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calculating plastic modulus Z thread507-195167

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hippo11 (Structural) 16 Aug

07 18:28

Can I do this without integrating?  For a rectangular section, it's easy, bt^2/4, but for a tee section for instance, is there an easy way to do this? And please don't tell me it's S * shape factor...:) thanks

StructuralEIT (Structural) 16 Aug

07 18:54

It is easy,  this has been covered before. Find the PNA (plastic neutral axis).  This is the axis about which there is an equal AREA of steel above and below. Now find the centroid of the area above and below the PNA. Now multiply the area of the steel above times the distance from the PNA to the centroid of the area above and add that to the product of the area below times the distance from the PNA to the centroid of the area below the PNA.   This will result in the area above OR below (which will be equal) times the distance between the two centroids. That is Z.

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Unt i t l ed

Pl ast i c Modul us

I t i s cal cul at ed.

For t he common cr oss sect i ons, t hese ar e t he equat i ons:

Rect angul ar - Z = . 25bh^2I sect i on - Z = ( bf ) ( t f ) ^3( d- t f ) + . 25( t w) ( d- 2t f ) ^2 ( St r ong Ax i s) Z = . 5( bf ) ^2( t f ) + . 25( d- 2t f ) ( t w) ^2

Sol i d Ci r cl e - Z = d^3/ 6Pi pe - Z = d^3/ 6( 1- ( 1- 2t / d) ^3)Hol l ow Rect - Z = bh^2/ 4( 1- ( 1- 2w/ b) ( 1- 2t / h) ^2)Di amond - Z = bh^2/ 12Channel - Z = bt ( h- t ) + . 25( h- 2t ) ^2

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Re: Plastic Section Modulus

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To: <seaint(--nospam--at)seaint.org>

Subject: Re: Plastic Section Modulus

From: "Gerard Madden, PE" <gmadden(--nospam--at)attbi.com>

Date: Thu, 2 May 2002 15:21:32 -0700

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It is calculated. For the common cross sections, these are the equations: Rectangular - Z = .25bh^2 I section - Z = (bf)(tf)^3(d-tf) + .25(tw)(d-2tf)^2 (Strong Axis) Z = .5(bf)^2(tf)+ .25(d-2tf)(tw)^2 Solid Circle - Z = d^3/6 Pipe - Z = d^3/6(1-(1-2t/d)^3) Hollow Rect - Z = bh^2/4(1-(1-2w/b)(1-2t/h)^2) Diamond - Z = bh^2/12 Channel - Z = bt(h-t) + .25(h-2t)^2 If you want, I can fax you a table, just give me your number -gerard Santa Clara, CA ----- Original Message ----- From: <RainCat1(--nospam--at)aol.com> To: <seaint(--nospam--at)seaint.org> Sent: Thursday, May 02, 2002 2:27 PM Subject: Plastic Section Modulus Is the plastic section modulus determined by calculation or by testing? My understanding is that it is determined by testing, and it has a constant ratio over the elastic section modulus for a given shape. Please enlightened me. Thanks! Rainier Catubig San Diego, CA * * This email was sent to you via Structural Engineers * Association of Southern California (SEAOSC) server. To * subscribe (no fee) or UnSubscribe, please go to: * * http://www.seaint.org/sealist1.asp *

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