Calculate strain from bending moment?

[LDC1972]

Homework Statement

Simply supported beam, all values known now I believe as this is the last question on it. I have spent a long time trying to work this out:

The bending moment is to be verified using a strain gauge bonded to the outer surface of the beam at the point of max bending moment.
Derive an equation which could be used to calculate the bending moment from the measured strain value.

Homework Equations

k = M/EI
ε(max) = kz,

The Attempt at a Solution

I know the position and value of the max bending moment, so I "think" this may be correct. But I've spent so long I have confused myself a lot. Please be gentle :-)

I have come up with this so far:

k = M/EI
ε(max) = kz,

and therefore ε(max)= (z) M/(EI)

I think I've typed the above equation correctly. I mean it as follows: strain(max) = z multiplied by the result of M divided by EI.

Z is the distance from the neutral layer to the outer layer in a tensile condition.
M is bending moment
EI is flexural stiffness (E is youngs and I is 2nd moment of area)
K is curvature of the beam or could be replaced with 1/R where R is the radius of curvature in radians.

Can anyone confirm the above or point me correctly?

 

[Chestermiller]

Homework Statement

Simply supported beam, all values known now I believe as this is the last question on it. I have spent a long time trying to work this out:

The bending moment is to be verified using a strain gauge bonded to the outer surface of the beam at the point of max bending moment.
Derive an equation which could be used to calculate the bending moment from the measured strain value.

Homework Equations

k = M/EI
ε(max) = kz,

The Attempt at a Solution

I know the position and value of the max bending moment, so I "think" this may be correct. But I've spent so long I have confused myself a lot. Please be gentle :-)

I have come up with this so far:

k = M/EI
ε(max) = kz,

and therefore ε(max)= (z) M/(EI)

I think I've typed the above equation correctly. I mean it as follows: strain(max) = z multiplied by the result of M divided by EI.

Z is the distance from the neutral layer to the outer layer in a tensile condition.
M is bending moment
EI is flexural stiffness (E is youngs and I is 2nd moment of area)
K is curvature of the beam or could be replaced with 1/R where R is the radius of curvature in radians.

Can anyone confirm the above or point me correctly?

Looks good.

 

[LDC1972]

Thank you! So much time spent and to have an expert say "looks good" makes it so rewarding!

Have clicked your thanks button ;-)

Thanks again!

 

[oxon88]

how would this be re-arranged for M?

M = I * ε_max * E / Z