1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Having some issues deriving internal force functions for a section.

  1. Dec 8, 2013 #1
    1. The problem statement, all variables and given/known data

    I have a 13 foot long beam supported by a pin at x = 0 feet and a roller at x = 9 feet.

    There is a triangular distributed load of 50 lb/ft from 0 ft to 9 ft. (Increasing as it approaches 9 ft)

    At the end of the beam there is a moment of 200 lb-ft counter-clockwise.

    2. Relevant equations

    ƩFx = 0
    ƩMr = 200 lb-ft

    Vertical Force at Pin: 52.78 lbs upward
    Vertical Force at Roller: 172.22 lbs upward
    Normal Force = 0

    3. The attempt at a solution

    For the first section, it seems my equations are correct;

    0 < x < 9:

    Shear: -.5(50/9)x^2 + 52.78
    Bending: -.5(50/9)x^3/3 + 52.78x


    This is where I'm having an issue with my Bending equation;

    9 < x < 13:

    Shear: -225 + 52.78 + 172.22
    Bending: 52.78x + 172.22(x-9) - 225(x-3)


    At exactly 9 feet, both bending functions should give a bending moment of -200 lb-ft but for some reason, I can't seem to get that answer with the second one. I tried to rework this function a few times but it's not happening.
  2. jcsd
  3. Dec 8, 2013 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    The applied couple (200 ft-lb) at the end of the beam (x = 13 ft) means there is a jump in the bending moment value at this location. However, for x > 9, there is zero shear. In your equations above, it's not clear what the factor (x-3) means, since the beam is 13 feet long and the right support occurs at x = 9 ft.
  4. Dec 8, 2013 #3
    (x-3) is the distance of the resultant force (225 lbs) from the distributed load at any given point between 9 and 13 feet. <---- I think this is my problem. It makes no sense.

    Since there is 0 shear after 9 feet, I'm just getting that the bending moment should be -200 lb-ft from 9 feet to 13 feet. This equation is not reflecting that though and I'm trying to figure out where I made my mistake. :(
    Last edited: Dec 8, 2013
  5. Dec 8, 2013 #4
    I think I got it... I need some sleep

    Bending Function: 52.78x + 172.22(x-9) - 225(x/3)
  6. Dec 8, 2013 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    No ... I don't know what you mean by 225(x/3).

    Also, what is 13 - 9 = ?
  7. Dec 8, 2013 #6
    4, I can't believe I botched that up.
  8. Dec 9, 2013 #7
    When you first calculated the reaction forces, did you check them by (say) taking moments about some axis not already used? You should show us all your working.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted