Q3. (a) A prismatic circular rod with one end fixed is acted on by the specified loadings as shown below. Discretise the rod with two equally long linear truss finite elements and calculate: (i) the global/system stiffness matrix and load vector, and (ii) the nodal displacements and element stresses. (b) The theoretically exact displacement, u(x), at any generic material point a distance x from the fixed end is given by the differential eqn. dx (x) =1,(x), 0 ≤x≤L, with the boundary coditions, [EA du(x)]=1,(x), when x = 0, u(0) = 0, and when x=L, EA du(L) P., and where dx E=30x106, A = 2.0, L = 60.0, ts(x) = 20.0/unit length, P= 50.0 Plot the variation of displacements of points along the length of the rod and critically compare these with your finite element results you have obtained in part (a). ts(x) +u(x) PX 0 Ans. 475x10" {0}= (475) 650×10 Q4. Solve Q3 when ts(x) = 10(1+x)/unit length. Also, find the reaction force at the fixed end and hence assess the validity of your finite element solution.

Mechanics of Materials (MindTap Course List)
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Chapter1: Tension, Compression, And Shear
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Q3. (a) A prismatic circular rod with one end fixed is acted on by the specified
loadings as shown below. Discretise the rod with two equally long
linear truss finite elements and calculate:
(i) the global/system stiffness matrix and load vector, and
(ii) the nodal displacements and element stresses.
(b) The theoretically exact displacement, u(x), at any generic material
point a distance x from the fixed end is given by the differential eqn.
dx
(x) =1,(x), 0 ≤x≤L, with the boundary coditions,
[EA du(x)]=1,(x),
when x = 0, u(0) = 0, and when x=L, EA
du(L) P., and where
dx
E=30x106, A = 2.0, L = 60.0, ts(x) = 20.0/unit length, P= 50.0
Plot the variation of displacements of points along the length of the rod
and critically compare these with your finite element results you have
obtained in part (a).
ts(x)
+u(x)
PX
0
Ans. 475x10"
{0}=
(475)
650×10
Q4. Solve Q3 when ts(x) = 10(1+x)/unit length. Also, find the reaction force
at the fixed end and hence assess the validity of your finite element
solution.
Transcribed Image Text:Q3. (a) A prismatic circular rod with one end fixed is acted on by the specified loadings as shown below. Discretise the rod with two equally long linear truss finite elements and calculate: (i) the global/system stiffness matrix and load vector, and (ii) the nodal displacements and element stresses. (b) The theoretically exact displacement, u(x), at any generic material point a distance x from the fixed end is given by the differential eqn. dx (x) =1,(x), 0 ≤x≤L, with the boundary coditions, [EA du(x)]=1,(x), when x = 0, u(0) = 0, and when x=L, EA du(L) P., and where dx E=30x106, A = 2.0, L = 60.0, ts(x) = 20.0/unit length, P= 50.0 Plot the variation of displacements of points along the length of the rod and critically compare these with your finite element results you have obtained in part (a). ts(x) +u(x) PX 0 Ans. 475x10" {0}= (475) 650×10 Q4. Solve Q3 when ts(x) = 10(1+x)/unit length. Also, find the reaction force at the fixed end and hence assess the validity of your finite element solution.
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