The element shown below is a bar element (subject to only axial deformation) that contains three nodes, also known as a higher-order element. (Note: This is NOT two elements!) L/2 L/2 Length L AE Constant U2 Assuming the following function for the displaced shape of the element: u(x) = co + c1x + c2x2 %3D Determine the three unknown constants co, C1, and c2 using the following boundary conditions: u(0) = u1 u(L/2) = u2 u(L) = u3 • Determine the [ N] and [B] matrices for the element. Derive the stiffness matrix [K] for the element.
The element shown below is a bar element (subject to only axial deformation) that contains three nodes, also known as a higher-order element. (Note: This is NOT two elements!) L/2 L/2 Length L AE Constant U2 Assuming the following function for the displaced shape of the element: u(x) = co + c1x + c2x2 %3D Determine the three unknown constants co, C1, and c2 using the following boundary conditions: u(0) = u1 u(L/2) = u2 u(L) = u3 • Determine the [ N] and [B] matrices for the element. Derive the stiffness matrix [K] for the element.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![The element shown below is a bar element (subject to only axial deformation) that
contains three nodes, also known as a higher-order element.
(Note: This is NOT two elements!)
1
2
3
L/2
L/2
Length L
AE
Constant
%3D
U2
U3
Assuming the following function for the displaced shape of the element:
u(x) = co+ c1x + c2x2
%3D
• Determine the three unknown constants Co, C1, and c2 using the following
boundary conditions:
u(0) = ui
u(L/2) - u2
u(L) = u3
• Determine the [N] and [ B] matrices for the element.
Derive the stiffness matrix [K] for the element.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52ff072a-02c9-4aa2-ab97-e9f4f5f3280d%2F9c498ec4-0c34-4653-bb16-19e7b98f141c%2Fl4b3pt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The element shown below is a bar element (subject to only axial deformation) that
contains three nodes, also known as a higher-order element.
(Note: This is NOT two elements!)
1
2
3
L/2
L/2
Length L
AE
Constant
%3D
U2
U3
Assuming the following function for the displaced shape of the element:
u(x) = co+ c1x + c2x2
%3D
• Determine the three unknown constants Co, C1, and c2 using the following
boundary conditions:
u(0) = ui
u(L/2) - u2
u(L) = u3
• Determine the [N] and [ B] matrices for the element.
Derive the stiffness matrix [K] for the element.
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