Q1The stiffness matrix for a Timoshenko beam-column element in its local coordinate system(where x is along the beam length) is:L²AL²Aī(1+$)-7 (1+ 4)126L-126LE I6LL²(4 + ¤)-6L L(2 – 4)[K'] =L²A(1 + 4)L³ (1 + Ø)L²A(1+ ø)I-12-6L12-6L6LL²(2 – $)-6L L2(4+ ¢)]12EIGAŞL?a) Derive the transformation matrix [T] for this element, such that the stiffness matrix of theelement can be transformed to the global coordinate system using the following relation:[K«] = [T<]*[K¢°][Te]

Given : To find : Transformation matrix

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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Concept explainers

Types of loading

In mechanical terminology, the term load indicates that external force/weight, either constant or variable, acts on a mechanical member/structure. The weight of an object of a specific material is also an external load, and the external force that works on a structure comes under the categories of loading. The external load generates its effects as stress and strain in the structure.

Question

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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