Figure 1 shows a stepped bar BCD made of steel material with the top end B rigidly fixed to a support at A and the bottom end D held at a distance of 0.001m from a steel surface E. Assume the steel surface E to be rigid and the weight of the bar is negligible. The Young's modulus of steel material is 200 GPa. The bar segments BC and CD have cross sectional areas 8x10¯³ m² and 4x10 m², and lengths 0.8m and 0.2 m, respectively. 0.8m 0.2m I 0.001m E Figure 1 It is intended to pull the end D downwards and weld it to the steel surface E. Determine the downward force to be applied at end D so that end D just touches the steel surface E. Model each of segments BC and CD as a single 'spring element’ for this purpose. (i) Show all details of your workings such as the finite element model, element stiffness matrices, how you assemble them to get the global equilibrium equations and how you apply the boundary conditions. Instead, if a downward force of 5000N is initially applied at C, what would be the downward force required at D so that end D just touches the steel surface E? (ii)

Figure 1 shows a stepped bar BCD made of steel material with the top end B rigidly fixed to a support at A and the bottom end D held at a distance of 0.001m from a steel surface E. Assume the steel surface E to be rigid and the weight of the bar is negligible. The Young's modulus of steel material is 200 GPa. The bar segments BC and CD have cross sectional areas 8x10¯³ m² and 4x10 m², and lengths 0.8m and 0.2 m, respectively. 0.8m 0.2m I 0.001m E Figure 1 It is intended to pull the end D downwards and weld it to the steel surface E. Determine the downward force to be applied at end D so that end D just touches the steel surface E. Model each of segments BC and CD as a single 'spring element’ for this purpose. (i) Show all details of your workings such as the finite element model, element stiffness matrices, how you assemble them to get the global equilibrium equations and how you apply the boundary conditions. Instead, if a downward force of 5000N is initially applied at C, what would be the downward force required at D so that end D just touches the steel surface E? (ii)

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 2.3.2P: A long, rectangular copper bar under a tensile load P hangs from a pin that is supported by two...

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A long, rectangular copper bar under a tensile load P hangs from a pin that is supported by two steel posts (see figure). The copper bar has a length of 2.0 m, a cross-sectional area of4S00 mm", and a modulus of elasticity Ec= 120 GPa. Each steel post has a height of 0.5 m, a cross-sectional area of 4500 mm2, and a modulus of elasticity E = 200 GRa. (a) Determine the downward displacement
A rigid triangular frame is pivoted at C and held by two identical horizontal wires at points A and B (see figure). Each wire has an axial rigidity EA = 120 kips and coefficient of thermal expansion a = 12.5 X 10-6/°F. (a) If a vertical load P = 500 lb acts at point D, what are the tensile forces TAand TBin the wires at A and B, respectively? (b) If both wires have their temperatures raised by 180°F while the load P is acting, what are the forces TAand TB (c) What further increase in temperature will cause the wire at B to become slack?
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