Statics question....

[AstroTerrapin]

Hey folks,

So i am designing a metal structure and i am having a little trouble figuring out the reaction forces in a rigid truss with the shown loading.

i'd appreciate some advice!

thanks folks

 

[msquared48]

If you know where your external support/restraint points are for the entire structure to prevent rotation and linear movement, you could just plug this into RISA 2D or 3D and solve for the reactions, internal forces, member end rotations and deflections.

Mike McCann, PE, SE (WA)

 

[Shu Jiang PEng SE]

The structure in the your case is indeterminate structure. It is hard to get solution manually.

 

[AstroTerrapin]

So this structure is sitting in the ground. That bottom member is on the ground.

This the restraining forces to horizontal displacement is friction between the bottom horizontal beam and the ground. Rotation is prevented by the bottom member (length of gamma) pressing against the ground.


I don't know what RISA is.

Is there really no way to calculate a solution by hand?

Thanks

 

[AstroTerrapin]

I think what I can do is treat it as being supported by a pin on the right bottom corner of the bottom horizontal beam and a roller on the bottom surface on the left of the bottom beam.

 

[msquared48]

RISA is a computer program that solves for both determinate and indeterminate structures, and is very user friendly.

Sounds like you may also need to perform a beam on an elastic foundation analysis here too for the bottom portion of the structure if it is sitting on the ground. You will need a spring constants for the soil matrix to solve for that ...

No, this not one for hand anlysis to get a reliable solution.

Mike McCann, PE, SE (WA)

 

[BAretired]

So this structure is sitting in the ground. That bottom member is on the ground.

This the restraining forces to horizontal displacement is friction between the bottom horizontal beam and the ground. Rotation is prevented by the bottom member (length of gamma) pressing against the ground.
I don't know what RISA is.

Is there really no way to calculate a solution by hand?

Perhaps not precisely, but probably close enough for practical purposes.

Remove M1 and M2 and calculate R1 and R2. Design top beam for resulting moments.

For bottom beam (length gamma), calculate pressure variation assuming the whole structure is a rigid body. This gives a trapezoidal distribution of soil pressure on the bottom beam from which moments may be calculated from statics, assuming zero moment in the two vertical supports.

If you need to get more precise than that, calculate the angle change in both beams at the vertical supports and conservatively estimate the bending moment in the verticals.

There is no guarantee that the bearing surface will be flat to begin with and you probably don't know the properties of the soil, so a fancy analysis is not warranted in my opinion.




BA

 

[rb1957]

so the bottom of the "truss" is sitting on the ground, at y = 0
ok, then the reaction would be some "funky" distributed load with a centroid under the load centroid.

at the place where you've sectioned it, sure there could be moments, by a first approximation would be axial load only. This'd show you (I think) that the LH end will have trouble staying in contact with the ground.

after that, if you want moments then it's a doubly cantilevered beam, doubly redundant (so you can't solve it with use equations of static equilibrium); not difficult to hand calc (my preferred solution is unit force method).

another day in paradise, or is paradise one day closer ?

 

[BAretired]

Neglecting the self weight of the members, the centroid of load occurs at 35" from the left end. The value of γ has not been given.

if γ/3 < 35 < 2γ/3 soil pressure is trapezoidal
if γ/3 = 35 OR 2γ/3 = 35 soil pressure is triangular over full length of bottom beam
if 2γ/3 < 35 < γ soil pressure is triangular over partial length of bottom beam
if γ < 35 structure will topple

BA