The stiffness matrix for a Timoshenko beam-column element in its local coordinate system (where x is along the beam length) is: L² A (1+ 4) L²A (1 + 0) 12 6L -12 6L E I 6L L²(4 + $) -6L L?(2 – 4) [K'] = L³ (1 + $) L²A L²A (1+ ø) 7(1+ $) -12 -6L 12 -6L 6L L2 (2 — Ф) -6L L2(4 + ¢)] 12EI GAĻL² a) Derive the transformation matrix [T] for this element, such that the stiffness matrix of the element can be transformed to the global coordinate system using the following relation: [K] = [T.]*[K°][7.]
The stiffness matrix for a Timoshenko beam-column element in its local coordinate system (where x is along the beam length) is: L² A (1+ 4) L²A (1 + 0) 12 6L -12 6L E I 6L L²(4 + $) -6L L?(2 – 4) [K'] = L³ (1 + $) L²A L²A (1+ ø) 7(1+ $) -12 -6L 12 -6L 6L L2 (2 — Ф) -6L L2(4 + ¢)] 12EI GAĻL² a) Derive the transformation matrix [T] for this element, such that the stiffness matrix of the element can be transformed to the global coordinate system using the following relation: [K] = [T.]*[K°][7.]
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![Q1
The stiffness matrix for a Timoshenko beam-column element in its local coordinate system
(where x is along the beam length) is:
L²A
L²A
ī(1+$)
-7 (1+ 4)
12
6L
-12
6L
E I
6L
L²(4 + ¤)
-6L L(2 – 4)
[K'] =
L²A
(1 + 4)
L³ (1 + Ø)
L²A
(1+ ø)
I
-12
-6L
12
-6L
6L
L²(2 – $)
-6L L2(4+ ¢)]
12EI
GAŞL?
a) Derive the transformation matrix [T] for this element, such that the stiffness matrix of the
element can be transformed to the global coordinate system using the following relation:
[K«] = [T<]*[K¢°][Te]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ed5c8a9-edb7-4932-9d05-88a89c1954d4%2F715a82d6-a033-4958-8482-a353edab9e6f%2Ffxa0gju_processed.png&w=3840&q=75)
Transcribed Image Text:Q1
The stiffness matrix for a Timoshenko beam-column element in its local coordinate system
(where x is along the beam length) is:
L²A
L²A
ī(1+$)
-7 (1+ 4)
12
6L
-12
6L
E I
6L
L²(4 + ¤)
-6L L(2 – 4)
[K'] =
L²A
(1 + 4)
L³ (1 + Ø)
L²A
(1+ ø)
I
-12
-6L
12
-6L
6L
L²(2 – $)
-6L L2(4+ ¢)]
12EI
GAŞL?
a) Derive the transformation matrix [T] for this element, such that the stiffness matrix of the
element can be transformed to the global coordinate system using the following relation:
[K«] = [T<]*[K¢°][Te]
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