Algebra Help - Concrete Neutral axis

[Cojack]

Probably a stupid question, but need some basic algebra help regarding elastic analysis of rectangular section.
Solve for k:

How do you get from
k^2/n(1-k) = 2p

to

k = (sqroot 2pn + (pn)^2)-pn

If someone could break that down that would be great.

 

[GregLocock]

multiply through by n(1-k), subtract 2p and you have a quadratic in k. My maths teacher would give zero for your answer, there are two alternatives.

Cheers

Greg Locock


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[rb1957]

well greg did two steps together ...

multiply by n(1-k) to get k^2 = 2pn(1-k)

then subtract the right hand side to get k^2+2pnk-2pn = 0

solution of quadratic k = -b+-sqrt(b^2-4ac)/2a ... k = -2pn+-sqrt((2pn)^2-4(-2pn))/2
k = -pn+-sqrt(4((pn)^2+2pn))/2
k = -pn+sqrt((pn)^2+2pn) ... the "-" gets an unreal -ve solution
that's nearly what you've written, with some "tolerance" on where the brackets are ...

another day in paradise, or is paradise one day closer ?

 

[Cojack]

Thankyou both. Rb1957 cheers for the extra steps