physics, mit 2.01x, mechanical engineering
posted by yo yo on .
MITx 2.091x
Can anyone help me on this question:
HW9_3: Design against buckling in a SD truss
We are considering again the truss in the figure, from homework problem HW4_2. The truss is loaded at joint C as indicated, and we had determined the axial forces in each of the bars using the method of joints.
From the solution to HW4_2, we had obtained:
N(AB)=2W
N(BC)=W
N(BD)=W
N(BE)=−2√W
N(CD)=−2√W
N(ED)=−W
Now you can take the magnitude of the applied load to be W=2 kN and the length L=4 m . Assume that the bars of the truss have a circular cross section and are made of steel, with a Young's modulus E=210 GPa and a failure strength (in tension and compression)
σ(f)=250 MPa
HW9_3_1
(24 points possible)
If you want a safety factor, SF=4 against both failure of the material, due to stresses that exceed its
failure strength, and collapse of the truss due to buckling of bars under compressive loading, obtain the numeric values, in mm, of the minimum radius of each of the bars of the truss.
r(AB) = not answered (in mm)
r(BC)= not answered (in mm)
r(BD) = not answered (in mm)
r(BE) = not answered (in mm)
r(CD) = not answered (in mm)
r(ED) = not answered (in mm)

If you tried to copy and paste the drawing or sketch of this truss here, it did not work because copy and paste is not allowed here.
From what you said, moment of inertia of the cross section must be increased or length of section reduced assuming you are doing Euler column bucking. As the question implies be careful going up on the diameter to avoid buckling and getting into simple excessive stress failure.
I am not about to get into MITx questions though. When the 8:01x students discovered this site we were swamped and the questions were clearly exam questions. As a graduate and former faculty member at MIT I was very unhappy with the performance. 
Its fine. Damon

Here is the image though.
courses.edx/c4x/MITx/2.01x/asset/images_HW9_3_1.png 
just add (dot)org after "courses.edx" in order to view the pictures of the truss.

Ltb