Plotting Skeleton Curves and Hysteresis Loops in MATLAB with Calculation of Cumulative Hysteretic Energy, Stiffness Degradation, and Strength Degradation

In structural engineering and earthquake engineering research, plotting and analyzing skeleton curves and hysteresis loops are crucial methods for evaluating seismic performance of structures. MATLAB provides efficient tools for visualizing these curves and calculating key parameters such as cumulative hysteretic energy, stiffness degradation, and strength degradation.

### Skeleton Curves and Hysteresis Loops The skeleton curve represents the relationship between maximum load-bearing capacity and corresponding deformation under cyclic loading, reflecting the overall stiffness and strength characteristics of a structure. Hysteresis loops record the load-displacement relationship during loading cycles, visually demonstrating the energy dissipation capacity and restoring force characteristics. In MATLAB implementation, these curves can be plotted using cyclic loading test data through interpolation methods (like interp1 function) or curve fitting techniques (using polyfit or fit functions).

### Cumulative Hysteretic Energy Cumulative hysteretic energy is a key indicator for assessing seismic performance, representing the structure's energy dissipation capacity under repeated loading. Calculation involves summing the areas of individual hysteresis loops. MATLAB can efficiently compute these areas using numerical integration methods such as the trapezoidal rule (trapz function) and accumulate the results through iterative summation in loops.

### Stiffness Degradation and Strength Degradation Stiffness degradation refers to the gradual reduction of structural stiffness under cyclic loading, which can be evaluated through slope changes in the skeleton curve or secant stiffness of hysteresis loops. Strength degradation describes the progressive decline in load-bearing capacity, typically quantified by changes in peak loads. In MATLAB, these degradation trends can be analyzed using piecewise linear regression (with lsqcurvefit) or moving average methods (movmean function) to track stiffness and strength evolution over loading cycles.

In summary, MATLAB provides powerful computational and visualization tools for seismic performance analysis, enabling researchers to gain deep insights into hysteretic behavior and degradation patterns of structures through systematic data processing and graphical representation.