Moment of Inertia Deflection equation

[JimCrown]

I am currently looking at moment of inertia. I don’t knowwhether this is right or wrong. Please help.




Maximumdeflection of a cantilevered beam with a uniform load is given by the followingequation

d = wL³/ (8EI)​

if E is 65x10⁹ PA

Deflection dis 12mm and beam is 3.5m long, w = 125Kg/m what size and units would I, themoment of inertia be?


3.5^3 = 42.875

125 x 42.875 = 5359.375



65 x 10^9 = 65000000000

65000000000 x 8 = 520000000000



12 = 5359.375 / (520000000000I)

Times both side of the equation by 520000000000I

12 x 520000000000 = 624000000000

6240000000000I = 5359.375



5359.375 / 6240000000000 = 8.588741987^-9 mm^4



Would 8.588741987^-9 mm^4 be the moment of inertia

 

[Ishuda]

I am currently looking at moment of inertia. I don’t knowwhether this is right or wrong. Please help.




Maximumdeflection of a cantilevered beam with a uniform load is given by the followingequation

d = wL³/ (8EI)
​

if E is 65x10⁹ PA

Deflection dis 12mm and beam is 3.5m long, w = 125Kg/m what size and units would I, themoment of inertia be?


3.5^3 = 42.875

125 x 42.875 = 5359.375



65 x 10^9 = 65000000000

65000000000 x 8 = 520000000000



12 = 5359.375 / (520000000000I)

Times both side of the equation by 520000000000I

12 x 520000000000 = 624000000000

6240000000000I = 5359.375



5359.375 / 6240000000000 = 8.588741987^-9 mm^4



Would 8.588741987^-9 mm^4 be the moment of inertia

As I understand it, the question is asking, in part, for units not the particular numerical answer. For example velocity has units of m/s (or equivalent other length units) and time has units of seconds s. So, given an initial distance of zero at time zero and the formula for distance
d = vt
we have
units of d = units of v times units of t = (m/s) s = metres

 

[JimCrown]

As I understand it, the question is asking, in part, for units not the particular numerical answer. For example velocity has units of m/s (or equivalent other length units) and time has units of seconds s. So, given an initial distance of zero at time zero and the formula for distance
d = vt
we have
units of d = units of v times units of t = (m/s) s = metres

Isn't moment of inertia always measure in mm^4 in SI units?

 

[stapel]

Isn't moment of inertia always measure in mm^4 in SI units?

Maybe, but the exercise didn't ask you for the customary units. It asked for the units in this particular case, given these particular inputs.