Poisson's ratio

please help on this formula how it has been arrived?

dA=A(1-m dL/L)^2-A

where m= Poisson's ratio
A=area of cross section
L=length

 

gauge factor

While deriving the formulae for Gauge factor of materials(resitors) in strain gauges it comes.In between they have given this formula.

First they told

R=PL/A

R=RESISTANCE
P=SPECIFIC RESISTANCE
L=LENGTH
A= AREA

Then,

dR=a(PdL+LdP) - P L da
-------------------
a^2

Divide L.H.S by R and R.H.S by PL/A we get

dR dL dP dA
-- = --- + ---- - ----- (eqn 1)
R L P A



And suddenly they give this formula

as

dA= A(1-m dL/L)^2 -A

m=poisson's ratio

they substituted this in equation (1)
and finally arrived at gauge factor (dR/R)/(dL/L)

 

Please I need a answer How this formula is obtained?

da=a(1-m dl/l)^2 - a

please help me.

 

Book reference

It is from "Transducer Engineering" by S.Renganathan

 

please provide me the proof for this formulae:

da=a(1-m dl/l)^2-a
i.e., da/a=(1-m dl/l)^2 -1
=1+m^2 (dl/l)^2-2m dl/l -1
=(m dl/l)^2 - 2m dl/l

so da/a= (m dl/l)^2 - 2m dl/l
=m dl/l(m dl/l -2)

so

(da/a)/(dl/l)=m^2 (dl/l)-2m

now atleast you can say me how we arrive at this formula.Because I don't know any of the mechanical concepts and also about Poisson ratio.If you find any material regarding these please send me.My e-mail Id is

saravanan_n@msn.com

 

Sorry for being impatient,Since I have test on this I have to hurry.
Now we get
DR/R=DL/L+DP/P-DA/A

Then we divide whole eqn by dl/l

(dr/r)/(dl/l)=1+(dp/p)/(dl/l)-m

so we can put
Gauge Factor=1+Piezoresistivity-Poisson ratio

Is this equation right?

 

Equation Not Agrreable

If you say Poisson Ratio =(da/a)/(dl/l)

then do you agree with this equation also

da=a(1-((poisson ratio) dl/l)^2)-a
(in whatever context it comes)

 

Thanks for the reply.I am very much pleased.Thank you!!!