Derive the element stiffness matrix for the nonprismatic bar, using quadratic shape functions N₁(x)=(x−L)(2x −L)/ Ľ², N₂(x)= 4x(L− x)/Ľ², and N₂(x)= x(2x −L)/ Ľ². Consider E = constant, and A(x) = A (2−x/L).
Derive the element stiffness matrix for the nonprismatic bar, using quadratic shape functions N₁(x)=(x−L)(2x −L)/ Ľ², N₂(x)= 4x(L− x)/Ľ², and N₂(x)= x(2x −L)/ Ľ². Consider E = constant, and A(x) = A (2−x/L).
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter1: Tension, Compression, And Shear
Section: Chapter Questions
Problem 1.4.13P: An L-shaped reinforced concrete slab 12 Ft X 12 ft, with a 6 Ft X 6 ft cut-out and thickness t = 9.0...
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Transcribed Image Text:Derive the element stiffness matrix for the nonprismatic bar, using quadratic
shape functions N₁ (x)=(x−L)(2x−L)/ Ľ², N₂(x)= 4x(L− x)/Ľ², and
N₂(x) = x(2x −L) / L². Consider E= constant, and A(x) = A₁(2-x/L).
Transcribed Image Text:X = 0
Node 1
Area = 2A₂
X = L/2
*
Element
Node 2
Area = A₂
Node 3
X = L
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