To calculate the base shear of a linear Multi-Degree-of-Freedom (MDOF) building, you can check the following code:
clear all
clc
% Define mass, stiffness, and damping matrices
m1 = 3; m2 = 2; m3 = 1;
k1 = 2; k2 = 2; k3 = 2;
c1 = 1; c2 = 1; c3 = 1;
M = [m1 0 0; 0 m2 0; 0 0 m3];
K = [k1+k2 -k2 0; -k2 k2+k3 -k3; 0 -k3 k3];
C = [c1+c2 -c2 0; -c2 c2+c3 -c3; 0 -c3 c3];
% State space model matrices
F = [-m1 -m2 -m3]';
inv_M = inv(M);
A = [zeros(3,3) eye(3); -inv_M*K -inv_M*C];
B = [zeros(3,1); inv_M*F];
Cc = eye(6);
D = zeros(6,1);
sys_s = ss(A,B,Cc,D);
% Define input motion
acc = [1; 2; 3; 4; 5];
u = acc;
dt = 0.01;
t = (0:length(acc)-1)*dt;
x0 = zeros(6,1);
[y,t,x] = lsim(sys_s,u,t,x0);
% Calculate base shear
base_shear = sum(M * x(:, 1:3)', 2);
% Display base shear
disp('Base Shear:');
disp(base_shear);
This code calculates the base shear by summing the contributions of the mass matrix and the displacements at each degree of freedom. You can adjust the input motion and other parameters as needed for your specific analysis.
Hope this helps.
