Mitesh Patel
MANE 6960 (Advanced Topics in Finite Elements)
Homework #5
Introduction
The COMSOL Multiphysics problem software has been used to determine the deflection of the simply
supported beam. The simply supported beam are of those types of beams that is pin supported or roller
supported either on one side or at both sides. This type of problems are commonly encountered in structural
discipline such as during construction of bridges. One of the most important physical quantities that is
commonly determined is the maximum deflection of the beam when an external load is applied to the beam.
Problem Statement
The beam is 5m long and it is supported by pins at both ends. The two points shown at the ends of the beam
are considered the pins, where the beam are supported. The goal of this problem is determine the maximum
deflection of the beam when an external load is applied at the top surface.
Figure 1
Finite Element Method Model
The beam is 5m long. The beam in the COMSOL Multiphyscis was created using the interpolation curve.
The beam is supported by pins at the both ends, and the external force of 100N/m per was applied at the
top surface of the beam. The material of the beam used was still with the following properties of the steel
in the table below.
The beam was constraint on the left side in such a way that the beam can deflect in x, y, and z directions.
This model was analyzed five time with the extremely coarse, coarse, normal, finer, and extremely fine,
which are shown in Figures 2, 3, 4, 5, and 6, respectively.
Figure 2: Extremely Coarser Mesh
Figure 3: Coarser Mesh
Figure 4: Normal Mesh
Figure 5: Finer Mesh
Figure 6: Extremely Finer Mesh
It was assumed that the material of the beam is steel. The following material properties were used as inputs
to build the model in the COMSOL Multiphysics.
Boundary Conditions
The beam are supported by pins at both ends. As such, the beam cannot deflect down at those ends. Other
than that, the beam can freely deflect downwards as it is not restricted by anything.
Analysis Results
The beam model was analyzed using the aforementioned five meshes. The plots and results obtained with
the five different meshes are shown in Figures 7, 8, 9, 10, and 11, and based on these figures it can be seen
that the maximum deflections in the negative y direction (downward) because of the applied external force
are 0.000827m, 0.000829m, 0.000829m, 0.000829m, and 0.000829m, respectively. The minimum
deflection in all the cases is zero at the pin supports at both ends. The deflection of the beam can also be
found based on the standard strength of material. The beam tries to deflect as it is acted up on by the external
force; however, due to the pin supports, the beam will be restricted from beam. As such, the beam will
experience the maximum stress at both pin supports, and thus, the beam can be failed first at pin supports
if the maximum stress limit exceed. Therefore, stiffeners are welded to beams, especially at supports, so
that the stiffeners will absorb significant loads.
Figure 7: Results with Extremely Coarse Mesh
Figure 8: Results with Coarser Mesh
Figure 9 Results with Normal Mesh
Figure 10: Results with Finer Mesh
Figure 11: Results with Extremely Fine
Validation
It can be seen that the maximum deflection converges to 0.000829m as the mesh density increases. The
results is in accordance with the standard strength of material.
Conclusion
The minimum deflection is zero at both pin supports and the maximum deflection at the midpoint of the
beam is 0.000829m. The steel is a ductile material, so it will go back to its original shape as long as the
applied external load does not exceed its maximum limits. If the applied external load exceeds the maximum
limit, then the beam, which is considered to be the steel here, will experience permanent deformation and
will not fail immediately, which will be the case in the brittle material.