Theatre Design & Technology - Summer 1987 - 23

MEASURING THE DEFLECTION OF YOUR MODULAR STAGING: PREDICTED AND ACTUAL

yield a single homogeneous component section of predictable behavior. Furthermore, this procedure examines the effect of the materials working together rather
than as separate components which is frequently the
approach used in simplified analytical methods.
The key to generating the proper transformed section
is to keep in mind that the new section must have the
same stiffness or bending resistance as the original section. In applying the transformed section procedure to
Platform C, we find Y-," AC plywood has the greater
stiffness (modulus of elasticity or E = 1/, X 10 161 psi),
while a 2 x 4 has an E value = 1.2 x 10 16 } psi. If the
2 x 4/plywood section were transformed to one consisting of plywood only, the 2 x 4 would become narrower
since it is less stiff than the plywood. Conversely, if the
plywood were to be transformed to the 2 x 4, its width
would increase to account for its greater stiffness. It is
important to note that the depth of the section remains
unchanged since the deflections occur in the vertical
axis and must be identical to those of the original section. The analytical procedure of transformed sections
theoretically reconfigures the section into a homogeneous T-shaped beam of the dimensions shown in
Figure 6.

1\
Key

Tesl 2

* * L DT (transducer)

Area-

,

/

T9

-!

T

3

T 12
T8
/

T 1

T2

r-

*

I

-,

Test
Area_

-,

T4

*

I

CT3

TS

T7

T

T6

T 10
Plan With Deck Removed
3/4 Ply Deck

Section Showing Sluc:lwalla

Figure 5: Plan and Section of Platform C Showing LVDT Placement

Where £[ = Modulus of elasticity of component to be
'transformed'
£2 =Modulus of elasticity of 'common'
component
WI = Thickness dimension of component to be
,transformed'
Ts =Thickness dimension of transformed
section
Ts

(~J 1.5"
1200000) 1
( I800000 .:J

The formula used to predict the center deflection of a
simply supported beam carrying a concentrated load at
its midpoint is:

PP

6=48EI

Where P = Magnirudeofconcentrated load (lb.) = 4001b.
All other variables repeat those in the formula for
uniform loads.
Platform C. E = 1800000
I = 14.56 in. 4

,-/1

Ts

I"

In the next series of calculations we apply standard
beam formulas. Here we consider the entire platform
surface, as acting as a single, simply supported beam.
The numbers generated are for Platform C when
stressed under typical static loading conditions, i.e., a
uniformly distributed load of 75 psf and a concentrated
load at the center of the span of 400 psf.
The formula used to predict the deflection of a simply
supported beam carrying a uniformly distributed load
over its entire surface is:

6

5WL1
=--

Distributed Load:

6

=

5 (600) 48 3

Concentrated Load:
6

400 (48 3 1
= ----'------'----

384 (1800000)14.56

6 = 0.0329 in.

48 (1800000)14.56
6

0.0351 in.

=

There is a considerable disparity between measured
and predicted results as shown in Table 3. This discrepancy implies that the behavior of stage platforming is

Figure 6: Transformed Section of Platform C

ORIGNAl S[CTION

TRANSFOR/"'{O S[CTION

3 4EI

Where 6 = Predicted deflection lin.l at center of beam
W = Total weight lIb.) = 75 lb. x frI = 600 lb.
L = Length of beam span lin.) = .+8 in.
E = Elastic modulus of beam material
I = Moment of inertia about centroid of beam
(in. 4 1
TD&T· SUMMER 1987

21



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
Theatre Design & Technology - Summer 1987 - 6
Theatre Design & Technology - Summer 1987 - 7
Theatre Design & Technology - Summer 1987 - 8
Theatre Design & Technology - Summer 1987 - 9
Theatre Design & Technology - Summer 1987 - 10
Theatre Design & Technology - Summer 1987 - 11
Theatre Design & Technology - Summer 1987 - 12
Theatre Design & Technology - Summer 1987 - 13
Theatre Design & Technology - Summer 1987 - 14
Theatre Design & Technology - Summer 1987 - 15
Theatre Design & Technology - Summer 1987 - 16
Theatre Design & Technology - Summer 1987 - 17
Theatre Design & Technology - Summer 1987 - 18
Theatre Design & Technology - Summer 1987 - 19
Theatre Design & Technology - Summer 1987 - 20
Theatre Design & Technology - Summer 1987 - 21
Theatre Design & Technology - Summer 1987 - 22
Theatre Design & Technology - Summer 1987 - 23
Theatre Design & Technology - Summer 1987 - 24
Theatre Design & Technology - Summer 1987 - 25
Theatre Design & Technology - Summer 1987 - 26
Theatre Design & Technology - Summer 1987 - 27
Theatre Design & Technology - Summer 1987 - 28
Theatre Design & Technology - Summer 1987 - 29
Theatre Design & Technology - Summer 1987 - 30
Theatre Design & Technology - Summer 1987 - 31
Theatre Design & Technology - Summer 1987 - 32
Theatre Design & Technology - Summer 1987 - 33
Theatre Design & Technology - Summer 1987 - 34
Theatre Design & Technology - Summer 1987 - 35
Theatre Design & Technology - Summer 1987 - 36
Theatre Design & Technology - Summer 1987 - 37
Theatre Design & Technology - Summer 1987 - 38
Theatre Design & Technology - Summer 1987 - 39
Theatre Design & Technology - Summer 1987 - 40
Theatre Design & Technology - Summer 1987 - 41
Theatre Design & Technology - Summer 1987 - 42
Theatre Design & Technology - Summer 1987 - 43
Theatre Design & Technology - Summer 1987 - 44
Theatre Design & Technology - Summer 1987 - 45
Theatre Design & Technology - Summer 1987 - 46
Theatre Design & Technology - Summer 1987 - 47
Theatre Design & Technology - Summer 1987 - 48
Theatre Design & Technology - Summer 1987 - 49
Theatre Design & Technology - Summer 1987 - 50
Theatre Design & Technology - Summer 1987 - 51
Theatre Design & Technology - Summer 1987 - 52
Theatre Design & Technology - Summer 1987 - 53
Theatre Design & Technology - Summer 1987 - 54
Theatre Design & Technology - Summer 1987 - 55
Theatre Design & Technology - Summer 1987 - 56
Theatre Design & Technology - Summer 1987 - 57
Theatre Design & Technology - Summer 1987 - 58
Theatre Design & Technology - Summer 1987 - 59
Theatre Design & Technology - Summer 1987 - 60
Theatre Design & Technology - Summer 1987 - 61
Theatre Design & Technology - Summer 1987 - 62
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https://www.nxtbook.com/nxtbooks/hickmanbrady/tdt_1965Dec
https://www.nxtbook.com/nxtbooks/hickmanbrady/tdt_1965Oct
https://www.nxtbook.com/nxtbooks/hickmanbrady/tdt_1965May
https://www.nxtbookmedia.com