Finite Element Analysis is not the only method for analyzing a tower. It is a relatively recent analytical tool that takes advantage of the computing power of computers to make the drudgery of number crunching easier and faster. This is a brief discussion of how this type of tool was used to facilitate the information presented in the Guyed Tower Study. It is not a "how to use FEA" discussion, but is meant to assist the reader of the tower study in understanding the basics of what was done to generate the information.
The FEA approach to analyzing mechanical structures is very much like the MiniNEC and NEC codes. The models are made up of discreet segments called "Finite Elements." The program looks at each individual segment in the model with the loads applied and computes how it behaves under its loads and how it interacts with the others under their loads.
The FEA models used in this exercise are the simplest models that can made. They are called "stick models." They are simply a collection of line elements from one point (node) to another. Each element has the properties of the section (tower or guy) that it represents. The tower elements in the "stick model" are not the actual tower sections, with all the leg and bracing detail. They are just line entities that have the same global section properties as the tower sections. The guy elements are similar, with their own set of properties.
This is suitable for the intended purpose of the study, to examine global tower behavior under a variety of load cases. To get to the actual loads in the members of the tower sections, the loads from the global tower analysis need to be taken and applied to detailed tower section models. The detailed section analyses were not done for this study, so the stress and buckling loads in the section members is unknown. Therefore, the information presented in the study does NOT represent an attempt to determine if any of the configurations are actually suitable for use.
Most FEA software is modular in nature. Different
modules of code are used to perform the various steps in the process.
1 - Creating the model
The modeling module is used to define the geometry of the structure and assign material properties and section geometries. This describes what is going to be analyzed.
The model geometry is defined by creating nodes at all the places where the user wants to connect elements. These are simply locations in 3-dimensional space. For these tower models, nodes were located at the top and base of the tower and at each guy connection to the tower and the ground.
Then the nodes are connected with elements, each with certain defined properties. Each element in the structure has its own user drefined properties.
The element properties are as follows:
Element Type - Beam elements,
which have rigid end connections, were used for the tower sections.
Truss elements, which have freely rotating end connections, were used for the guys.
Element Material - Steel (elastic modulus = 29 Msi) was used for the tower sections and EHS guys, Kevlar (elastic modulus = 18 Msi) was used for the aramid guys.
Element Geometry -
Cross sectional area
Moment of inertia in the x axis - Ix
Moment of inertia in the y axis - Iy
Polar moment of inertia - J
Critical fiber distance in the x axis - Cx
Critical fiber distance in the y axis - Cy This is the distance from the section's centriod to the outermost surface of the section.
The tower element properties were taken from the information in the Rohn drawings with the cross sectional area adjusted to cause the correct tower weight to be developed in the analysis via the application of -1G acceleration to the model.
The guy properties used the formulas and
data offered by the MacWhyte Wire Rope Company, Kenosha, WI., to find
a solid diameter for the EHS cables that would accurately provide stretch
behavior with an elastic modulus of 29 Msi. The properties for the aramid
guys were determined from data sheets published by Philadelphia Resins Corp.,
the manufacturers of Phillystran aramid cable. One should view the
information available at the Guy Cable Link on this site, to understand how the guy properties
2 - Defining the Constraints, Calculating and applying the loads
The constraints and loads are applied using the "load" module in the software.
The loads on the tower and guys are reacted by the tower base and the guy anchors. These reaction locations need to be defined for the FEA models. This is done by applying constraints at these locations.
Constraints are defined methods
of fixing, or holding fast, a location (or node) in the model.
There are six possible ways (commonly referred to as degrees of freedom) to fix a node in the model. Constraints in Fx Fy Fz are connections that prevent movement along the X, Y & Z axes. Constraints Mx My Mz are connections that prevent rotation about the X Y & Z axes.
The guy anchors in all models used only Fx Fy Fz constraints. The tower base constraints are given for each model, and represent two different types of tower base connection. The Fx Fy Fz Mx My Mz connections represent a fixed base, where the tower is buried in the concrete footing. The Fx Fy Fz base connections represent a "pier pin" base, where the tower is free to rotate about all axes, while being held from moving along any axis.
The tower geometry, guy sizes, feedlines,
antenna projected areas, and basic wind speed were entered into a set of
linked spreadsheets to calculate the loads to be applied to the models. The
loads applied to the towers were calculated in accordance with ANSI/EIA RS-222-F.
The calculated loads were applied to the models via several load application options:
Point Loads are discreet loads applied to a single node in the model. These loads can be applied along each of the 3 axes, and were used to apply the antenna, and guy loads. These loads can be seen in the model image at the beginning of the tower study. They are the individual arrows at the guy connection points on the tower and at the top.
Distributed Loads are ones that are spread along the length of an element. They can also be applied along each of the 3 axes, and were used to apply the wind loads to the tower. These loads appear in the model image as arrows that are connected together.
Accelerations are more commomly
used in modeling the dynamic behavior of a model. In the tower study models,
-1G of acceleration was applied to simulate gravity to get the tower section
weights to be applied to the tower.
Step 3 - Analyzing the Tower
Running the analysis is the easiest part
of the process. The solver portion of the software is invoked and it solves
the problem. If there is a problem with geometry or the constraints, the
solver will not be able to solve the problem and it will issue an error message.
The user goes back to the modeling or load modules and corrects the problem
and reruns the solver. The models in the tower study are pretty simple so
it only took the solver 10-15 seconds to solve them. This is not the case
with complex models that have hundreds or thousands of nodes and elements..
Step 4 - Obtaining the Results
The post processor provides access to the
results of the analysis. The bending moments in two axes, shear in two axes,
axial loads, and deflections at the nodes are available in the analysis output
file. This data is entered into another spreadsheet to calculate the resultant
bending moments, shear and the combined tower stresses and safety factors
along with the guy safety factors.
The FEA software used for the tower study is a linear finite element code called GBEAM. It is quite nice for software that resides at the very affordable end of the spectrum. The shareware version is quite adequate for most simple problems. Those interested in obtaining more information can go to http://www.grapesoftware.mb.ca
Linear FEA code is ok for analyzing structures
that do not experience large deflections. Non-linear software needs to be
used when the deflections are large.
Most of the tower deflections in the study are close to the width of the tower face, so the analyses are expected to be acceptable. Questionable models are noted.
Updated May 5, 2001
Copyright © 2001-2004 Kurt Andress, K7NV All Rights Reserved