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Rearrange formula

spikeybrummy

New member
Joined
Dec 23, 2014
Messages
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:


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
Joined
Jun 18, 2007
Messages
18,087
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
Please provide the missing equations.
 

spikeybrummy

New member
Joined
Dec 23, 2014
Messages
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
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,087
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
Joined
Dec 23, 2014
Messages
6
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
 

HallsofIvy

Elite Member
Joined
Jan 27, 2012
Messages
4,715
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.
 

spikeybrummy

New member
Joined
Dec 23, 2014
Messages
6
Thank you HallsofIvy, you are a star.:p
 

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
2,750
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
Joined
Jun 18, 2007
Messages
18,087
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?
 
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