# Rearrange formula

#### spikeybrummy

##### New member
Hi,

I have an engineering question in a struggling to solve.

I have a Second Moment of Area question, where I need to replace a solid cylindrical beam with a hollow one.

For the solid beam, the second moment of area is:

For the hollow beam, the external diameter (D) needs to be x2.5 the internal diameter (d), therefore d=D/2.5

The formula I need to rearrange to make "D" the subject is:

Any help is much appreciated
Kind regards

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi,

I have an engineering question in a struggling to solve.

I have a Second Moment of Area question, where I need to replace a solid cylindrical beam with a hollow one.

For the solid beam, the second moment of area is: Your gr
aphics is missing

For the hollow beam, the external diameter (D) needs to be x2.5 the internal diameter (d), therefore d=D/2.5

The formula I need to rearrange to make "D" the subject is: Your gr
aphics is missing

Any help is much appreciated
Kind regards

#### spikeybrummy

##### New member
Apologies:

The formula I need to rearrange is: I=(pi*D^4/64)-(pi*d^4/64)

"D" is the external diameter and "d" is the internal diameter.
As the external diameter is 2.5times the internal, I can substitute "d" with "D/2.5"
I (second moment of area) = 9.5*10^-6

#### Subhotosh Khan

##### Super Moderator
Staff member
Apologies:

The formula I need to rearrange is: I=(pi*D^4/64)-(pi*d^4/64)

"D" is the external diameter and "d" is the internal diameter.
As the external diameter is 2.5times the internal, I can substitute "d" with "D/2.5"
I (second moment of area) = 9.5*10^-6
I*64/π = D[SUP]4[/SUP] - d[SUP]4[/SUP]

I*64/π = D[SUP]4[/SUP] - D[SUP]4[/SUP]/(2.5)[SUP]4[/SUP]

I*64/π = D[SUP]4[/SUP] - D[SUP]4[/SUP]/39.0625

Now continue....

#### spikeybrummy

##### New member
Hi Subhotosh Khan,

Thank you for the quick reply. Unfortunately my transposition is pretty poor and I cannot figure out the next step. If I take the denominator of 39.0625 over to the left, does that just leave "D^4 - D^4" on the right, which would then cancel each other out?

Sorry if this is basic stuff, I just can't see it.

#### HallsofIvy

##### Elite Member
Hi Subhotosh Khan,

Thank you for the quick reply. Unfortunately my transposition is pretty poor and I cannot figure out the next step. If I take the denominator of 39.0625 over to the left, does that just leave "D^4 - D^4" on the right, which would then cancel each other out?

Sorry if this is basic stuff, I just can't see it.
No, they don't cancel. You would be right if it were (D- D)/39.0625= 0. But what you have is $$\displaystyle D- D/39.0625= D- \frac{D}{39.0625}$$. That is, the "39.0625" is dividing only one of the "D"s, not both. What I would do is "factor out" the "D" and write this as D(1- 1/39.0625)= D(1- 0.0256)= 0.9744D.

#### spikeybrummy

##### New member
Thank you HallsofIvy, you are a star.

#### Jomo

##### Elite Member
Remember that a - a/b = (ab -a) / b
and a -a/b is not 0/b=0. Remember that before you can add or subt fractions you need to have common denominators.

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi,

I have an engineering question in a struggling to solve.

I have a Second Moment of Area question, where I need to replace a solid cylindrical beam with a hollow one.

For the solid beam, the second moment of area is:

For the hollow beam, the external diameter (D) needs to be x2.5 the internal diameter (d), therefore d=D/2.5

The formula I need to rearrange to make "D" the subject is:

Any help is much appreciated
Kind regards
Are you an engineering student?

If you are - what level of math have you had taken?