Beam - Curved Spring; Bending stress, force & deflection Calculation
Beam - Curved Spring; Bending stress, force & deflection Calculation
(OP)
I am designing a bent spring ;
http://files.engineering.com/getfile.aspx?folder=519f7b2d-4dc6-447c-9e16-72038deeef43&file=Capture.JPG
A simplified version is illustrated in the above link. It consists of two straight sections and a curved section in the middle.
Multiple springs will hold an object in place.
I am looking for some formulae/ method to calculate the deflection, force and bending stress in the beam.
Essentially the spring force at each location.
I had a relatively similar problem last year and posted here;
http://www.eng-tips.com/viewthread.cfm?qid=292578
Desertfox offered a 'strain energy method'
I am wondering how this might apply to my current problem or maybe someone could suggest a calculation method for this problem.
Thank you





RE: Beam - Curved Spring; Bending stress, force & deflection Calculation
Tobalcane
"If you avoid failure, you also avoid success."
“Luck is where preparation meets opportunity”
RE: Beam - Curved Spring; Bending stress, force & deflection Calculation
as above, you can use curved beam equations, but i'd be surprised if your geometry really is a curved beam problem.
you're doing all this 'cause you're interested in the deflection of the end, ie the stiffness of the part ?
i mean, from a strength perspective, the critical section is at the edge of the fixed support.
this assumption (a fixed support) is probably going to be the biggest variable in matching with the real world.
RE: Beam - Curved Spring; Bending stress, force & deflection Calculation
RE: Beam - Curved Spring; Bending stress, force & deflection Calculation
Simply decompose the load into a transverse and an axial force and the sloped part is directly calculated; then apply the load and the moment to the horizontal portion, calculate it directly and then sum the deflections for the two portions.
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads
RE: Beam - Curved Spring; Bending stress, force & deflection Calculation
From sketch small curvature neglected, all strain energy in 2 sections
E= integral of M^2/2EI ds=(Mx +My)^2/2EIds
My=Fy*x 0<x< 8
Mx=Fx*xsin@ x<6
Mx=Fx*6*sin@ x>6
Fx= fictitious x force, zero in this case but neede for the x deflection
s=x/cos@ for x< 6mm
ds =dx/cos@ for x<6
ds=dx for x>6
y deflection=partial derivative of E WR to Fy
x deflection =partial derivative of E WR to Fx , then set Fx=0
E=INT[(Fy*x+Fx*x*sin@)^2*dx/(2EIcos@)] limits 0>x<6
+INT [(Fy*x+Fx*6*sin@)^2)*dx/(2EI] limits 6>x<8
ydefl=part of E WRT Fy=INT[(Fy*x^2)*dx/(EIcos@)] limits 0>x<6
+INT [Fy*x^2)*dx/(EI] limits 6>x<8
xdefl=INT[sin@*Fy*x^2/EI*dx] limits 0 to 6
+INT[6*x*sin@Fy*dx/EI limits 6 to 8
RE: Beam - Curved Spring; Bending stress, force & deflection Calculation
for the sloping piece, i think you need to convert the load into it's components (one component compressing the spring, the other bending it)
like prex suggested above.
RE: Beam - Curved Spring; Bending stress, force & deflection Calculation
RE: Beam - Curved Spring; Bending stress, force & deflection Calculation
Work as attached, Curved Beam Theory slightly bastardized for our application.
Regards,
Cockroach
RE: Beam - Curved Spring; Bending stress, force & deflection Calculation
In my opinion to within engineering accuracy the beam effectively behaves like a straight one 8 mm long, in displacement and stress .
The reason is that at each x the moment is the same, and the difference in section properties is irrelevantly small at the tip, and non existent at the important bit.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Beam - Curved Spring; Bending stress, force & deflection Calculation
I tried to find an attachment which showed a sketch, and had no luck until I saw Cockroach’s sketch. Otherwise, I agree with your statements on the matter.
RE: Beam - Curved Spring; Bending stress, force & deflection Calculation
The reason is that at each x the moment is the same, and the difference in section properties is irrelevantly small at the tip, and non existent at the important bit. "
You are almost right for the angle shown, but for steeper angles the solution is not within engineering accuracy.
I got
y=F*(296+216/cos@)/3EI
in mm units
where you see the dependence on @.
RE: Beam - Curved Spring; Bending stress, force & deflection Calculation
in first post
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Beam - Curved Spring; Bending stress, force & deflection Calculation
Prex, RB1957 & GregLocock thank you, Zekeman thank you for the details and Cockroach thank you so much for the neat upload!
I need to digest this and maybe get back with a question or two when I get a chance to take this information in.
Have a nice weekend guys