Consider the following steel I?beam, which has a constant cros
2) Consider the following steel I‐beam, which has a constant cross‐section as described below, and a modulus of E = 200 GPa. The distance a = 0.2 m. The distributed load has a value of w=12 kN/m and the point load, P=400 N
EGM 302 Finite Element Analysis
Fall 2022 HW 2: Beams and Frames
1) Connection constraints
The physical construction of two different beam connections are shown:
a) An I‐beam is connected to a floor slab through a slotted bolt hole
b) An I‐beam is connected to a column through an angle bracket.
What simplified support conditions would you use to represent the physical construction in the two
cases? Explain your reasons.
2) Beam with distributed and point loads (MATLAB, LISA, ANSYS)
Consider the following steel I‐beam, which has a constant cross‐section as described below, and a
modulus of E = 200 GPa. The distance a = 0.2 m.
The distributed load has a value of w=12 kN/m and the point load, P=400 N
a) By hand/using MATLAB with 2 elements and the standard shape functions determine:
the reaction forces at the two walls
the deflection, the bending moment and the bending stress at the two locations of interest:
o the location of the point mass
o the location a meters from the right wall
Your solution must include:
A. Elemental stiffness matrix for each element
B. The global stiffness matrix for the entire beam
C. The load vector for the entire beam
D. The boundary conditions the entire beam
E. Write out the FEA system in matrix form and clearly explain what each matrix represents.
F. Nodal displacement solution
G. The reaction forces
H. The deflection at the two selected points
I. The bending moment and bending stresses at the two selected points
J. The Matlab script and comments providing detailed explanation of each line of code (Note
that you will be building on this code for the next problem, so be sure to comment your code
well)
b) Use LISA to perform the same analysis, but use a total of 4 elements to complete the model, placing a
node at the specified locations. Compare the following between the MATLAB and LISA solution:
Nodal displacements
Bending Moment
The reaction forces
c) Use ANSYS to perform the same analysis as LISA. Confirm the nodal displacements and the bending
moments between the LISA and ANSYS solutions. Explain, based on the underlying model used why the
answers may not be identical.
3) Frame with point load and distributed load (MATLAB, LISA)
The plane frame is almost identical to the beam in the previous
problem, except that the portion of the frame without the
distributed load is mounted at an angle as shown.
a) Describe the differences in the assembly of the global stiffness
matrix for this problem compared to the previous beam problem.
b) Clearly describe all of the nodal variables that can be
calculated and explain why there are more than in the previous
problem.
c) Using both MATLAB and LISA, find and compare the nodal values associated with node 2 and clearly
explain what they represent, and why they are reasonable.
Note: you should be able to reuse most of your code from problem 2 with modifications.
4) Frame with point load and distributed load (LISA, ANSYS)
The bike frame shown in the figure below has hollow circular tubes (24 mm outer diameter and 2 mm
thick) and is made of aluminum alloy with E = 70 GPa.
a) Can a reasonably accurate model be developed for this model in 2D space? Provide rational for your
answer.
b) Use either LISA or ANSYS Workbench to determine the deformation and stresses using a 2D frame
model for this bicycle.
c) Use LISA to determine the deformation and stresses of the frame members for the model as shown.
Compare your LISA results with the following ANSYS results and identify any differences in nodal
displacements, and element stresses, as well as differences in the way that the results are interpolated
between Nodes.
The total deformation plot for the bicycle frame: The direct stress plot:
d) Compare the results from b) and c), assess your answer to part a) and explain any differences.
Notes for using LISA:
1. To fix the rotation at a node, select the desired node, and then use the “On selected nodes” command
to apply an New rotz of zero.
2. Model the distributed load by applying the equivalent force and moment on each of the nodes.
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