+6 07 553 86 86 arazin@utm.my
Bar |
k1 = E*A/L * [1 -1 ; -1 1]
r1 = [q*L/2 ; q*L/2]
Beam |
ka = 12*E*I/L^3
kb = 6*E*I/L^2
kc = 4*E*I/L
kd = 2*E*I/L
k1 = [ ka kb -ka kb;
kb kc -kb kd;
-ka -kb ka -kb;
kb kd -kb kc]
q1 = [q*L/2; q*L^2/12; q*L/2; -q*L^2/12]

Truss | 

c = cos(B); s = sin(B);
k1 = E*A/L* …
[c^2 c*s -c^2 -c*s;
c*s s^2 -c*s -s^2;
-c^2 -c*s c^2 c*s;
-c*s -s^2 c*s s^2]

Frame | 

ka = EA/L
kb = 12*EI/L^3
kc = 6*EI/L^2
kd = 4*EI/L
ke = 2*EI/L
k1p = [ka 0 0 -ka 0 0;
0 kb kc 0 -kb kc;
0 kc kd 0 -kc ke;
-ka 0 0 ka 0 0;
0 -kb -kc 0 kb -kc;
0 kc ke 0 -kc kd]

c = cosd(B); s = sind(B);
T = [c s 0 0 0 0;
-s c 0 0 0 0;
0 0 1 0 0 0;
0 0 0 c s 0;
0 0 0 -s c 0;
0 0 0 0 0 1];

k1 = T’*k1p*T

q1p = [0 q*L/2 q*L^2/12 0 q*L/2 -q*L^2/12]’
q1 = T’*q1p

Buckling |
kg1 = 1/(30*L) * …
[36 3*L -36 3*L;
2*L 4*L^2 -3*L -L^2;
-36 -3*L 36 -3*L;
3*L -L^2 -3*L 4*L^2]

Free Vibration | 

m1 = rho*A*L/420 * …
[156 22*L 54 -13*L;
22*L 4*L^2 13*L -3*L^2;
54 13*L 156 -22*L;
-13*L -3*L^2 -22*L 4*L^2]