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[answered] BME303 HW 6 Due: 12/7/2016 1. A rod is under the loading wi


The topic of assignment is calculation of?beam buckling and bending. Can anyone please solve these questions with details? Thank you.


BME303 HW 6 Due: 12/7/2016 1. A rod is under the loading with two boundary conditions 1) pinned two ends, 2) fixed

 

end at the bottom and free at the top, and 3) following condition (2) but guided top

 

(Figure). The critical buckling load PCr can be expressed as

 

PCr = ?2 EI / L2 for condition (1) PCr = ?2 EI / (4L2), for condition (2)

 

PCr = 2.05?2 EI / L2 for condition (3) respectively. Assuming the cross section of the beam is an I shape with defined geometry in figure.

 

E = 60 GPa, L = 1200 mm. Calculate the critical load for above three cases and clearly

 

indicate which way the bending would occur (e.g., rotate along which axis). (Hint:

 

consider Izz and Iyy) P P (1) (2) P (3) Y 8 mm

 

20 mm

 

10 mm Z

 

20 mm 2. A rod is under the loading with multiple boundary conditions (Figure).

 

(1) Please calculate the Pcr, and indicate initial buckling section.

 

The parameters are L1= 60mm, L2= 90mm,

 

Cross section is a cylinder, R= 8mm, r= 5mm, E = 10GPa.

 

L1

 

(2) If the modulus of L1 section is changed to E1= 18GPa,

 

and L2 section retained same, what Pcr would be and where is it

 

located? P L2 3. A cylinder beam is under the axial loading, P = 3000 N. The dimension is assumed as

 

R = 25 mm and r = 20 mm. E = 20 GPa. The total length of the beam is L. A design

 

decision shall be made for the total length, L, in which the axial stress xx shall be

 

controlled at the transitional stress (at the point of buckling). Please calculate this critical

 

length. (Hint: calculate both axial stress and buckling stress, and compare)

 

z P

 

L

 

y x

 


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