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# Re: Diaphragm Calculations

• To: mtv(--nospam--at)skilling.com
• Subject: Re: Diaphragm Calculations
• From: Seaintonln(--nospam--at)aol.com
• Date: Fri, 9 Jul 1999 01:25:33 EDT
• Cc: seaint(--nospam--at)seaint.org

```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:

deformation of the diaphragm.  Here is how the equation is derived.

Assume:
Simple span beam
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

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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>>

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