Derivation of the Curvature Equation
The compatibility equation is as follows:
The slope at the top ends are taken from the Beam Deflection Formula tables. For the first analysis shown, a simple force load at the end is transmitted to the column.
The second analysis shows a 1 k-ft moment at the tip of the column which is multiplied by the real Moment at "B." This take usage of flexural (beam) theory.
The total degree change when added up is zero. This allows for the calculation of the real moment at the top of the column.
The moment diagram of each system was created. The sum of the moment equations of each gave the moment of the column as a function of x-- x being the vertical axis. The curvature equation was calculated in this manner.
Research Schedule
Week 11/15 - 11/19
- check formula
- finish 1.1-1.3 of Ch. 1
Week 11/22-11/26
- Finish Ch. 1 & send draft to Barroso/Hurlebaus
- Read Ch. 7: Modelling of Smart Structures (Antisymmetric Configuration) and apply the curvature equation.
- Re-read "Adaptive Control to Mitigate Damage Impact on Structural Response" (Bitaraf, Maryam) to refresh on the Bouc-Wen Model
- Start writing the Bouc-Wen Model on Matlab/Simulink*
- Assume MR is 10kN for now
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