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:

Elements Of Electromagnetics

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ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Concept explainers

Thermal Properties of Materials

In mechanical engineering, the thermal property is represented as the physical quantity that is relevant to the application of heat. The thermal properties are evaluated by variations in any specific material due to low heat or high heat. The quantities that influence the thermal property of the materials are mass, density, temperature, and many others.

Question

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 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:
0.2 m
X
N₁
N4 =
9
30 kN
(1-5)(-5²)
N₂-271-5)(1-²)
№3 = 27+5)(1-5²)
1 + 5) (1 − 5²)
0.2 m
16(1
20 KN
0.2 m
Figure Q1a.
b) The stiffness matrix is found to be:
ƏN₁
JE 16
=
ƏN ₂
d
=
ƏN 3
JE
ƏN4
JE
=
CROSS
SECTIONAL
AREA
X
A = 0.03- 40
A in m², x in m
(185-2752+1)
(-185+8152-27)
(27-
1
7/6 (-1 + 185+275²)
7-185-8152)
Figure Q1b
a) Determine the strain shape function matrix, [B], for this element.
11.625 -14.6875 3.875 -0.8125
K = 106-14.6875 30.375 -18.5625 2.875
3.875 -18.5625 23.625 -8.9375
-0.8125 2.875 -8.9375 6.875
By applying appropriate boundary conditions, use this stiffness matrix to find the
displacements 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.

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