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Cracks, movements and joints in buildings: record of the DBR Building
Science Seminar, autumn 1972
Baker, M. C.; Hutcheon, N. B.; Latta, J. K.; Handegord, G. O.; Plewes, W.
G.; Crawford, C. B.
NATIONAL RESEARCH COUNCIL OF CANADA DIVISION OF BUILDING RESEARCH
CRACKS, MOVEMENTS AND JOINTS TN BUILDINGS
Record o f t h e DBR B u i l d i n g S c i e n c e Seminar, Autumn 19 72 P r o c e e d i n g s No. 2 o f t h e D i v i s i o n o f U u i l d i n g Research Ottawa, September 1976
The DBR Building Science Seminar of Autumn 1972 dealt with the
topic "Cracks, Movements, and Joints in Buildings." It was presented
twice in Ottawa and once in Calgary.
As there has been a continuing demand for information on this
topic it was decided to publish a record of the talks given at these
meetings. The papers presented in this report are essentially the
slide/talks as given, with only minor editing. All the talks save
one
-
the resume by M.C. Baker
-have been included. In the case of
two of the talks
-one by J.K. Latta and one by G.O. Handegord
-
CBD 171 and 155 have been included in their stead because these two
publications of the Division of Building Research present essentially
the same information in a more concise form.
Ottawa
September 1976
C
.
B. Crawford
TABLE OF CONTENTS
-
...
I n t r o d u c t i o n t o t h e Problem M.C. Baker ( I )...
S t r e s s - S t r a i n R e l a t i o n s h i p s N . B . Hutcheon...
Dimensional Changes due t o Temperature J . K . L a t t a ( I )
...
Dimensional Changes due t o Moisture G . O . Handegord ( I )
...
D e f l e c t i o n s due t o Loads W . G . Plewes ( I ) V e r t i c a l Movement o f B u i l d i n g
. . .
Frames and Cladding W . G . Plewes (11)
. . .
Deformations due t o Foundation Movements C . B. Crawford
...
The Accommodation o f P o t e n t i a l Movements J . K . L a t t a (11) The Design of W e a t h e r t i g h t J o i n t s
...
J . K . L a t t a (IV)...
The R e c o g n i t i o n o f J o i n t s i n t h e System M . C . Baker (11) I n a c c u r a c i e s i n C o n s t r u c t i o n (CBD 171)
. . .
J . K . L a t t a...
J o i n t Movement and S e a l a n t S e l e c t i o n (CBD 155) G . O . Handegord and K . K . K a r p a t i
D i v i s i o n o f B u i l d i n g Research
INTRODUCTION TO THE PROBLEM OF CRACKS, MOVEMENTS AND JOINTS IN BUILDINGS
by Maxwell C. Baker
Based on s l i d e / t a l k p r e s e n t a t i o n g i v e n a t t h e DBR B u i l d i n g S c i e n c e Seminar,
"Cracks, Movements and J o i n t s i n B u i l d i n g s
,"
Autumn 1972.Baker I
INTRODUCTION TO THE PROBLEM OF CRACKS, MOVEMENTS AND JOINTS IN
BUILDINGS
by Maxwell C. Baker
A whole building is produced by assembling small or large
building components, necessitating joints between adjoining
components. Stated in other terms, we can say that joints are
required in building design to assist the designer to obtain
functional and visual flexibility, when combining building
materials and components to produce whole buildings. Joints also
provide locations where movements of components can be accommodated,
to prevent or control cracking of materials.
Cracks in materials are due to forces set up by restraints to
movement, occasioned by fixing in relation to adjacent components,
that are sufficient to break chemical and physical bonds between
the atoms and molecules of the materials. Movement and dimensional
changes take place in materials because of intentional or
unintentional loading, or because of chemical and physical changes
occasioned by the environment to which they are exposed.
It is a common fallacy to think of materials as good or bad,
durable or non-durable, strong or weak as if these were inherent
properties of the materials. It is seldom that simple or definite.
These terms are relative; durability is related to the conditions
of exposure. The service life for any particular usage will depend
on the severity of the conditions to which the material is exposed.
No materials are infinitely strong; all will crack and fail under
some definite level of applied load. If we do not want materials to
crack, we must assure that they are not subjected to that level of
1
oad ing
.
Materials are broken down in nature by progressive cracking as
a result of chemical, physical and biological activity. Given time,
mountains can be worn away to dust. Time is also a factor in
relation to changes in properties sometimes leading to deterioration
that takes place for all practical materials used in buildings.
What we attempt to do to increase service life is to control the
rate of change and prevent cracking by limiting or controlling the
forces. Although we cannot prevent movement it can usually be
allowed for by suitable joints and connections. When we are
unsuccessful in predicting where joints are required, Nature often
indicates by cracking where they should have been located.
Design that does not recognize the nature of materials is unlikely to produce problem-free buildings, except by chance. Even when the designer knows as much as possible about the
properties of materials, he still may not always be successful in combining them into building elements if they are later subjected to forces that he was not able to foresee. Since much knowledge is available about materials, and there is general understanding of failure mechanisms and the forces to which materials are subjected, there would appear to be no excuse for gross failure. Anticipated minor failure might sometimes be tolerated when
economies or some other such factor dictates choice.
That many buildings become disfigured soon after their completion from cracking of glass and finishes, spalling of surfaces, failures of sealants at joints, and occasionally the breaking loose of a material from those surrounding it is an indication that there may be considerable misunderstanding among designers concerning cracking and movement of building materials.
Obviously no designer would knowingly design buildings so that materials rapidly crack and deteriorate immediately after completion.
If such things happen, and they do all too frequently despite the availability of unprecedented expertise and knowledge, it must be due to the designer's inability to predict the result of his design decisions and his choices and arrangements of materials or his inability to control the construction process.
Cracks and spalling of building materials are almost always unsightly. In addition, cracks on exterior finishes usually represent a loss of weathering quality, which can allow rain penetration and severe wetting. This in turn could lead to freeze-thaw breakdown of the material and serious structural weakening of a building element, as deterioration proceeds with further wetting.
Mechanisms Res~onsible for Cracking
The mechanisms responsible for cracking of materials are
usually associated with deformations in materials due to changes in moisture content and temperature, deflections under loading, or chemical action. Many common building materials have a porous structure and can absorb water more or less readily. Most
materials expand with wetting and contract again on drying. Some materials, such as concretes, mortars and plasters have a very high initial shrinkage on drying, that is far in excess of any following reversible deformation. Wetting or drying on one face of a material can cause warping.
Temperature changes also tend to cause deformations in materials, with expansion resulting from heating and contraction
Baker I
from cooling. For materials that are unrestrained and free to
move it is easy to calculate the amount of deformation for any
range of temperature to which the material is exposed. If the
materials used are restrained, however, considerable judgement and
experience are necessary to estimate the stress induced in a
component, or the actual movement of the component. Variation of
temperature from face to face can also cause warping.
Deflections of structural elements or components may result
from soil settlement, wind pressure or vertical loading. Such
deflections will be transferred to the building components of the
enclosure through the fixings. This may cause stresses to develop
in the components or differential movement between the components.
Shrinkage during the curing process, post hydration,
carbonation, corrosion or some other chemical action on materials
can also cause irreversible dimensional changes that can affect
the supporting structure, or that may directly affect the
components
Cracking occurs when stresses are induced in the material that
are greater than the strength of the material. The induced
stresses may often be due to restraints to deformation that is
provided by the fixing of the material to adjacent materials. When
cracking occurs there is a re-distribution of stress; the amount of
opening of the cracks will depend on how the new system adjusts to
resist the loads. It is possible to avoid cracking by using a
material strong enough to resist the stresses developed.
It is also possible to control the size of cracks by
reinforcing a weak tensile material with materials having high
tensile strength.
Areinforced concrete beam is an example of the
crack control technique by reinforcement. The steel wires or rods
used for this purpose do not stop the cracking. In fact they act
to restrain movement and so induce stress in the concrete. Once
cracking has occurred, the tensional stress previously developed in
the concrete is taken up by the reinforcement which tends to keep
the cracks from opening. Individual cracks will probably be very
narrow, but there are likely to be a large number of them
distributed along the bottom of a beam.
Traditional vs Industrialized Building
Traditionally, buildings have always had joints and this will
continue in industrialized building. In traditional building all
materials were man-handled which meant small components put
together with
amultitude of joints, e.g., a typical masonry
building. This meant a large linear footage of joints, but also a
small amount of movement at each joint. Because of this, and
perhaps some other reasons, such walls usually performed adequately
except where weathering conditions were extremely severe.
Many modern buildings and industrialized building systems utilize large components that greatly reduce the linear footage of joints, but this results in differential movements at the joints that may be very large. The traditional methods also of course allowed for some adjustment when laying up the materials on site, whereas large component construction is only viable if cutting and fitting is largely eliminated from site operations. For these reasons the consideration of joints and joint
performance has become an essential and unavoidable aspect of building design activity.
If the designer is to take systematic account of the factors that are fundamental to the process of fitting and joining
building components, he obviously must be able to identify them. This is easy to state but in fact may not be easy to do, since
specific knowledge of building movement and the interrelations of the various types of building movement is fairly limited and only recently has it become the object of study by building research organizations and others. There are also various kinds of inaccuracies in buildings that must be studied and defined.
There may be considerable difference between the intended and the actual sizes and positions of building components. This is due to manufacturing inaccuracies and inaccuracies of setting out and erection on construction sites. These inaccuracies might be described as man-made, and may be avoidable to some extent. In addition, there are unavoidable dimensional changes from thermal and moisture conditions that relate to the inherent
properties of the materials used. Although unavoidable, they are reasonably predictable and can be allowed for.
Location and Requirements
Convenience and cost are both involved when considering the location of joints. For materials manufactured off-site, the size of components may well be determined by transport restrictions. On-site, the factor that determines the size is likely to be the handling ability, which relates to the convenience of the
contractor. When man handling is involved, components need to be restricted to relatively small or, if large, relatively light
units. Cranes are almost universally used nowadays on construction, however, so that large and heavy units can be lifted. Even if a whole building or a whole wall cannot be made of one piece, the designer today can consider making large areas of the wall from one material without joints. The joints that are provided between components might be described as convenience joints.
There are some other building joints that are essential: where there is a change in construction material or a change of component type. This occurs, for instance, where the designer puts windows or doors in walls, thus necessitating a joint between
Baker I
t h e g l a s s and frame, and between t h e frame and w a l l . S i m i l a r l y , j o i n t s a r e unavoidable a t t h e j u n c t i o n o f w a l l s t o r o o f , w a l l s t o f l o o r s , and p a r t i t i o n s t o f l o o r s and c e i l i n g s . When t h e t h i c k n e s s o f t h e e n c l o s u r e elements i s made o f o f more t h a n one m a t e r i a l , t h e r e a r e a l s o j o i n t s o r i n t e r f a c e s between t h e m a t e r i a l s , e . g . , between i n s u l a t i o n and a back-up w a l l .
A l l o f t h e s e e s s e n t i a l j o i n t s s h o u l d be c o n s i d e r e d by t h e d e s i g n e r . The i n t e r i o r j o i n t s have been handled r e a s o n a b l y
s u c c e s s f u l l y i n a t r a d i t i o n a l way by t h e d e v i c e s o f a r c h i t e c t u r a l d e t a i l i n g , such a s , cove and b a s e mouldings and c o v e r s t r i p s . These have g e n e r a l l y proved s a t i s f a c t o r y from an a e s t h e t i c p o i n t of view, and where s e p a r a t i o n f u n c t i o n s o f such j o i n t s have n o t been c r i t i c a l . The r e q u i r e m e n t s f o r j o i n t s i n t h e e x t e r i o r e n c l o s u r e s o f b u i l d i n g s a r e , however, u s u a l l y more c r i t i c a l .
One approach t o l o c a t i n g j o i n t s i n t h e e x t e r i o r o f an
e n c l o s u r e i s t o make t h e convenience j o i n t s ( n e c e s s a r y t o reduce components t o a r e a s o n a b l e s i z e ) c o i n c i d e w i t h t h e e s s e n t i a l j o i n t s t h a t o c c u r a t changes of m a t e r i a l s . T h i s may mean having j o i n t s a t t h e j u n c t i o n s o f windows and w a l l p a n e l s . T h i s may n o t n e c e s s a r i l y be t h e most l o g i c a l approach; i n some i n s t a n c e s it may be b e t t e r t o produce w a l l p a n e l s t h a t i n c o r p o r a t e windows and d o o r s , s i n c e t h e c r i t i c a l j u n c t i o n can t h e n b e factory-made under more o r l e s s i d e a l c o n d i t i o n s . The movement o f r a i n w a t e r o v e r t h e f a c e o f t h e b u i l d i n g and o v e r t h e p a n e l s and j o i n t s , however, must b e c a r e f u l l y c o n s i d e r e d i f s t a i n i n g and r a i n p e n e t r a t i o n a r e t o b e avoided.
The e x t e r i o r e n c l o s u r e (wall o r r o o f ) must a c t a s a s e p a r a t o r o f two environments, t h e one we wish t o m a i n t a i n i n s i d e t h e b u i l d i n g , and t h e one t h a t r e s u l t s a s a consequence o f l o c a l c o n d i t i o n s and c l i m a t e . A s a s e p a r a t o r o f two environments it h a s c e r t a i n
performance r e q u i r e m e n t s . I t must c o n t r o l a i r , h e a t and w a t e r vapour flows; and p r e v e n t r a i n , r a d i a t i o n , n o i s e , f i r e , vermin and i n t r u d e r p e n e t r a t i o n , w h i l e p r o v i d i n g s t r e n g t h and d u r a b i l i t y , and a p l e a s i n g appearance. And a l l t h i s a t an economical c o s t . J o i n t s between e x t e r i o r w a l l components w i l l have one o r more o f t h e same r e q u i r e m e n t s , depending on t h e d e s i g n , and may i n some c a s e s have t o s a t i s f y a l l o f t h e r e q u i r e m e n t s .
Types o f &Toints
There a r e s o many c l a s s e s and t y p e s o f j o i n t s r e l a t e d t o t r a d i t i o n a l a s well a s t o modern b u i l d i n g , t h a t it i s d i f f i c u l t t o c l a s s i f y them i n a meaningful way. For d i s c u s s i o n p u r p o s e s , however, a l l j o i n t s might be s e p a r a t e d i n t o two fundamental t y p e s r e l a t e d t o t h e a d j a c e n t components: j o i n t s between i n t e r l o c k i n g components and j o i n t s between s e p a r a t e d components. I n t e r l o c k i n g j o i n t s would i n c l u d e t h o s e where components p e n e t r a t e i n t o each o t h e r (tongue and grooved b o a r d s ) , o v e r l a p a t t h e edges ( s h i n g l e s o r t i l e s ) o r
TONGUE SHIPLAP SHINGLE & GROOVE INTERLOCKING COVER PLATE S E A L A N T G A S K E T S T W O S T A G E
Baker I
Slide 1
Slide 2
overlap and are mechanically fastened (coverplate applications in
engineering).
(Slide 1)
When the components are separated by a space, a degree of
continuity as required by the joint function can only be obtained
by filling the space between the flat edge faces, or between
grooved or rebated edge faces with some other material (Slide 2).
Components that interpenetrate require a precision in joint
geometry and a degree of dimensional control that may be difficult
to attain with many materials and components.
Overlapping joints for siding and roofing are a successful
age-old solution to joining problems that still deserves serious
consideration for large components and heavier construction.
No great accuracy is required in dimensions and for some
applications no other product is required to fill the space
between units. Movement can be allowed for in the method of
fixing and one component can slide over the other at the overlap.
The coverplate-type joint is not used very much in building, but
is commonplace in engineering and might well be used to a greater
extent.
Tolerances
For the separated component type of joint to perform as
intended, the width of the separation must be within certain
limits. The lower limit may be dictated by the least width of
sealant material that can accommodate the expected movement or by
the least width that can accommodate gaskets and baffles that are
to be used. If a gun-applied sealant is to be used, there will
be a narrow limit below which application is not practicable and
a wide limit above which the material may slump. If too wide,
gaskets will not have sufficient lip seal pressure and baffles in
grooves may not engage adequately.
Two things are involved: the width of the joint required for
successful performance of the joint material, and the width
dictated by the unavoidable inaccuracies of manufacture and
construction. The first is very simple and depends largely on the
nature of the sealant materials. It is easy therefore to
prescribe the joint width and the range of movement that the joint
filler can tolerate. Putty for instance has a movement capability
of +1 per cent and polysulfide about +25 per cent.
Achieving the joint width required may not be so easy.
No component can be economically manufactured exactly to the
design dimensions and unusual care is required to achieve precise
placement of a component in its space in the assembly. Some
degree of inaccuracy is inevitable both in manufacture of
components and in their assembly on site. If the inaccuracies
are not kept within limits, problems of fit arise which slow down
P A N E L F I T T I N G B E T W E E N O T H E R P A N E L S 2 C R I T I C A L D I M E N S I O N S C U P B O A R D F I T T I N G R E C E S S I N W A L L 2 C R I T I C A L D I M E N S I O N S 6a - B a k e r I
Baker I
Slide 3
Slide 4
construction, make interchangeability of components impossible, and even affect the strength and performance of the wall or building as a whole.
At present in the construction industry in most countries, there is limited information available on tolerances, little agreement on appropriate values and seldom are they appropriately specified. Generally also architects believe that the standards of accuracy achieved on construction are unsatisfactory, and contractors think that architects have a poor understanding of construction and often specify levels of accuracy that are unnecessarily high or completely unattainable.
Dimensional Constraints
This brings up the whole question of the need for accuracy, and the possibility of avoiding the need for accuracy. Every
detail of the building must be carefully looked at by the designer, in relation to the number of dimensional constraints that are
required, and thus the need for close dimensional control. If the constraints can be reduced the problem of fitting will be eased.
Let us now consider the constraints that are involved in fitting of components. In the simplest case of fitting a cupboard unit onto a wall, or two components together that are lap-jointed, dimensional control is not critical. (Slide 3 ) Dimensional
control becomes important when a component has to be fitted between other components, or a cupboard has to be fitted into a recess in a wall (Slide 4). The dimensions of the gap or the recess, and the dimensions of the component or cupboard, at least in one
I I I I ' I
//
P R E F A B R I C A T E D S T A I R C A S E I N W E L LSlide
5
Slide 6
Baker
I
direction become critical and tolerance control is necessary. When a window has to fit into a wall opening, or a floor-to-ceiling cupboard has to fit into a wall recess, there are four critical dimensions involved and fitting may become difficult. (Slide
5)
When a component has to fit in three directions as would be involved for a prefabricated staircase required to fit a floor opening and match floor levels at top and bottom, the problem is extremely difficult and expensive fitting on site is almost certain to be required (Slide 6). This type of three-dimensional fit
frequently arises in building design and the designer should be constantly on the lookout for such problems. Constraints can be reduced to a minimum by prgviding dimensional adjustments in some of the directions involved.
The foregoing has outlined some of the many factors involved in the design of buildings to control movements and reduce or eliminate undesirable cracking. Most of these factors will be
considered in greater detail in the other talks in these Proceedings. The problem is one of providing the designer with as much knowledge as possible about this important topic, so that he can apply it to specific building situations. He is the one who usually must make decisions on the selection and combination of materials, and is often the only one in a position to judge what is intended and what is likely to be satisfactory. Obviously if he can modify his designs to prevent cracking and deterioration of materials and components, he will want to do so.
D i v i s i o n o f B u i l d i n g Research .. STRESS-STRAIN RELATIONSHIPS by N. B. Hutcheon Based on s l i d e / t a l k p r e s e n t a t i o n given a t t h e DBR B u i l d i n g S c i e n c e Seminar,,
"Cracks, Movements and J o i n t s i n B u i l d i n g s , Autumn 1972.
S l i d e 1
S l i d e 2
S l i d e 3
STRESS-STRAIN RELATIONSHIPS by N.B. Hutcheon
A l l m a t e r i a l s e x h i b i t small dimensional changes w i t h changes
i n load and temperature. Some m a t e r i a l s move w i t h changes i n moisture c o n t e n t . Others expand o r c o n t r a c t because of chemical o r p h y s i c a l e f f e c t s brought on by t h e c o n d i t i o n s t o which t h e y a r e exposed. This means, i n t u r n , t h a t e v e r y component of a b u i l d i n g , and indeed t h e b u i l d i n g i t s e l f , i s c o n s t a n t l y changing i n dimension.
The obvious q u e s t i o n a t t h i s p o i n t i s , "How does one judge whether t h e s e dimensional changes a r e important?" The answer cannot always be s i m p l e , s i n c e t h e r e can be s o many d i f f e r e n t e f f e c t s . I n g e n e r a l , t h e d e s i g n e r must be concerned t h a t he h a s a n t i c i p a t e d a l l t h e important ones and h a s planned s o t h a t t h e y can be accommodated i n a t o l e r a b l e way i n h i s d e s i g n .
We must, i n a t t e m p t i n g t o e s t a b l i s h a q u a n t i t a t i v e b a s i s f o r t h e e v a l u a t i o n o f movements and c r a c k i n g , i n q u i r e i n t o t h e
t o l e r a b l e and l i m i t i n g s t r e s s e s and s t r a i n s f o r m a t e r i a l s . Engineering mechanics i s based e x t e n s i v e l y on t h e assumption of an i d e a l m a t e r i a l obeying Hookets Law, which s a y s t h a t deformation o c c u r s i n p r o p o r t i o n t o l o a d . The c o n c e p t s o f stress and s t r a i n , d e f i n e d i n terms of u n i t dimensions, a r e a s s o c i a t e d w i t h t h i s s u b j e c t , a s i s t h a t o f modulus of e l a s t i c i t y which may be regarded a s t h e h y p o t h e t i c a l s t r e s s r e q u i r e d t o produce u n i t s t r a i n i n u n i t l e n g t h o f m a t e r i a l .
Real m a t e r i a l s do n o t always obey Hookets Law, b u t most o f them do s o , o r can u s e f u l l y be assumed t o do s o , o v e r t h e u s u a l working s t r e s s r a n g e s . The c h a r a c t e r i s t i c performance of modern s t r u c t u r a l s t e e l s i s shown i n S l i d e 2. We may n o t e t h a t t h e average s t r a i n a t f r a c t u r e i s about 0.20 ( i . e . , 20% e l o n g a t i o n ) . When t h e s t r e s s s t r a i n curve (shown h e r e f o r t e n s i o n only) i s drawn t o accommodate t h i s r e l a t i v e l y l a r g e s t r a i n , t h e e l a s t i c p o r t i o n becomes h i g h l y compressed. The expanded s c a l e of S l i d e 3
shows t h i s e l a s t i c p o r t i o n more c l e a r l y . The s t r a i n a t t h e y i e l d p o i n t f o r a G40.12 s t e e l i s seen t o be about 0.0015, o r 0.15%. The g r e a t c a p a c i t y of s t e e l t o y i e l d p l a s t i c a l l y b e f o r e f a i l u r e e n a b l e s it t o a d j u s t t o c o n c e n t r a t i o n s of s t r e s s and t o w i t h s t a n d shock loads.
It was evident in Slide 2 that an A514 steel, with a yield point of 100,000 psi, shows almost the same elongation at
Slide
4
fracture (i-e., 20%) as the G40 steels of only half the strength. In annealed carbon steels, however, as the carbon content and the strength are increased, the elongation at fracture decreases. That is, such steels become harder and stronger, with acharacteristic change in the nature of the fracture. Although the strain at yield increases in proportion, as the yield
strength increases, the capacity to adjust to stress concentrations through local, plastic yielding, and to absorb impact loads, is decreased.
Materials which do not deform plastically to any appreciable extent are said to be brittle and are very sensitive to impact loads and to the effects of stress concentrations, such as those Slide 5 produced intentionally in the cutting of sheet glass. Concrete
is moderately brittle. It usually deviates markedly from Hooke's Law, exhibiting a non-linear stress-strain curve shown somewhat exaggerated in Slide
4.
The modulus of elasticity must now be approximated by a tangent (OT) or a secant (OD) to the curves, as appropriate.It is useful, at this point, to look at a comparison of the relevant properties of some common materials, as in Table I. The values given must be regarded as average or typical ones, since there can be wide variations for any one material.
The yield point of ordinary mild steel is 30,000 psi and designs are usually based on stresses somewhat below this. The corresponding strain is 0.001 or 0.1%. That is, it is 1 in 1,000 or about 1 inch in 100 ft. The elongation at rupture, we may recall from previous slides, can be up to 200 times this value, i.e., up to 20%. This capability of steel to deform plastically is one of its useful properties, since it provides for the
redistribution of stresses and loads, and imparts a large measure of protection against sudden failure. As we shall see, however, the limiting plastic deformation of a component is affected by a number of factors and so may not always be in direct proportion to that shown in a tensile test.
Aluminum has about the same useful working stress as steel and can also be made to deform plastically. Since its modulus of elasticity is only one-third of that of steel, it always deforms three times as much, for the same stress. This can be an
important consideration in design. The strength and elongation characteristics depend on composition and treatment and, as in the case of steel, increased strength is usually accompanied by reduced elongation at fracture.
Hutcheon TABLE I S t r e n g t h and Deformation o f M a t e r i a l s M a t e r i a l Approximate Working Modulus o f L i m i t E l a s t i c i t y , p s i S t r e s s , S t r a i n , p s i % Common D u c t i l e Metals S t e e l - o r d i n a r y 30 X
l o 6
30,000T 0.10 Common B r i t t l e B u i l d i n g M a t e r i a l s Glass-
o r d i n a r y 10 xlo6
4,000T 0.04 Concrete-
o r d i n a r y 2 . 5 x 10 6 2,500C 0.10 250T 0.01 Brick Dense Limestone 3 Xl o 6
6 , OOOC 0.20 SOOT 0.016 Some Organic M a t e r i a l s Reinforced P o l y e s t e r 1 . 5 xlo6
15,000T 1 . 0 Range of P l a s t i c s Unreinforced Douglas F i r Compr. a l o n g f i b r e s 1 . 5 xlo6
4,000 0.25 Compr. a c r o s s f i b r e s 65 0 G l a s s , c o n c r e t e , b r i c k and s t o n e a r e r e l a t i v e l y q u i t e b r i t t l e . G l a s s i s unusual because o f i t s extreme b r i t t l e n e s s , b u t it a l s o has a q u i t e s u b s t a n t i a l t e n s i l e s t r e n g t h , h i g h enough t o make it u s e f u l i n r e s i s t i n g t e n s i o n and bending l o a d s , a s w e l l a scompressive ones. O r d i n a r y c o n c r e t e h a s a working l i m i t s t r a i n o f about 0.1%. (Concrete, i n g e n e r a l , f r a c t u r e s a t s t r a i n s o f 0.4% t o 0.8% i n compression.) C o n c r e t e , b r i c k and l i m e s t o n e , a s shown, have t e n s i l e s t r e n g t h s which a r e no more t h a n 10% o f t h e i r
compressive s t r e n g t h s , making them prone t o e a r l y c r a c k i n g when loaded i n t e n s i o n .
Hutcheon
The term "plastics1' covers a wide range of organic materials, often with markedly different properties, which are also capable of modification through changes in formulation and processing. They are characterized generally by low modulus of elasticity and thus exhibit quite high strains at working stress levels. We may note that even when reinforced with glass fibre, a polyester will exhibit up to 1% elongation at the working limit, compared to steel and concrete at 0.1%.
Wood, being a natural product, varies both within species as well as between species. Its strength and modulus vary also with moisture content and other factors, and finally it has a marked variation in properties measured by loading parallel to the grain from those measured transverse to the grain. The strengths and moduli measured along the grain reflect the fibre strength, while the much lower values cross-grain result from crushing of the wood cells. The transverse strengths and corresponding moduli are less than those longitudinally by factors of 5 to as much as 20.
The strain limits we have been discussing are valid as a basis for assessing the importance of strains imposed as a result Slide 6 of temperature, moisture and other changes
--
to be discussed inmore detail in subsequent presentations. There are, however, some complications to be noted. When a material tends to shrink due to cooling or drying under restraint of some kind, tensile stresses and strains are induced in the same way as if the material were loaded progressively. If carried far enough, tensile failure in the form of cracking occurs. Thus, instead of the material being strained until it increases to some new dimension, as shown in Slide 6, it shrinks so that its new, unstrained dimension decreases while it is held at its original length.
Materials which are perfectly brittle, that is, which fail in tension without plastic deformation, will follow closely the
Slide
7
simple prediction of failure by cracking based on an experimentally determined failure stress. Materials which only show moderate plasticity at high stress levels show a similar kind of brittle fracture, but those like steel, which are highly ductile, deform and neck down locally before final fracture. The results ofloading the cast iron and steel specimens of Slide
7
are shown in Slide 8 Slide 8. The normal cast iron and steel specimens showcharacteristic brittle and ductile failure patterns. In the sharply notched steel bar, the plastic deformation is confined to the root of the notch so that the overall elongation is greatly reduced. The strength, however, is increased since there is little reduction in cross-section. Thus, a notched steel bar exhibits a kind of false brittleness.
Slide 9 When we look more closely at the stresses in a load-carrying member having a marked change in cross-section, we find that there
Hutcheon
a r e v e r y s e r i o u s s t r e s s c o n c e n t r a t i o n e f f e c t s . A s we have j u s t seen, t h i s may have l i t t l e i n f l u e n c e on breaking load o r may a c t u a l l y i n c r e a s e i t , i n t h e c a s e o f s t e e l , which can withstand v e r y g r e a t p l a s t i c deformation l o c a l l y , b u t t h e o v e r a l l s t r e t c h i n g o r e l o n g a t i o n o f t h e member may be g r e a t l y reduced a t f a i l u r e i n comparison t o t h a t o f a member which i s o f t h e same c r o s s - s e c t i o n everywhere along i t s l e n g t h . B r i t t l e m a t e r i a l s , on t h e o t h e r hand, respond t o t h e s e c o n c e n t r a t e d s t r e s s e s , t h u s f r a c t u r i n g a t t e n s i l e l o a d s which a r e reduced i n t h e r a t i o o f t h e s t r e s s c o n c e n t r a t i o n f a c t o r s .
D u c t i l e m a t e r i a l s may n o t be g r e a t l y i n f l u e n c e d by s t r e s s c o n c e n t r a t i o n s under s t e a d y l o a d i n g , b u t may o f t e n be markedly S l i d e 10 a f f e c t e d by them when s u b j e c t e d t o r e p e a t e d s t r e s s c y c l e s , a s i n t h e c a s e of r o t a t i n g p a r t s which a l s o c a r r y t r a n s v e r s e l o a d s . Some e f f e c t i v e s t r e s s c o n c e n t r a t i o n f a c t o r s a t p o i n t s o f a b r u p t change i n c r o s s - s e c t i o n f o r s h a f t s a r e shown. S l i d e 11 S l i d e 12
There i s a n o t h e r e f f e c t , a time-dependent one, which can complicate f u r t h e r t h e p r e d i c t i o n o f f a i l u r e s t r a i n s , a s well a s s t r e s s - s t r a i n r e l a t i o n s h i p s . Most m a t e r i a l s when r e l a t i v e l y h i g h l y s t r e s s e d w i l l c o n t i n u e t o e x h i b i t i n c r e a s i n g s t r a i n , even when h e l d a t c o n s t a n t l o a d , i n a way which v a r i e s w i t h time and with s t r e s s l e v e l . When t h e s t r e s s i s s u f f i c i e n t l y h i g h , t h e
t e r t i a r y c r e e p s t a g e develops and l e a d s t o f r a c t u r e i n time without f u r t h e r i n c r e a s e i n l o a d . I t i s a p p a r e n t t h a t c r e e p can occur a l s o i n t h e c o u r s e o f l o a d i n g i n a t e s t i n g machine. L o a d - s t r a i n c u r v e s f o r c o n c r e t e c y l i n d e r s i n compression a t t h r e e d i f f e r e n t l o a d i n g r a t e s a r e shown i n S l i d e 12. The l i m i t i n g s t r a i n a t f r a c t u r e , i n t h i s c a s e f o r c o n c r e t e i n compressive loading, i s a f f e c t e d i n a complex way by t h e h i s t o r y o f t h e s t r a i n i n g . Creep r a t e s a r e u s u a l l y v e r y small a t low s t r e s s l e v e l s , but can be expected t o i n c r e a s e markedly f o r most m a t e r i a l s a s t h e y become more h i g h l y s t r e s s e d . The p o s s i b i l i t y o f s i g n i f i c a n t deformations, a s a r e s u l t of such i n c r e a s i n g s t r a i n , w i t h t i m e , may j u s t i f y a r e d u c t i o n i n t h e working s t r e s s i n o r d e r t o keep them w i t h i n t o l e r a b l e l i m i t s .
We must now a s k whether f a i l u r e o f a m a t e r i a l o c c u r s because of s t r c s s o r because o f s t r a i n . The answer i s t h a t , s i n c e s t r e s s and s t r a i n a r e c l o s e l y r e l a t e d , we may u s e whichever i s t h e more convenient. When we a r e a b l e t o i d e n t i f y t h e l o a d s and s t r e s s e s , we may u s e them i n p r e d i c t i n g t h e imminence o f f a i l u r e . When t h e imposed s t r a i n i s t h e f a c t o r which i s known, it w i l l obviously be more convenient t o compare it d i r e c t l y w i t h t h e known s t r a i n l i m i t s f o r t h e m a t e r i a l . Indeed, t h i s l a t t e r approach w i l l
g e n e r a l l y be t h e one most a p p r o p r i a t e f o r many j o i n t problems and f o r many o t h e r c a s e s i n which c r a c k s and movements may be involved. We may a l s o q u i t e p r o p e r l y gauge t h e s t r e s s e s involved by comparing t h e imposed s t r a i n with t h e working l i m i t s t r a i n . The phenomenon
of creep, that is, increase of strain with time alone, will be a
complication in relating stress and strain precisely in all cases
in which it occurs, since the time and history of loading must be
taken into account.
There can be a further complication in estimating the strain
levels induced in practice when the degree of restraint against
movements is not readily predictable. If there is no restraint to
the expansion or contraction of a component occurring because of
factors other than load, there will be no stress, and therefore no
strain induced. The over-all change in dimension may not be
acceptable for other reasons, but it will not induce stress or
strain. If, on the other hand, the component is fully restrained
while the conditions change, the component will be held to a
constant dimension. That is, there may be no measurable movement,
even though the material is being progressively loaded and strained
Stress and strain must always be considered in relation to the
unloaded condition. Thus it is the change in strain which will
occur when the restraint is removed, which determines the state of
stress in a material under the restrained condition, regardless of
the movement which may have taken place.
The examples thus far have ignored the difficulties of
restraining fully a member in tension so that it will fracture.
The special end conditions required in a tensile test illustrate
this. There are a large number of practical cases in buildings,
however, where the arrangement of the material or the component or
the structure is inherently self-restraining, and this produces
self-loading, or internal loading, as the shrinkages and expansions
due to temperature or moisture or other effects occur.
Considerations of restraint become very important in
estimating the failure of structural members under conditions of
fire exposure. One or two beams or columns, highly heated by a
confined fire, will tend to expand, but may be restrained by the
remainder of the structure. The rest of the structure will always
give way to some degree under the loads produced, but this may
provide little relief when it is very stiff relative to the part
under fire exposure.
On the other hand, the restraint may be
insignificant if the restraining structure deforms readily. Thus,
it is seen that the degree of restraint in any given situation is
determined by the relative ease of deformation of the restrained
and the restraining members. When both are equally resistant, the
deformations will be shared equally between them.
When the unrestrained shrinkage or expansion is uniform
throughout a piece of material, the overall change in dimension
does not result in any final strain. If, however, the movement
within the material is non-uniform, the less highly strained parts
provide restraint for the rest, stresses are produced, and in
extreme c a s e s c r a c k i n g r e s u l t s . Thus, when a s o l i d p i e c e o f m a t e r i a l i s s u b j e c t e d suddenly t o a c o o l e r environment, it w i l l cool and s h r i n k a t t h e s u r f a c e . The more r a p i d l y t h i s i s c a r r i e d on t h e g r e a t e r w i l l be t h e s t r a i n which i s produced. T h i s
d i f f i c u l t y w i l l be a p p r e c i a t e d a s one of t h e main problems o f t h e g l a s s manufacturer who must anneal and cool h i s product slowly. He a l s o t a k e s advantage o f t h e low r e s t r a i n t o f semi-molten g l a s s t o impose an i n t e n t i o n a l s e t of i n i t i a l compressive s t r a i n s i n t h e g l a s s s u r f a c e by c o o l i n g it r a p i d l y t o produce toughened g l a s s . S l i d e 1 3 M a t e r i a l s , l i k e wood, which expand and c o n t r a c t markedly with
changes i n moisture c o n t e n t , experience s e r i o u s i n t e r n a l s t r a i n s upon drying. Wood, however, h a s a f u r t h e r i n t e r e s t i n g complication s i n c e it e x h i b i t s d i f f e r e n t shrinkages i n t h e t h r e e p r i n c i p a l
d i r e c t i o n s i n t h e t r e e , namely, along t h e l e n g t h ( o r g r a i n ) and r a d i a l l y and t a n g e n t i a l l y with r e s p e c t t o t h e l o g c r o s s - s e c t i o n . The changes a r e about 0.1, 5 and 7 p e r c e n t , r e s p e c t i v e l y , from green t o over-dry. Even i f a l o g i s d r i e d slowly, i t w i l l almost always crack s i n c e t h e c i r c u m f e r e n t i a l shrinkage i s g r e a t e r t h a n t h a t r a d i a l l y . Cracking can be avoided o n l y by c u t t i n g t h e l o g i n t o lumber and by slow and c a r e f u l d r y i n g .
When two d i f f e r e n t m a t e r i a l s having d i f f e r e n t p r o p e r t i e s a r e p u t t o g e t h e r , t h e y may induce l o a d i n g and s t r a i n i n one a n o t h e r when a change i n load, temperature o r moisture c o n t e n t i s imposed. One common example i s provided by maps and photos p a s t e d t o one s i d e o f a paper board which o f t e n r e q u i r e t o be "balanced" by a s i m i l a r s h e e t glued t o t h e back.
Plywood provides an example of a f u r t h e r complication, s i n c e t h e veneers from which i t i s made have markedly d i f f e r e n t moisture response p r o p e r t i e s i n t h e two-grain d i r e c t i o n s i n t h e p l a n e of t h e s h e e t . Two-ply m a t e r i a l warps s o b a d l y a s t o be unusable. The c o n s t r u c t i o n must be "balanced" with odd numbers o f p l i e s arranged symmetrically i n t h e p l a n e o f t h e s h e e t a s t o g r a i n d i r e c t i o n . Cracking and checking of plywood veneers may occur i n s e r v i c e i f t h e f a b r i c a t i o n i s c a r r i e d o u t a t moisture c o n t e n t s above t h o s e a t which t h e m a t e r i a l w i l l be used.
S t i l l on t h e s u b j e c t o f wood, t h e d a i l y , weekly and seasonal moisture changes i n wood s i d i n g can l e a d t o dimensional changes t r a n s v e r s e t o t h e g r a i n i n excess of 1%. Such changes occur i n a l l l o g b u i l d i n g s , with some a t t e n d a n t d i f f i c u l t i e s when wood elements a r e a p p l i e d t o l o g s a c r o s s t h e g r a i n . Horizontal l o g s a r e
s e l f - a d j u s t i n g t o shrinkage, while c r a c k s a r e bound t o open up between l o g s p l a c e d v e r t i c a l l y . Problems occur i n t h e c r a c k i n g of wide weather boards, i f t h e y a r e s o l i d l y n a i l e d a t both edges. S l i d e 14 The Norwegians have a s p e c i a l n a i l i n g method f o r wide board s i d i n g
t o avoid t h i s , which h a s been a p p l i e d i n t h e c a s e shown i n S l i d e 14. The wide boards a r e n a i l e d o n l y i n t h e c e n t r e , while t h e b a t t e n s a r e h e l d by c r o s s e d n a i l s p a s s i n g between t h e gaps i n t h e wide boards
These and o t h e r p o t e n t i a l problems w i t h wood a r i s e because i t e x h i b i t s a r e l a t i v e l y v e r y h i g h s h r i n k a g e and expansion a c r o s s t h e g r a i n w i t h changes i n moisture c o n t e n t . I t would be v e r y much l e s s u s e f u l , however, i f it e x h i b i t e d s i m i l a r movements a l o n g i t s l e n g t h i n s t e a d o f t h e low v a l u e s o f 0.1% from wet t o d r y .
S l i d e 15 Bricks a r e r e l a t i v e l y v e r y s t a b l e , d i m e n s i o n a l l y , s o f a r a s temperature and m o i s t u r e a r e concerned. I n a few c a s e s , b r i c k s made with p a r t i c u l a r combinations o f raw m a t e r i a l and f i r i n g temperature show expansions when used s h o r t l y a f t e r burning i n
amounts up t o 1 o r 2 i n c h e s p e r 100 f t . While t h i s i s n o t e x c e s s i v e , being o n l y 0.2%, it induces compressive s t r e s s e s which can l e a d t o l a r g e f o r c e s which a r e n o t r e a d i l y r e s t r a i n e d , u n l i k e s h r i n k a g e which i s o f t e n q u i c k l y r e l i e v e d by c r a c k i n g a t r e l a t i v e l y low t e n s i l e s t r e s s l e v e l s . Brickwork i s r e l a t i v e l y b r i t t l e and r i g i d and s o can show s e r i o u s c r a c k i n g a s a r e s u l t o f foundation and o t h e r g r o s s b u i l d i n g movements. Cracking w i l l normally f o l l o w t h e c l o s e l y spaced mortar j o i n t s , s i n c e t h e mortar i s u s u a l l y much weaker t h a n t h e b r i c k s , b u t when s t r o n g mortar i s used, even good q u a l i t y b r i c k s may be cracked.
S l i d e 16 Concrete u n i t masonry c o n s t r u c t i o n , l i k e b r i c k masonry, i s
q u i t e r i g i d and i s r e a d i l y a f f e c t e d by b u i l d i n g movements.
Cracking and movement problems a r i s i n g from d r y i n g s h r i n k a g e a r e not u s u a l l y s e r i o u s i f t h e b l o c k s e x h i b i t no more t h a n 0.04% shrinkage from s a t u r a t e d t o d r y c o n d i t i o n . Blocks made o f
l i g h t w e i g h t a g g r e g a t e may show h i g h e r s h r i n k a g e up t o . 0 8 % o r even h i g h e r and may e x h i b i t s e r i o u s c r a c k i n g problems u n l e s s used i n such a way a s t o c o n t r o l t h e m o i s t u r e changes subsequent t o l a y i n g . Masonry made from c o n c r e t e b r i c k s may a l s o be s u b j e c t t o c r a c k i n g .
The hardened cement p a s t e which i s normally used o n l y i n c o n j u n c t i o n w i t h a g g r e g a t e of some kind e x h i b i t s r e l a t i v e l y high shrinkage up t o 0.4% with extreme m o i s t u r e changes and w i t h c a r b o n a t i o n . Foamed cement p r o d u c t s , which r e f l e c t s t r o n g l y t h e shrinkage p r o p e r t y of t h e cement p a s t e , w i l l e x h i b i t c o r r e s p o n d i n g l y high s h r i n k a g e s u n l e s s t h e y a r e cured i n an a u t o c l a v e with steam.
These v a r i o u s s h r i n k a g e v a l u e s f o r c o n c r e t e a r e o f p a r t i c u l a r i n t e r e s t t o u s s i n c e we a r e looking f o r guidance i n judging t h e importance o f movements i n m a t e r i a l s . We may n o t e , f i r s t , t h a t c o n c r e t e and s t e e l b o t h e x h i b i t about t h e same working l i m i t s t r a i n s , i . e . , 0.1%. This means t h a t t h e y work w e l l t o g e t h e r i n t h e form o f r e i n f o r c e d c o n c r e t e , a s w e l l a s i n o t h e r s t r u c t u r a l combinations. However, t h e l i m i t i n g t e n s i l e s t r a i n i s o n l y 0.01%, which may be compared w i t h t h e p r a c t i c a l s h r i n k a g e l i m i t f o r
b l o c k s j u s t quoted of 0.04%, and t h e p o t e n t i a l s h r i n k a g e o f cement p a s t e o f 0.40%.
Carbonation o f t h e lime i n cement by carbon d i o x i d e from t h e a i r l e a d s t o a v e r y s u b s t a n t i a l s h r i n k a g e , b u t p r o c e e d s v e r y s l o w l y from t h e s u r f a c e i n t h e c a s e of normal dense c o n c r e t e , p e n e t r a t i n g a t a r a t e o f about 1 i n c h i n 50 y e a r s . Long-time
c a r b o n a t i o n s h r i n k a g e o f o t h e r c o n c r e t e p r o d u c t s t a k e s p l a c e a t r a t e s which a r e dependent on t h e i r p e r m e a b i l i t y t o carbon d i o x i d e . S l i d e 17 Concrete o c c a s i o n a l l y e x h i b i t s expansion a s a r e s u l t o f
unusual chemical r e a c t i o n s between t h e cement and a g g r e g a t e , which c a u s e t h e l a t t e r t o expand. S l i d e 17 shows t h e e f f e c t s o f one such r e a c t i o n i n v o l v i n g t h e a l k a l i i n t h e cement and a p a r t i c u l a r a g g r e g a t e . Laboratory t e s t s c a r r i e d o u t w i t h v a r y i n g amounts of S l i d e 18 a l k a l i produced t h e r e s u l t s shown i n S l i d e 18. There a r e s e v e r a l
a c c e p t a b l e s o l u t i o n s t o t h e problem.
The r e s u l t i n g c h a r a c t e r i s t i c map, c r a c k i n g a t t h e exposed s u r f a c e , i s produced by expansion o f t h e u n d e r l y i n g m a t e r i a l which h a s been k e p t i n a damp c o n d i t i o n . Experience w i t h s e v e r a l c a s e s o f t h i s kind l e a d s t o t h e i n t e r e s t i n g f i g u r e o f 0 . 2 % a s t h e
expansive l i m i t a t which t h e c o n c r e t e i t s e l f b e g i n s t o d i s i n t e g r a t e a s a r e s u l t o f t h i s growth from w i t h i n .
S l i d e 19 Problems can be e n c o u n t e r e d w i t h c o a t i n g s , f i l m s and s h e e t s a p p l i e d o r bonded t o b o a r d s , p a n e l s , and decks o f v a r i o u s k i n d s . The c o a t i n g , b e i n g t h i n and adhered t o t h e s u r f a c e , may have t o f o l l o w t h e movement o f t h e r e l a t i v e l y t h i c k and s t r o n g s u b s t r a t e . I f t h e s u b s t r a t e c r a c k s , a r e l a t i v e l y h i g h l o c a l s t r a i n i s developed which i s v e r y l i k e l y t o c a u s e f a i l u r e a l o n g t h e c r a c k i n t h e c o a t i n g a l s o , u n l e s s it h a s a p p r e c i a b l e c a p a c i t y f o r e x t e n s i b i l i t y o r s u f f i c i e n t s t r e n g t h t o f o r c e a d h e s i o n f a i l u r e on e i t h e r s i d e of t h e c r a c k , t h u s i n c r e a s i n g t h e l e n g t h o f m a t e r i a l f r e e t o s h a r e t h e imposed deformation. Such c a s e s a r i s e f r e q u e n t l y w i t h r o o f i n g membranes l a i d d i r e c t l y on c o n c r e t e decks and w i t h p a i n t on e x t e r i o r wood. I t must be a p p r e c i a t e d t h a t t h e l i m i t i n g s t r a i n f o r t h e c o a t i n g o r membrane may have t o be v e r y g r e a t i f it i s t o s u r v i v e w i t h o u t r u p t u r e a t c r a c k s i n a s u b s t r a t e t o which it i s s t r o n g l y adhered.
Let u s , i n c l o s i n g , remind o u r s e l v e s o f some o f t h e s i g n i f i c a n t s t r a i n r e f e r e n c e l e v e l s , s o t h a t we may judge t h e
s i g n i f i c a n c e o f v a r i o u s k i n d s and amounts o f movements i n m a t e r i a l s . A key f i g u r e i s t h e one o f 0.1% s t r a i n , which i s i n d i c a t i v e o f t h e t o l e r a b l e l i m i t i n many common b u i l d i n g m a t e r i a l s and t h e
c o n s t r u c t i o n s made from them. T h i s l i m i t i s a rough measure a l s o o f t h e g e n e r a l dimensional s t a b i l i t y o f o u r b u i l d i n g s . Induced s t r a i n s i n e x c e s s o f t h i s w i l l u s u a l l y be s e r i o u s , and i n many c a s e s c r a c k i n g and o t h e r d i f f i c u l t i e s may a r i s e w i t h even lower l e v e l s o f s h r i n k a g e s i n c e many common m a t e r i a l s a r e b r i t t l e and r e l a t i v e l y weak i n t e n s i o n .
Hutcheon
We have noted t h e d i f f i c u l t i e s i n c a l c u l a t i n g o r e s t i m a t i n g t h e l i m i t i n g s t r a i n s beyond which f a i l u r e o r u n s a t i s f a c t o r y s e r v i c e can be expected. We s e e t h a t b r i t t l e m a t e r i a l s , while p r e d i c t a b l e i n some ways, a r e s u s c e p t i b l e t o s t r e s s c o n c e n t r a t i o n s . D u c t i l e m a t e r i a l s have a l a r g e r e s e r v e s t r a i n c a p a c i t y beyond
normal working limits, but t h i s does not always mean t h a t t h e component o r t h e s t r u c t u r e has a s i m i l a r r e s e r v e . Creep and t h e e f f e c t s of f a t i g u e i n t r o d u c e added complications. These a r e unavoidable f a c t o r s f o r c o n s i d e r a t i o n i n design, i f a p r e d i c t a b l e r e s u l t i s t o be obtained. They o f f e r a g r e a t and e x c i t i n g
c h a l l e n g e which a l l t o o f r e q u e n t l y has been ignored i n b u i l d i n g design. The r e s u l t s of i g n o r i n g them can range from annoyance t o d i s a s t e r .
D i v i s i o n o f B u i l d i n g Research
DIMENSIONAL CHANGES DUE TO TEMPERATURE
by J . K . L a t t a
Based on s l i d e / t a l k p r e s e n t a t i o n given a t t h e DBR B u i l d i n g S c i e n c e Seminar,
"Cracks, Movements and J o i n t s i n Buildings
,"
Autumn 1972.DIMENSIONAL CHANGES DUE TO TEMPERATURE by J . K . L a t t a
I am s u r e t h e r e a r e v e r y few who do n o t know t h a t i f you warm a m a t e r i a l it w i l l expand, i f it i s f r e e t o do s o , and t h a t i f you cool i t , it w i l l c o n t r a c t . Most o f u s l e a r n e d t h i s s o long ago t h a t we have f o r g o t t e n t h a t t h e r e was e v e r a time when we d i d n o t know i t . There i s n e v e r t h e l e s s even i n t h i s simple s t a t e m e n t a p o i n t which i s o f t e n overlooked. The m a t e r i a l w i l l o n l y change i n dimension i f it i s f r e e t o do so. I f i t i s n o t f r e e t o change i n dimension a s t r e s s w i l l be induced i n it. A gas i n a c l o s e d r i g i d c o n t a i n e r w i l l undergo a change i n p r e s s u r e with a change i n
temperature. A s t e e l b a r f i x e d between immovable abutments w i l l have a compressive s t r e s s induced i n i t on being h e a t e d and d e s p i t e being s t r o n g i n compression it may r e l i e v e t h e s t r e s s by buckling.
I n o r d e r t o a s s e s s t h e s e v e r i t y o f t h e problem o f dimensional changes due t o temperature changes t h r e e t h i n g s must be known. 1. The response o f t h e m a t e r i a l t o a given change i n t e m p e r a t u r e ,
2 . The change i n temperature t o which it may be s u b j e c t e d ,
3 . The freedom i t has t o change dimension i n r e s p o n s e t o a change i n temperature.
The f i r s t o f t h e s e t h r e e items i s e a s i l y o b t a i n e d . The change i n l e n g t h o f a m a t e r i a l (which i s f r e e t o move) f o l l o w i n g a change i n temperature o f one degrec i s c a l l e d t h e c o e f f i c i e n t o f l i n e a r expansion o f t h e m a t e r i a l . T h i s i s u s u a l l y well e s t a b l i s h e d and v a l u e s a r e a v a i l a b l e i n many r e f e r e n c e books. Average v a l u e s f o r some common b u i l d i n g m a t e r i a l s i n c l u d i n g s e v e r a l p l a s t i c s a r e given i n Table I.
I t can be seen t h a t t h e r e i s a range o f 7 : l between wood and aluminum and over 40:l between wood and p o l y e t h y l e n e . The change i n l e n g t h of a 1 0 - f t l e n g t h of m a t e r i a l s u b j e c t e d t o an a r b i t r a r i l y chosen temperature change of 1 0 0 ~ ~ can e a s i l y be c a l c u l a t e d and t h e r e s u l t s a r e l i s t e d i n t h e t h i r d column. They a r e shown i n b a r S l i d e 1 graph form i n S l i d e 1.
L a t t a I
TABLE I
Coef. of Exp. Deformation, i n c h e s M a t e r i a l p e r O F x p e r 1 0 ft/lOO°F
Wood (along t h e g r a i n ) Brick
Marble
E
Dense Limestone Normal Dense Concrete Sandstone S t e e l Copper Aluminum Reinforced P o l y e s t e r Foamed Polyurethane P.V.C. Foamed P o l y s t y r e n e (Extruded) Foamed Urea-Formaldehyde A. B. S. P o l y e t h y l e n eA 1 0 - f t - l o n g wood s t u d would expand 0.024 i n . , which f o r most p u r p o s e s is n e g l i g i b l e . The c l o s e n e s s o f t h e v a l u e s f o r s t e e l and c o n c r e t e a t about 0.08 i n . a r e w e l l known and t h i s i s one r e a s o n why t h e two can be used t o g e t h e r i n r e i n f o r c e d c o n c r e t e . A 1 0 - f t l e n g t h o f aluminum would expand about t w i c e a s much a t 0.168 i n . b u t a 1 0 - f t p o l y e t h y l e n e p i p e would expand more t h a n one i n c h . E q u a l l y i t would c o n t r a c t t h e same amount on c o o l i n g 100°F s o i f you p l a n t o p u t a w a t e r system i n t o y o u r c o t t a g e i n summer u s i n g p o l y e t h y l e n e p i p e be s u r e t h a t you a l l o w f o r t h i s movement
o t h e r w i s e t h e j o i n t s may p u l l a p a r t when e v e r y t h i n g i s c o l d i n w i n t e r . Vinyl s i d i n g made from p o l y v i n y l c h l o r i d e would need t o be i n s t a l l e d w i t h s p e c i a l s l i d i n g j o i n t s t o a l l o w f o r t h e p o s s i b l e movement of n e a r l y 1/2 i n . under t h e c o n d i t i o n s s p e c i f i e d , o r a l t e r n a t i v e l y it c o u l d b e h e l d f i r m l y i n p l a c e t o r e s i s t i t .
I t can a l s o b e s e e n t h a t a l l o f t h e more t r a d i t i o n a l b u i l d i n g m a t e r i a l s - wood, b r i c k , s t o n e , s t e e l and c o n c r e t e
-
have f a i r l y-
3- L a t t a IS l i d e 2
aluminum which one normally t h i n k s of a s b e i n g h i g h l y e x p a n s i v e a r e r e l a t i v e l y s t a b l e compared w i t h some o f t h e newer p l a s t i c m a t e r i a l s . However, t h e deformation o f a m a t e r i a l which i s f r e e t o expand i s o n l y p a r t o f t h e s t o r y and f r e q u e n t l y it i s t h e f o r c e s o r s t r e s s e s induced by t h e r e s t r a i n t o f such a m a t e r i a l which a r e i m p o r t a n t . Here one must t a k e n o t e o f t h e d e f o r m a t i o n , o r would be d e f o r m a t i o n , i n r e l a t i o n t o t h e modulus o f e l a s t i c i t y o f t h e m a t e r i a l concerned.
Let u s , by way o f i l l u s t r a t i o n , s e l e c t f o u r m a t e r i a l s w i t h d i f f e r e n t d e g r e e s o f expansion; s a y s t e e l , aluminum, p o l y v i n y l c h l o r i d e and p o l y e t h y l e n e ; whose u n r e s t r a i n e d movements a r e shown i n t h e t o p diagram i n t h i s s l i d e . Now i f we t a k e a modulus o f e l a s t i c i t y f o r s t e e l o f 30 x
l o 6
p s i t h e s t r e s s induced by f u l l yr e s t r a i n i n g a p i e c e o f s t e e l s u b j e c t e d t o a 100°F t e m p e r a t u r e change would be 21,000 p s i . Although aluminum expands t w i c e a s much a s s t e e l i t s modulus i s o n l y 1 0 x
lo6
p s i o r one t h i r d t h a tof s t e e l and so it i s l e s s h i g h l y s t r e s s e d a t 14,000 p s i . P o l y v i n y l c h l o r i d e w i t h a modulus o f 0.2 x
lo6
p s i would bes t r e s s e d t o about 1,700 p s i , and when we g e t t o t h e p o l y e t h y l e n e t h e induced s t r e s s would be a mere 380 p s i s i n c e i t s modulus i s down t o 0.04 x
l o 6
p s i , which i s o n l y 1 / 7 5 t h o f t h a t o f s t e e l . I f t h e s e s t r e s s e s a r e now r e l a t e d t o t h e u l t i m a t e t e n s i l e s t r e s s o f each m a t e r i a l we s e e t h a t t h e s t e e l i s a t about 50 p e r c e n t o f i t s u l t i m a t e s t r e s s , t h e aluminum a l t h o u g h l e s s h i g h l y s t r e s s e d i s a t 70 p e r c e n t o f i t s u l t i m a t e , t h e p o l y v i n y l c h l o r i d e a t 21 p e r c e n t and t h e p o l y e t h y l e n e a t o n l y 16 p e r c e n t a s i s shown i n t h e bottom diagram.Thus we can s e e t h a t w h i l e it may be d i f f i c u l t t o r e s t r a i n t h e s t e e l f u l l y because o f t h e c o n s i d e r a b l e f o r c e s developed it may n o t be t o o d i f f i c u l t t o f i x v i n y l s i d i n g i n p l a c e d e s p i t e i t s r e l a t i v e l y high c o e f f i c i e n t o f expansion.
Now t h i s i s r e a l l y a r a t h e r t o o s i m p l i s t i c approach t o what can be a v e r y complex s u b j e c t . The modulus o f e l a s t i c i t y o f s t e e l may n o t change v e r y much o v e r t h e 1 0 0 " ~ t e m p e r a t u r e change
( a l t h o u g h i t can s u f f e r b r i t t l e f r a c t u r e a t low t e m p e r a t u r e ) b u t t h a t o f t h e p o l y e t h y l e n e w i l l change c o n s i d e r a b l y . The s t r e s s i n t h e p o l y e t h y l e n e may t h e r e f o r e be much h i g h e r t h a n t h e 380 p s i . On t h e o t h e r hand t h e m a t e r i a l w i l l have a c r e e p e l o n g a t i o n , because o f t h e slow a p p l i c a t i o n o f t h e l o a d , which w i l l r e l a x t h e s t r e s s . U n f o r t u n a t e l y , t h i s may a l s o lower t h e b r e a k i n g s t r e s s ; and s o we c h a s e t h e problem round and round i n c i r c l e s .
I n f a c t a l l t h e s e f i g u r e s f o r c o e f f i c i e n t s o f expansion, e l a s t i c moduli, induced s t r e s s e s and f a i l u r e s t r e s s e s a r e o n l y r e p r e s e n t a t i v e v a l u e s and most m a t e r i a l s have a wide range o f
