Finding M & T Using Mohr's Strain Circle

[arghstar]

Hi, desperately need help with this assignment question as its in for 2moro!

"At a point on the surface of a shaft with diameter of 100mm, a 45deg rosette strain gauge is positioned with the middle gauge along the axis of the shaft. The gauges measure strains of a= -0.00015, b = 0.0003, c = 0.00005. Use Mohr's strain circle to determine the value of M(bending moment) and T(torque). E = 210GPa and u = 0.29."

I've drawn a mohr's circle to find principle strains of 0.00032 and -0.00042. From this i can get the principle stresses, but I do not know what formula to use to find the bending moment and torque?

Any help would be much appreciated thankyou!

 

[FredGarvin]

Don't double post. I answered in the Engineering section.

 

[piercas]

Hello, thank you for reaching out for assistance with your assignment. I understand the importance of using appropriate methods and equations to accurately determine values such as bending moment and torque. In this case, we can use the equations for bending moment and torque in terms of principle stresses and strains to solve for M and T.

For bending moment, we can use the equation M = (E/2(1+u)) * (σ1-σ2) * (ε1-ε2), where E is the modulus of elasticity, u is the Poisson's ratio, σ1 and σ2 are the principle stresses, and ε1 and ε2 are the principle strains. Plugging in the given values, we get:

M = (210GPa/2(1+0.29)) * (0.00032-(-0.00042)) * (0.0003-(-0.00005))
M = 0.000023 Nm

For torque, we can use the equation T = (E/4(1+u)) * (σ1+σ2) * (ε1+ε2), where E, u, σ1, σ2, ε1, and ε2 are the same as before. Plugging in the given values, we get:

T = (210GPa/4(1+0.29)) * (0.00032+(-0.00042)) * (0.0003+(-0.00005))
T = -0.000012 Nm

I hope this helps you solve your assignment question. Remember to always use the appropriate equations and units when solving for values in scientific problems. Best of luck!