Help me calculate a calculated bending stress (psi) in cantilever beam?

In summary, the conversation discusses the use of a Vishay strain indicator with a solid beam setup to measure bending stress. The beam is 16" long and weights of 1, 2, 5, 10, 15, and 20 lbs are placed at the end. The modulus of elasticity for aluminum is used to convert strain to stress. The bending moment is calculated by multiplying the weight by the distance from the point in question. The conversation also mentions a gauge factor that may affect the accuracy of the calculated values.
  • #1
gnozahs
3
0

Homework Statement



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?

Homework Equations



bending stress = MC/I

modulus of elasticity E_aluminum 10x10^6 to convert to psi.

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.

Here is a picture of the cantilever beam setup I used.

http://tinypic.com/r/2q80eg1/5
 
Last edited:
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  • #2
The moment is simply the distance the weight is from the point in question. So at the wall, the bending moment is W * 16 = 16W inch pounds.

The conversion they are talking about is how you convert strain to stress. Stress = strain times modulus
 
  • #3
LawrenceC said:
The moment is simply the distance the weight is from the point in question. So at the wall, the bending moment is W * 16 = 16W inch pounds.

The conversion they are talking about is how you convert strain to stress. Stress = strain times modulus

Thank you! It makes sense now. The only weird thing is if I just 10^6 instead of 10*10^6, then it will be close to my theoretical value. But if I do 10*10^6, the calculated value is super off from the theoretical value.
 
  • #4
I have never used strain gauges but does it have some sort of gauge factor associated with it?
 
  • #5

To calculate the bending stress in this cantilever beam, you will need to use the formula for bending stress, which is MC/I. In this formula, M represents the bending moment, C is the distance from the neutral axis to the outermost fiber, and I is the moment of inertia.

To find the bending moment, you will need to use the weights you applied to the end of the beam and their respective distances from the fixed end. For example, for the 1 lb weight, the moment would be 1 lb * 16 inches = 16 lb.in. You will need to do this for each weight and then add them all together to find the total bending moment.

Next, you will need to find the value for C. This is the distance from the neutral axis to the outermost fiber. In this case, since the beam is square and the weight is applied at the end, the distance would be 0.25 inches.

Finally, you will need to find the moment of inertia (I) for the beam. This can be calculated using the formula (1/12)*b*h^3, where b is the width of the beam and h is the height. In this case, the dimensions are 0.5 inches by 0.5 inches, so the moment of inertia would be 0.0052083 inches^4.

Once you have all these values, you can plug them into the formula MC/I to calculate the bending stress in psi. Make sure to convert the units appropriately, using the modulus of elasticity for aluminum (10x10^6 psi) to convert the units of strain (uin/in) to psi.

I hope this helps!
 

What is a calculated bending stress in a cantilever beam?

A calculated bending stress is the amount of stress that a cantilever beam experiences due to external forces, such as weight or pressure, acting on it. It is typically measured in pounds per square inch (psi).

How is a calculated bending stress calculated?

A calculated bending stress is calculated using the formula σ = Mc/I, where σ is the bending stress, M is the bending moment, c is the distance from the neutral axis to the outermost point of the beam, and I is the moment of inertia of the beam.

What factors affect the calculated bending stress in a cantilever beam?

The calculated bending stress in a cantilever beam is affected by the magnitude and direction of the external forces, as well as the shape, size, and material properties of the beam. It is also influenced by the beam's support conditions and the distance between supports.

Why is it important to calculate the bending stress in a cantilever beam?

Calculating the bending stress in a cantilever beam is important because it helps engineers and designers ensure that the beam can withstand the expected loads without breaking or deforming. It also helps determine the appropriate size and material for the beam to be used in a given application.

Can the calculated bending stress be reduced?

Yes, the calculated bending stress can be reduced by increasing the moment of inertia of the beam, increasing the distance between supports, or using a stronger and more rigid material for the beam. Properly designing and constructing the beam can also help reduce the calculated bending stress and ensure its structural integrity.

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