My Math Forum  

Go Back   My Math Forum > College Math Forum > Linear Algebra

Linear Algebra Linear Algebra Math Forum


Thanks Tree1Thanks
  • 1 Post By skipjack
Reply
 
LinkBack Thread Tools Display Modes
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)
Attached Images
File Type: png Attachment1.PNG (8.9 KB, 6 views)
File Type: png Attachment 2.PNG (2.0 KB, 25 views)
hatchelhoff is offline  
 
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 $d = 2\sqrt{\dfrac{P_{cr}}{\pi S_y} + \dfrac{S_yl^2}{C\pi^2E}}$.
Thanks from Country Boy
skipjack is offline  
August 19th, 2017, 08:36 AM   #3
Member
 
Joined: Nov 2011

Posts: 71
Thanks: 0

Thank skipjack
hatchelhoff is offline  
Reply

  My Math Forum > College Math Forum > Linear Algebra

Tags
formula, transposition



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Transposition of formula carbonkid1985 Applied Math 1 May 10th, 2016 05:12 AM
Transposition of formula maths moth Algebra 1 March 19th, 2016 07:38 AM
simple transposition rightsidedbrain Algebra 3 June 3rd, 2014 01:16 AM
Transposition of Formula, Real Life Applications manich44 Algebra 1 December 27th, 2011 09:29 PM
Transposition of Formula pauliewalnuts Calculus 2 May 6th, 2008 09:09 PM





Copyright © 2017 My Math Forum. All rights reserved.