Need a book? Engineering books recommendations...

Return to index: [Subject] [Thread] [Date] [Author]

Re: Diaphragm Calculations

[Subject Prev][Subject Next][Thread Prev][Thread Next]
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 

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

<< Dennis:
 The deflection term you are asking about represents the flexural 
 deformation of the diaphragm.  Here is how the equation is derived.
 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.
<<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 
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 

What am I missing???????


 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