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Re: Diaphragm Calculations
[Subject Prev][Subject Next][Thread Prev][Thread Next]- 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: 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. ******************************************************* <<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 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 >>
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