To start, the code and building from Module 5 were reused. The code was then added to in order to get the new parameters (everything is from module 5 except the bottom yellow, red, light blue sections, and loop inputs/outputs).
For this assignment, I was interested in doing an analysis that relates to the class in Earthquake Resistant Design (CEE 287) that I am currently taking. Two important parameters in seismic design are the following:
- Building Period
- Seismic Base Shear
Two new parameters of Floor Unit Mass and Lateral Stiffness were added to allow for these to be calculated. These were input as variable parameters to see the effects of each.
In a real world building, the difference in unit mass can be the difference between a steel and concrete structure, since concrete is so much heavier. The lateral stiffness is also a parameter that can be changed and is based on the lateral system of the structure. However, the values chosen here are just representative and are not necessarily real values for mass and stiffness. The main point of interest is how they affect the output parameters.
In order to estimate the period of the building, the mass and stiffness need to be known. To simplify the problem, the building is approximated as a single degree of freedom (SDOF) system. The equation for period is the following:
This is coded in grasshopper with the following expression:
The multiplication takes the floor area and multiplies it by the unit mass factor. That factor, along with the stiffness, is from the loop and excel sheet (initialized in the bottom red and yellow sections).
Lastly, the values are re-input into the end-loop function and output. Final output parameter spreadsheet values are at the bottom of the page.
Seismic Base Shear
Seismic Base Shear is taken from ASCE 7-22 as:
To find Cs, the design spectrum from ASCE 7-22 is used along with the periods just found. The site is assumed to be where the classroom is (Y2E2, 473 Via Ortega, Stanford, California, 94305), the site class is Class D (found in CEE 287), and the risk category is II. The following spectrum is produced.
The two period spectrum was used as opposed to the new ASCE 7-22 multi-period spectrum because the calculations are made easier. The values of spectral acceleration from this are based on the parameters above and simple equations.
In grasshopper, the this was done with the block below, with the python script holding the spectrum calculations.
Finally, the base shear can be found by multiplying the Cs value by the building weight. The total mass from the period calculation is used and multiplied by a scale factor of 32.2 ft/s^2 to get weight.
The task of designing a structure is a balancing act of many parameters. A light structure with high stiffness does not necessarily mean lower base shear because it creates lower periods which lead to higher spectral acceleration values. Base shear is generally the most important parameter when evaluating performance, with the value of period being a parameter to calculate it with.
The results from this study show that generally, higher mass is leads to higher periods, but also higher base shear. Although the values of Cs decrease with increasing period, the extra weight matters more.
The more interesting result is with the stiffness. Generally the thought is that a stiffer structure is preferred, however the higher values of lateral stiffness lead to higher base shears. This is because higher stiffness values result in lower periods, but lower periods lead to higher spectral acceleration values.
To achieve the smallest base shear, the recommended building structural properties are the lighter mass and lower lateral stiffness. In term of height, scale factor, and floor area, the lower numbers lead to smaller base shears in all cases however that is more of an architectural decision and isn’t the primary focus of this study.