I have a cantilever steel beam of 1m length. I want to determine the strain near fixation due to the bending moment of a dead weight on the tip of the beam.
I plan to place 3 strain gauges near fixation and close to each other on the same line level.
I have some doubts about managing the data. Shall I take the average reading and consider it representative of the strain on the beam?
I believe that each strain gauge measures the strain in the zone it is placed on.
Any ideas?
Actually a strain gage gathers data about the exact place that you attached it on. So the data of a certain strain gage is the strain of that exact point. Even a strain gage also averages the strain over a finite length due to its own dimensions. So averaging three results might not be a good choice, maybe you can use results seperately and then you can have a strain distribution over the axis of your beam. Sincerely.
Dear Ahmed,
If you put 3 strain gauges parallel to 3 Cartesian directions at one level (e.g. same longitudinal distance from the fixed support) you will get exact strains for mounting locations at x, y and z. There is no need to averaging the output data.
But if you put all 3 gauges in one direction, utilizing the average output may be meaningful, I'm not sure.
Your statement "strain on the beam" is a little confusing because strain goes from high to zero has you move from root to tip. I'm assuming the "fixation" you refer to is the root of the cantilever. When a cantilever is rooted very well and you can measure strain in the root area you'll see strain go from zero to very high over a very small distance at the root. Because a strain gage gives a strain reading that is actually an average of what it is measuring underneath of it, you can incorrectly measure the maximum strain at the root (you'd get lower measurements than what is actually there). Most measurements involving cantilevers stay away from the root because of the difficulty in setting up a good root and because of the difficulty of making a good measurement at the root.
Dear Ahmed,
simple linear strain gauges give the strain in its direction. So in case of bending of a steel cantilever of constant cross section, loaded by a transverse force F at extremity, bending moment is given by M=-F(L-z), where z is the centroidal axis of beam, x, y are the inertia principal directions of cross section. Origin of coordinates (G,x,y,z) is in the initial fixed section (left).
Strains are given by formula (6.34) of paragraph 6.4.2 of my book of Solids and Structural Mechanics by McGraw-Hill attached to this answer.
Maximum of strains of direction z af axis are attained in the fixed section, where bending moment is maximum, and in points whit maximum and minimum value of y (top and bottom of beam),
But you could also read strains in different points and directions. The strain tensor E allows you to predict strains in whatever point and direction on the beam.
If you need more suggestions, do not hesitate to give me more details on your problem writing an e-mail to [email protected] . I will help you.
Regards,
Luciano Nunziante.
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