Results 1 to 9 of 9

Thread: Rearrange formula

  1. #1

    Rearrange formula

    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

  2. #2
    Elite Member
    Join Date
    Jun 2007
    Posts
    17,784
    Quote Originally Posted by spikeybrummy View Post
    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.
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
    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

  4. #4
    Elite Member
    Join Date
    Jun 2007
    Posts
    17,784
    Quote Originally Posted by spikeybrummy View Post
    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....
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  5. #5
    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

  6. #6
    Elite Member
    Join Date
    Jan 2012
    Posts
    4,610
    [QUOTE=spikeybrummy;368110]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 [tex]D- D/39.0625= D- \frac{D}{39.0625}[/tex]. 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.

  7. #7
    Thank you HallsofIvy, you are a star.

  8. #8
    Senior Member
    Join Date
    Dec 2014
    Posts
    2,218
    Quote Originally Posted by Denis View Post
    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.

  9. #9
    Elite Member
    Join Date
    Jun 2007
    Posts
    17,784
    Quote Originally Posted by spikeybrummy View Post
    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?
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

Tags for this Thread

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •