4. Given a 1D elasticity problem shown in (a) of the figure below. The bar is constrained at both ends (A and C). Its cross-section area is constant (A=0.1 m²) on segment AB and varies linearly as A=0.05(x- 2) m? on BC. The Young's modulus is E=2×107 Pa. A distributed load b=5 N/m is applied along AB and a concentrated force P=100 N is applied at the mid-point of BC. Fixed boundaries are applied to both sides of the bar and all dimensions are in meters. AB is modeled using a 3-node quadratic element and BC is modeled using a 2-node linear element. Numbering of nodes and elements are shown in (b) of the figure below. a. Construct the global force matrix. b. Construct the global stiffness matrix. c. Approximate the displacement and stress fields in the whole domain. b=5N/m E = 2x107 Pa P=100N (a) A В C XA=2 Xg=4 Xc=5 (b) D В C 1 3 4 (1) (2)

4. Given a 1D elasticity problem shown in (a) of the figure below. The bar is constrained at both ends (A and C). Its cross-section area is constant (A=0.1 m²) on segment AB and varies linearly as A=0.05(x- 2) m? on BC. The Young's modulus is E=2×107 Pa. A distributed load b=5 N/m is applied along AB and a concentrated force P=100 N is applied at the mid-point of BC. Fixed boundaries are applied to both sides of the bar and all dimensions are in meters. AB is modeled using a 3-node quadratic element and BC is modeled using a 2-node linear element. Numbering of nodes and elements are shown in (b) of the figure below. a. Construct the global force matrix. b. Construct the global stiffness matrix. c. Approximate the displacement and stress fields in the whole domain. b=5N/m E = 2x107 Pa P=100N (a) A В C XA=2 Xg=4 Xc=5 (b) D В C 1 3 4 (1) (2)

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 2.2.19P: Two pipe columns (AB, FC) are pin-connected to a rigid beam (BCD), as shown in the figure. Each pipe...

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