Structural Analysis: Max & Min Stresses, Loads, Euler Buckling

[nickenrite]

Hi few questions I am stuck on.
If the table top weighs 60kg, find the max and min stresses on the 75mm tube.

if the steel tube has an ultimate stress of 200Mpa, will it take the loads applied (110kg to the far left edge of the table top).

if the table weighs 100kg total, will the eccentricload over turn the table.
calculate the euler critical bucking load for the colomn.


If working could be shown that would be great so can work myself through question.
Cheers

 

[PhanthomJay]

Hi few questions I am stuck on.
If the table top weighs 60kg, find the max and min stresses on the 75mm tube.

if the steel tube has an ultimate stress of 200Mpa, will it take the loads applied (110kg to the far left edge of the table top).

if the table weighs 100kg total, will the eccentricload over turn the table.
calculate the euler critical bucking load for the colomn.


If working could be shown that would be great so can work myself through question.
Cheers

Your image doesn't show the 100kg 'load' at the table edge, but i assume it is a 110kg mass or an applied downward force of 1100N.
What attempt have you made so far at a solution? You need to find the axial load and bending moment on the tube, and compute the combined max/min stresses accordingly. What is the axial load and moment at the top of the column?

 

[nickenrite]

yes a mass of 110kg applied to left edge of table

 

[PhanthomJay]

OK, using g=10m/s^2 for simplicity, that's a force of 1100N applied at the edge of the table. Replace that force with a downward force at the top of the tube, and a couple. Add in the table top weight at the top of the column, and check the stress in the column for the combined axial load and bending moment. You have to show some work before we can be of further assistance. I'm sure you have studied axial and bending stresses, have you not?

 

[mathmate]

Perhaps I am mistaken, but wouldn't the table be overturned when the 110kg load is applied at the edge of the 60kg table?
The 100kg table-top will sustain that load though.

 

[PhanthomJay]

Perhaps I am mistaken, but wouldn't the table be overturned when the 110kg load is applied at the edge of the 60kg table?
The 100kg table-top will sustain that load though.

The table top 'weighs' 60kg, but the entire table, including the tabletop and base, 'weighs' 100kg. As long as the Normal force lies within the table base, it won't overturn.

 

[mathmate]

You'd need the basic equations such as:
Stress = Force/area. This will take care of the axial load.

It looks to me you can calculate the moment, so no problem there.

No information is available on the table top, so you cannot be of big help there (to see if the table top withstands the force).

Now calculate the I for the steel tube using the standard formulae.
I=pi/4(r2^4-r1^4)
See for example http://en.wikipedia.org/wiki/List_of_area_moments_of_inertia

The formula for stress due to moment is My/I, where y is the distance from the neutral axis. For a pure moment load, the neutral axis is at the centre, by symmetry. With added compressive axial load (force/area), the neutral axis shifts towards the tensile edge. Once you get the neutral axis, the above My/I formula will give you the maximum (compressive) stress which you can compare with the ultimate value (no load factor yet).

The Euler buckling load is the easy part, assuming the two ends of the steel tube are simply supported.
Pcr=EI pi^2/L^2
(The Young's modulus E is required, but not supplied in the given question.)
See for example
http://www.efunda.com/formulae/solid_mechanics/columns/columns.cfm