Calculating Bending Stress for a Cantilever Beam

In summary, the conversation was about calculating bending stress for a cylindrical beam with a point mass on its tip. The person was unsure of their answer and asked for clarification. They shared their calculations and mentioned using the formula for bending stress. However, they used the wrong values and the expert advised using the formula S = W*L/Z for the correct answer.
  • #1
NuclearPink
1
0
Hi, I'm trying to calculate bending stress for a cylindrical beam. I'd like to have my result double checked because I got an answer that doesn't make sense to me. All of this is personal research, so I'm not very confident in my answer.

It's a cantilever beam with a point mass of 347.4 oz. on its tip. The distance from the load to the other end is 2 in., and the beam has a radius of 1/8". This is the calculation I found for bending stress:

bending stress (psi) = bending moment (lbs. in.) * distance from load to edge (in.) / second moment of inertia (in^4)

I researched the second moment of inertia to be (pi/4)*r^4 for a solid cylinder. So I plugged that in...

((21.7125 lbs. * 2 in.) * 2in.) / (pi/4 * (1/8 in.)^4)

...and got a result of about 450,000 psi. This feels like way too high a number, so I'd like to know what I'm doing wrong here. Thank you!
 
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  • #2
I am not sure why you doubled the load W and used the second moment of inertia.

What you will find in any engineering reference is that you should be using the formula S = W*L/Z for the max stress at the base attachment point where Z is the section modulus and for round bar Z = π*d^3 / 32 = π*(2*r)^3 / 32. By doing so you will get an answer of 28,308.7 psi.
 

1. How is bending stress calculated for a cantilever beam?

The bending stress for a cantilever beam can be calculated using the formula σ = (M * c) / I, where σ is the bending stress, M is the bending moment, c is the distance from the neutral axis to the outermost fiber, and I is the moment of inertia.

2. What is the moment of inertia and why is it important in calculating bending stress for a cantilever beam?

The moment of inertia (I) is a measure of an object's resistance to changes in rotational motion. In the context of a cantilever beam, it represents the beam's cross-sectional shape and dimensions. It is important in calculating bending stress because it affects the distribution of stress and strain along the beam, with a larger moment of inertia resulting in lower bending stress.

3. How does the position of the load affect the bending stress on a cantilever beam?

The position of the load can greatly affect the bending stress on a cantilever beam. Placing the load closer to the fixed end of the beam will result in higher bending stress, while placing it closer to the free end will result in lower bending stress. This is because the moment arm, or the distance from the load to the fixed end, plays a significant role in the calculation of bending stress.

4. What are the units for bending stress and how do they relate to the units for the other variables in the bending stress formula?

The units for bending stress are typically expressed in pounds per square inch (psi) or newtons per square meter (N/m^2). These units are directly related to the units for the other variables in the formula. The bending moment is typically measured in pound-feet (lb-ft) or newton-meters (N-m), while the distance (c) is measured in inches or meters and the moment of inertia (I) is measured in inches^4 or meters^4. Therefore, the units for bending stress are derived from the units of the other variables in the formula.

5. Can the bending stress on a cantilever beam be negative?

Yes, the bending stress on a cantilever beam can be negative. This occurs when the beam experiences compression instead of tension, resulting in a negative value for the bending stress. Negative bending stress can occur in certain situations, such as when a cantilever beam is subjected to a distributed load or a combination of loads acting in opposite directions.

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