Three-point bending

For a three point bend test, the bending angle of the beam has to be small - so small that (theta)=tan(theta).... this is necessary to make a substitution of the reciprocal radius of curvature 1/R = M/EI... which then can be assumed to be the second derivative of the beam deflection.

Might sound stupid, but would the bending angle assumption be measured in degrees or radians?

Im trying to bend amyloid fibrils (dia ~5nm over a 100nm trench). My data suggests that I get approx 10nm of deflection for a low applied load (~200pN). Therefore, the subtended bending angle tan(theta)=10/50=0.2; theta=11degrees... so would violate the bending theory derivation

however in radians, 11degrees is 0.19, which would suggest is within the boundaries of acceptability.

Any thoughts? experience etc..

Cheers

Colin

 


Ying Li's picture

Only the angle is in radians, tan(theta) equals theta.

Ying Li
Department of Engineering Mechanics
Tsinghua University
Beijing, 100084, P. R. CHINA


Sanjay Govindjee's picture

Advice

Collin,

First the answer:  Radians (Such that x = tan(x) for small x, x must first be non-dimensional for dimensional homogeneity.  Radians are non-dimensional.  However you can have a "better" physical reason if you understand beam theory first.)

So, second, some advice: Get a book on elementary mechanics and read it or hire an engineer to help you in your project.

 

 

Prof. Dr. Sanjay Govindjee
University of California, Berkeley