continuous beam supported on springs
continuous beam supported on springs
(OP)
I have multi-span beam that is fixed on one end and is supported on 4 spring supports: |------3-----3-----3----3 the beam is not on ground. I want to analyze this beam with K value of the beam is known. Is there a theory or procedure to know the reactions and displacements of the springs for statically indeterminate beams, load is hydrau-static with maximum at fixed end.






RE: continuous beam supported on springs
Licensed Structural Engineer and Licensed Professional Engineer (Illinois)
RE: continuous beam supported on springs
RE: continuous beam supported on springs
"Is there a theory or procedure to know the reactions and displacements of the springs for statically indeterminate beams" ... yes, moment distribution, FEA, even hand calcs (but that'd be a chore ven using excel to do the matrix math)
"load is hydrau-static with maximum at fixed end" ... linear increasing distributed load ?
"It sounds like a homework problem. " ... does, doesn't it ?
Quando Omni Flunkus Moritati
RE: continuous beam supported on springs
Licensed Structural Engineer and Licensed Professional Engineer (Illinois)
RE: continuous beam supported on springs
I would be inclined to remove the four spring supports and solve the cantilever beam for deflections at each of the spring locations, then calculate the four deflections for a unit load at each point and finally solve for the four reactions using four simultaneous equations. Those equations can be solved by computer without structural analysis software.
BA
RE: continuous beam supported on springs
That is a really good point, Hard cross typically deals with joint stiffness, not spring stiffness. Now I'm wondering if there is a way to model that. The distribution factor for the springs is relative to the other springs as well as to the beam stiffness.
Does your method assume that the springs are all equally stiff?
Licensed Structural Engineer and Licensed Professional Engineer (Illinois)
RE: continuous beam supported on springs
it might be easier just to do trial and error ... set up a spread sheet, i'd start with the simple cantilever then add one support reaction (=k*d1) ... so far no guessing ! then with these two reactions (the FE and 1 spring) add another (initial guess = k*d2) but this'll change the deflections at both but with a little tweeking you should be able to get balanced (so that the reactions = k*d) and then the 3rd. yes, i know this sounds like a bit of a farce but it is an alternative to solving the matrix (required for the triply reducdant beam).
Quando Omni Flunkus Moritati
RE: continuous beam supported on springs
Each spring may have a unique stiffness or they can all be equal. A unit load will deflect each spring according to its own stiffness.
rb1957,
I agree that you could solve the problem by trial and error, but the solution of a 4 x 4 matrix is trivial with a computer and not too onerous by hand.
BA
RE: continuous beam supported on springs
Quando Omni Flunkus Moritati
RE: continuous beam supported on springs
Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin
RE: continuous beam supported on springs
BA
RE: continuous beam supported on springs
http://newtonexcelbach.wordpress.com/2012/09/06/co...
will do what you want.
It uses the method described by BARetired (i.e. calculate deflections for a cantilever then solve simultaneous equations so that:
Support deflection = -Reaction/Spring stiffness.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: continuous beam supported on springs
BA
RE: continuous beam supported on springs
The actual system I am designing is soldier piles and lagging for 35 ft deep excavation that terminates on top of rock. The tiebacks have ~300 Kips/in stiffness and I would like use W 14X233 or equal steel section for soldier piles. anchoring the soldier piles into rock is also an option. The system is a continuous beam (soldier pile) which is fixed at rock socket and supported by tiebacks. My rephrased question would be: could I consider the tiebacks to be pin supports for the system or spring supports and is there a difference in tieback reactions between pin and spring (I need justified answer to present to structural engineer)? load per tieback is 150~200 Kips (mainly because of bathtub condition).
RE: continuous beam supported on springs
BA
RE: continuous beam supported on springs
RE: continuous beam supported on springs
Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin
RE: continuous beam supported on springs
If the point of fixity is known, then considering each tieback as a pin instead of a spring will be somewhat conservative with respect to tieback reactions but not with respect to the fixed end moment.
BA
RE: continuous beam supported on springs
RE: continuous beam supported on springs
RE: continuous beam supported on springs
BA
RE: continuous beam supported on springs
RE: continuous beam supported on springs
I'd suggest doing the analysis with upper bound anchor stiffness (i.e. pinned supports) and lower bound stiffness, as a starting point.
If this is modelling loads due to excavation, with anchors placed as excavation proceeds, the results of any single stage analysis are going to be substantially different from what occurs in the actual structure, but if you cover the envelope of possible loads you will be OK.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: continuous beam supported on springs
RE: continuous beam supported on springs
modelling as springs mean you're accounting for compression, yes? ... why not ?
fixity to the rock is one thing, fixity at the horizontal beam is something not being talked about (maybe 'cause you guys know) ... is it s single point attmt (ie pinned) or a multiple fastener (ie some moment capability) ?
if the choice is critical to the structure ... why not choose the most conservative ? by that i mean analysis the various models, and pick the most conservative result at each point (ie not consistently fixed or pinned, but which ever model produces the local maximum load) ?
Quando Omni Flunkus Moritati
RE: continuous beam supported on springs
Tiebacks are usually cables anchored into the soil or rock and in this case, prestressed to 100 kips. They can be horizontal or angled downward.
Where the cable intersects the pile, it is hinged but the cable will strain with additional load. The total magnitude of strain in inches is expected to be P/300 where P is the cable tension in kips. Cables should be modeled as springs.
BA
RE: continuous beam supported on springs
Just trying to think my way through this.
Drill holes, drop soldier piles in holes, place concrete in the rock to embed the pile.
Pile is not in contact with undisturbed soil, it is a cantilever sticking up from the rock. Is the hole flooded?
Excavate to first tieback level, place and pre-tension the tieback.
The pile is a cantilever being pulled towards the soil it is to retain. This soil must be dewatered or else it would pour in during excavation.
When the second level of tiebacks are tensioned, it will relieve the installed tension in the first level, and so on with each level. They probably go back and adjust with a torque wrench.
The retained soil still is not against the lagging but when dewatering stops, the gap will fill with water, I think.
I know this doesn't answer the question.
Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin