Installation and Safety Guidelines Page 21
pro.Bose.com Appendix
Example Free Body Diagram Determination of WLL:
The following example shows a free body diagram determination of the working loads for a RoomMatch™ array of RM7005, RM7010,
RM9010, RM9020, and RM12020 modules with a 0-degree frame pitch.
Step 1. Determine the array center of gravity in the X-axis using the equation:
X
COG
= ∑ X
M
* W
M
Where: X
COG
= X-axis distance of array COG from reference fastener
W
A
X
Mn
= X-axis distance from reference to module COG for module n (n = 1 to 8)
W
M
= Weight of module (example: 56.7 kg)
W
A
= Weight of total array (example: 283.5 kg)
(6.51)*(56.7) + (10.69)*(56.7) + (21.08)*(56.7) + (38.8)*(56.7) + (66.69)*(56.7)
X
COG
= = 28.75 cm
(283.5)
Step 2. Free Body Review. Assuming the front fastener is a pivot point and the rear fastener is bearing the entire load (a conservative
approach), the following free body diagram can be developed for one side of the top module:
Where: M
1
= Moment (rotational) force about front module fastener
F
1
= Force applied on rear-module fastener
F
COG
= Force applied by total array per side (1/2 of total weight)
X
1
= X-axis distance from front to rear fastener (15 cm)
X
COG
= X-axis distance from array center of gravity to front fastener
Reference fastener
6.51 cm (X
M1
)
10.69 cm (X
M2
)
21.08 cm (X
M3
)
38.80 cm (X
M4
)
66.69 cm (X
M5
)
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