Theatre Design & Technology - Spring 1981 - 21

Mmax

Maximum facing bending stress =

ht,

where h = t e + t,
t e = core thickness
t f = thickness of one facing
If maximum does not exceed allowable, the final check is core
shear stress.
Allowable core shear stress =
core shear stress x 80%
(from tables)
Safety Factor
Shear stress is simply the tendenc)l of a material or structure
to separate in two. The two blades of a scissors apply enough
force to opposite faces of paper that it shears in two. Shear
forces exist both parallel and perpendicular to the plane of the
material. Because plywood is a laminate the veneers in a
panel must be securely joined or they will slide past each
other-sliding shear. Interestingly, an adhesive can actually
increase the shear resistance of a laminate over a solid piece
of the same thickness. Honeycomb sandwich beams face the
same problem-the paper core offers relatively small surface
contact with the facings so sound adhesion of all cell edges is
essential to prevent the material from submitting to shear
forces. To account for possible poor adhesion or any cell deformation the core shear stress value is taken at 80% of the
table value.
Vmax
Maximum core shear stress = - h When none of these maximum values have exceeded the allowables, the beam meets the design's structural demands.
Modifications can now be made in materials selection for
more efficient use if the maximum stresses appear exceedingly far below the allowable values.
This analysis involves considerable calculations with every
trial. Without a familiarity with the sandwich components in
finished form, extensive trial and error may be necessary before arriving at a workable combination of facing and core
thicknesses. Facility with math is also an asset. Lacking either, a first time user may be reluctant to begin analysis of a
sandwich beam design. I reacted this way when it was suggested we try using honeycomb core for a variety of scenic
elements at UC Santa Cruz. For reasons of both safety and
economy I wanted hard data on this new structural material.
During my initial exposure to honeycomb sandwich structures
I attempted to calculate each intended use longhand, but this
method proved lengthy and random. After four productions
applying this tedious method, both George Smith of Honeycomb Structural Products and Tom Corbett urged me to translate these formulas into a series of programs which would derive beam and column analysis for a variety of scenic
applications using our most common materials and loading
criteria.
The following graphs illustrate part of the output of these
programs by demonstrating suggested core and facing material combinations for the given range of load and span situations in a simple beam, uniform load structure. In addition, a
table of deflection values accompanies each graph. These are
supplied to allow for adapting the materials choice if more
headway between allowed and maximum is desired. In the calculations a safety factor of 1.8 is used to modify the allowable
values for facing bending stress and core shear stress. Additionally, 80% of the core's modulus of rigidity value is used in
computing maximum deflection, and as was noted earlier,
80% of the table value is figured in allowable core shear
stress. These steps, under moderate load conditions, and with
proper fabrication techniques, should provide sufficient safety
margin for most short term use. Using the deflection tables is
an option on the part of the user to increase this margin and
allow for a varying degree of fabrication skill, loading circumstances, and use conditions. The graphs alone, however, do
provide accurate information for general applications.

Although the data in these graphs and tables reflect only
the use of plywood facings-1 /8", 1/4", 3/8", 1/2" (APA
Species Group 1 or 2, Grade Stress Level S-1, Exterior
glues}--other facing materials could be used and would produce different but possibly more desirable structural values.
Where extreme rigidity is needed masonite or other hardboard
would be a good facing choice, however, its weight contributes a negative factor to the finished unit's dead load. Sheet
steel or aluminum would provide substantial increase in beam
strength if properly joined to the paper core.
The other material choice represented here is the cell size
of the core. All these graphs demonstrate values for untreated
80 lb. Kraft Paper honeycomb with a 3/4" cell cross-section-1 /2" to 8" thick in 1/2" increments. Larger celled core
results in lower structural values; smaller cells in higher values. Cell sizes smaller than 3/4" are very difficult to manually
expand or stretch out from the unexpanded or compressed
state in which they are manufactured and shipped. KP3/4-80
(O)E expands easily without special tools and you will find it
the most versatile size for most scenic applications.
To demonstrate use of the graphs and tables, let us design
a scenic platform-a honeycomb sandwich beam. The design
criteria require a sixteen foot span, four feet wide (16 ft x 4 ft
= 64 ft2) and the capability of carrying a maximum of twelve
actors averaging 150 Ibs (12 x 150 Ibs = 1800 Ibs live load).
If, because it is relatively inexpensive, we choose 1/4 inch
ADX plywood as facing material, from the chart below we can
add approximately 25 Ibs per sheet of dead load to the beam
(two sheets top and bottom = 4 x 25 Ibs = 100 Ibs.).

Thickness
1/8"
1/4"
3/8"
1/2"

WEIGHT OF PL YWOOD
psf
0.4
0.8
1 .1
1.5

x 8' panel
12.81bs
25.61bs
35.21bs
48 Ibs

The weight of the core in its expanded form is:
Thickness
f
10
ps.
For an estimate, take the weight of six inch core (0.6 Ibs x 64
2
ft = 38.4 Ibs.). When this is added to the plywood weight the
dead load equals 138.4 Ibs and the total load is 1938.4 Ibs.
To determine the uniform load divide this by the area of the
platform:
1938.4 Ibs = 30 29
f
64 ft2
.
ps .
Now, refer to Graph 2, which plots core thickness at uniform load levels for 1/4" plywood facings. From 16 on the xaxis (ft of span) follow the line up until it intersects the 30 psf
tracing. From this point move horizontally to the left and read
the core thickness value on the y-axis, 6 Y2". This combination
would provide a structure adequate for your needs. Similarly,
if you chose 1 /8",3/8", or 1 /2" facings, the graphs indicate
you should use 7%", 6", and 6" thick core, respectively.
The final step in this design process is to examine the deflection values for your probable combination of core and facing thickness in the tables. (Tables 1-4 list the deflection values only for the facing and core combinations on Graphs 1-4:
the core thickness is omitted here for clarity.) In the span column find sixteen feet and move right. Read the allowable deflection:
16
. h
240 = 0.8 Inc es.
This value remains constant regardless of load. Compare this
to the maximum deflection on the same line under the 30 psf
column of Table 2: .713005 inches. This allows a margin of
around 10% between allowable and maximum, and unless
shock forces or center loading are anticipated, such a margin
should be sufficient. By contrast, in this same case (16 ft
span, 30 pst) considerably less deflection margin exists for ei-

Table of Contents for the Digital Edition of Theatre Design & Technology - Spring 1981