(b*x)*x/2=mAst(d-x) ....help me to find X if b ,m ,Ast,d are known..file is attached

[krishna Prakash]

(b*x)*x/2=mAst(d-x) ....help me to find X if b ,m ,Ast,d are known..file is attached

 

[Nebu]

Hi:

What is your expected result.

Thanks

 

[Hui]

(b*x)*x/2=mAst(d-x)
Applying a bit of high school algebra

expand
bx^2/2=mAst(d-x)

expand
bx^2/2 = dmAst - xmAst

subtract dmAst - xmAst from both sides
bx^2/2 - dmAst + xmAst =0

divide both sides by b/2
x^2 - 2dmAst/b + 2xmAst/b = 0

add 2dmAst/b to both sides
x^2 + 2xmAst/b = 2dmAst/b

add mAst^2/b^2 to both sides
x^2 + 2xmAst/b + [mAst]^2/b^2 = 2dmAst/b + [mAst]^2/b^2

Write the left side as a square
(x+mAst/b)^2 = 2dmAst/b + [mAst]^2/b^2

take the square root of both sides
x+mAst/b = +/- Sqrt(2dmAst/b + [mAst]^2/b^2 )

Subtract mAst/b from both sides
x = Sqrt(2dmAst/b + [mAst]^2/b^2 ) -mAst/b
and
x = mAst/b - Sqrt(2dmAst/b + [mAst]^2/b^2 )

Note the two solutions

 

[krishna Prakash]

Hi:

What is your expected result.

Thanks

The Result of x is 234.6

 

[Hui]

which cells are
b ?
m ?
Ast ?
d ?

 

[krishna Prakash]

Thanks for your valuable response.....Its very helpful to me...I got the exact answer.
Is it possible to solve the equation (b*x)*x/2=m*Ast(d-x) directly in excel...

 

[krishna Prakash]

its a design of concrete rectangular beam.. b is the breadth of beam, d depth of beam, ast-area of steel used in the beam,m-modular ratio its a constant value..its value is 13.33...The value of b is 300 d is 550 ast is 1963.....
please see the attachemet of excel sheet

 

[Hui]

So my Algebra is spot on and returns 234.59

 

[krishna Prakash]

super sir,...u gave me the derived equation of (b*x)*x/2=mAst(d-x) as

= Sqrt(2dmAst/b + [mAst]^2/b^2 ) -mAst/b , i got he exact answer from this eqaution.

Is there any option in excel to get the answer directly without deriving this formula (b*x)*x/2=mAst(d-x) to Sqrt(2dmAst/b + [mAst]^2/b^2 ) -mAst/b,

Is is possible to solve an equation directly if we have equal symbol at the middle (E.g) (b*x)*x/2=mAst(d-x)

 

[Hui]

Yes, But you need to use Goal Seek
I15: X=
J15: 1
I16: =(D10*J15)*J15/2
J16: =D17*D15*(D13-J15)
K16: =I16-J16

Then goto the Data, What-If_Analysis, Goal Seek tab


Ok

After a few seconds


Enjoy

You can read about this here:
http://chandoo.org/wp/2013/09/19/how-to-solve-an-equation-in-excel/

 

[krishna Prakash]

Sir can you send me the solved excel worksheet.

 

[Hui]

Yes
It is your file from above with my instructions applied ?

 

[krishna Prakash]

Ya,Thank You very Much Sir,I noted it,Actually Goal seek function is new to me,That's the reason it take some time for me to get into it..Now i am very clear,You just helped me a lot...Thank very much from my side and my friends thanked u for helping me,because i was disturbing them for past 1 week to get this result in excel......

 

[krishna Prakash]

Sir Can i get ur name

 

[Hui]

http://chandoo.org/wp/about-hui/