Need help with more indepth beam theory?

[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.

 

[SteamKing]

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.