Bending Strain Determination from Strain Gauge Data 2

[struclearner]

For structure under bending loading, strain gauges are placed at the top and bottom, or across the wall of the structure member depending upon the bending mode, and the strain gauges data showing tension on the top and compression on the bottom verifies the loading type as bending.
What are the Bending Strain and how these can be calculated from axial strains?
For example, in the case of determining stresses on the bolts, 4 strain gauges are placed on the bolt shank, around the periphery, in case of tensile loading, all the strain gages output will be axial strain, in case of bolt bending, how the bending strain of the bolt will be calculated.

Thanks a lot for your insights and help.

 

[SWComposites]

Bending strain is proportional to the difference in strains on the opposite surfaces. If you have a plate with strain gage A on one surface and strain gage B on opposite surface at same location:
Midplane axial strain = (A + B)/2
Bending strain = (A - B)/2

 

[rb1957]

and in your bolt example, the axial strain is the average of the 4 (A+B+C+D)/4
and the "bending" strain is the difference between opposing pairs … (A-C)/2
but the interesting thing (I think) you want is the moment on the bolt … (A-C)/2*E*I/D/2
and axial load … (A+B+C+D)/4*E*Area

another day in paradise, or is paradise one day closer ?

 

[struclearner]

Hello SWComposites and rb1957,
Thanks for the clarification.
For Bending Strain determination, considering bolt example, in the case of bending, the strain on one surface will be negative, and two negatives will make the positive of -B in the equation of (A-B)/2, and for symmetric section, the equation gives the value of either side strain.
In case of no bending load acting on the bolt, the equation will give zero strain, confirming the absence of the bending.
Again thanks for your time and response.

 

[rb1957]

not at all clear with your reply !

don't confuse things with +ve and -ve signs.

the "bending" strain is 1/2 the difference of the two s/g.

if A = 100, and B = 100 … then (A-B)/2 = 0, hence no bending (as is obvious for the s/g readings)
if A = 100 and B = -100 then (A-B)/2 = 100, hence pure bending (and zero endload).

a different way to look at things is the average of the s/g is the endload … (A+B)/2
and the bending strain is A-(A+B/2) = (A-B)/2
note, the "other" bending strain is B - (A+B)/2 = (B-A)/2 … ie one will be +ve and the other -ve … which is which depends on the sign of the moment (putting tension or compression at s/g A).

another day in paradise, or is paradise one day closer ?

 

[struclearner]

Hello rb1957,
Thanks for your very useful explanation!

 

[struclearner]

In the case of Bolts, which has pre-load stresses, we need to investigate the stresses at locations A, B, C, D, which are 90 degree apart on Bolt shank, A is opposite to B, C is opposite to D.
The bolts have pre-load stresses in addition to the stresses due to external load applied.
In case of pure tensile load applied to the joint, the stresses on locations A,B,C,D on one bolts will almost be the same and there wont be any bending stresses, i.e (A-B)/2 and (C-D)/2 will almost be negligible.
In case of bending moment applied to the joint, the bolts will also see the bending stresses and the average axial stresses will be (A+B+C+D)/4 and bending stresses will be (A-B)/2 and (C-D)/2 in case of biaxial bending.
The bolts of the bolts pattern (circular) under bending moments seeing the tensile loads (members of the joint are being separated) will have axial stresses higher than axial stresses due to pre-load.
The bolts of the bolts pattern (circular) under bending moments seeing the compressive loads (members of the joint are being compressed more) will have axial stresses lower than axial stresses due to pre-load.
Is this possible that any of the stresses on A,B,C,D locations on a bolt could be much lower than the axial stresses due to pre-load of the bolt?
Is this possible that any of the stresses on A,B,C,D locations on a bolt could become negative, even in the presence of axial stresses due to pre-load of the bolt?
I am looking for FEA stresses at the stress recovery points of the beams representing the beams. The beam element stress recovery points corresponds to A,B,C,D locations, where the strain gauges are placed.
The stresses calculated from FEA, the superposition stresses obtained from adding the axial stresses and bending stresses in biaxial direction are becoming negative for some bolts of a circular bolt pattern under bending load.
The combined Axial + Bending (Biaxial) stresses are obtained for superposition of the stresses by adding all these stresses together.
Thanks for your input and help.

 

[rb1957]

as near as I can tell …
"The bolts of the bolts pattern (circular) under bending moments seeing the tensile loads (members of the joint are being separated) will have axial stresses higher than axial stresses due to pre-load." … yes
"The bolts of the bolts pattern (circular) under bending moments seeing the compressive loads (members of the joint are being compressed more) will have axial stresses lower than axial stresses due to pre-load." … no, but maybe … I don't see compressive loads directly affecting the bolts.
Is this possible that any of the stresses on A,B,C,D locations on a bolt could be much lower than the axial stresses due to pre-load of the bolt? … yes, bending
Is this possible that any of the stresses on A,B,C,D locations on a bolt could become negative, even in the presence of axial stresses due to pre-load of the bolt? … yes … significant bending.
I am looking for FEA stresses at the stress recovery points of the beams representing the beams. The beam element stress recovery points corresponds to A,B,C,D locations, where the strain gauges are placed. … ok
The stresses calculated from FEA, the superposition stresses obtained from adding the axial stresses and bending stresses in biaxial direction are becoming negative for some bolts of a circular bolt pattern under bending load. … ok?
The combined Axial + Bending (Biaxial) stresses are obtained for superposition of the stresses by adding all these stresses together. ... sure?

another day in paradise, or is paradise one day closer ?