A statically determinate truss is one of the early problems addressed in sophomore staticsclasses. A typical problem is shown in figure below:2Fapplied√30°F₁F3F2023L.HingeRollerThe applied force has a magnitude of 1000 N at an angle of 30° from the horizontal, as shownin the figure. The inner angles ₁ and 2 are 45° and 65° respectively. Determine the values ofthe forces in each member of the truss, and the reactive forces experienced at the hinge and theroller (nodes 2 and 3). Set up the problem using a simultaneous equation system. Use themethod of the inverse matrix taught in the lectures. Follow the steps a) to e) as indicatedbelow (assume "S" as the matrix representing the previous system.a) Calculate the matrix of minors of S.b) Calculate the matrix of cofactors of S (name it H)c) Calculate the determinant of S.d) Calculate the Adjoint of matrix of S using adj S = HTe) Calculate the inverse of matrix S using S₁ = adj S/|S|

To solve the problem, we first need to draw the free-body diagram of the truss and label all the…

a) Calculate the matrix of minors of S. b) Calculate the matrix of cofactors of S (name it H) c) Calculate the determinant of S. d) Calculate the Adjoint of matrix of S using adj S = HT e) Calculate the inverse of matrix S using S₁ = adj 5/|S|

a) Calculate the matrix of minors of S. b) Calculate the matrix of cofactors of S (name it H) c) Calculate the determinant of S. d) Calculate the Adjoint of matrix of S using adj S = HT e) Calculate the inverse of matrix S using S₁ = adj 5/|S|

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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Question

A statically determinate truss is one of the early problems addressed in sophomore statics
classes. A typical problem is shown in figure below:
2
Fapplied
√30°
F₁
F3
F2
02
3
L.
Hinge
Roller
The applied force has a magnitude of 1000 N at an angle of 30° from the horizontal, as shown
in the figure. The inner angles ₁ and 2 are 45° and 65° respectively. Determine the values of
the forces in each member of the truss, and the reactive forces experienced at the hinge and the
roller (nodes 2 and 3). Set up the problem using a simultaneous equation system. Use the
method of the inverse matrix taught in the lectures. Follow the steps a) to e) as indicated
below (assume "S" as the matrix representing the previous system.
a) Calculate the matrix of minors of S.
b) Calculate the matrix of cofactors of S (name it H)
c) Calculate the determinant of S.
d) Calculate the Adjoint of matrix of S using adj S = HT
e) Calculate the inverse of matrix S using S₁ = adj S/|S|

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Step 1: Free-body diagram of the truss and label all the forces acting on it

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Step 2: matrix of cofactors

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