My Math Forum Formula Transposition

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August 17th, 2017, 11:47 PM   #1
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Formula Transposition

I need to solve the Equation for Pcr/A to find d.
The equation for Pcr/A is given in Attachment_1.
The answer that I need to get is given in Attachment_2.
note
A represents Area which is (PI(D^2))/4)
K represents radius of gyration which is (d/4)
Attached Images
 Attachment1.PNG (8.9 KB, 6 views) Attachment 2.PNG (2.0 KB, 25 views)

 August 18th, 2017, 04:38 AM #2 Global Moderator   Joined: Dec 2006 Posts: 19,162 Thanks: 1638 The second equation implies $\displaystyle 4AS_y = 4P_{cr} + 4Abl^2/k^2\!$. Replacing $4A$ with $\pi d^2$ and $k^2\!$ with $(d/4)^2\!$ gives $\displaystyle \pi d^2S_y = 4P_{cr} + \pi d^2bl^2/(d/4)^2 = 4P_{cr} + 16\pi bl^2$. Replacing $b$ with $\dfrac{S_y^2}{4\pi^2CE}$ gives $\displaystyle \pi d^2S_y = 4P_{cr} + 4\dfrac{S_y^2l^2}{\pi CE}$. Dividing both sides by $\pi S_y$ gives $d^2 = 4\left(\dfrac{P_{cr}}{\pi S_y} + \dfrac{S_yl^2}{C\pi^2E}\right)$. Hence $d = 2\sqrt{\dfrac{P_{cr}}{\pi S_y} + \dfrac{S_yl^2}{C\pi^2E}}$. Thanks from Country Boy
 August 19th, 2017, 07:36 AM #3 Member   Joined: Nov 2011 Posts: 72 Thanks: 0 Thank skipjack

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