Theatre Design & Technology - Summer 1987 - 24

MEASURING THE DEFLECTION OF YOUR MODULAR STAGING: PREDICTED AND ACTUAL

Table 3: Measured Versus Calculated
Deflections for Concentrated (400 Ibs.) &
Uniformly Distributed Loads (75 psf)

Platform!
Test
Measured

Predicted Difference % Discrepancy

I

A-I

0.1181

0.0-+73

0.708

16-\

B-1

0126

0.0382

00878

229

C-I

01151

00351

0.08

227

0-1

0.0769

0.0328

00-\-\1

13-\

A-2

0.16-\-\

0.0-\-\-\

0.12

270

B-2

I 01967

0.0363

0.160-\

-\51

C2

0.1-\9

0.0329

01167

35-\

0-2

0115-\

0.0308

008-\6

27-\

Note: All measurements in inches; all measuremems taken at
LVDT#3.
Test I is for concemrated load; Test 2 is uniformly distributed load.

not analagous to the textbook behavior of simplysupported beams. Figure 7 illustrates one possible reason
for this discrepancy.
Beam analysis assumes that a beam (or platform) is
rigidly supported at each end, a condition not common
to theatre staging with the exception of stud wall supports. The conventional platform module, suspended on
four points, deflects alnng all four edges. Its center deflection is influenced by these edge deflections and is
consequently far greater than anticipated. This suggests
that the platform reacts to the imposed loads in the
manner of a plate, the plane of which, when loaded,
deforms much like the canvas sheet of a trampoline.
In an attempt to reconcile the discrepancy between
actual and predicted values, we investigated an approach
that subtracted the deflections measured at the edges
[LVDTs 6 & 9) from the deflection recorded at the center
of the 4 x 4 module (LVDT 3). This action should in effect
"cancel" the edge deflections. Evidence that is does not is

Figure 7: Schematic Showing Deformation of a Plate Supported on Four
Corners, All Edges Unsupported.

B

/

-- T

/'----

/

E~ge

x

TD&T . SUMMER 1987

Acknowledgements:
I. Our research has been supported thus far by grants from the
University of Wisconsin Graduate School and US ITT, which
awarded this project the first USITT Endowment Fund grant.
2. We owe a debt of gratitude to Professor Bronislaw Sammler,
head of the Yale Technical Production Department, through

Table 4: A Comparison of Actual and
Predicted Center Deflections Corrected for
Edge Deflections; UDL of 75 psf

/

"

*/
)-

",- Eoge
Oeflectlon

Relative
Center
Predicted
Percent
Deflection Cnrr. DeL Discrepancy

Platform!
Test

Measured
Deflections

A-3

T.3=0.164-\
T.6= 0.0839
T.9=0.0915

0.0767

0.0-\-\-\

72.7%

B-3

T.3=0.1967
T.6=0.1092
T.9=01222

00810

0.0363

123.1%

C-3

T.3=0.1-\9
T.6=0.1129
T.9=0.1387

0.0232

0.0329

67.8%

0-3

T.3 = 0 115-\
T.6=0.0811
T.9 = 0.087/

0.0313

0.0308

11.-\%

/'/

_~//ID

---~--

Deflection

22

7'-

/

- /-'
. .- - - - -...----/-,;./..."I~
'----

- - -

1. Given a four-foot span between supports, a modular 4' x 8' st3ge platform constructed with a
2 x 4 frame on2' centers [beam orientation parallel with the short side) and %" AC plywood deck
is capable of sustaining a uniformly distributed
load of approximately 100 psf. Additional stiffness, up to 125 psf, can be obtained by substituting %" OSB in place of the plywood.
2. Rectangular steel tubing (1"x2", 16 ga.) is capable of sustaining approximately 90 psf under the
same conditions as in No.1 above; it is not as stiff
as the 2 x 4 lumber frame.
3. No easily-manipulated mathematical model exists that accurately predicts the behavior of theatre staging since it does not appear to behave in
accordance with simple beam theory. Rather, it
more closely resembles plate theory which is a
considerably more difficult mathematical
model, requiring substantial effort to employ.
4. It would be enormously useful to the theatre
community to have available a working set of
guidelines which, in essence, functions as a design code. This set of performance standards
could serve as a point of departure for all
applications.

(

Center ~
<- /,deflection

--

shown in Table 4. Although Platform D exhibits values
similar to the prediction, there are such significant discrepancies in the other three predictions as to suggest
that standard beam formulas are inappropriate tools for
analysis of stage platforming supported by discrete column legs.
In summary, our investigation thus far has led us to
draw the following conclusions:

Notes: I. All displacements shown in inches
2. RCD = T3 -IT6 + T9j12
3. Percem Discrepancy = RCD!PD



Table of Contents for the Digital Edition of Theatre Design & Technology - Summer 1987

Contents
Theatre Design & Technology - Summer 1987 - 1
Theatre Design & Technology - Summer 1987 - 2
Theatre Design & Technology - Summer 1987 - 3
Theatre Design & Technology - Summer 1987 - Contents
Theatre Design & Technology - Summer 1987 - 5
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