Problem 5.4Given a one-dimensional elasticity problem as shown in Figure 5.20. The bar is constrained at both ends(A and C). Its cross-sectional area is constant (A = 0.1 m²) on segment AB and varies linearlyA = 0.5(x-1)m² on BC. The Young's modulus is E = 2 × 107 Pa. A distributed load b = 10 Nm isapplied along the left portion of the bar AB and a point force P 150 N acts at point B. The geometry,material properties, loads and boundary conditions are given in Figure 5.20a. Use a three-node element onAB (nen=3) and a two-node element on BC (nen=2) as shown in Figure 20b. The dimensions in Figure 5.20are in meters.=a. Construct the element body force matrices and assemble them to obtain the global force matrix.b. Construct the element stiffness matrices and assemble them to obtain the global stiffness matrix.c. Find and sketch the finite element displacements.d. Find and sketch the finite element stresses.(a)Ab = 10 Nm-1E = 2×107 PaP = 150 NB(b)XA = 1UXB= 3x = 5DB134(1)2(2)xFigure 5.20 (a) Geometry, material properties, loads and boundary conditions for a bar with a variable cross-sectionalarea (b) the finite element model.

bar is constrained at both endsA-CA=0.1m2B-CA=0.5(x−1)m2young modulusE=2×107pab=10Nm-1VDL=…

Answered: Problem 5.4 Given a one-dimensional…

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter2: Axially Loaded Members

Section: Chapter Questions

Problem 2.3.5P: A vertical bar is loaded with axial loads at points B, C, and D. as shown in the figure. The bar is...

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A vertical bar is loaded with axial loads at points B, C, and D. as shown in the figure. The bar is made of steel with a modulus of elasticity E = 29,000 ksi., The bar has a cross-sectional area of 8.24 in2. Calculate the displacements at points B, C, and D. Ignore the weight of the bar
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