Help Analyzing Frame Homework: Find Forces & Best Angle

[rock.freak667]

Homework Statement

http://img571.imageshack.us/img571/2026/framekq.jpg

I need some help with finding the forces associated with this structure. I drew it badly from how a friend described it.

A point load would be placed on it so, a weight W would be at the centre + the weight of the metal at that point + another point load to simulate a person standing on the structure near the edge.

I am to assume that the entire frame is made out of iron, and the legs are welded onto to the rectangular top and it is resting on the ground. The distance from the ground to the rectangular top should be 15 feet. It will also be subjected to a wind load as well.

I'd like to know how to perform an analysis that will show me the best angle to have the legs at and if the structure can withstand the forces.

Homework Equations

∑F_x=∑F_y=∑F_z=∑M=0

σ_b=My/I

The Attempt at a Solution

Weight of point load = W
Weight of person = w
Weight of material = m_ng

I can get the properties of the metal and whatnot, I'd just like some help in starting the analysis.

Mostly the reactions at the joints is where I get confused, normally I'd think the ones where the legs are joined to the top plate are the same, but that would get confusing when I consider the reactions due to the ground.


EDIT:

Summing vertical forces: W+w-4m₁g+m₂g= 4R+4N

(R= reaction due by the joints and N= reactions at the ground)

Now this is assuming all the joint reactions are equal and all of the ground reactions are equal.

Now if I take moments about the load W, all of my reactions will cancel out. This means that what I am doing is wrong.

 

[pongo38]

Is this a real practical problem, or a theoretical one? If a practical one, you will hardly ever get the four feet to match the assumptions made in a theoretical treatment, because of 'lack of fit'. If theoretical problem, then you must recognise this is a statically indeterminate problem, and this requires a number of assumptions. What would they be? This is what we call a sway structure, and you should be more interested in bending moments than forces. Are you sure you know enough to cope with this question?

 

[rock.freak667]

Are you sure you know enough to cope with this question?

Not really, I was just told the structure has to support some machine and must be able to support a person so that they can do maintenance on it, it must also look like how I drew it, more or less.

 

[pongo38]

Sorry but this is not a job for an amateur. There are many things to consider, including vibration, stability on 3 levels (overall, member, and local), deflections and fatigue, even if you can get the stresses right. You haven't given any dimensions or loads, and it is not reasonable to expect this kind of help on this forum. The discussion would be interminable. You need a specialist who carries professional indemnity insurance, because I doubt if you could get it yourself. So I'm out of this one.

 

[rock.freak667]

Well I can get the values of the weights and loads, if that will help.

 

[nvn]

rock.freak667: If your structure is symmetric, and your applied loading is on at least one axis of symmetry, then you have two unknowns for the reactions at the bottom of the legs, which is statically determinate. Draw a good, dimensioned free-body diagram, and solve for the reactions. Afterwards, assume the plate is rigid, and use the maximum reaction to compute the bending stress on the weldment at the upper end of the leg. Ignoring the axial force for now, use this bending stress to size the weldment (and leg). To analyze the plate, it would be easier to use finite element analysis, if you can.

 

[pongo38]

If a rigid object with four legs has settlement in the ground under one of the legs, the reactions on the remaining legs can double. That's why you need a healthy factor of safety. I'm afraid nvn's advice, though well-meaning, ignores wind load. And we don't yet know if the machine to be supported is a vibrating machine or not. Please be wary of over-simplified advice.

 

[pongo38]

The trouble is you are presenting this as a problem in analysis when in fact it is a problem in design. In analysis, everything is well-defined in terms of geometry and material properties, but here, that is not the case, yet. Design will generally require compromises. For example, the best angle for legs is vertical for a vertical load, but inclined for a lateral load (with a point of concurrence at the centroid of the lateral load, because that puts the legs into axial force, which is the most efficient). There is no way of arriving at the 'right' answer without compromising conflicting ideals.

 

[rock.freak667]

The trouble is you are presenting this as a problem in analysis when in fact it is a problem in design. In analysis, everything is well-defined in terms of geometry and material properties, but here, that is not the case, yet. Design will generally require compromises. For example, the best angle for legs is vertical for a vertical load, but inclined for a lateral load (with a point of concurrence at the centroid of the lateral load, because that puts the legs into axial force, which is the most efficient). There is no way of arriving at the 'right' answer without compromising conflicting ideals.

Ah I always forget that designing has compromises in it. Well I don't believe the legs can be vertical since there will be a wind load present. The structure is for a vertical wind turbine.

 

[WhoWee]

Ah I always forget that designing has compromises in it. Well I don't believe the legs can be vertical since there will be a wind load present. The structure is for a vertical wind turbine.

Are you making any progress on your design?

 

[rock.freak667]

Are you making any progress on your design?

I sort of stopped bothering with it at the moment.