Need help with more indepth beam theory?

• Kristopher Horn
In summary, the goal of the project is to design a beam using 1018 steel to achieve a certain deflection under one load and not fail under a larger load. The design is similar to a cantilever beam with a variable cross section, and the Euler-Bernoulli beam theory was used to determine the proper dimensions. However, the deflection values obtained from ANSYS were significantly different from those calculated using beam theory. It is suggested to double check the application of beam theories and ensure consistent units are used. Additionally, the use of degrees as arguments in the tangent function in MathCAD should be verified.
Kristopher Horn
I have a project for a class and our goal is to design a beam using 1018 steel to achieve a certain deflection under one load and not fail under an even larger load.

The design I have come up with is very similar to a cantilever beam, but is has a variable cross section. I have used the Euler-Bernoulli beam theory to find the proper dimension to minimize the volume and achieve the goals. I then built my design in ANSYS and my deflection values varied GREATLY. With beam theory I was getting about 3.655 inch deflection, ANSYS was giving me about a .031 inch deflection. That is all under a 60 lbf load

Is there a more elaborate beam theory or more correct one that I could use?

Attached is a pdf of my work in MathCAD and picture of my ANSYS model if that would help.

Attachments

• Bracket_Design_Work.pdf
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Kristopher Horn said:
I have a project for a class and our goal is to design a beam using 1018 steel to achieve a certain deflection under one load and not fail under an even larger load.

The design I have come up with is very similar to a cantilever beam, but is has a variable cross section. I have used the Euler-Bernoulli beam theory to find the proper dimension to minimize the volume and achieve the goals. I then built my design in ANSYS and my deflection values varied GREATLY. With beam theory I was getting about 3.655 inch deflection, ANSYS was giving me about a .031 inch deflection. That is all under a 60 lbf load

Is there a more elaborate beam theory or more correct one that I could use?

Attached is a pdf of my work in MathCAD and picture of my ANSYS model if that would help.

It's not clear, from what I can piece together from your attachments, that you need a new beam theory, you just need to make sure the beam theories you are using have been applied correctly.

Why have you used only 60 ksi for Young's Modulus (E)? E for steel is going to be on the order of 30,000 ksi.

In the quantity M / EI , you must use consistent units. If M is in inch-lbs, then I must be in in4 and E must be in lbs / in2, not ksi.

One other thing to check is to make sure the tangent function in MathCAD accepts degrees as arguments.

1. What is beam theory?

Beam theory is a mathematical model used to analyze the behavior of beams under various loading conditions. It involves simplifying the complex three-dimensional structures of beams into one-dimensional systems, making it easier to calculate the stresses and deflections in the beam.

2. What are the assumptions made in beam theory?

Beam theory is based on several assumptions, including that the beam is straight, the cross-section remains constant and free from warping, and that the material is homogenous and isotropic. It also assumes that the beam is subjected to small deformations and that the loading is applied gradually.

3. What are the different types of beams in beam theory?

The three types of beams commonly used in beam theory are cantilever beams, simply supported beams, and continuous beams. Cantilever beams are supported at one end and have a fixed connection, while simply supported beams are supported at both ends and have a free connection. Continuous beams have multiple supports along their length.

4. How is beam theory used in structural engineering?

Beam theory is an essential tool in structural engineering as it allows engineers to predict the behavior of beams under different loading conditions and make informed design decisions. It is commonly used in the design of bridges, buildings, and other structures to ensure their stability and safety.

5. What are the limitations of beam theory?

While beam theory is a useful tool, it has its limitations. It is only applicable to slender beams with constant cross-sections and uniform material properties. Beams with complex geometries or non-uniform material properties require more advanced analysis methods. Additionally, beam theory does not consider the effects of shear deformation, which can be significant in some cases.

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