4. 1B: MAGNITUDE OF DEFLECTION AT
CENTER OF BEAM FOR FOUR MODELS
(LUMPED LOAD)
# ELEMENTS DEFLECTION
WRT
LUMPED
LOAD (in)
2 0.0144
4 0.0159
8 0.0163
16 0.0164
5. 1C: MAGNITUDE OF DEFLECTION AT
CENTER OF BEAM FOR FOUR MODELS
(CONSISTENT LOAD)
# ELEMENT DEFLECTION
WRT
CONSISTENT
LOAD (in)
2 0.0165
4 0.0165
8 0.0165
16 0.0165
6. 1D: VALUES OF DEFLECTION AT THE
CENTER OF THE BEAM
TABULAR FORM
# ELEMENTS DEFLECTION WRT
LUMPED LOAD(in)
DEFLECTION WRT
CONSISTENT LOAD (in)
2 0.0144 0.016515
4 0.0159 0.0165
8 0.0163 0.0165
16 0.0164 0.0165
7. 1D: VALUES OF DEFLECTION AT THE
CENTER OF THE BEAM
GRAHPICAL FORM
+x
+y
8. 1E: DISCUSSION
• The value of deflection at the center of the beam
gets closer the theoretical one, because of
number of elements added to FEA lumped one. In
addition, closer deflection value converges the
theoretical deflection value, since the addition of
number of elements.
• In consistent method, the use of number of
elements always matches with the theoretical
deflection values. But, in Lumped method, it
requires enough number of elements to get
matched with theoretical values.
9. 1F: PLOT OF DEFORMED SHAPE OF
BEAM SUPERIMPOSED ON ORIGINAL
SHAPE OF BEAM AND DEFORMED
BEAM
PLOT
+x
+y
11. 1G: REASON TO USE MORE THAN 16
ELEMENTS TO MODEL THIS BEAM? YES
OR NO? AND WHY?
• Its not required to use more than 16 elements, because
1. In the consistent method, we have seen the exact
analytical solution wrt number of elements used. In
coda, we can say that it is more correct/ accurate
method.
2. In lumped method, the use of 16 elements has made
the deflection values approximately converged to the
analytical one which means more the elements,
approximate values we will get wrt analytical one.
16. 2D: COMPARISON OF TRANSLATION
AND SLOPE WITH DISCUSSION
TABULAR FORM
FACTORS CALCULATIONS BY
HAND
MATRIX FORM RESULT FROM FEA
TRANSLATION (in) 0.23487 0.2349 0.2348
SLOPE OF A (rad) 0.003523 0.0035 0.0035
SLOPE OF B (rad) -0.00704 -0.0070 -0.00704
17. DISCUSSION
• The FEA, stiffness matrix, and hand calculated
values are almost same which shows the
answers are correct by any method. Also, the
results which we got wrt the elements 2,4,
and 12 are almost same.
• In conclusion, we can use any kind method to
find translation and slopes of the beam (i.e.
hand calculation, stiffness matrix, and or FEA).
18. REFERENCES
1. PART 1:
• CLASS NOTES BEAM PROJECT and CHAPTER #5
• class handed notes for FEMAP written by
James Sherwood.
2. PART 2:
beam project class notes by James Sherwood
The slope: The translation:
