Combined Axial & Bending Stress In Column

[SBSDesign]

I have written an Excel spreadsheet to solve the equation

fc/Pc + fbc/(Pbc(1-fc/Pe))<=1

It works by using the 'Goalseek' command in a macro to make the answer 0.99 (i.e. <1) by varying the value of fc. HOWEVER depending on where you start with the value of fc it can find up to 3 solutions to the above equation which work!

The reason I've done it this way is because fc appears in the formula twice which makes it a trial error exercise to find the solution.

Is there anyone who knows how to re-arrange the above formula to get fc on its own?

Thanks

 

[Drej]

Try: fc <= (Pbc-fbc)/((1/pc)+(pbc/pe))

 

[SBSDesign]

Thanks Drej. Gave it a try, but it doesn't seem work.

 

[desertfox]

Hi SBSDesign

I have rearranged the formula and I get the same answer as
Drej, can you give anymore information ie :- what are the
Pbc, pc, etc in terms of numbers and units.


regards desertfox

 

[Denial]

I do NOT get the same answer as Drej and desertfox. I get a rather unattractive quadratic equation to be solved for fc, whose result is beyond my presentation powers in this medium. A quadratic is exactly what one would expect, given that fc appears in the numerator of one of the terms and in the denominator of the other. The work involved is not difficult, merely tedious and error-prone.

 

[desertfox]

Hi Denial,SBSDesign
You are correct Denial it is a quadratic, I realise now I
misread the original equation I thought that the equation

was :- fc/Pc + fbc
----------- <=1
Pbc(1-fc/Pe)

Assuming I have read it correctly this time I get this Quadratic equation:-


-(Pbc*fc^2/(Pc*Pe)) + Pbc*fc*(1/Pc + 1/Pe) + Pbc + fbc


SBSDesign if you can work all the coefficients other than the fc you could use the formula below to solve the above


-b +/- [b^2-4*a*c]^0.5
----------------------
2*a



regards Desertfox

 

[SBSDesign]

Thanks Denial & Desertfox,

Desertfox,

You'll have to forgive my ignorance. It's 10yrs since I did HNC Building and 20 years since I did 'O' level maths!!

The term 'quadratic equation' rings faint bells somewhere in the depths of my very dodgy memory. However, I haven't got the foggiest idea what you're talking about.

Where did a, b & c come from? I'm sorry but I'm totally confused now. It looks like something used to calculate the orbit of Mars Express to me!

Can you explain further to a Maths beginner?

Thanks (in worried anticipation).

SBSDesign.

 

[SRO]

Try entering

fc/Pc + fbc/(Pbc(1-fc/Pe))

in a cell as the eq. then use the SOLVER comand from the tool menu. It is a very useful add in.

click TOOLS-->ADD INS
CHECK &quot;SOLVER ADD-IN

then you should be good to go

 

[desertfox]

Hi SBSDesign

Thanks for your reply, the a,b,c as you put it are the coefficients of the formula which you calculate from your other values ie:- Pbc,Pe etc


for example :- 2x^2 - 8x + 3 = 0

then a=2

b=-8

c=3
the formula is standard for solving a quadratic equation and usually gives two roots for the unknown &quot;x&quot;


so -(-8) +/- [-8^2 - 4*2*3]^0.5 8+/- 6.32455532
-------------------------- = ---------------
2*6 12

therefore x= 1.19371... or 0.13962039

so where I have &quot;x&quot; you need to have fc in place, and work out the numerical values of the other symbols so the quadratic equation in the earlier post reads
similar to the example here.

ie (- 84fc^2 + 45fc + 10)

hope this helps

regards desertfox