In his name is the judge
I want to build some parametric structures. my objects is period of first mode, eccentricity and (frequency of torsional mode/frequency of transitional mode). So I decide to use NSGAII for make my parametric structure.
Inputs of optimization are transitional mass, rotational mass, length and width of structure and objects are period of first mode and (frequency of torsional mode/frequency of transitional mode) and in each one I assume eccentricity constant.
So I think there is a problem. I think there is a relation between rotational mass and transitional mass with respect to length and width of structure and eccentricity of mass.
If my guess is true I have to remove rotational mass from my inputs and use the relation instead.
So my big question is
Is there any formula to evaluate rotational mass based on dimension, eccentricity and transitional mass in rectangular plan?
wish you best
Take refuge in the right.
I even didn't read the full question but copy/pasted the title in Open AI chat. Here's what AI has to say about your inquiry (neither I, nor AI will accept any responsibility for the results but if it helps, you are welcome):
Yes, there is a formula that can be used to evaluate the rotational mass of a rectangular plan based on its dimensions, eccentricity, and transitional mass. The formula is as follows:
Rotational mass = (length * width * height * density) / (2 * PI * eccentricity)
In this formula, "length" and "width" refer to the dimensions of the rectangular plan, "height" refers to the height of the plan, "density" refers to the density of the material from which the plan is made, and "eccentricity" refers to the distance between the center of mass and the center of rotation of the plan. The formula uses these values to calculate the rotational mass of the plan, which is a measure of its resistance to changes in rotational motion.
This formula is based on the principles of classical mechanics and assumes that the rectangular plan is a uniform, solid object with a constant density. It may not be accurate for objects with more complex shapes or varying densities, and it may not take into account other factors that can affect the rotational mass of an object. However, it can provide a rough estimate of the rotational mass of a rectangular plan based on its dimensions, density, and eccentricity.
If your structure is an 'office' or 'hospital' type building with concrete floors, so that the floors form rigid diaphragms at each storey, mass is associated with the translational response, and mass moment of inertia (MMI) is associated with the torsional response. You need to study an appropriate text on this, or an ETABS program manual, etc. Attached are formulae for calculating the MMI for typical floor shapes, including how to allow for these shapes being offset from the overall centre of mass.
Hi
thank all of you for sharing your idea with me
dear Janis Barbars actually i need a formula for concentrated mass with eccentricity
dear @John Scarry yeah i used to use this formula but unfortunately the answer of this formula give different mass moment of inertia from etabs
dear @Marc Brijs thanks I'll check it and let you know what happen
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