Finite Element Study to Compare the Performance of
Composite and Steel Angle Bars
by
Kayla Kruper
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Ernesto Gutierrez-Miravete, Project Advisor
Rensselaer Polytechnic Institute
November, 2015
(For Graduation December, 2015)
i
CONTENTS
LIST OF TABLES………………………………………………………………………………………...iii
LIST OF FIGURES……………………………………………………………………………………….iv
LIST OF SYMBOLS………………………………………………………………………………………v
KEYWORDS……………………………………………………………………………………………..vi
ACKNOWLEDGEMENT……………………………………………………………………………..…vii
ABSTRACT………………………………………………………………………………………………viii
1.0 INTRODUCTION………………..…………………………………………………………………....1
1.1
Background…………………………………………………………………………………..1
1.2
Problem Description…………………………………………………………………………2
2.0 THEORY/METHODOLOGY………………………………………………………………………...3
2.1
Theory………………………………………………………………………………………..3
2.2
Finite Element Analysis…………………………………………………………………….4
3.0 RESULTS……………………………………………………………………………………………..9
3.1
Composite Angle Bar vs. Steel Angle Bar – Deflection Comparison…………….…….9
CONCLUSION……………………………………………………………………………………….….14
REFERENCES……………………………………………………………………………………..……15
APPENDICES……………………………………………………………………………………...……16
ii
LIST OF TABLES
Table 1 – Material Properties of Fiberglass……………………………………………………………6
Table 2 – Material Properties of Steel………………………………………………………………….7
iii
LIST OF FIGURES
Figure 1 – Example of Angle Bar Application
Figure 2 – Steel Angle
Figure 3 – Typical Installation View of Angle Bar Used to Route Cable
Figure 4 – Cable Lay on Angle Bar
Figure 5 – Example of Angle Bar Detail
Figure 6 – Partition Geometry Added to Angle Bar
Figure 7 – Angle Bar Modeled into Abaqus/CAE
Figure 8 – Pressure Applied to Angle Bar
Figure 9 – BC 1: Mounting Angle Bar to Structure
Figure 10 – Angle Bar Mesh
iv
LIST OF SYMBOLS
Symbol
Definition
Units
P
Pressure
psi
F
Force
lbf
A
Area
in2
m
Mass
lbs
a
Acceleration of Gravity
ft/s2
v
KEYWORDS
Keyword
Definition
Finite Element Model (FEM)
Representation of an object using finite elements
American Wire Gauge (AWG)
A standardized wire gauge system used since 1857
predominantly in North America for the diameters of
round, solid, nonferrous, electrically conducting wire
vi
ACKNOWLEDGEMENT
I would like to thank Professor Ernesto Gutierrez-Miravete for his guidance in these early stages
of my master’s project. I would also like to thank the faculty of Rensselaer Polytechnic Institute
at Groton for all the support throughout the Master’s program. And finally I would like to thank
my family and friends for their guidance and encouragement throughout my academic career
thus far.
vii
ABSTRACT
The purpose of this project is to perform an elastic finite element analysis of composite and
steel materials. In this project, the performance of glass-reinforced plastic (GRP) and steel will
be examined in an everyday building material, an angle bar. Angle bars can vary with the
material used to build them. This project will focus on creating a finite element model that will be
used to compare the effects that the material has on the strength performance of angle bars.
Figure 1 – Example of Angle Bar Application
viii
1.0
1.1
INTRODUCTION
Background
Steel angle, or commonly referred to as angle bar, is one of the most popular hot rolled, low
carbon steel shapes used in manufacturing, fabrication, and repair products. From truck beds to
farm implements and construction equipment, angle bar has thousands of uses and
applications. Its 90 degree angle shape adds strength and rigidity to any product for a lower
price compared to other shapes and types of metals. It is easy to weld, cut, form, and machine
with the proper equipment and knowledge.
Figure 2 – Steel Angle
Traditional angle bar is used on various platforms from building designs to shipbuilding and
more and are typically made from steel. The purpose of the angle bar is to route and protect
cables from one area to another. However, corrosion remains a problem in all different
environments, particularly in marine applications. Composite materials are beginning to be
introduced in harsh environments as a non-corrosive alternative to stainless steel. Specifically,
glass fiber reinforced resins are used widely in the building and construction industry.
1
Figure 3 – Typical Installation View
of Angle Bar Used to Route Cable
1.2
Problem Description
This project will use finite element analysis (FEA) to assess the performances of glassreinforced plastic (GRP) and steel. This project will consist of modeling an angle bar in
Abaqus/CAE. Once the modeling is accomplished, the models will be modified with different
physical properties such as the type of material, the distributed mass loading of cable, and the
angle bar size.
2
2.0
2.1
THEORY/METHODOLOGY
Theory
Pressure is a physical quantity characterizing the intensity of normal forces (perpendicular to the
surface) with which one body acts on another’s surface. If the forces are distributed uniformly
over the surface, the pressure P on any part of the surface is:
𝑃=
𝐹
𝐴
[1]
The pound-force is the English Engineering unit of force or weight, properly abbreviated to lbF.
The pound-force is equal to a mass of one pound multiplied by the standard acceleration due to
gravity on Earth (approximately 32.174 ft/s2).
𝐹 =𝑚∗𝑎
[2]
Main feeder cable, usually 4/0 or 2/0 american wire gauge (AWG) copper cable, carries power
from the power source to the set. Generally, cable bigger than 4/0 AWG is not used. In order to
handle larger loads, the number of 4/0 AWG conductors used for each phase and neutral wire is
increased.
4/0 AWG copper cable weighs approximately 660 lbm/1000 ft, or 0.66 lbm/ft and has an outer
diameter of 0.522 inches [1]. As many as nine cables could be stacked and routing as depicted
in Figure 4 below.
Figure 4 – Cable Lay on Angle Bar
3
Using Equation [2] above with the combination of using nine 4/0 AWG copper cables and
accounting for the length of the angle bar being 2 feet, the pound-force is calculated to be
382.23 lbF. As the angle bar used in this analysis was created with both legs being equal with a
2” width and a thickness of 0.25”, the surface area the force is distributed uniformly over is
calculated to be 42 in2 (1.75 in x 24 in). Using Equation [1], the uniform pressure is calculated as
approximately 9 psi.
2.2
Finite Element Analysis Methodology
Finite element analysis (FEA) is a numerical method for finding an approximate solution to
engineering and mathematical boundary value problems. It uses subdivision of a whole problem
domain into simpler parts, called finite elements to solve the problem. FEA is useful for
problems with complex geometries, material properties, and loads when it is difficult to obtain an
analytical solution. The FEA software utilized in this project is Abaqus/CAE which is used to
develop the models of the angle bars.
Once the angle bar is finalized, material properties are assigned to create a part with a
randomized fiber matrix and isotropic material properties. This model is assigned material
properties to simulate layered fiberglass with alternating fiber angles. Boundary conditions are
applied to simulate having the angle bar mounted to a structure. A pressure is then applied
simulating cable being banded the length of the angle bar.
A similar model is made using the same angle bar. This model is assigned material properties of
that of steel.
2.2.1
Part Geometry
A three-dimensional model of angle bar was created using Abaqus/CAE after common angle
bar dimensions. Each leg, dimensions A and B, was created with a 2” width. The thickness,
dimension t, is 0.25” thick [2].
4
Figure 5 – Example of Typical Angle Bar Detail
Next a partition geometry was created to simulate the bounding of the material to what is
typically frame spacing of the structure the angle bar is mounted to. The partition geometry can
be seen in Figure 6. Final dimensions of the angle bar created can be seen in Figure 7.
Figure 6 – Partition Geometry Added to Angle Bar
5
Figure 7 – Angle Bar Modeled into Abaqus/CAE
2.2.2
Materials
Two different materials were used for the angle bar. Fiberglass material properties were used
for the composite material modeling. Creating a model of an orthotropic layered fiberglass angle
bar in Abaqus requires creating a material with lamina properties. The layered fiberglass
material used for this analysis is glass-reinforced plastic, which is starting to be used in
corrosive applications. Using fiberglass, a composite ply layup is created to assign individual
layer thicknesses, region assignments, and fiber angle orientations. Table 1 states the material
properties used as inputs for the fiberglass.
Table 1 – Material Properties of Fiberglass
Material Properties of Fiberglass [3]
Material
E1
(x 106 psi)
E2
(x 106 psi)
v12
G12
(x 106 psi)
G13
(x 106 psi)
G23
(x 106 psi)
Glass-reinforced
plastic (fiberglass)
8.34
2.727
0.25
1.08
1.08
1.05
Steel is the most popular angle bar material; therefore, the comparative angle bar in this
analysis will use material properties based on steel. The steel angle bar is modeled with elastic
material properties. Elastic material properties for steel are shown in Table 2.
6
Table 2 – Material Properties of Steel
Material Properties of Steel [4]
Material
Young’s Modulus E
(x 106 psi)
Density (lb/in3)
Poisson’s Ratio
Steel
29
0.284
0.28
2.2.3
Loads and Boundary Conditions
A pressure load of 9 psi is applied to the top surface of the angle bar as shown in Figure
8. This is the pressure force derived in Section 2.1 to simulate the force of cable banded in to
angle bar.
Figure 8 – Pressure Applied to Angle Bar
One boundary condition is used in this analysis. To simulate having the angle bar attached to
frame structure to allow banding of cable, one boundary condition is assigned.
Boundary Condition 1:
All degrees of freedom (DOFs) are constrained on the back side
of the angle bars to prevent movement and rotation in all
directions (Figure 9).
7
Figure 9 – BC 1: Mounting Angle Bar to Structure
2.2.4
Mesh
Since the layered fiberglass and steel angle bars are constructed from the same shell geometry,
the two angle bars are assigned identical meshes. The element used is the S4R, which is a 4noded doubly curved shell element with reduced integration, hourglass control, and finite
membrane strains. The mesh density is an approximate global seed size of 0.5” (Figure 10).
Figure 10 – Angle Bar Mesh
8
3.0
3.1
RESULTS
Composite Angle Bar vs. Steel Angle Bar – Deflection Comparison
In Progress
Results for Composite Angle Bar
9
10
Results for Steel Angle Bar
11
12
13
4.0
CONCLUSION
In Progress
14
REFERENCES
[1] http://www.engineersedge.com/copper_wire.htm
[2] Engineering Toolbox Website, http://www.engineeringtoolbox.com/steel-angles-d_1322.html,
2015
[3] Y.W. Kwon, D.H Allen, R. Talreja, “Multiscale Modeling and Simulation of Composite
Materials and Structure”, 2008
[4] Engineering Toolbox Website, http://www.engineeringtoolbox.com/stress-strain-d_950.html,
2015
Abaqus 6.13 User’s Manual
Barbero, Ever. Finite Element Analysis of Composite Materials Using Abaqus. Boca Raton:
CRC Press, 2013.
Chawla, Krishan. Composite Materials. New York: Spring, 2013.
Jones, Robert. Mechanics of Composite Materials. New York:Taylor and Francis Group, 1999.
15
APPENDICES
16