MAE 456 West Virginia University CAD Finite Element Analysis Questions Consider a Beam Element system, as the one shown in the figure below. Use the “Simpl

MAE 456 West Virginia University CAD Finite Element Analysis Questions Consider a Beam Element system, as the one shown in the figure below. Use the “Simplex
Beam Element Matrix and the linear spring matrix to solve for the displacements and reactions
at the supports.In developing your solution, make sure that you show the following:
– Write the element matrices of each and all elements (including the springs)
– Write the Global Matrix in the sequential order
– Rewrite the global matric with Partitions for Fixed and Free degrees of freedom
– You can invert the “D” matrix using any solver (MATLAB, Mathematica or any other
solver)
– Write the solution (Displacements and reactions) clearly and Box it.
– Do a shear and moment diagram of each beam set (upper and lower sets) MAE456 CAD/Finite Element Analysis
Assignment # 2 Due, June 1st, 2020 by noon (This is an individual assignment)
Assignments are to be submitted in the form of a PDF document (use either computer screen
captures or your cellphone to paste READABLE pictures of your work on paper). Your
Assignment must be sent by email to vhmucino@mail.wvu.edu with a title as follows;
MAE456-Asg2-InitialLastname.pdf
(in my case it would be MAE456-Asg2-VMucino.pdf)
Student Name: _________________________________________________________
Pr. 1. Consider a Beam Element system, as the one shown in the figure below. Use the “Simplex
Beam Element Matrix and the linear spring matrix to solve for the displacements and reactions
at the supports.In developing your solution, make sure that you show the following:
– Write the element matrices of each and all elements (including the springs)
– Write the Global Matrix in the sequential order
– Rewrite the global matric with Partitions for Fixed and Free degrees of freedom
– You can invert the “D” matrix using any solver (MATLAB, Mathematica or any other
solver)
– Write the solution (Displacements and reactions) clearly and Box it.
– Do a shear and moment diagram of each beam set (upper and lower sets)
Before you start, Make a table for the following parameters and loads
E1= E2= E3= E4 = E5 = 10 x 106 psi
L1, L2, L3, L4, L5 = Your choice (use inches)
I1= I2= I3 = Your Choice for a rectangular cross section, sketch it (use inches2)
I4= I5 = Your Choice for a circular cross section sketch it (use inches2)
Kspring = Your Choice (use lb/in)
F2 and M3= Your Choice (use lb and lb-in respectively)
6 L − 12 6 L   y1   F1 
 12
 6 L 4 L2 − 6 L 2 L2     M 
EI 
  1  =  1 
3
L − 12 − 6 L 12 − 6 L   y2   F2 

2
2 
 6 L 2 L − 6 L 4 L   2  M 2 
The generic stiffness matrix
of a beam element
The Beam system to solve:
1
2

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