simple "crane" problem 1

[dkastz]

Dear friends

I got stuck into simple crane problem, which deals moments and rotation around an axis. Imagine you have two “cranes” – with equal mass and similar dimensions W1 = W2 and L1 = L2, therefore only difference is in shape and thickness t1 and t2. Mass center of both is always in the middle (a1 = b1 and a2 = b2).

Which one can handle bigger load F before roll over point A

thanx in advance and kind regards

 

[jayrod12]

Smells like homework.

 

[Lomarandil]

If bearing on a rigid medium, I don't know that there's a difference analytically.

If bearing on an elastic medium, configuration 1 might have an advantage because of not losing bearing area as quickly once the heel lifts off.

 

[LittleInch]

but unless the "mass" is radically different densities, the two masses cannot be the same. The ring type will be significantly higher in section and this will impact on the moment. Hence t2 will be about twice t1.

Still looks like homework...

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[dkastz]

haha i wish a homework, but I am 31 now...

it is a simplification of a more complex problem, my worries were if differently distributed mass has different moment of inertia around given axis, therefore the load capacity is different... or all depends from mass center location

 

[jayrod12]

If Mass is independent of thickness of base, then in theory in a straight vertical pull scenario, the capacity would be equivalent.

 

[SlideRuleEra]

Is this for a fixed crane, say on a dedicated concrete foundation, or a mobile crawler or truck crane? My preference will be the same, but the reasons differ.

http://www.SlideRuleEra.net

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[dkastz]

mass and mass center distance to pivot are the same in both cases. only difference is in moments of inertia of the two bodies

 

[racookpe1978]

If L1 = L2, and W1 = W2, then the area of the single simple square will be larger than the area of the ring. Since mass carried would be the same (if the two cranes were equal capacity) then the pounds per square foot of each is higher for the ring. So, the net force into the ground per sq foot of ground resisting the crane's load - regardless of the moment of intrtia of either - is much greater for the ring. So the ring needs to be rated lower if they are on the same ground/pavement/concrete slab.

Now, if the ground/slab/steel they were on could carry both 100% into the ultimate ground, then the ground load per sq foot would not matter. But moment of inertia of the crane foundation matters only for a dynamic twisting effect acting through a member - like in a boom or a cantilever arm.