 (59) . = 79 in.4 Maximum Positive Moment = )3(59) = 78 in.4 Average I,= (79+78)/2 = 78.5 in.4 D
35、eflection due to D + L _ (0.175)(164)(123) max X= (186-6DO)m = 0.37 in. i.e. Temperature gradient results in 60% increase in deflection under dead + live load (ii) Thermal moments based on I, calculated for service loads MT = 7.13 x .g, =4.19 ft.kips/ft. MT at 3/8 L= 1.57 ft.kips/ft. Therefore maxim
36、um positive moment for D + L + T = 3.15 + 1.57 =4.72 ft.kips/ft. Ie = 93 in.4 Average Ie= (79+93)/2 = 86 in.4 Deflection due to D + L _ max = 0.33 in. SUMMARY AND CONCLUSION Deflections caused by temperature change can have adverse effects on serviceability of concrete structures. Measures should be
37、 taken at the design stage to alleviate these effects, usually by providing adequate joint details to permit relative movement where required. Calculation procedures to estimate changes in stiffness and temperature-induced deflections are outlined in the report. 10 ACI Committee 435 For uncracked me
38、mbers,effects of temperature can be included in deflection calculations in a relatively straightforward manner. For statically indeterminate systems after cracking, the deflections,stiffness, and temperature are inter-related, and an iterative procedure is required for a correct solution. However a
39、simplified direct procedure is given in the report for calculation of temperature-induced deflections after cracking occurs. Temperatures and temperature gradients for use in design are specified in several codes. Suggestions for selecting these design quantities are given in the report for cases wh
40、ere the temperatures to be considered are not specified by the governing code. Some data are available in the literature concerning field measurements of temperatures in structures. Additional data would be of value in developing appropriate temperature gradients for standard design situations. ACKN
41、OWLEDGEMENT The committee acknowledges the significant contribution made to this report by J.R. Libby, former Chairman of ACI Committee 435. Conversion Factors - Inch-Pound to SI A b D E h I Icr Ie Ig 1 in. = 25.4 mm 1 lb (mass) = 0.4536 kg 1 lb (force) = 4.488 N 1lb/sq in. = 6.895 kPa 1 kip = 444.8
42、 N 1 kip/sq in. = 6.895 MPa 1 in.-kip = 0.1130 Nom NOTATION = cross-sectional area = width of beam = dead load = modulus of elasticity = depth of member, blacktop thickness = moment of inertia = moment of inertia at cracked section = effective moment of inertia = moment of inertia of gross concrete
43、section Temperature-Induced Deflections 11 k L M Mcr n P = constant = Live load, span length = bending moment = cracking moment = distance of neutral axis from bottom of beam = axial load t, _ t = temperature difference T wD wL Y O( _ Ea Et cp 0 1. 2 3. 4. 5. = effects of temperature = uniformly dis
44、tributed dead load = uniformly distributed live load = distance from bottom of beam = coefficient of thermal expansion = deflection = axial strain at centroid = strain due to temperature change, t = curvature = stress REFERENCES DeSerio, J.N.,“Thermal and Shrinkage Stresses - They Damage Structures!
45、“ (SP-27) pp. 43-49. Martin, I.,“Effects of Environmental Conditions on Thermal Variations and Shrinkage of Concrete Structures in the United States“, (SP-27) pp. 279-300. Fintel, M. and Khan, F.R., “Effects of Column Exposure in Tall Structures - Temperature Variations and Their Effects“, ACI Journ
46、al,Proceedings V. 62, No.12, Dec 1965, pp. 1533-1556. ASCE Monograph on the Planning and Design of Tall Buildings, Volume CB, “Structural Design of Tall Concrete and Masonry Buildings,American Society of Civil Engineers, 1978, p. 468. Zienkiewicz, O.C., “The Finite Element Method in Engineering Scie
47、nce“. McGraw-Hill. 1977. 435.7R-12 MANUAL OF CONCRETE PRACTICE 6. Dilger, W.H., Ghali, A., Chan, M., Cheung, M.S., and Maes, M.A., “Temperature Stresses i n Composite Box Girder Bridges“, Journal of Structural Engineering, ASCE, Vol. 109, No. 6, June 1983, pp. 1460-1478. 7. Priestley, H.J.N., “Therm
48、al Stresses i n Concrete Structures“, Proceedings of the Canadian Structural Concrete Conference, University of Toronto, September 1981, pp. 255-283. 8. Mentes, G.A., Bhat, P.D., and Ranni, A.I., “Thermal Effects i n Reinforced Concrete Structures“, ASCE Specialty Conference i n Civil Engineering an
49、d Nuclear Power, Knoxville Tennessee, September 15-17, 1980. 9. Branson, D.E., “Deformation of Concrete Structures“, McGraw H i l l International, 1977. 10. ACI Committee 349, “Reinforced Concrete Design for Thermal Effects on Nuclear Power Plant Structures“, ACI Journal, Proceedings V. 77, Nov-Dec 1980, pp. 399-428. 11. Branson, D.E., and Trost, H., “Unified Procedures for Predicting the Deflection and Centroidal Axis Location of Partial ly Cracked Nonprestressed and Prestressed Concrete Members“, ACI Journal, Proceedings V. 79, No. 2, March-April 1982, pp. 119-130.
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