1. The problem statement, all variables and given/known data
I am using a Vishay strain indicator with it hooked up to a strain gage hooked up 1" away from the wall on the solid beam. The beam is .5" by .5", and it is solid. The beam is 16" long and I am putting weights at the end of the beam. The weights are 1, 2, 5, 10, 15, and 20 lbs. On each weight, I recorded a strain(uin/in). It states to use the modulus of elasticity E_aluminum 10x10^6 to convert to psi. My question is how do I calculate the M part for the bending stress?
2. Relevant equations
bending stress = MC/I
modulus of elasticity E_aluminum 10x10^6 to convert to psi.
3. The attempt at a solution
For C, .5/2= .25
For I, (1/12)*b*h^3 or (1/12)*.5*.5^3 = .0052083
How do I find my M?
For 1 lb, would it be M-1lb(16")=0 or M=16 lb.in but I don't get it why it says to use E_aluminum = 10x10^6 psi to convert.
To calculate the bending stress, you need to determine the value of M, which represents the moment applied to the beam. In this case, M can be calculated by multiplying the weight applied at the end of the beam by the distance from the point of application to the point where you are measuring the strain.
Assuming you are measuring the strain 1 inch away from the wall, the distance from the point of application to your measurement point is 16 - 1 = 15 inches.
For the 1 lb weight, the moment, M, is given by:
M = 1 lb * 15 inches = 15 lb·in
Now, regarding the use of the modulus of elasticity, E_aluminum, to convert the strain to psi, let me explain.
The strain, which is measured in microinches per inch (uin/in), gives you an indication of how the length of the beam changes under the applied load. However, to calculate the bending stress, you need to convert the strain to a stress, which has units of pounds per square inch (psi).
The modulus of elasticity, E_aluminum, is a material property that relates the stress and strain for aluminum. It allows you to convert the strain to stress using the following formula:
Stress = E_aluminum * Strain
In your case, E_aluminum is given as 10x10^6 psi. So, to calculate the bending stress for each weight, you multiply the strain (in uin/in) by E_aluminum (in psi) to obtain the stress (in psi).
For example, let's say the strain for the 1 lb weight is 1000 uin/in. To calculate the bending stress, you would use:
Stress = (10x10^6 psi) * (1000 uin/in) = 10^9 psi·uin/in
The value obtained for the stress has units of psi·uin/in, which represents the bending stress per inch of the beam length. To convert it to psi, you divide by the length of the beam:
Bending Stress (psi) = Stress (psi·uin/in) / Beam Length (in)
I hope this explanation helps you understand how to calculate the M part for the bending stress and how to convert the strain to psi using the modulus of elasticity for aluminum.