k = 200kN/m k = 300kN/m EXAMPLE m = 1.0 ton m = 1.0 ton Schematic of two-story building frame 4m 4m m₂ ü₁ + (k₁ + k₂)u₁k₂u₂ = 0 m₂ U₂ -k₂U₁ +k₂U₂ = 0 0 +k₂ [₁ ₂] + [*₁ +² -k2²] (u)-0 -k₂ k₂ The mass and stiffness matrices are []=[]=[¹] tom [k] = [k₁ + k₂ = K₂ k₂ 0 500 -2001 200 Determine the period and modal matrix. [k₁ +K₂ -m₁w₁² -K₂ det kN/m -k₂ k₂ - m₂Wn² MADE4LE THE = 0 FRAMEWO Ca = 0.40 Cv = 0.56 N-S 4 k4= 31.49 KNIM k3=46.16 KNIM 1₂=59.46 kN /m 3 2 1 k₁= 85.47 kN/m] My = 0.89 ton M3= 1-22 ton M₂ = 1.47 ton M₁= 1.62 ton W-E k3= 102.05 K4 = 57.37 kN/m] 3 (4) My = 0.89 ton 12=141-27 K₁=214.97 M₁ = 1-22 ton 2 M₂ = 1.47 ton (1) M₁ = 1.62 ton
k = 200kN/m k = 300kN/m EXAMPLE m = 1.0 ton m = 1.0 ton Schematic of two-story building frame 4m 4m m₂ ü₁ + (k₁ + k₂)u₁k₂u₂ = 0 m₂ U₂ -k₂U₁ +k₂U₂ = 0 0 +k₂ [₁ ₂] + [*₁ +² -k2²] (u)-0 -k₂ k₂ The mass and stiffness matrices are []=[]=[¹] tom [k] = [k₁ + k₂ = K₂ k₂ 0 500 -2001 200 Determine the period and modal matrix. [k₁ +K₂ -m₁w₁² -K₂ det kN/m -k₂ k₂ - m₂Wn² MADE4LE THE = 0 FRAMEWO Ca = 0.40 Cv = 0.56 N-S 4 k4= 31.49 KNIM k3=46.16 KNIM 1₂=59.46 kN /m 3 2 1 k₁= 85.47 kN/m] My = 0.89 ton M3= 1-22 ton M₂ = 1.47 ton M₁= 1.62 ton W-E k3= 102.05 K4 = 57.37 kN/m] 3 (4) My = 0.89 ton 12=141-27 K₁=214.97 M₁ = 1-22 ton 2 M₂ = 1.47 ton (1) M₁ = 1.62 ton
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
Determine the 4 storey period and modal matrix.(Derive) (i need the RED CIRCLED)
P.S.An example is given but it is only a 2-storey period and modal matrix
![k = 200kN/m
k = 300kN/m
EXAMPLE
m = 1.0 ton
m = 1.0 ton
Schematic of two-story building frame
4m
4m
m₂ ü₁ + (k₁ + k₂)u₁k₂u₂ = 0
m₂ U₂ -k₂U₁ +k₂U₂ = 0
0
+k₂
[₁ ₂] + [*₁ +² -k2²] (u)-0
-k₂
k₂
The mass and stiffness matrices are
[]=[]=[¹] tom
[k] =
[k₁ + k₂
= K₂
k₂
0
500 -2001
200
Determine the period and modal matrix.
[k₁ +K₂ -m₁w₁²
-K₂
det
kN/m
-k₂
k₂ - m₂Wn²
MADE4LE
THE
= 0
FRAMEWO](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd2b7248-e1b4-405c-b30d-764232b6038c%2F56580003-37c6-408c-a8fb-2242b8c46945%2F8cwcqe_processed.png&w=3840&q=75)
Transcribed Image Text:k = 200kN/m
k = 300kN/m
EXAMPLE
m = 1.0 ton
m = 1.0 ton
Schematic of two-story building frame
4m
4m
m₂ ü₁ + (k₁ + k₂)u₁k₂u₂ = 0
m₂ U₂ -k₂U₁ +k₂U₂ = 0
0
+k₂
[₁ ₂] + [*₁ +² -k2²] (u)-0
-k₂
k₂
The mass and stiffness matrices are
[]=[]=[¹] tom
[k] =
[k₁ + k₂
= K₂
k₂
0
500 -2001
200
Determine the period and modal matrix.
[k₁ +K₂ -m₁w₁²
-K₂
det
kN/m
-k₂
k₂ - m₂Wn²
MADE4LE
THE
= 0
FRAMEWO
![Ca = 0.40
Cv = 0.56
N-S
4
k4= 31.49 KNIM
k3=46.16 KNIM
1₂=59.46 kN /m
3
2
1
k₁= 85.47 kN/m]
My = 0.89 ton
M3= 1-22 ton
M₂ = 1.47 ton
M₁= 1.62 ton
W-E
k3= 102.05
K4 = 57.37 kN/m]
3
(4) My = 0.89 ton
12=141-27
K₁=214.97
M₁ =
1-22 ton
2 M₂ = 1.47 ton
(1) M₁ = 1.62 ton](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd2b7248-e1b4-405c-b30d-764232b6038c%2F56580003-37c6-408c-a8fb-2242b8c46945%2Fqj5ay7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Ca = 0.40
Cv = 0.56
N-S
4
k4= 31.49 KNIM
k3=46.16 KNIM
1₂=59.46 kN /m
3
2
1
k₁= 85.47 kN/m]
My = 0.89 ton
M3= 1-22 ton
M₂ = 1.47 ton
M₁= 1.62 ton
W-E
k3= 102.05
K4 = 57.37 kN/m]
3
(4) My = 0.89 ton
12=141-27
K₁=214.97
M₁ =
1-22 ton
2 M₂ = 1.47 ton
(1) M₁ = 1.62 ton
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