Confused on a few things for a beam and cycles to failure

[bradk2fan]

I have a problem which is a beam with 2 machines on the beam and one of them has an operating frequency between 200 and 600 rad/s that transmits a force to the beam. I have to determine the number of cycles to failure of the beam. It's stated in the problem statement to account for the mean stress that arises from the weight of the machines and the beam.

I've found out the bending moments for the transmitted force and the weights of each machine and for the beam's weight. And then used that to determine the stresses. I've calculated that the stresses from just the weights add up to roughly 72 MPa. And the stress from just the transmitted force is 113 MPa.

Now I'm told to use the soderberg failure criterion.
σ_soderberg=-(σ_fatigue/σ_yield)σ_mean+σ_fatigue
σ_alternating≤σ_soderberg

I'm given the yield stress and I need to find the fatigue stress to calculate for cycles to failure. So I need to calculate the mean and alternating stresses. From what I've learned is that the mean stress is (σ_max+σ_min)/2 and alternating stress is (σ_max-σ_min)/2. I'm confused on my problem on what the min and max is. Well obviously the min would be 72 for the weight of the beam when the machine isn't transmitting a force. Would the max be 113 or would it be the total of the stress from weight plus the stress from the transmitted force for 185 MPa.

The other part I'm confused on is that I need to also find the cycles to failure from factors of safety for 1, 1.25, 1.5, 1.75, 2. Now I know to take that into account in a basic problem. You would take the yield stress over the factor of safety to find the working stress. But I'm not sure how to apply it for the soderberg equation?

If anyone could help me out that would be so greatly appreciated. Thanks.

 

[Achy47]

Hello,

Thank you for sharing your problem with us. I would like to offer some clarification and suggestions on how to approach this problem.

Firstly, it is important to understand the Soderberg failure criterion and how it applies to your problem. This criterion is used to determine the failure of a material under both static and cyclic loading conditions. In your case, you are dealing with a cyclic loading situation, so the Soderberg criterion is appropriate.

The Soderberg criterion states that the alternating stress (σalternating) should be less than or equal to the Soderberg stress (σsoderberg). The Soderberg stress takes into account the mean stress (σmean), fatigue stress (σfatigue), and yield stress (σyield). In order to calculate the Soderberg stress, you will need to know the values for σmean, σfatigue, and σyield.

You have correctly calculated the mean stress (σmean) as (σmax + σmin)/2, where σmax is the maximum stress and σmin is the minimum stress. In your case, the minimum stress is 72 MPa, which is the stress caused by the weight of the beam and the machines. The maximum stress (σmax) would be the sum of the stress caused by the weight of the beam and the machines (72 MPa) and the stress caused by the transmitted force (113 MPa). Therefore, σmax would be 72 + 113 = 185 MPa.

Next, you will need to calculate the fatigue stress (σfatigue). This value is dependent on the material properties and the number of cycles to failure. In order to determine the number of cycles to failure, you will need to use the Goodman diagram or other fatigue analysis methods. Once you have determined the number of cycles to failure, you can use it to calculate the fatigue stress using the Soderberg equation: σfatigue = σyield * (Nf)^(-1/k), where Nf is the number of cycles to failure and k is a material constant.

Once you have calculated σmean, σfatigue, and σyield, you can plug these values into the Soderberg criterion to determine if your beam will fail under the given loading conditions. If the alternating stress (σalternating) is less than or equal to the Soderberg stress (σsoderberg), then the beam will not fail. If σalternating