August 18th, 2017, 12:47 AM  #1 
Member Joined: Nov 2011 Posts: 71 Thanks: 0  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. Can you solve Attachment_1 and see if your answer matches Attachment_2. note A represents Area which is (PI(D^2))/4) K represents radius of gyration which is (d/4) 
August 18th, 2017, 05:38 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,245 Thanks: 1439 
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 $d = 2\sqrt{\dfrac{P_{cr}}{\pi S_y} + \dfrac{S_yl^2}{C\pi^2E}}$. 
August 19th, 2017, 08:36 AM  #3 
Member Joined: Nov 2011 Posts: 71 Thanks: 0 
Thank skipjack


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