Tension in three point loaded beam for Fracture calculation

[Supernovah]

A beam with dimensions 10x10x50mm is loaded in it's middle with a load F and it's supported by two wedges at either end

Given it's fracture toughness say 500MPa, what is the largest load that it can hold?

I am assuming that the underside of the beam will go into Tension and to calculate the largest F will be related to this but to choose a "underside" dimension accurately means to the level of the unit cell dimension and we don't know the material of the beam.

So to do this question, is it is simple as Force/Area = Fracture Stress, Solving for Force?

 

[Mapes]

No, it's not quite that simple. Do you know how to make a shear and moment diagram for the beam, and then to calculate the stress due to bending moment? That's how I'd solve the problem.

 

[oswaler]

I would like to clarify a few points before providing a response. Firstly, it is important to note that the fracture toughness of a material is a measure of its ability to resist fracture under stress. It is typically measured in units of MPa√m. This means that a material with a higher fracture toughness will be able to withstand higher levels of stress before fracturing.

In the given scenario, a beam with dimensions 10x10x50mm is loaded in its middle with a load F and supported by two wedges at either end. The beam will experience tension on its underside due to the load, and the maximum load it can hold will be related to the fracture toughness of the material it is made of. However, the specific material of the beam is not mentioned, making it difficult to accurately determine the largest load it can hold.

To accurately determine the largest load that the beam can hold, we would need to know the material properties such as its Young's modulus, yield strength, and ultimate tensile strength. These properties, along with the dimensions of the beam, can be used to calculate the maximum load it can withstand before fracturing. Simply using the formula Force/Area = Fracture Stress and solving for Force will not provide an accurate answer without knowing the material properties.

In summary, to accurately determine the largest load that the beam can hold, we would need to know the material properties of the beam in addition to its dimensions. Without this information, it is not possible to accurately calculate the maximum load it can withstand before fracturing.