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RE: C&C vs MWFRS pressures

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Thanks to Christopher Banbury for further insight to C&C vs MWFRS pressures.

The ASCE7 commentary quoted by Harold Sprague seemed relatively clear:

... The engineer needs to use appropriate loadings for design of components,
which may require certain components to be designed for more than one type
of loading, for example, long-span roof trusses should be designed for loads
associated with MWFRSs, and individual members of trusses should also be
designed for component and cladding loads [Ref. C6-1]. ...
<end quote>

Which seems to be what you are saying.


Also the commentary to ASCE7-05 with respect to MWFRS says:

<quote>
More specifically, the following structural actions were
evaluated:
1. Total uplift.
2. Total horizontal shear.
3. Bending moment at knees (two-hinged frame).
4. Bending moment at knees (three-hinged frame).
5. Bending moment at ridge (two-hinged frame).

 ... involved developing sets of "pseudo" pressure
coefficients to generate loading conditions that would envelope
the maximum induced force components to be resisted for all
possible wind directions and exposures. Note, for example, that
the wind azimuth producing the maximum bending moment at the
knee would not necessarily produce the maximum total uplift.
The maximum induced external force components determined
for each of the preceding five categories were used to develop the
coefficients. The end result was a set of coefficients that represent
fictitious loading conditions, but that conservatively envelope the
maximum induced force components (bending moment, shear,
and thrust) to be resisted, independent of wind direction."
<end quote>

Which some what confuses the meaning of transverse and longitudinal pressure
distributions, if there is independence of direction. It does however
suggest the MWFRS pressure gives an appropriate uplift force on a truss.

My initial objection to using C&C pressures for truss design or anything
beyond immediate support of cladding was based on the description of C&C
pressures being derived by enveloping extreme values as a model revolves 360
degrees in a wind tunnel. In Australia we use the angle theta for direction
of wind loading: theta=0 gives transverse pressures and theta=90 give
longitudinal pressures. We are required to check 4 orthogonal directions:
theta=0,90,180,270. Adopting notation (roof1,roof2), where roof1 is
coefficient on roof surface 1.

Then for:
Theta= 0 get say (-0.7,-0.3)
Theta=180 (-0.3,-0.7)

ASCE7-05 then envelopes the extremes on each surface to give (-0.7,-0.7),
which is not a realistic distribution for design of anything with multiple
surfaces. But for cladding and purlins, and other immediately supporting
elements, only want the extreme value for the roof surface, and the
differing zones on that surface. To AS1170.2 for each of the 4 orthogonal
directions we work out which surface experiences the worst pressure and
adopt that for design of cladding and immediate supporting structure, and
apply local pressure factors k[l] for turbulent zones. It seems using
ASCE7-05 the C&C pressures are already worked out giving the worst case for
all directions: so if direction theta=45 gives the highest pressure on a
given surface that is the C&C pressure listed.

My eventual agreement with Scott, with using C&C for small residential
trusses was shifting my focus away from the transverse distribution. If
longitudinal distribution also considered then get extremes of (-0.9,-0.9)
as the distribution on the surfaces, if this is enveloped with the
transverse, then it becomes the C&C pressures, and is a valid symmetrical
distribution. But this assumes that theta=45 or some other angle is not
producing the extreme pressures. (NB: for simplicity I am ignoring the edge
zones: To AS1170.2, I simply set k[a]=1, no area reduction allowed, and
local pressure factor k[l] is given different values for each surface zone
eg. typically k[l]=1 for interior zones, k[l]=1.5 for distance 'a', and
k[l]=2 for distance a/2). 

To AS1170.2 we have area reduction factor k[a], and as the tributary area
increases k[a] gets less than 1. For cladding and immediate supporting
structure k[a]=1. However to AS1170.2 it is not just a matter of defining
edge zones: the pressures in these zones are only applied to areas 'a/2 x
'a/2' and areas 'a x a'. These areas can occur any where along the length of
say a purlin. Now whilst k[l] is explicitly stated as being for cladding and
immediately supporting structure, it doesn't have to be taken so literally.

If there really are short lived, intermittent small area spikes in pressure
occurring in turbulent zones over a surface: then where k[l] cuts out and
becomes insignificant can be left to the designer. On a large structure the
assumption is that the purlin can be adequately fastened to the rafter, and
that the connection is the only item of concern. The rafter has a large
tributary area, and is deep below the building surface, and a short lived
spike in pressure on the building surface has little influence on the
rafter. Using AS1170.2 local pressure areas, the insignificance of a spike
to any given element could be evaluated: it isn't but it could be.

>From a practical viewpoint for a small structure, the supporting elements
may not be adequate to accommodate connection forces traced back from
cladding and immediate supporting structure, and also inadequate to support
the forces when behaving as a beam or other structural element: and
therefore it may be necessary to design these elements for the peaks in
pressure. From a practical viewpoint designing small trusses for C&C
pressures may be justified, as long as appropriately compared against the
results of MWFRS pressures. Practical and conservative doesn't however, make
it a code requirement. The ASCE7 C&C pressures however appear only to be
defined for edge zones defined by dimension 'a', not small 'a x a' areas
within those zones. So the ASCE7 pressures are applied to the full tributary
width of a truss, not some small portion of it: for small closely spaced
trusses may not be an issue but for larger trusses it starts becoming
uneconomical.

My other opposition to C&C pressures for design of trusses was the internal
pressure coefficients used by ASCE7. First the C&C pressure coefficients
ignore transverse and longitudinal loading, and then the internal pressure
coefficients also ignore such direction. To AS1170.2 we have either enclosed
buildings, enclosed with dominant openings, or free roofs. Ignoring
simplified assessment of internal pressure coefficients: the internal
pressure coefficient is equal to the external pressure coefficient on the
surface where the dominant opening is located. This means that openings
remove symmetry from a building shape.

If have a gable building and place doors in the longitudinal side. Then say
transverse pressure distribution on roof is direction theta=0, (-0.7,-0.3),
and for longitudinal direction theta=90 (-0.9,-0.9), then the external
pressure coefficient in the wall will say be -0.5 for theta=90, but -0.3 for
theta=270. That is the door is closer to one gable end than the other. With
no doors in the gable ends, the (-0.9,-0.9) cannot be combined with a
positive internal pressure coefficient, only with internal suctions. For
transverse loading there will be windward wall pressure of +0.7 and equal
internal generated, but for theta=180 the door now on leeward face and
produces say suction of -0.3. ASCE7-05 simply says internal pressure
coefficients are (-0.55, +0.55) for partially enclosed. To combine these
with the non-directional C&C pressures for truss design and tie-down is
potentially getting really over conservative. From a practical viewpoint
allowing for a future opening in a gable end wall may be worthwhile, if it
is possible to put one there in the future. If not then a more economical
structure can be designed by appropriate location of openings.

Now I understand Andrew Kester's preference for designing trusses for such
conservative loads, I believe he is in Tornado territory, and wind loading
codes simply say: designer needs to consider, but not giving you any
guidance. On the other hand it maybe a great deal of unnecessary expense for
a structure which is still not going to survive being hit by a tornado. Our
wind codes are equally deficient on guidance for violent downdrafts from
thunderstorms. Tornados and thunderstorms are issues requiring more
research. For tornados defensive structures in the environment, may be
better than strengthening houses: large concrete sculptures which remove
debris, absorb energy and smooth airflow: a community issue like flood
mitigation.

As for Scott Maxwell's concern about load reversal. As I said here we have
to check four orthogonal directions theta=0,90,180,270, and if the structure
is symmetrical the effect of reversal is obvious.

The need to decide whether an element is C&C or MWFRS seems an unnecessary
complication. The air flows over the building and pressures are generated on
the buildings surfaces, some how the actions of these pressures needs to be
resisted. For all buildings both C&C and MWFRS pressures need to be
considered irrespective of size.

I believe the point is that C&C pressures start at the cladding surface, and
are traced back through the multiple layers of support structure until their
influence is insignificant. The components are treated as relatively
isolated and independent elements. That is the purlin on the windward roof
plane is not dependent for its resistance on the purlin on the leeward roof
plane: so the pressure distribution across the roof is of little relevance.
The MWFRS pressures are applied to all surfaces at the same time, and the
combined actions on the multiple layers of structure are assessed. For some
elements the MWFRS pressures will control design, for others the C&C
pressures will control design. With ASCE7-05 Clause 6.5.12.1.2 being a guide
to when the influence of the C&C pressures cease to influence the design of
an element. (Commentary Figure C6-6 is a useful guide.)

Also for simplistic design, the roof and wall top and bottom plates have
large tributary areas. The projected area of the roof multiplied by the
extreme value MWFRS pressure should give a conservative estimate of wind
uplift. Even though the ASCE7 pressures are averaged, it is still the case
that the whole of the building does not experience the MWFRS pressures given
on all surfaces at the same time, nor across a given surface. By definition,
50% of values are less than the mean, and 50% greater than the mean value:
at any point in time the whole surface is not at the same pressure: even if
the code gives us a uniform pressure.

Locally however, near the surface of the building, the turbulence and
resulting spikes in pressure can have significant influence. The
cantilevered overhang of a roof truss, in the turbulent edge zones, the C&C
pressures may determine the size of the truss top chord. But such is a
simple cantilever design, not an over all analysis of the truss.

Our loading codes are generally not written so that we can place loads onto
surfaces, and then distribute sensibly to supporting elements. As I reduce
the spacing of my purlins to reduce the effects of wind loading, my applied
constructional live loading increases: it is inversely proportional to area.
If I was to create a 3D frame model, and apply loads to the purlins, then my
main frames would be oversized, because it is not the intent that the main
frames carry the same magnitude of constructional live load as the
individual purlins. The loading of the main frames doesn't come directly
from the reactions from the purlins. Also here we typically apply the wind
loading as a UDL to our main frames, and ignore making any correction for
the actual point loading from the purlins: the wind load is after all a best
guess of what the building will really experience. For large structures the
error is small, for small structures with few purlin point loads the error
can be large. And for those small structures it may be that the C&C
pressures control the size of element. This result being a practical output
of applying the code: not a direct requirement of the code.

As far as I can tell everyone is in rough agreement, and arguing in parallel
namely: caution needs to be exercised when assessing an element, its
function and tributary area, and the importance of the influence of C&C
pressures versus MWFRS pressures.

It is also important to know when you are using a conservative
interpretation of the code, and to avoid arguing that the guy down the
street has got it wrong and I don't know how they can get away with it.

Since I use AS1170.2 not ASCE7-05, I may just see what happens when I apply
k[l] to everything, not just the cladding and immediate supports. Noting
that for small buildings the dimension 'a' is dependent on the footprint of
the building, but for large footprint buildings it becomes dependent on the
building height. That is a point is reached at which 'a' is a constant and
further increase in footprint, makes 'a' an increasingly smaller and smaller
portion of the building surface. A spike in pressure in this zone has less
and less effect. Cannot do this with ASCE7 since don't have windward and
leeward C&C pressures. 

Just thinking out aloud.



Regards
Conrad Harrison
B.Tech (mfg & mech), MIIE, gradTIEAust
mailto:sch.tectonic(--nospam--at)bigpond.com
Adelaide
South Australia 



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