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III DISCUSSION A. GENERAL A building is a dynamic product subjected to a host of conditions that keep its various elements in a constant state of stress, strain, and displacement. During design, displacement must be evaluated and, when necessary, controlled to ensure that the building will perform as intended throughout its expected life without the need for unanticipated large-scale maintenance. Expansion joints introduced by the designer to avoid the effects of large lateral dis- placements are relied upon to limit the internal stresses caused by expansion and contraction and the actual movement of building elements, permit relative motion of the building members without disturbing functional continuity, and affect a complete structural separation without disturbing structural integrity. Experience indicates that appropriate use of expansion joints presents a rather complex design problem and requires a thorough understanding of those factors that dictate their need as well as those that affect their ultimate performance after installation. The design, location, and performance of expansion joints can be influenced by such factors as building form, function, and economics; construction techniques; the varying characteristics of the different materials employed, changes of these characteristics under varying environmental conditions, and the physical relationship of one to the other; and the ability to withstand stresses resulting from dimensional changes. The problem is further complicated by recent trends and developments in structural engineering. A better understanding of the behavior of materials and an evolution in the precision of structural analysis of buildings, coupled with the advent of computers that permit economical, rapid, and accurate analyses, have encouraged designers to include a mixture of mate- rials and a variety of jointing systems in most major structures. These factors make it possible to generally decrease the dimensions of resisting structural elements from those customarily used in past practice. As a con- sequence, structures are less likely to be overdesigned than in the past; therefore, the risk of their reaching the threshold of structural failure is greater, giving emphasis to the importance of adequate expansion joints. Previously developed empirical rules for expansion joint spacing are not necessarily compatible with these recent trends and developments. If desired margins of safety are to be maintained, it appears that the need for thermal expansion joints should be determined as part of the structural analysis of a building and that special attention should be given to the potential impact 9

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of horizontal dimensional changes* on structural integrity and building serviceability. Factors that are considered to be most significant with respect to the design and location of expansion joints, and which are treated herein, include dimensions and configuration of the building; design temperature change; provision for temperature control; type of frame, type of connection to the foundation, and symmetry of stiffness against lateral displacement; and materials of construction. 1. Dimensions and Configuration of the Building The dimensions of a building are obviously an overriding parameter with regard to the need for expansion joints because the problem of expansion joints arises when the dimensions become substantial. The configuration of a building is a parameter influencing the severity of the effects of temperature changes on a building and, as such, should be given consideration during the design process. Rectangular buildings and buildings with two axes of symmetry in plan with no internal open courts experience temperature-induced stresses that have relatively simple pat- terns, while buildings with a more complex configuration, such as U-shaped or L-shaped buildings, experience horizontal dimensional changes that result in complex stress patterns, particularly at re-entrant corners. 2. Temperature Change Since construction is carried out over a considerable period of time, the various elements of the structure are installed at different temperatures. The temperature changes causing displacements and stresses in a structure are changes from these installation/erection temperatures, over which the designer has little, if any, control. Yet, while it is apparent that temperature change is one of the most important factors influencing the potential linear expansion/contraction of a building, there is no possi- bility of establishing exactly the maximum expected temperature change because this change is not the same for all parts of the structure and is not known during the design phase for any one particular part of the structure. a. Computation of design temperature change To properly account for the effects of temperature on buildings requires a procedure that uniquely defines the temperature differ- ences for which a building in a given locality should be designed. Currently, however, there is no one established procedure for deter- mining this design temperature change with precision; therefore, the *While the scope of this report is concerned only with horizontal dimensional changes, the analysis also should be supplemented by consideration of dimen- sional changes in the vertical direction of buildings and of methods used to fasten nonstructural elements to the structural frame of the building. 10

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following guidelines were developed by the Committee to serve as an aid in its computation until a more definitive procedure is developed: . It should be assumed that structures will be built when the minimum daily temperatures are above 32 OF. Mean temperatures (Tm) should be based on only the construction season--the contiguous period* during which the minimum daily temperatures are above 32 OF. This season varies for different localities (see Table 1) and, except for southern areas, the mean construction season temperature is different from the mean annual temperature. The anticipated high-temperature extreme (Tw) should be con- sidered as the temperature that is exceeded, on the average, only 1 percent of the time during the summer months (June through September) in the locality of the building. The anticipated low-temperature extreme (Tc) should be con- sidered as the temperature that is equaled or exceeded, on the average, 99 percent of the time during the winter months (December through February) in the locality of the building. . Using the data described above, the design temperature change (At) can be uniquely defined according to At = (TW-Tm) or (Tm-TC), whichever is greater. The Tw, Tm, and TO values for many localities in the United States are presented in Appendix B. TABLE 1 Mean Construction-Season Temperatures for Various Localities Locality From . Birmingham, Alabama Anchorage, Alaska Jan 1 April 24 Almose, Colorado May 8 Daytona Beach, Florida Jan 1 Dec 31 Oct 8 Sept 28 Dec 31 Construction Season Mean Temperature ___ ~ 50.6 60.4 70.3 Annual Mean Temperature (OF) 63.2 35.5 42.2 70.3 *Obtained from Decennial Census of United States Climate--Daily Normals of Temperature and Heating Days, Climatography of the United States No. 84, U.S. Department of Commerce, Weather Bureau, Washington, D. C. (19633.

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b. Differential temperature effects on a building element As illustrated in Figure 2, the differential temperature profile of a member can be assumed to consist of the superposition of two tem- perature profiles: (1) A uniform temperature change (At") equal to the temperature change that takes place along the axis of the member,and (2) A differential temperature change [~(At)] equal to the differ- ence of the temperature change at one face of the member less the temperature change at the opposite face of the member; i.e., d(At) = (At2-Atl) = (a+b) iAti ~b: ~9 \~ l l ~ At2 ~: + b a Differential Temperature = Uniform Temperature + Differential Temperature Profile of a Member Change Atg Change dI1\t} FIGURE 2 Differential temperature effects on a building element. When viewed in this manner, it becomes apparent that the differential temperature change [d(At)] causes no change in the length of the member along its axis. Instead, it tends to cause curvature in the member, which, to the extent it is resisted, results in internal stresses. However, neither the curvature nor the ensuing internal stresses propagate and cause a cumulative increase in the length of the structure as do those stresses and deformations brought about by uniform temperature change. Thus, with respect to expansion joint requirements, a differential temperature profile can be replaced by the superposition of a uniform temperature change corresponding to the change at the level of the centroidal axis of the member and a differential temperature change that causes no change in the overall length of the member. 12

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From this discussion it becomes evident that the uniform temperature change component (At) of the differential temperature profile is the principal cause of building distress due to temperature changes. For a symmetrical member, the effective uniform temperature change will be equal to the average of the temperature changes on the oppo- site faces undergoing differential temperature changes. In members with nonsymmetrical cross sections, the effective uniform tempera- ture change obviously will have an intermediate value between the temperature changes on the two opposite faces. 3. Provision for Temperature Control 4. Properly functioning heating and air conditioning in a building will maintain a relatively constant temperature within the building and, thus, reduce the potential for adverse temperature change effects on internal and peripheral members. However, buildings that are heated but not air conditioned are subject to substantial changes in temperature during the summer and these must be taken into account. Buildings that are both heated and air conditioned can be considered only theoretically immune to the effects of extreme temperature fluctuations since malfunctions or intentional shutdowns of mechanical equipment could lead to sudden injurious temperature variations. Thus, the potential for such also must be considered during expansion joint design. Type of Frame, Type of Connection to the Foundation, and Symmetry of Stiffness against Lateral Displacement Thermal effects on buildings with fixed-column bases are likely to be more severe than on buildings with hinged-column bases. Comparison of the behavior of two identical tall buildings, one with fixed-column bases and one with hinged-column bases, subjected to the same tempera- ture changes indicates that both buildings underwent virtually the same dimensional changes in all levels above the first. However, in the case of the fixed-column building, temperature-induced stresses (shear forces, axial forces, and bending moments) at critical sections within the lowest story were almost twice as high as those at corresponding locations in the hinged-column building. The extent of stresses and deformations in a building also will be greatly influenced by the symmetry of the building in terms of stiffness against lateral displacement. A building with main structural frames having approximately the same stiffness against horizontal displacement from the center to the right as from the center to the left will be sub- ject to smaller stresses and deformations than a similar building with main structural frames having columns or a shear wall at one end sub- stantially stiffer against horizontal displacement than the rest of the columns. Therefore, the design of expansion joints should be influenced by the type of frame, type of connection to the foundation, and the stiffness against lateral displacement of the structural framing, each of which is discussed in greater detail subsequently. 13

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5. Materials of Construction - The type of material used in the construction of the frame (e.g., steel, concrete, masonry) can influence the effects thermal changes will have on the building. For example, comparison of the effect of thermal changes in two similar frames with identical moments of inertia, one of which has beams with greater cross-sectional area than the other, indi- cates that the frame with the greater cross-sectional area develops the greater axial forces, shear forces, and bending moments at the critical sections of both beams and columns. Consequently, considering that the ratio of the cross-sectional area to the moment of inertia is greater for concrete frames than for steel frames, it would be reasonable to expect that the thermal effects on structures would generally result in higher stresses in concrete frames than in steel frames. Therefore, a designer would need to be somewhat more conservative in evaluating poten- tial thermal effects when using concrete as a structural material than when using steel, unless of course, he conducts a more complete analysis of the structure for all forces, including thermal effects, and provides explicitly for the critical loading conditions. Shrinkage of concrete members accounts for a portion of the dimensional change in a building frame. However, shrinkage usually takes place during a relatively short period of time following concrete placement. Its extent can be estimated with reasonable accuracy, and its effects can be controlled by proper planning of the construction sequence of the building. Consequently, concrete shrinkage has not been considered in this study but should be taken into account when planning the construc- tion sequence of concrete frames of lengthy buildings. B. DETERMINATION OF NEED FOR EXPANSION JOINTS Although the need for expansion joints can be determined empirically in many cases, in certain situtations it would be determined best through analytical evaluation. The empirical approach is likely to be the simpler of the two, but is the more conservative. The analytical method requires that the designer fully evaluate and account for in the overall design the effects of all factors influencing the need for expansion joints (discussed in Section III.A). The basic elements, concepts, and/or procedures involved in each are discussed below. 1. The Empirical Approach a. Current practices and existing data With the exception of criteria currently used by some federal agencies in determining building expansion joint requirements and a report concerning a one-year (1943-1944) experiment examining expansion joint movement, a search of the literature revealed no significant quantitative data or specifications. Considerable infor- mation on the design of the actual expansion joint for a variety of 14

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specific building components and materials is available in engineering/architectural aids and specifications; however, through the years, the decision concerning the number and location of expan- sion joints, as well as the ultimate design, has been left primarily to the judgment of the designer on the basis of his intuition and experience. Individual agencies have examined the performance of buildings that seemed to lack appropriate expansion joints and have provided remedies for such problems on a case-by-case basis. Unfor- tunately, the results relating cause and effect were not formally documented. An examination of the federal agency criteria for expansion joints indicates that they are very basic in concept. These criteria are based on the assumption that the maximum allowable linear dimension of buildings is a function of two parameters: (l) The maximum difference between the mean annual temperature at the locality of the building and the maximum or minimum expected temperature, and (2) The provision for heat control in the building under considera- tion. The first parameter causes the dimensional change, while the second reflects the ability of the building to dampen, and thus to reduce, the severity of the effects of outside temperature changes. Curves for heated and unheated buildings (Figure 3) are used to relate the maximum allowable length of a building without expansion joints as a step function to design temperature changes. a, O - ~ (~' _ A ~ ~ a, O 0 4- U) N ~ ~ ~ O Q t X U,l ~ CK5 ~ a, .c c' ' ~ a) ~ O C) - ~ ~ ~ Q God) ~ _ u, ~ a, .E.E ~ ~ x x ~ ~ ~ ~ 0 - ~ ~ to 600 500 400 200 / Step Unheated Buildings ~ 1 .1 10 20 Preheated Buildings ~ Step / 1 1 1 1 1 30 40 50 60 70 TEMPE RATU R E CHANGE ( F) FIGURE 3 Expansion joint spacing criteria of one federal agency. 15 1 .1 80 90

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There is little doubt that a step function cannot represent the behavior of a physical phenomenon, such as thermal effect, that has evident characteristics of continuity. However, while the maximum allowable building length can be expected to decrease as the design temperature change increases, the definition of the exact nature of their relationship requires more rigorous and elaborate quantitative data than is available at present or is expected to become available. Therefore, the limits of 600 and 200 feet in the linear dimensions of buildings are assumed to reflect the considered consensus of long experience within the engineering profession. Consequently, without any further experimental or theoretical justification, they are used herein as boundary values. Taking the above factors into consideration, the curves in Figure 1 have been developed and are recommended in Section II as an aid in the empirical determination of the need for expansion joints in buildings. These curves are within the 600- and 200-foot bounds and assume a linear change (in the absence of any evidence justifying curves of other shapes) in allowable maximum length with regard to design temperature change. For relatively small temperature changes (up to 25 F) the maximum allowable length is permitted. In addition, factors can be used to modify the maximum allowable building lengths obtained from Figure l for parameters other than heating (e.g., air conditioning, type of support, type of configuration, and type of material used) to account in a conservative manner for their influ- ence. These factors were listed in Section II, Recommendation A.2, and are based on a qualitative assessment; the following sections of this report provide the rationale for their adoption. b. Findings of a previous study on expansion joints Structural engineers of the Public Buildings Administration* investi- gated expansion joint movement over a period of one year (September 1943 to August 19443 in nine federal buildings to obtain measurements of dimensional changes over a complete cycle of seasons.** Although some of the assumptions made in the analysis are questionable and data collected are not sufficiently complete to serve as a basis for definitive statements, several important conclusions relative to this report can be drawn from that investigation and those considered most significant are presented below. (1) There is a considerable time lag (2 to 12 hours) between the maximum dimensional change of a building and the peak ambient temperature associated with this dimensional change. The inves- tigators theorized that the time lag was due to the temperature *Now the Public Buildings Service of the General Services Administration. **Public Buildings Administration, Movement of Expansion Joints in Nine Federal Buildings in Washington, D. C. (September 10, 1943-August 29, 1944), unpublished. 16

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gradient between the outside ambient temperature and the inside temperature of the building, the resistance to the transfer of temperature change (insulation), and the duration of the ambient temperature at its extreme levels. Since such parameters deter- mine the rate of temperature change at the axis, this theory appears to be valid. (2) The maximum temperature change and the maximum linear dimension of a building are not the only parameters affecting the extent of dimensional change in the building. For example, the effec- tive coefficients of thermal expansion appear to vary widely from building to building and even within a single building. (3) The effective coefficient of thermal expansion of the first floor level is approximately one-third to two-thirds that of the upper floors. (4) The dimensional change of each building at the upper level corresponds, in most cases, to an effective coefficient of thermal expansion between 2 and 5 per million degrees Fahren- heit. Given the value for this coefficient of 3.3 for brick, 5.5 for concrete, and 6 for steel and the uncertainty of the assumption used to evaluate the temperature change on the basis of which the range from 2 to 5 was derived, the investigation seems to confirm that the upper levels of buildings undergo dimensional changes corresponding to the coefficient of thermal expansion of the principal material of which each is constructed. c. Explanation of structural expansion by statics The problem of structural expansion due to temperature change can best be understood in light of the basic mechanics involved. A fun- damental analysis of the problem can be made by utilizing statics. Assume for this purpose a one-bay simple bent (Figure 4), free in the two-dimensional space and subjected to uniform positive tempera- ture change. Intuitively, it becomes obvious that the bent ABED will expand as shown in Figure 4a to the new configuration A B C D with no accompanying stresses since the expansion is completely unre- strained. If bent AlBlClDl is fixed at the ground, expansion of the bent will occur as shown in Figure 4b. In its deformed position (AlBlClDl) the bent will be under stress. Supports A1 and D1 will develop horizontal thrust H1 and fixing moment M, thus subjecting beam BlC1 to an axial compressive force. Due to this internal force, the expansion BlBl of Figure 4b will be smaller than BB of Figure 4a. If, on the other hand, the bent is hinged at the bottom, as shown in Figure 4c, there will be no support moment and horizontal thrust H2 will be smaller than H1. As a result, the compression of B2C2 will be smaller than that of BlCl. The elongation, B2B2, of Figure 4c therefore will be greater than BlBl of Figure 4b but 17

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smaller than BB of Figure 4a. Similarly, the compression of B2C2 will be between the zero compression of BC and the compression HI of BlCl. B, A, ~ 1 B C A' Bath --- C \ B1 C1 ~ \ \ A D C ' j H it ASH I H2 ~ M M ~ 1 B2 ' ~C2 lB: C2 1 1 1 l l ~ A2 D2 ~ (a) (b) (c) 1 H2 ' FIGURE 4 Analysis of one-bay simple bent subjected to uniform temperature change: (a) bent completely unrestrained; (b) bent fixed at ground; (c) bent hinged at ground. In the multistory and multibay frame conditions illustrated in Figure 5, a temperature increase will produce a pattern of stresses and deformations similar to those of the single bent of Figure 4. Although it is more difficult to visualize the mechanics, it remains possible to predict the relative intensities of the thrusts and hori- zontal joint movements. Due to symmetry, the intensity of the thrusts tH1, H2, ... in Figure 5a and H1, H2, ... in Figure 5B) is maximum at the extreme ends and approaches zero at the center. Simi- larly, the horizontal displacements of the joints within each floor are maximum at the ends and approach zero at the center of the frame. These progressive changes of magnitude are a result of the cumulative effect of elongation from the center to the outside. It can be reasoned that the beams near the center of the frame are subjected to maximum axial stresses while the columns near the edges of the frame are subjected to maximum bending moments and shear forces. However, the intensity of these forces, and the accompanying elon- gations, may vary from story to story and their assessment will require analytical study. d. Analyses of stresses and deformations in frames An analytical study was formulated and conducted by the Committee to investigate the effects of uniform temperature change on typical two- dimensional elastic frames. It was anticipated that, with the aid of a computer program for two-dimensional stress analysis, the study would facilitate the understanding and evaluation of the temperature effects on joint displacement and forces (shear, axial, and bending) in a long building. 18

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: `~ H1 7; , H2 7 H3 ~W ~ ~ Axial Forces Are / Maximum Here _ - H3 r 7= H4 - ~ ~7~ Hs ~'7 Hs ~H4 _ ~ ~ ~ ~ _ (a) ~ Axial Forces Are / Maximum Here v A l - 1 H4 Hs ~7 H5 _ _' H4 ~ _ , H1 Hr 2 H3 . H1 7- , H2 (b) H' 1 FIGURE 5 Analysis of multistory and multibay frame subjected to uniform temperature change (x = points of maximum bending moments and maximum shear forces): (a) frame fixed at ground; (b) frame hinged at ground. 19

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has a horizontal displacement ratio less than the unity value corresponding to an unrestrained frame but greater than the 0.71 value for a fixed column. If columns are hinged rather than fixed at the base, the maximum deformation of the frame at the first floor increases by approximately (87-71) ~ 23%. 71 Comparison of analyses 1-1 to 2-1 and 3-1 to 4-1 in columns 7, 8, 9, and 10 of Table 2 reveals that the maximum forces associated with the fixed-column and the hinged-column cases vary in the following ratios: For For 24 x 24-in. 16 x 16-in. Columns Columns For beam moments (70-453/45 = 55% For beam axial forces (135-77~/77 = 75% For column moments (600-2503/250 = 140% For column shears (60-19~/19 = 150% (53-25~/25 = 110% (70-25~/25 = 180% (70-75~/75 = 130% (22-63/6 = 250% Analyses of the results of the various computer runs (Table 2) allow the following observations to be made: The horizontal displacements (~) of all stories except the lower one is almost identical to the displacement, AO, that would develop in a totally unrestrained frame (i.e., ANGLO). Therefore, if both ends of a frame are equally free to displace, the hori- zontal displacement of the outside joints of upper stories will be equal to one half of the unrestrained elongation of the frame corresponding to a temperature change, At, and a coefficient of thermal expansion, a; that is, A ~At~l/2L) = 1/2~At)L, (53 where ~ = coefficient of thermal expansion, AO = horizontal displacement of a joint at a distance l/2 L from the center of the frame, and L = total length of the frame. In a frame that is restricted from side displacement at one of its two ends, the unimpeded horizontal displacement of the other end will be equal to Ao = Itch, (6) since the total expansion of the full length, L, of the frame will be reflected in displacement of only the unrestricted end of the frame. A comparison of the data obtained in analyses A-1 and A-2 indicates that for a given frame an increase in the relative cross-sectional area of the beams (not associated with a 22

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simultaneous increase in the moment of inertia of the beams) results in a substantial increase in the deformation of the first floor as well as the maximum forces developed in the frame. This is based on the fact that in temperature-induced stressing a force resulting from the structural restraints and the temperature change is proportional to the cross-sectional area of the restrained members (in this case the beams since the frame is not restrained in the vertical direction). Con- sidering that the rate at which cross-sectional areas increase for a given increase in moment of inertia is faster in concrete members than in steel members, it can be anticipated that a concrete frame will suffer somewhat more than a steel frame from the consequences of thermal expansion. Finally, a comparison of the results of analyses 1-1 and M-2 indicates that hinges placed at the top and bottom of the exterior columns of the frame reduce the maximum stresses that can be expected to develop in the frame. However, such an arrangement permits an increase in the horizontal expansion of the first floor because it reduces the resistance to such movement. These analytical studies of temperature effects have quantita- tive value in the sense that they provide valid bounds of stresses and deformations caused by temperature changes and help to define relative values of stress and deformation among the various locations of a structural frame for given ranges of temperature change. 2. The Analytical Method The difficulties of categorizing every conceivable building configuration and the complexity of the stress and deformation patterns created by thermal change effects in buildings with other than a rectangular con- figuration make it impracticable to always determine the need for expan- sion joints on an empirical basis. Also, the designer may wish to exceed the limits on lengths of a building without expansion joints established by the empirical approach described above. In all such cases a detailed structural analysis needs to be performed to support the design. The analysis should incorporate the following basic concepts of and proce- dures for the design of buildings against the effects of thermal change, regardless of building type or configuration. a. Uniform design temperature change (CA:) _ When establishing for design purposes the effective maximum tempera- ture change to which a structure is likely to be subjected, the influence of heating and air conditioning must be considered as well as the extreme range of outside temperature. However, there are no available experimental or theoretical data or procedures that will 23

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permit the quantitative evaluation of the influence of heating and air conditioning in reducing the effects of outside temperature fluctuations on a structure. Even if such could be quantified, only a portion of the dampening effect of temperature control on tempera- ture fluctuation could be recognized safely during frame design in view of the lack of temperature control during the construction phase and during periods when the heating/air-conditioning equipment is likely to be inoperative because of mechanical failure or service and maintenance operations. For these reasons, the calculation of the design temperature change for heated and/or air-conditioned buildings should include a minimum empirical coefficient that will reduce the maximum temperature change to which the structure is expected to be exposed but will not give full value to the influence of internal temperature control. In the absence of technically sound data that dictate otherwise, the uniform design temperature change, CAt, can be satisfactorily determined by considering At = (TW-Tm) or (Tm-TC), whichever is greater, and C = 1.0 for buildings not provided with temperature control, 0.70 for buildings heated but not air condi- tioned, and 0.55 for buildings heated and air conditioned. Any deviation from these values should be quantitatively justified. b. Suggested procedures for design of buildings against thermal changes As in most structural problems, the investigation of thermal effects on a building is reduced to a basic understanding of distributed forces and deformation within the structure. If deformations are resisted the resulting force system in structural members may well exceed the members' strength and cause structural failure; if they are not resisted the change of geometry in the structure may inter- fere with its overall performance. Therefore, the designer's task is to select one of the following three broad but basic approaches: (1) Limit the potential for deformation in the structure (without causing failure) by designing the appropriate members to be substantially stiffened and strengthened. (2) Allow for substantial movement of the building's structural members and nonstructural components such that ultimate building performance will not be adversely affected. Such a structure will require practically no additional strength of members to withstand thermal effects. (3) Strike a compromise between capacity to resist stress and ability to withstand deformation without sacrificing building performance. The first approach is quite unrealistic for buildings above two stories. Stiffening and strengthening the lower floors will only transfer the adverse thermal effects to the stories above, and, in effect, the upper floors would then be resting on a rigid artificial base instead of on the ~round. Conversely, this approach is inherent 24

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in low, long and massive masonry buildings that have a low tolerance to movement. Their structural frames are designed to maintain building integrity by withstanding the substantial thermal forces that challenge structural strength rather than deformation. Most field experiences indicate that buildings with continuous masonry bearing walls should be provided with expansion joints at intervals not exceeding 200 feet and with additional subjoints in accordance with the recommendations of the Brick Institute of America and the National Concrete Masonry Association.* The portions of walls at and near the intersection of two walls, surfaces likely to be weakened by numerous openings for doors and windows, and the rigid connections between horizontal elements (par- ticularly concrete or other stiff roofs) and massive walls are most sensitive to the effects of thermal change. In all such cases either expansion joints or very strong elements that can successfully resist the tendency to deform without yielding must be provided. The forces assumed to be generated under these circumstances can be derived by analyzing the forces necessary to cause elastic deformations compa- rable to the deformations caused in an unrestricted structure by corresponding temperature changes. Thus, these forces can be deter- mined by the very elementary formula: F = step, (7) where F = axial force that develops in a member when it is restrained from changing to temperature change, ~ = coefficient of thermal expansion, E = modulus of elasticity, A = cross-sectional area, and t = temperature change. If the member is completely restrained, F will become the maximum axial force which can develop in a member. However, if the member is completely free to expand, F will be equivalent to zero. In actual structures the completely restrained and completely unrestrained con- ditions are unattainable. Physically, the problem can be interpreted through two superimposed conditions. Thermal changes cause a total change of length, Ant, given by the equation: At = ALL, where L = the affected length of the member. (83 Forces resisting the change of length will cause a change in length, Off, in the direction opposite Aft; AQf is given by Hooke's Law: ~Qf EA *See p. 4 for publication references. 25 (9)

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The net change of length will be: (6tt if); (1 O) therefore, if AT = Aft (i.e., AQf = 0 or unrestricted change), then F = 0 and if AN = 0 (fully resisted change), AQf = Aft or F = step. In all real situations F therefore lies between these two extremes; i.e., O OCR for page 9
It should be noted that the maximum resisting force will depend not on the maximum tolerable fraction 0, but rather on the fraction ~ that will develop as a result of the physical restraints and redun- dancy of the structure. This value, 6, may well be substantially smaller than the maximum a structure can tolerate. The discrepancy between ~ (tolerable) and ~ (developed) is easily recognized in the low-level massive masonry building that can tolerate a great deal of elongation but is so rigid and monolithic that the ~ that does develop is a small fraction of the value that could be tolerated. The result is a buildup of very high internal forces (F) that can produce failures at the weak points of the structure. These failures are normally brittle in nature, indicating that they were caused by forces exceeding capacity rather than excessive deformation. In such cases the designer has few options for adapting his structure, which is inherently too stiff, and instead, he must design to allow expan- sion by reducing the effective length (L) that determines the funda- mental parameter, Aft = GIL. The lowest allowable value of maximum L obviously depends on the maximum expected temperature change (t) since the elongation will be proportionate to both L and t. Con- versely, when considering flexible buildings with a frame consisting mostly of slender flexural members, the designer can influence the (developed) value (i.e., the amount of the maximum change of length that will develop in a building). This can be done by an interplay of strength and flexibility. In general, strong but slender flexible members will allow greater changes of length [i.e., higher ~ (devel- oped) values], and in these situations, ~ (developed) will approach the ultimate deformation tolerable to the structure. This combina- tion will ensure that the building will perform with a minimum of distress due to temperature change. C. THE DESIGN OF EXPANSION JOINTS _ The following principles are considered basic to sound expansion joint design. 1. The width of the expansion joint should exceed the maximum potential dimensional changes by an amount sufficient to prevent the complete closing of the joint and, simultaneously, provide for construction toler- ances and nature of filler material. The maximum potential dimensional change can be computed either empirically (point 2 below) or by using the formulas given for Aft and AQf [Eq. (8) and (93] and by an accurate evaluation of the forces, F (see p. 25), in the structural system through appropriate structural analysis. 2. The upper bound, UB, of the maximum joint closing obviously will depend on the coefficient of thermal expansion of the material of the frame, the maximum temperature change (i.e., the effective temperature increase Ate = TW-Tm) that the structural frame is assumed to undergo, and the 27

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effective length, L, of the structural segments converging at the joints. The effective length, L, can be computed utilizing the following empirical guidelines 'in conjunction with Figure 6: a. If both the building segments converging on the joint have symmetri- cal stiffness, only one half of the dimensional change of each segment will affect the joint separation (Figure 6a), hence, L = 1/2 (L1+L23. (11) b. If, however, either segment has one end substantially stiffer than the other, the dimensional change resulting from temperature fluc- tuation will be distributed unevenly between the two ends of such a segment with comparatively less deformation 'developing at the stiff end. In such cases, L = 1/2 tKL1+L2), (12) where K = 1.5 (i.e., the length of the unsymmetrically stiff segment will be increased by 50 percent if the stiff end is farthest away from the joint; see Figure 6b) or K = 0.67 (i.e., the length of the unsymmetrically stiff end will be decreased by 33 percent if the stiff end is the one abutting the joint; see Figure 6c). L:: L 1 )(: L2 l (a) (b) | L1 al L2 l (c) FIGURE 6 Computation of effective length L of building segments adjacent to the expansion joint: (a) building segments with symmetrical stiffness, L = 1/2 (L1+L23; (b) one segment with unsymmetrical stiffness and the stiff end farthest from the joint, L = 1/2~1.5L1+L23; (c) one segment with unsym- metrical stiffness and the stiff end abutting the joint, L = 1/2~0.67L1+L2> 28

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The coefficient of thermal expansion of concrete and steel (the principal materials used for buildings with column-and-beam frames) can be con- sidered approximately the same and equal to 6-10-6 per degree Fahren- heit. The upper bound, UB, of the maximum joint closing can be computed from the expression: UB = (6 10 )Ate-L, where Ate and L are as previously defined. (13) 3. The actual width of the expansion joint must be greater than the UB to provide for construction tolerances and for the width and compressibility or expandability of the joint filler. The UB is likely to develop in those buildings that are not temperature controlled; for this condition, a joint width equal to twice the UB probably would be required. Because the maximum horizontal movement in temperature-controlled buildings is expected to be lower than that in noncontrolled buildings,the joint width can be narrower. Joint widths equal to 1.7 times the UB for buildings heated but not air conditioned and equal to 1.4 times the UB for build- ings both heated and air conditioned should be sufficient. 4. For buildings with exterior bearing walls of continuous clay masonry the required joint width, W. can be determined by the expression: W = CleL(50F+~\te) (4~10 ), where C1 = 2.0 for buildings with no heat control, 1.7 for buildings heated but not air conditioned, and 1.4 for buildings both heated and air conditioned and Ate and L are as previously defined. (14) In this expression 4~10 6 is a coefficient approximateing the coefficient of thermal expansion of clay masonry. The term 50 OF in the factor (50F+Ate) represents a temperature equivalent to the dimensional changes resulting from potential of swelling of clay masonry under mois- ture conditions. Finally, the coefficient C1 is intended to provide for construction tolerances, compressibility and expandability of the joint filler, and the dampening effects on the effective Ate of temperature control. The values for C1, which are based on the judgment of the Committee members, are comparable to the correction factors recommended for use with Figure 1 when buildings are provided with temperature control. The rationale for the values is the same as for the Figure 1 correction factors. Notwithstanding the above procedures, practical limits on the width of an expansion joint need to be adopted. It seems reasonable that, in general, an expansion joint should not be narrower than 1 inch. On the other hand, an expansion joint that, according to the computations above, requires greater than 2 inches of width should be specially designed to 29

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ensure that these relatively large dimensional changes can take place without any loss of building serviceability. During architectural design and filler material selection, care must be taken to ensure that the functional and aesthetic requirements of the building are satisfactorily met and that the joint will be sufficiently flexible to guarantee durable and trouble-free operation. 6. It is necessary that an expansion joint extend all the way to the footing because, as is indicated by the analytical studies conducted on two- dimensional frames, a large percentage (on the order of 75 percent) of the maximum dimensional change due to temperature fluctuation develops in the lowest story of a structure and almost the maximum change develops in all the stories above. 7. An expansion joint requires protection from potential accumulation of foreign material or debris that could interfere with the proper func- tioning of the two parts of the joint. The joint should be designed in such a way that it can be maintained and inspected without difficulty to ensure that it remains effective. D. AREAS OF FUTURE RESEARCH For convenience, the scope of the Committee's study was limited to expansion joints that separate structural frames of buildings in order to relieve excessive temperature-induced stresses. The practices and procedures sug- gested herein are considered to be sound and should guide the designer in producing a more efficient building system than in the past. Also, they have been based for the most part on experience and educated judgment. Tem- perature fluctuations also effect dimensional changes in the vertical direc- tion and the performance of the nonstructural building components; while such effects are not considered in this report, they cannot be ignored during design. Execution of the most efficient design with respect to the total effects of temperature changes on building performance requires criteria developed on a data base more technically sound than exists at present. Thus, research should be undertaken immediately to provide urgently needed information and data that: 3. 1. Reflect building damage directly attributable to temperature fluctuation. Permit the correlation of ambient temperature with temperatures of building components (structural and nonstructural) at the periphery and within buildings for different building types and materials. Permit the correlation of ambient temperature fluctuations with tempera- ture gradients existing within building components under different conditions of exposure and insulation of these components. 30

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Also needed are analytic and experimental investigations that will lead to the correlation of stresses in the various building components with the different patterns of temperature fluctuations and gradients and with the different types of assembly component (connectors). Buildings supported on masonry walls require special examination since effects of temperature changes on the performance of such buildings will vary according to the type of masonry material or combinations of material used. Each type and combination should be investigated with respect to construc- tion details, connections of walls to horizontal and vertical components (roofs, floors, walls, and partitions at right angles), optimal spacing of joints, and extent of joints. 31

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