Register to reply

Geometry of a curved beam

by Jerry1989
Tags: beam, curved, geometry
Share this thread:
Jun10-14, 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 y-direction.
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 X-displacement of 55mm. What would that radius R be?

So far, I've tried an arc-length menthod, and I tried looking at the circles, but I just can't figure it out. Can you guys help me out?
Attached Thumbnails
Phys.Org News Partner Mathematics news on
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture
Iranian is first woman to win 'Nobel Prize of maths' (Update)
Jun10-14, 11:50 AM
Sci Advisor
HW Helper
PF Gold
P: 6,474
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':

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.
Jun12-14, 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
T-section for curved beam Engineering Systems & Design 0