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# Re: Diaphragm Calculations

• To: mtv(--nospam--at)skilling.com
• Subject: Re: Diaphragm Calculations
• From: Seaintonln(--nospam--at)aol.com
• Date: Thu, 15 Jul 1999 14:33:14 EDT
• Cc: seaint(--nospam--at)seaint.org

```Mike, I was reviewing your calculation for the conversion of the diaphragm
deflection (simple span part) and came up with a different solution than you.
Can you please review my notes below and let me know where I may have gone
wrong?

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

<< 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.
*******************************************************
<<Dennis>> Mike, I may be confused by your Moment of Inertia term I which you
define as:

I = (A b^2 ) / 2

Since the basic formula for I is (base * height^3)/12  we can assume the base
to be the span between shear elements or gridlines (L) and the height to be
the depth of the diaphragm (b). Therefore the formula changes to I = (L
b^3)/12.
If the area is L*b the formula reduces to:  I = (A*b^2)/12

combining all of the terms:

Deflection = 5*2 v b L^4 12  / (384 E A b^2) which then reduces to:

Deflection = 5 v L^3 / (16 E A b)

This still does not balance to match the deflection formula 5 v L^3 / (8 E A
b)

What am I missing???????

Dennis

*************************************************************
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