Three springs, A, B and C, are connected as shown below, with one end of A and C attached to rigid supports. All springs are interconnected by a light, inextensible bar that is constrained from rotating. Also, forces of 250 N and 175 N are applied to the springs as shown. The stiffness of A, B and C are 100, 150 and 200 N/mm, respectively. By modelling each spring as a linear simplex finite element, determine: (a) (b) (c) the global assembly the elongation of the springs the reactions at the supports_

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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Please show all possible workings, such as how the matrix was derived and how the answer was reached. Use finite element analysis.
1.
Three springs, A, B and C, are connected as shown below, with one end of A and C
attached to rigid supports. All springs are interconnected by a light, inextensible bar that
is constrained from rotating. Also, forces of 250 N and 175 N are applied to the springs
as shown. The stiffness of A, B and C are 100, 150 and 200 N/mm, respectively. By
modelling each spring as a linear simplex finite element, determine:
(a)
(b)
(c)
the global assembly
the elongation of the springs
the reactions at the supports
(Ans: (b) u, = 1.417 mm, u, = 1.667 mm, uc = 11.417 mm (c) Ren = 141.67 N,
left, Riaht = 283.33 N, left)
B
250 N
wwww-→
A
175 N
Transcribed Image Text:1. Three springs, A, B and C, are connected as shown below, with one end of A and C attached to rigid supports. All springs are interconnected by a light, inextensible bar that is constrained from rotating. Also, forces of 250 N and 175 N are applied to the springs as shown. The stiffness of A, B and C are 100, 150 and 200 N/mm, respectively. By modelling each spring as a linear simplex finite element, determine: (a) (b) (c) the global assembly the elongation of the springs the reactions at the supports (Ans: (b) u, = 1.417 mm, u, = 1.667 mm, uc = 11.417 mm (c) Ren = 141.67 N, left, Riaht = 283.33 N, left) B 250 N wwww-→ A 175 N
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