Register to reply 
Geometry of a curved beam 
Share this thread: 
#1
Jun1014, 11:25 AM

P: 4

Hey Guys,
I'm stuck with this problem, we want to compare the curve of a beam to it's horziontal deflection, it's for an experiment we're performing on a very elastic beam. In the attachment you see a flexibel beam getting deflected by a force, this causes displacement x. We don't know (or can't measure) displacment in vertical ydirection. However, we can assume the beam bends in a way that it's curvature resembles a circle with radius R. Now, if we have an L0 of 120mm and an Xdisplacement of 55mm. What would that radius R be? So far, I've tried an arclength menthod, and I tried looking at the circles, but I just can't figure it out. Can you guys help me out? 


#2
Jun1014, 11:50 AM

Emeritus
Sci Advisor
HW Helper
Thanks
PF Gold
P: 6,306

Most beam theories which are used in structural analysis are what are known as 'small deflection' theories. Because of the mathematics involved with relating the bending moment in the beam to its curvature, a great simplification in calculating the deflection of the beam is obtained when the slope of the beam is very small. For very flexible beams, where the slopes can no longer be considered small, the 'small deflection' theories can no longer be applied, and more complicated 'large deflection' theories must be used for analysis.
What you are looking for is called 'elastica theory': http://en.wikipedia.org/wiki/Elastica_theory For obvious reasons, most structural engineers don't deal with such theories, but some engineers, like those involved in laying submarine pipelines, may be familiar with the necessary mathematics. 


#3
Jun1214, 08:47 AM

P: 4

thanks, I'm looking into it.
So far, it's looking t be more of a trigonometry problem. But a tricky one.. 


Register to reply 
Related Discussions  
Cantilever beam with curved beam on the end.  General Engineering  1  
How do you calculate Stress of a curved beam?  Mechanical Engineering  2  
Electrostatic Force curved beam  Advanced Physics Homework  1  
Deflection equation of a curved beam  Mechanical Engineering  0  
Tsection for curved beam  Engineering Systems & Design  0 