Representing Beam as a Spring and positioning it, to achieve same deflection value.
Representing Beam as a Spring and positioning it, to achieve same deflection value.
(OP)
Hallo Engineers,
I really need your help urgently.
I have this problem as part of my project work.
I have a beam fixed on the wall and on-top of that beam, another beam with more less 1/3 or the total length of the initial beam. The two are attached together. with this, i will have two different stiffness xEI for the (attached beam + the mother beam) and the remaining 2/3 of the mother beam with EI. I used the method of super-positioning to achieve the total deflection. BUT my aim is to represent the beam on the top using a Spring and position it withing the 1/3 of the mother beam, to achieve the total deflection as when the two beams were attached
I have attached a file on this thread to give you a clear view of the problem.
Any tips with highly be appreciated as soon as you can. Thank you in advance
I really need your help urgently.
I have this problem as part of my project work.
I have a beam fixed on the wall and on-top of that beam, another beam with more less 1/3 or the total length of the initial beam. The two are attached together. with this, i will have two different stiffness xEI for the (attached beam + the mother beam) and the remaining 2/3 of the mother beam with EI. I used the method of super-positioning to achieve the total deflection. BUT my aim is to represent the beam on the top using a Spring and position it withing the 1/3 of the mother beam, to achieve the total deflection as when the two beams were attached
I have attached a file on this thread to give you a clear view of the problem.
Any tips with highly be appreciated as soon as you can. Thank you in advance






RE: Representing Beam as a Spring and positioning it, to achieve same deflection value.
If the two beams are continuously welded together such that the combined EI is equal to xEI, the problem has no solution because it is not possible to generate a bending moment diagram which satisfies the correct end deflection for all values of P.
BA
RE: Representing Beam as a Spring and positioning it, to achieve same deflection value.
So, how do you go about it to find the Spring which will represent the upper beam for the CASE 1 that you just described. My problem is how to generate that spring and to position it. guide me on the steps further if you have some time. any attachments if POSSIBLE. Thank you.
RE: Representing Beam as a Spring and positioning it, to achieve same deflection value.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Representing Beam as a Spring and positioning it, to achieve same deflection value.
N/B the most important result is that the deflection achieved when i have the full model, SHOULD correspond to the deflection achieved when i model the flange as a beam. As per now, am trying to model the beam as a spring to enable me to position it TO achieve the goal.
That's my goal Sir.Thank you.any reply will be appreciated highly.
RE: Representing Beam as a Spring and positioning it, to achieve same deflection value.
If it is attached at a point like you suggest. You equate the two deflections.
Delta(top beam) = function of P1 at attachment point
Delta (bottom beam) = function of P1 at attachment and P at end
Delta (top beam) = Delta (bottom beam)
Solve for P1
Spring stiffness is P1/Delta
Spring location is at attachment point
RE: Representing Beam as a Spring and positioning it, to achieve same deflection value.
then you can iterate ... assume P, how much deflection for the upper beam ? solve the lower beam (a cantilever with two loads), how much deflection at the desired pt ?
or you can think about setting up the equations for the lower beam, knowing that the force and the deflection at the desired pt are related.
RE: Representing Beam as a Spring and positioning it, to achieve same deflection value.
RE: Representing Beam as a Spring and positioning it, to achieve same deflection value.
i'd solve this iteratively ... assume P = 100 (1000?) lbs, calc the upper cantilever deflection. for the lower beam (a cantilever with two loads), calc the deflection at the common pt). then re-guess P and continue untill the deflection of the upper beam matches the lower beam.
knowing the upper beam results, a simple cantilever, you could derive a general result for the lower beam and get deflection as a function of P for the lower beam and solve the two beams.
RE: Representing Beam as a Spring and positioning it, to achieve same deflection value.
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: Representing Beam as a Spring and positioning it, to achieve same deflection value.
Mike McCann
MMC Engineering
http://mmcengineering.tripod.com
RE: Representing Beam as a Spring and positioning it, to achieve same deflection value.
We know that the upper and lower beams are fixed at the left end, but we do not know how the two beams are attached to each other. If they are attached continuously, the problem is not soluble because no combination of spring location and stiffness in Setup 2 can simulate Setup 1.
If (a)the two beams are attached at a point by a tension member which can carry only vertical load and (b) the lower beam is free to flex between the left end and the attachment, the problem is easily solved by substituting a spring with proper stiffness at the same location in Setup 2.
Please tell us clearly how the two beams are fastened together.
BA
RE: Representing Beam as a Spring and positioning it, to achieve same deflection value.
RE: Representing Beam as a Spring and positioning it, to achieve same deflection value.
RE: Representing Beam as a Spring and positioning it, to achieve same deflection value.
F = kx
where
x is the displacement of the spring's end from its equilibrium position;
F is the force exerted by the spring; and
k is the spring constant
From the above equation, k = F/x.
As stated by structSU10, the spring constant,
k = 3EI/L3
where I is the moment of inertia of the upper beam and L is the distance from the fixed end to the tension member connecting the upper and lower beams. The spring must be located at distance L from the fixed end.
The gap between upper and lower beam must be sufficient to allow the lower beam to flex freely. Otherwise, Setup 1 will behave differently than Setup 2.
BA
RE: Representing Beam as a Spring and positioning it, to achieve same deflection value.