- #1
bugatti79
- 794
- 1
Folks,
I am trying to understand the balance of units for this eqn
## \displaystyle \frac{d^2}{dx^2}(E(x)I(x) \frac{d^2 w(x)}{dx^2})+c_f(x)w(x)=q(x)##
where ##E## is the modulus of Elasticity, ##I## is the second moment of area, ##c_f## is the elastic foundation modulus, ##w## is deflection and ##q## is the distributed transverse load.
Based on the above I calculate the units to be
## \displaystyle \frac{d^2}{dx^2}[\frac{N}{m^2} m^4 \frac{d^2 m}{dx^2}]+\frac{N}{m^2} m=\frac{N}{m}##
gives
##\displaystyle {Nm^3} +\frac{N}{m}=\frac{N}{m}##
##LHS \ne RHS##...?
I am trying to understand the balance of units for this eqn
## \displaystyle \frac{d^2}{dx^2}(E(x)I(x) \frac{d^2 w(x)}{dx^2})+c_f(x)w(x)=q(x)##
where ##E## is the modulus of Elasticity, ##I## is the second moment of area, ##c_f## is the elastic foundation modulus, ##w## is deflection and ##q## is the distributed transverse load.
Based on the above I calculate the units to be
## \displaystyle \frac{d^2}{dx^2}[\frac{N}{m^2} m^4 \frac{d^2 m}{dx^2}]+\frac{N}{m^2} m=\frac{N}{m}##
gives
##\displaystyle {Nm^3} +\frac{N}{m}=\frac{N}{m}##
##LHS \ne RHS##...?