The Interconnected Physics of Roof Components

The Interconnected Physics of Roof Components

Lyle D. Hogan, PE, FRCI, RRC
Lip-attached roofs
RESPOND DIFFERENT IY
Abstract:
Roof construction is
founded in physics. As
disturbing as that may
be, the concept is
encountered daily.
Behavior of roof assemblies
(including the various
substrate types) is
somewhat predictable
when examined in the
backdrop of physics.
A related notion,
mechanics of solids, proceeds
upon inescapable
constants such as gravity
and mass (at least
regarding construction
on this planet). This
treatise is not intended
as a comprehensive discussion
of the physical
sciences. Instead, the
concepts offered are
meant to illustrate the
relationships between
and among roof assembly
components.
Examples of other building
construction components
are used as analogies.
Inertia
The bulk or mass of roof components can be
understood by inertia. Consider the difficulty in
accelerating or bringing to a halt an element of
a roof deck. An earthquake is a type of natural
event which can induce acceleration. Plywood
decks on wood structures behave radically different
from a cast-in-place concrete deck during
such exposure. The shock energy will be transmitted
and reflected through these media at a
rate governed by density of the materials used
and the fixity of connections (among other variables).
Similarly, a vertical load may create identical
deflections in plywood and steel decks. This
would suggest that they are equally capable substrates
for a given project. Yet, abrupt vertical
loading may induce far different instantaneous
deflection with attendant susceptibility for irreversible
deformation and membrane rupture.
Inertia is the phenomena responsible for this
difference in behavior.
Inertia can be witnessed by analyzing the
various corrugations of steel roof decks. Span
tables confirm that for any gauge of deck, load
capabilities differ, varying only with the fluting
configuration (i.e. shape, profile, spacing, and
opening).
A related aspect is thermal inertia. This is
the tendency of some decks to serve as a thermal
sink better than others, responding slowly
to top side temperature changes. A concrete
deck slightly less than five inches thick will
have five times greater thermal inertia than
some other lightweight substrates examined
(Beech & Saunders, 1985). Separate research by
Kunzel and Petersson confirmed that underside
temperatures (of heavy concrete decks,- see
Figure 1) changed little with wide changes in the
external environment. Roof coverings should be
appropriately matched to perform in the setting
of several parameters. Deck inertia is important
among them.
Thermal storage capacity should be considered
in surfacings as well. Gravel surfacing has
the capacity to act as a thermal “flywheel.”
Removal of the surfacing and replacement with
a mineral-surfaced cap sheet will generate a new
behavior of the substrate (Duchene, 1985).
Modulus
Young’s Modulus of Elasticity (E) is the slope
of a graph plotting deformation against the ten-
Figure 1. Concrete decks have high thermal
inertia. When compared to other substrates,
ROOFTOP TEMPERATURE CHANGES ARE
TRANSMITTED SLOWLY INTO THE BUILDING.
18 • Interface April 1999
sile load per unit area. This works well for examining
solid materials,- however, some roof materials do
not behave as pure solids through a reasonably
expected service temperature range. That is, the
value for E would vary greatly with changes in temperature.
A modulus of elasticity is therefore not
meaningful for these materials, but a load-strain
relationship nonetheless exists (albeit quite temperature
sensitive). Bitumen is an example of a material
having engineering properties which range according
to temperature. This is the basis for studying
the rheological properties of materials.
Anyone having drilled, punched, or sheared
stainless steel is well aware of its hardness in comparison
with other metals. For this reason, many
suppose that stainless steel is stronger than the same
thickness of carbon steel. Its tensile strength is well
in excess of that for carbon steel (85,000 psi compared
to 60,000 psi). Yet the modulus for the stainless
is 28,000 ksi compared to 29,500 ksi for carbon
steel (Eshbach & Souders, 1974). Carbon steel,
then, has a greater slope for load-strain relationships,
deforming less for a stated load. This difference
can be viewed in span tables contrasting stainless
with carbon steel roof deck sheets. The concept
is better appreciated if the surface hardness of stainless
is neglected for the moment.
One-ply membranes also behave according to
modulus values. For instance, wind-induced oscillation
(flutter) imparts energy to the fasteners. Other
factors being constant, the higher modulus membranes
transmit this energy more effectively than
lower-modulus, more flexible products (i.e. EPDM).
A highly-reinforced, lap-attached, sheet membrane
would apply much different loads to the fastening
devices during wind events than would a thick,
bituminous, adhered membrane (Figure 2). Yet, the
working pressure of the prevailing wind is the same.
The varying modulus values of the two products
hold part of the explanation.
Membrane modulus values also played a part of
deck span tables as various products were implemented.
Designers were told, for instance, to size
structural elements so as to limit vertical deflections
to 1/180, 1/240, etc. This was in an effort to avoid
rupturing of a high modulus bituminous membrane
(built-up roof), the hands-down system of choice
for decades. This author is unaware of any current
polymeric membrane product incapable of withstanding
vertical deflections of the substrate well in
excess of the figures above. Many such products
have had performance problems, but the resilient
nature (low modulus) of the coverings is largely
immune to damage from deck deflection.
Moment
A force times its measured distance from some
point of influence is considered the moment value
acting about that point. Comparatively
hard or brittle materials are
well capable of transmitting
moment. Further, rigid materials
“attract” moment. Consider two
types of pitch pocket filler surrounding
an iron penetration
(Figure 3). Movement of the iron is
transmitted through the material.
Rigid fillers (like cementitious
grout) impart more separation
stress to the sides of the pitch
pocket form than more resilient
polymeric products.
Steel deck sheets may be installed spanning
across three, four, or more bar joists. That arrangeFigure
3.
Rigid filler in a pitch
ment is intended to transmit moment induced (by
loads in one area) across the supports into other
POCKET ATTRACTS AND
TRANSMITS MOMENT
regions. Multiple single spans may work apart at the
sheet endlaps. Distribution of the moment is
appealing management of an influence that might
split a comparatively rigid membrane.
BETTER THAN A RESILIENT
PRODUCT. SUSCEPTIBILITY
FOR SPLITTING AND
SEPARATION THEN
BECOMES APPARENT.
Shear Diaphragm
A structure having only horizontal and vertical
members would be unstable, even when fastened
appropriately to adjacent members. Lateral loads
imparted (by wind and earthquake acceleration)
induce horiand
result in twisting or torsional behavior within
the structure. Resistance is provided in several locations
in a structure by using a diaphragm and/or
diagonal bracing (Figure 4). Bracing (bridging) may
be found between and among wood joists and steel
purlins. This, however, is to control potential rotation
of the members and should not be confused
with shear diaphragm elements.
A plywood roof deck is an excellent shear
diaphragm when anchored properly into framing
members. This is also the reason plywood is used at
corners of framed wood walls, substituting for other
types of sheathing found elsewhere in the same
construction (Figure 5).
Figure 4.
A STRUCTURAL SYSTEM
HAVING ONLY VERTICAL
AND HORIZONTAL
MEMBERS MUST BE
STIFFENED AGAINST
HORIZONTAL LOADS.
Shown here is
ORDINARY DIAGONAL
BRACING USING STEEL
SECTIONS.
April 1999 Interface *19
Coefficients Of
Figure 6.
Structural metal roofs are carried on
A SYSTEM OF CONCEALED CUPS, ALLOWING
LONGITUDINAL MOVEMENT OF THE PANS.
Being, therefore, separated from the
STRUCTURE, THE ASSEMBLY IS INCAPABLE
OF SERVING AS A SHEAR DIAPHRAGM.
Figure 5.
Plywood is used at corners of
FRAMED WOOD WALLS, SUBSTITUTING
FOR ORDINARY SHEATHING USED
ELSEWHERE. THE PLYWOOD IMPARTS
HORIZONTAL SHEAR RESISTANCE TO
THE FRAMING.
A structural metal roof, by
definition, has no deck or substrate.
Modern standing seam
coverings are carried on a system
of concealed clips which accommodate
thermal movement
(Figure 6). This appealing divorcement
of the roof covering from
the framing elements, however,
renders standing seam assemblies
incapable of serving as a shear
diaphragm. Such resistance must
be gained elsewhere in that type
of structure such as with the
diagonal elements described
above. Note that even conventional steel decks do not develop
full diaphragm capability until side lap stitching screws are in
place (Figure 7).
Fluid Dynamics
Those things that flow can be examined in a study of fluid
dynamics. A substance does not have to be in “liquid” form to be
a fluid. For roofing analysis, wind is the fluid of interest. Wind
tunnels all whistle the same tune, and the influence on construction
surfaces can be modeled reliably. Bernoulli’s Energy Equation
is the form used to express working pressure as a function of
fluid velocity. Modified appropriately for the density of air, the
influence is generally in the form:
P = 1/2 p(v)2
where: P = the pressure of the wind acting on the surface
p = the density of air
v = the wind speed
Simplified, the pressure acting on a surface varies as the
square of the wind velocity. This is pivotal in understanding why
roofs come off (even though most should not). Try holding your
hand from the window of an automobile moving at both 40 k/hr
and 80 k/hr. The velocity has doubled, but the difference in
pressure experienced has increased exponentially. Such an example
ratifies the velocity pressure curve, a parabolic function
because the formula is a second degree equation (Figure 8).
Roof design for wind resistance embodies a shape factor
analysis. That is, we convert the pressure acting normal to a wall
surface to an influence over the top of a structure. Such converting
incorporates a 50% escalation of the working pressure for
design purposes (1.5 times the wall surface pressure). Other escalations
and factors are applied later.
Thermal Movement
The movement of various
construction materials as a
function of temperature is well
known. A coefficient of thermal
expansion has been determined
for virtually everything
used in roof construction.
Joining certain materials occasionally
results in mismatch,
particularly where long-term
Figure 7.
Conventional steel decks do not develop full diaphragm
CAPABILITY UNTIL SIDE LAP STITCHING SCREWS ARE IN PLACE.
waterproofing is required. Sheet metal accessories integrated into
membrane products is a classic case where this union is crucial.
Consider light-gage (0.032 inch) aluminum and how it compares
with bulk (0.125 inch) aluminum of the same length. Note
that the coefficient of thermal expansion is unrelated to the
thickness of the material (Hogan, 1993). That is, the amount of
movement has nothing to do with the gage of the material. The
difference in performance is the amount of shear force exerted
on the fasteners used to secure the accessories.
The force acting on the fasteners (of bulk thickness metals)
may be substantial, potentially shearing the attachment devices
and/or elongating fastener holes. The force actually at work is
identical to the force required to stretch it by the same amount
(Beiser, 1991). Because of this, the thicker bulk metals are
divorced from a membrane while light gage metals may be functionally
restrained by frequent fastening.
20 • Interface April 1999
Summary Remarks
Nonperformance of various
roof types may be explained
when the properties of one component
are not well matched to
others in the composite. The
interaction of the components has
been explored by several
researchers. Van Wagoner (1989)
has examined the membrane and
insulation combination. The deck
and structure have played a pivotal
role in the observations of
this writer. I will not attempt to
improve on Griffin (1982) who
postulated:
“The characteristic problems
of roof system designs are a combination
of incompatible materials
rather than isolated failures of single
components. Two or more
components may satisfy their
Figure 8. The velocity pressure curve is parabolic
BECAUSE IT IS THE PLOT OF A SECOND DEGREE EQUATION.
The pressure varies as the square of velocity.
individual material requirements to perfection and yet, in combination,
fail disastrously.”
Successful integration of the multiple components is crucial
to achieving the optimum roof service life. A better understanding
of physics will lead the way to improved system performance.
REFERENCES
Beech, J. C., and Saunders, G.K., “The Performance of
Lightweight Inverted Flat Roofs,” (proceedings from the)
Second International Symposium on Roofing Technology,
1985, pg. 285.
Beiser, Arthur, “Chapter 13: Thermal Properties of Matter,”
Physics, 1991, pg. 354.
Duchene, Claude, “Repair of Roofing
Membrane Systems,” (proceedings
from the) Second International Symposium
on Roofing Technology, 1985, pg. 14.
Eshbach, Ovid W. and Souders, Mott,
“Chapter 16: Properties of Materials,”
Handbook of Engineering Fundamentals, 3rd
edition, 1974.
Griffin, C. W., ‘The Roof As A System,”
Manual of Built-up Roof Systems,
McGraw-Hill, 1982, page 13.
Hogan, L. D., “Detailing Accessory
Metal Components,” Interface,
May/June, 1993, page 7.
Van Wagoner, John D., “Compatibility of
Roofing Insulations and Membranes,”
(proceedings from the) Ninth Conference
on Roofing Technology, 1989, pp. 27-30.
This article is reprinted from the proceedings of
the Energy Efficient Building Association’s
(EEBA) Conference Oct. 28-31, 1998 in
Washington, DC.
About the Author
Lyle Hogan is a senior engineer with
Geoscience Group, Inc., working out of the
firm ‘s Greensboro, NC office. He is a registered
engineer, Registered Roof Consultant,
licensed home inspector, and Fellow of the
Roof Consultants Institute. His technical
articles have been published in numerous
technical journals and conference proceedings.
He is Senior Editor of Interface Journal.
Lyle D. Hogan
PE, FRCI, RRC
Rollin’… Moving forward in continuous revolutions
‘HE HEAT IS ON WITH OUR NEW 1 O FOOT WIDE SHEETS • THE HEAT IS ON WITH OUR NEW 1 O FOOT WIDE • THE HEAT IS ON WITH OUR NE
April 1999 Interface • 21