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OCR for page 9
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
OCR for page 10
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
OCR for page 11
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.
OCR for page 12
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
OCR for page 13
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
OCR for page 14
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
OCR for page 15
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
OCR for page 16
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
OCR for page 17
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
OCR for page 18
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
OCR for page 19
: `~
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
OCR for page 22
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
OCR for page 23
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
OCR for page 24
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
OCR for page 25
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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Representative terms from entire chapter:
expansion joints
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
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
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
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(50°F+~\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
(50°F+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
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
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
