Rearrange formula

spikeybrummy

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Joined
Dec 23, 2014
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6
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:
HEqQAAAKgA5AwAMAiQMwDAIPwHnlRzznsNj oAAAAASUVORK5CYII=


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:
AfBpFHfeF LQgAAAABJRU5ErkJggg==


Any help is much appreciated
Kind regards
 
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
HEqQAAAKgA5AwAMAiQMwDAIPwHnlRzznsNj oAAAAASUVORK5CYII=
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
HEqQAAAKgA5AwAMAiQMwDAIPwHnlRzznsNj%20oAAAAASUVORK5CYII=
aphics is missing
AfBpFHfeF LQgAAAABJRU5ErkJggg==


Any help is much appreciated
Kind regards

Please provide the missing equations.
 
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
 
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 = D4 - d4

I*64/π = D4 - D4/(2.5)4

I*64/π = D4 - D4/39.0625

Now continue....
 
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.
Thanks in advance
 
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.
Thanks in advance[/QUOTE
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.
 
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:
HEqQAAAKgA5AwAMAiQMwDAIPwHnlRzznsNj oAAAAASUVORK5CYII=


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:
AfBpFHfeF LQgAAAABJRU5ErkJggg==


Any help is much appreciated
Kind regards

Are you an engineering student?

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