What’s the answers and explanation for this please ? A tapered bar with a solid circular cross section is held rigidly at either end. As shown in FigureQ1a, axial loads of 30 kN and 20 kN are applied to the bar. The bar material has a Young'smodulus of 200 GN/m². The bar is to be modelled using a single one dimensional cubic element.The shape functions and their derivatives for this type of element are shown in figure 1b:0.2 mXN₁N4 =930 kN(1-5)(-5²)N₂-271-5)(1-²)№3 = 27+5)(1-5²)1 + 5) (1 − 5²)0.2 m16(120 KN0.2 mFigure Q1a.b) The stiffness matrix is found to be:ƏN₁JE 16=ƏN ₂d=ƏN 3JEƏN4JE=CROSSSECTIONALAREAXA = 0.03- 40A in m², x in m(185-2752+1)(-185+8152-27)(27-17/6 (-1 + 185+275²)7-185-8152)Figure Q1ba) Determine the strain shape function matrix, [B], for this element.11.625 -14.6875 3.875 -0.8125K = 106-14.6875 30.375 -18.5625 2.8753.875 -18.5625 23.625 -8.9375-0.8125 2.875 -8.9375 6.875By applying appropriate boundary conditions, use this stiffness matrix to find thedisplacements of the points where the loads are applied.c) Using the displacements found in part (b) and the strain shape function matrix found in part(a), determine the strain in the bar at the point where the 20 kN load is applied.

Given Data: A=0.03-x40 To Find: (a) Determine the strain shape function matrix. (b) Displacements…

A tapered bar with a solid circular cross section is held rigidly at either end. As shown in Figure Q1a, axial loads of 30 kN and 20 kN are applied to the bar. The bar material has a Young's modulus of 200 GN/m². The bar is to be modelled using a single one dimensional cubic element. The shape functions and their derivatives for this type of element are shown in figure 1b:

A tapered bar with a solid circular cross section is held rigidly at either end. As shown in Figure Q1a, axial loads of 30 kN and 20 kN are applied to the bar. The bar material has a Young's modulus of 200 GN/m². The bar is to be modelled using a single one dimensional cubic element. The shape functions and their derivatives for this type of element are shown in figure 1b:

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 1.6.7P: A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The...

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