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Re: Diaphragm Calculations

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Finally, a rational human being. Thank you, thank you, thank you. For some 
reason I tried to work it the same way but forgot about the Moment of Inertia 
term and my denominator did not reduce to 96 which through me off. 

Now, why couldn't this have been told to us up front rather than try to skirt 
the issues. 

Have you looked at the nail slippage terms. This is the only one that does 
not seem to balance. If you can solve this one, then the entire equation does 
balance and is therefore justified.

Again, you used your intelligence instead of trying to convince us to accept 
this on faith and I really appreciate your efforts for this. I hope you don't 
mind, but others want to know this as well and I am posting your response to 
the list. 

I am greatful to you.

Regards,
Dennis


In a message dated 7/8/99 6:54:19 PM Pacific Daylight Time, mtv(--nospam--at)skilling.com 
writes:

<< Subj:	 Re: Diaphragm Calculations
 Date:	7/8/99 6:54:19 PM Pacific Daylight Time
 From:	mtv(--nospam--at)skilling.com (Michael Valley)
 To:	Seaintonln(--nospam--at)aol.com
 
 Dennis:
 
 The deflection term you are asking about represents the flexural 
 deformation of the diaphragm.  Here is how the equation is derived.
 
 Assume:
 Simple span beam
 Uniformly distributed load
 Base diaphragm moment of inertia on chords only
 
 Maximum deflection = ( 5 w L^4 ) / ( 384 E I )
 Maximum shear force, V = w L / 2
 Maximum unit shear, v = V /  b
 
 I = sum (A d^2), where d = b / 2
 
 So, I = (A b^2 ) / 2
 
 Substituting (and simplifying),
 
 Maximum deflection = (5 v L^3 ) / ( 96 E A b )
 Given the units noted in the code, the deflection is in feet.
 
 Max defl (inch) = (5 v L^3 ) / ( 8 E A b )
 
 or,  = (5/8) (v L^3 ) / ( E A b )
 
 As a point of interest, this also highlights the limitations 
 (assumptions) of the formula.  If we say that for all load conditions 
 and all boundary conditions,
 
 Max defl (inch) = X (v L^3 ) / ( E A b )
 
 X is 5/8 for single, simple span with uniformly dist load, but can 
 range from 1/8 (fixed-fixed, unif load) to 1 (pin-roller, centered 
 point load).
 
 The second term of the deflection is based on a similar derivation 
 for the deflection due to shearing of the "web".
 
 The equation for shear wall deflection (flexural and shear) is 
 derived based on a cantilever column with a concentrated load at the 
 top.
 
 -Mike
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 Michael Valley                                   E-mail: mtv(--nospam--at)skilling.com
 Skilling Ward Magnusson Barkshire Inc.                  Tel:(206)292-1200
 1301 Fifth Ave, #3200,  Seattle  WA 98101-2699          Fax:        -1201
 
 
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