Column buckling example problem #2: both ends fixed

[@livenletdie0]

For the buckling in the Y-Z plane calculation, E should be N/m^2 not m^4. Thanks for the videos, they are a great help.

[@Engineer4Free]

Whoops, thanks for point it out! I made a note of it in the description, and have pinned your comment.

[@aliakmal5249]

I am afraid you forgot to divide the load calculated by yield stress in the end with the factor of safety. I believe the step should be shown nevertheless the critical load selected in the end is correct.

[@Engineer4Free]

Hey Ali, yeah in the second last line, I write FS = ult / all. Referring to Factor of Safety = Ultimate Load / Allowable Load. I rearrange to find the Allowable Load = 9.36kN. I realize now while watching it that I don’t come back and mention that despite the column having the tenancy to buckle before yielding, that neither will happen if we respect the maximum allowable load of 9.36kN. Thanks for the comment! Any I hope this clarifies the question for others if they see your comment too 👍

[@rublie1426]

Could you maybe explain to me why you can ignore forces in the x-y-plane for this exercise?

[@rublie1426]

Do you also have a video on deriving the P_crit formula?

[@Engineer4Free]

Yeah please watch videos 50 - 56 here: engineer4free.com/mechanics-of-materials 50 and 51 go over the basics and then throughout the ither examples I talk about the formulas too

[@eth4nkeebs]

Hi there i got one question if the column isnt rectangular but its Cylindrical, the calculation for I just follow the Radius of gyration? like ( I=A·R^2 )?

[@abdulkadirhassanahmed956]

I am afraid i don't think the formula for fixed fixed end condition is properly followed this supposed to be Pcr= 4Pie2EI/Le2

[@Engineer4Free]

Hmm. I follow the method from Mechanics of Materials by Beer & Johnston. This PDF wp.optics.arizona.edu/optomech/wp-content/uploads/sites/53/2016/10/OPTI_222_W18.pdf has diagrams and formulas copied right out of the textbook, you can see there that they use Pcriit=(π^2)(EI)/((Le)^2).

[@Engineer4Free]

You might have a 4 in the numerator if you switch Le for L in the denominator. Le = 0.5L for fix-fix. Dividing by 0.5^2 is the same as multiplying by 4.

[@RJ47_AeroMechEngg]

WHAT HE DID IS CORRECT

[@mohamedaliahmed5983]

Abdulkadir Hassan ahmed somali

[@Aviator168]

Does this assume the load is on the centroid of the column? How to calculate if the load is on side of the column?

[@mohammadaslamkorai5699]

This is not correct formula for this problem

[@RJ47_AeroMechEngg]

IT IS CORRECT

[@abdib5446]

sometimes there are more than 1 formulas but the method and answer is correct in this .