Download CEE 379 Frame Example: Structural Stiffness Matrix - Prof. Marc Eberhard and more Study notes Civil Engineering in PDF only on Docsity!
(ALL UNITS ARE KIPS AND INCHES)
Member AB
Input Properties XN Y (^) N XF Y (^) F A E I w 0 0 72 144 16.8 29000 758 0. Calc Properties L λx λy 161.0 0.447 0. Local Coordinate System dNx' dNy' θNz' dFx' dFy' θFz' qo q = T Q qNx' 3026.1 0 0 -3026 0 0 0 25.51 k qNy' 0 63.211 5088.4 0 -63.21 5088.4 10.062 9.35 k m (^) Nz' 0 5088.4 546147 0 -5088 273074 270.0 244.64 k-in.
k' qNFx' -3026 0 0 3026.1 0 0 0 -25.51 k
qF (^) y' 0 -63.21 -5088 0 63.211 -5088 10.062 10.78 k m (^) Fz' 0 5088.4 273074 0 -5088 546147 -270.0 -359.87 k-in.
T 0 0 0 0.4472 0.8944 0 T t^ 0 0 0 0.44721 -0.894 0
T t^ k' 0 5088.4 546147 0 -5088 273074
Global Coordinate System D 1 D 2 θ 3 Q 0 = Tt^ q 0 D kD Q 655.8 1185.2 -4551 -655.8 -1185 -4551 -9 0 12.0503 3.05 k 1185.2 2433.6 2275.6 -1185 -2434 2275.6 4.5 0 22.5 27.00 k
k = -4551 2275.6 546147 4551.2 -2276 273074 270 0 -25.3629 244.64 k-in.
Tt^ k'T (^) Q 1 -655.8 -1185 4551.2 655.8 1185.2 4551.2 -9 0.0031 -12.0503 -21.05 k Q 2 -1185 -2434 -2276 1185.2 2433.6 -2276 4.5 -0.011 -22.5 -18.00 k M 3 -4551 2275.6 273074 4551.2 -2276 546147 -270 -2E-04 -89.8742 -359.87 k-in.
A
B C
6 ft 12 ft 6 ft D
1500 lbs/ft
12 ft
1500 lbs/ft
3000 lbs/ft
All Members A = 16.8 in^2 I = 758 in. 4 E = 29000 ksi
Member BC
Input Properties XN Y (^) N XF Y (^) F A E I w 72 144 216 144 16.8 29000 758 0. Calc Properties L λx λy 144.0 1.000 0. Local Coordinate System dNx' dNy' θNz' dFx' dFy' θFz' qo q = T Q qNx' 3383.3 0 0 -3383 0 0 0 21.05 k qNy' 0 88.341 6360.5 0 -88.34 6360.5 18.000 18.00 k m (^) Nz' 0 6360.5 610611 0 -6361 305306 432.0 359.87 k-in.
k' qNFx' -3383 0 0 3383.3 0 0 0 -21.05 k
qF (^) y' 0 -88.34 -6361 0 88.341 -6361 18.000 18.00 k m (^) Fz' 0 6360.5 305306 0 -6361 610611 -432.0 -359.87 k-in.
T 0 0 0 1 0 0 T^
t 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1
3383.3 0 0 -3383 0 0 0 88.341 6360.5 0 -88.34 6360.
T t^ k' 0 6360.5 610611 0 -6361 305306
Global Coordinate System D 1 D 2 θ 3 D 4 D 5 θ 6 Q 0 = Tt^ q (^0) D kD Q Q 1 3383.3 0 0 -3383 0 0 0 0.0031 21.0503 21.05 k Q 2 0 88.341 6360.5 0 -88.34 6360.5 18 -0.011 9.3E-15 18.00 k
k = M 3 0 6360.5 610611 0 -6361 305306 432 -2E-04 -72.1258 359.87 k-in.
Tt^ k'T (^) Q 4 -3383 0 0 3383.3 0 0 0 -0.003 -21.0503 -21.05 k Q 5 0 -88.34 -6361 0 88.341 -6361 18 -0.011 -9.3E-15 18.00 k M 6 0 6360.5 305306 0 -6361 610611 -432 0.0002 72.1258 -359.87 k-in.
Structural Stiffness Matrix
D 1 D 2 θ 3 D 4 D 5 θ 6 Q 1 4039.1 1185.2 4551.2 -3383 0 0 Q 2 1185.2 2521.9 4084.9 0 -88.34 6360.
K 11 M 3 4551.2 4084.9 1E+06 0 -6361 305306
Q 4 -3383 0 0 4039.1 -1185 4551.2 k/in. Q 5 0 -88.34 -6361 -1185 2521.9 - M 6 0 6360.5 305306 4551.2 -4085 1E+
0.0043 -0.002 8E-08 0.0042 0.0019 1E-06 -9 k -0.002 0.0013 -9E-07 -0.002 -9E-04 -2E-06 22.5 k
K 11 (inv 8E-08 -9E-07 9E-07 1E-06 2E-06 -2E-07 Q 01 162 k-in.
0.0042 -0.002 1E-06 0.0043 0.002 8E-08 9 k 0.0019 -9E-04 2E-06 0.002 0.0013 9E-07 22.5 k 1E-06 -2E-06 -2E-07 8E-08 9E-07 9E-07 -162 k-in.
0 k 9 k D 1 0.00311 inches 0 k -22.5 k D 2 -0.01098 inches
Qk 0 k-in. Qk -Q 01 -162 k-in. Du θ 3 -0.00024 radians
0 k -9 k D 4 -0.00311 inches 0 k -22.5 k D 5 -0.01098 inches 0 k-in. 162 k-in. θ 6 0.00024 radians
