Moment of Inertia, working backwards

[Niall]

I've to work out b & d in this equasion.

I=bd^3/12

I know that the ratio between b & d in this case is 1.166 and I am given the value of I.

It is an engineering problem as the software will only allow the use of square/rectangular or round section but we are using H section and we are allowed to substitue a rectangle of the same h/w ratio and moment of inertia.

This kind of thing was never what I was much good at although I believe it may be possible to work out but I don't know how.
Thanks

 

[DrClaude]

I know that the ratio between b & d in this case is 1.166 and I am given the value of I.

Do you mean $\frac{b}{d} = 1.166$? Then $b = 1.166d$, put that into your equation for the moment of inertia, and solve for $d$.

 

[Niall]

Yes , I managed to figure it out a few min ago.

Ixx = (D (1.116) * D ^ 3) / 12

D^4 = I * 12 * 1.116

D = 4√ I * 12 * 1.116

 

[HallsofIvy]

In your original post you used "d". In your response you used "D". It is a bad idea to switch symbols like that.

 

[CellCoree]

for reaching out with your question. I would approach this problem by first defining the variables and understanding the equation. Moment of inertia is a measure of an object's resistance to changes in rotation. In this equation, I represents the moment of inertia, b represents the width of the object, and d represents the depth of the object.

To work backwards and solve for b and d, we can rearrange the equation to isolate b and d on one side. First, we can multiply both sides by 12 to get rid of the fraction:

12I = bd^3

Next, we can take the cube root of both sides to get rid of the exponent on d:

(12I)^(1/3) = d

Now, we can substitute the given ratio of 1.166 for b/d into the equation:

(12I)^(1/3) = (1.166d)^3

Solving for d, we get:

d = (12I)^(1/9) / 1.166

To solve for b, we can use the given ratio again:

b = 1.166d

Substituting the value of d we just solved for, we get:

b = 1.166(12I)^(1/9) / 1.166

Simplifying, we get:

b = (12I)^(1/9)

So, to summarize, to solve for b and d in this equation, we first rearrange the equation and isolate d. Then, we substitute the given ratio for b/d and solve for d. Finally, we use the given ratio again to solve for b. I hope this helps and good luck with your engineering problem!