INSTRUCTIONS FOR INPUT OF DATA IN EXCEL
SPREADSHEETS
1. Rectangular Footing
In Spreadsheet “A” you enter English units for
dimensions “b” and “d” as measured in inches. Enter allowable soil
bearing pressure, “q”, in kips per square inch. See Capacity Curve in
English and SI units.
Sheet “B” shows the Capacity Curve of the
footing when θ = 0.
Sheet “C” shows the Capacity Curve of the
footing when θ = π/2.
2. Circular Footing
You enter in the spreadsheet English unit for
dimension “R” as measured in inches. Enter allowable soil bearing
pressure, “q”, in kips per square inch. See Capacity Curve in English
and SI units.
3. Uniform Surcharge Load
You enter in the spreadsheets dimensions “a”
and “b” as measured in inches. For dimension “h” enter the English unit
of measurement of feet. For allowable soil bearing pressure, “q”, enter
kips per square foot. See graph of the vertical stresses as this surface
loading is distributed through depth.
4. Triangular Surcharge Load
For dimensions “a” and “b” enter measurement
in inches. For dimension “h” enter measurement in feet. For allowable
soil bearing pressure, “q”, enter kips per square foot. See graph of the
vertical stresses as this surface loading is distributed through depth.
5. Steel Pipe
You enter in the spreadsheet the values of
radius, “R” and thickness, “t” as measured in inches. Enter the value of
steel yield stress, “f_{y}” in kips per square inch. See the
Capacity curve of the steel pipe.
NOTE: For further details and other
solutions in structural analysis, please see the book entitled
“Structural Analysis: The Analytical Method” published by Taylor and
Francis, Boca Raton, 2007.
We have computers now! We do not have to
“count our fingers” anymore nor copy someone else’s work! We can find
the truth by using basic mathematics, physics of the problem and
Microsoft Excel to do all the calculations. Structural engineers that I
know would like to find out the truth if only they can. Well there is
now a way to find the truth as I have enumerated the steps above.
Apply basic mathematics, physics of the
problem and Microsoft Excel to do all the numerical calculations in the
equations derived by the analyst. If you cannot do these basic steps
with your computers, then you are relegated to copying others and not
knowing the truth about the veracity of the articles you are copying.
If you like to see how these steps worked
for me you may consult my 3^{rd} book published by Xlibris
Corporation dated April, 2012. Here is the book trailer if interested.
Recommendations for “The Analytical Method”
Apply the 3 tools that I mentioned i.e., basic mathematics (algebra,
trigonometric identities, analytic geometry and differential and
integral calculus), physics (laws derived from observed facts) and
Microsoft Excel of the computers to find the truth in anything that you
meet in your profession. There is now a new paradigm required from the
approximate to the exact method because of the availability of personal
computers. If you have to copy existing literature because you have no
choice just like me when I was still active as a professional engineer,
you can always find the truth about the article you are copying and make
the right decision as a professional.
For structural engineers, you have to apply Leonhard Euler’s principle
which states that “any section is subjected to an axial load and a
moment” using basic mathematics as well as physics of the problem.
Superimpose the stress strain ratio of the material in the problem. Then
you can integrate the axial forces and bending moments about the centroid. You can then compare your external load with the yield
capacity of the material. Then you can get your real factor of safety
versus the yield capacity. There is no more “factor of ignorance” as
practiced worldwide using the standard interaction formula. You can do
this because you were trained in school to have a working knowledge of
the tools above-mentioned.
For your information
I am the only one in the world doing the “rotation
of axes” to a given concrete and steel section. These terms were never
mentioned in my books but it is evident that this principle was
indicated in all the figures and equations shown in my books.
You may follow my lead as exposed in my books or you can apply the 3
tools above-mentioned to find the truth about the article you are
copying and determine whether it is true or not. We do not have to apply
approximate methods anymore nor copy existing literature or someone
else’s work. There is a saying “seek ye the truth and the truth shall
make you free” that should be followed by a serious researcher.
We are now in the age of computers and
there are no more justifications for approximate methods. Every engineer
who has a working knowledge of basic mathematics and physics can now
update his information in engineering accurately using the analytical
method I started since 1980.
My goal in becoming a member of
Linkdin
is to inform my fellow engineers that it is now time to implement the
analytical method in structural analysis because we have computers to do
all our numerical calculations.
Unfortunately, we have been buried for
many years in copying existing literature and others in the approximate
methods given to us by experts, well intentioned authors and professors
that we thought expediency and practicality as well as credentials is
the proof of the veracity of everything in our profession. Computers can
now expose the truth in our profession and basic math and physics of a
problem can produce the correct solution in anything that we do.
We can no longer copy nor blame others or
credentials for any mistakes discovered when we apply our basic
principles and knowledge that we learned in college. The practice of
expediency and practicality worldwide can no longer be relied on if the
methods employed are approximate. Tests results maybe slanted or not
following the correct theory of structures.
We can now easily discover any mistake by
analyzing the standard interaction formula copied worldwide. Use the
Leonard Euler’s principle that any section is subjected to an axial load
and a moment. This principle and basic mathematics will facilitate the
calculations of the yield capacity of any given concrete or steel
section for all eccentricity using Microsoft Excel. All that is needed
by the analyst is the determination of the external load which can vary
locally and compared to the yield capacity determined by Microsoft
Excel.
We can now determine the real factor of
safety versus yield capacity of the material and not rely on what I call
‘factor of ignorance’ using the standard interaction formula and the
principal axes. I am the only one in the world who has done the
‘rotation of axes’ to obtain the correct solution of a structural
problem. If an engineer cannot do the free body diagrams or the required
mathematics to solve a problem, he or she may refer to my books where
the analytical method is illustrated and the required parameters
considered in the solution. The discovery of the truth by the engineer
may be shared with others to spare them the trouble of doing the math or
thinking of the correct solution. Computers can remember all the
equations and any shortcuts developed by the analyst can be stored for
reference.
Experts, authors and professors are
welcome to comment and give a plausible reason for being silent all
these years in the use of the analytical method in structural analysis.
You may check the international proceedings of ISEC (Honolulu, Rome,
Shunan, Melbourne and Zurich), SEMC (Cape Town, South Africa), ASCE
(Cancun, New York, Nashville and Montreal), RILEM (Moscow 2005) Global
Concrete, Scotland 2005 and HKIE 2005 Journal. These were my efforts in
exposing the truth in engineering since I retired in 2000 from the NYCTA.
I am not expected to solve everything in life but I have shown the way
for the analytical method. You may follow my lead to discover other
truths.
The
approximate method in structural analysis has been in practiced for so long
world wide that it has shown itself in codes especially, ACI, AISC, ASCE and
AASHTO as well as codes of other countries in some form or another.
Basically, it is based on an assumption that the sum of the ratios of
biaxial stress and axial load should equal unity or less. This ratio has
been adjusted to account for results of tests. This is based on the standard
flexure formula and essentially approximates a point in the capacity of a
given section in the orthogonal axes X and Y. The true free body diagram of
a given section as a result cannot be drawn properly for an external biaxial
bending and axial load. This method has been copied over and over since the
slide-rule era that it has become true to the copier.
The exact
method is the true method to follow given stress-strain property of the
material and given geometry of the section. For steel, it is known that the
stress-strain is a straight line. For concrete, the stress-strain is
parabolic. The equations of the stress-strain curve and the equations of the
rectangle and circle can be written from analytic geometry. Once these
equations are known, we can use calculus to compute the forces and moments
that can be developed in a section. The solutions might take hundreds of
equations but we have computers now to program these equations. The Excel
program is very much suited to this task. All the given parameters of a
section can be substituted and the minimum capacity due to biaxial bending
and axial load can be shown in a curve known as the minimum capacity curve.
The minimum capacity for a rectangular section is defined when the axis
falls on the diagonal of the enclosing rectangle of the section. Most of the
resultant falls inside the sector defined by the horizontal axis and the
diagonal. The analyst can easily determined the truth about this procedure
if he just applies basic mathematics. He does not need the mediocre
approximate method above to verify the truth.
By using the
exact method the capacity of a given section is determined using basic
mathematics and the given parameters including the angle for minimum
capacity for biaxial bending and axial load. The resulting curve is the
capacity of a section to resist external loads. It is computed only once by
the Excel method.
Knowing the
capacity curve requires the analyst to determine the external load and plot
against this curve. If inside the curve, the given section is adequate. If
outside the curve, a bigger section is assumed by the analyst. He can
determine his factor of safety within the curve and the decision to accept
or reject is his decision.
You can see
from above arguments that the approximate method has no relation to the
analytical method. It is pure guesswork and has no relation to the true
capacity of a section. This method has been copied by authors for many
years; it is now time to apply the true method of analysis because we have
computers now to integrate all the forces in a given section without
guessing.
The author
has produced two books defining the analytical approach outline above. These
books are:
Jarquio,
R. V., Structural Analysis: The Analytical Method, 1^{st} ed.,CRC
Press/Taylor & Francis, Boca Raton, Florida, 2007
Jarquio, R. V., Analytical Method in Reinforced Concrete, 1^{st}
ed., Universal Publishers, Boca Raton, Florida, 2004.
Anyone interested in the truth and the analytical approach
may consult these books and questions maybe emailed to the author as
desired.
“The
Analytical Method in Structural Analysis”
I am still waiting for the questions that researchers
would like to ask me about my books. They may not know what questions to
ask since we have been brainwashed and buried for many years accepting
literature done by authors and professors using the approximate method.
We are now in the age of computers and this practice is no longer
correct. I may not solve everything in life but I showed the way in my
books to find the truth in anything. Note that I am the only one in the
world doing the ‘rotation of axes’ while everyone is copying the
principal axes to any section. The following are my tips for
their understanding of the things exposed in my web site at
http://www.ramonjarquio.com and the
equations in my books which were published by Universal Publishers in
2004, the second one was by CRC Press/Taylor and Francis in 2007 and the
third one published by Xlibris in March, 2012.
For structural analysis, apply the Leonhard
Euler’s principle which states that any section is subjected to
‘an axial load and a moment’. Note: This refers to the capacity
of any rectangular or circular section at all eccentricities.
Apply basic mathematics and physics learned in
school to derive the equations involved in any problem. From
analytic geometry, the equation of a circle and rectangular section
is known.
From physics we know the equation of parabola to
define the stress/strain relation for concrete. For steel the
stress/strain ratio is linear.
Draw the free body diagrams with ‘rotation of
axes’ to enable the engineer to analyze for equilibrium of
internal and external forces.
Use our knowledge of differential and integral
calculus to derive the equations for axial load and moment to any
rectangular or circular section. The stress/strain diagram over the
given section for any position is given in the free body diagram and
therefore we can integrate the volume generated for axial load and a
moment at the centroid of the section.
The Microsoft program can now do the numerical
calculations of the equations derived above at all eccentricities.
The graph produced is now what we call capacity of any section.
There was no need to define ‘short’ or ‘long’ column as
others do. However, if you want to do that, a short column is that
which the given section is at full compression. A long column can
then be defined as that where the stress at the section is now
compression and tension. The external load when plotted in this
envelope will define itself whether it is short or long.
Therefore, we do not need the short or long column terms.
My discovery is that the minimum capacity of a
rectangular section is at a diagonal. For a circular section
reinforced with steel bars the minimum capacity is between
reinforcement. However, for a circular section, assume a
diameter through the center of any bar as the capacity axis since
the variation between any two reinforcing bars is very small.
Now that the capacity of any section in
rectangular and circular section is known from Microsoft Excel
solutions, we can now determine the real factor of safety
from the yield capacity versus the external load which can vary due
to local regulations and applicable codes. Worldwide the practice is
still what I call the ‘factor of ignorance’ in determining
the factor of safety.
Apply the 3 tools of basic mathematics,
physics and the computer that we learned in college to find the
truth in anything that we encounter in our profession. The
educational system must be revamped for a student to be familiar in
the use of these 3 tools for discovery of the truth in anything that
we do.
I started the exact analysis in 1980 and I
was able to finish my research and produced my books after
retirement from the TA. I would like all engineers to know the truth
now that we have computers to perform all the numerical
calculations. A new paradigm from the approximate to the
exact method can now be implemented if one is interested in the
truth. Expediency and compliance with regulations is not always the
best approach in finding the truth. ‘Seek ye the truth and the truth
shall make you free’ should be followed for enlightenment.
There are 3 basic tools that you need
to find the truth about anything! Here they are:
(1) Basic mathematics which includes
Algebra, Trigonometry, Analytic Geometry and Differential and Integral
Calculus.
(2) Physical principles involved in a
problem - for structural the Euler's principle which states that "any
section is subjected to an axial load and a moment" should be employed. The
equilibrium equations and the stress/strain equation of the material are
always included in the analysis.
(3) Microsoft Excel to do all the
calculations required in the equations derived from (1) and (2) above.
The procedure looks so simple yet no
expert in the world including all authors and professors have employed "the
rotation of axes" for any section except me in this case! Everyone is
copying from one another without knowing the truth about anything. It seems
that credential is more important than the basic tools themselves.
The rotation of axes allows the
analyst to employ the equilibrium equations so that the external load is
made equal to the capacity of the section. The governing external load is
different for each locale and analyst, but the centroid of the resultant
external load is known from “ Pythagorean Theorem” when the moment about
the orthogonal axes are known. However, the minimum capacity is at the
diagonal of the rectangular section since the capacity decreases from the
horizontal axis to the diagonal. It is this minimum capacity of the
rectangular section that the author recommends when computing the real
safety factor from the yield capacity of the member. The resultant external
load can be compared to this resultant capacity of the rectangular section.
The model sample for testing and the
results obtained therefore should be related to the minimum capacity of a
rectangular section. This is not done by anyone and therefore the
conclusions arrived by experts not related to the minimum capacity can be
erroneous and therefore slanted to the ones they know from existing
literature.
I am not expected to solve everything
in life but what I did in my books was to show the proper way to follow my
lead in finding the truth! People are satisfied to just copy literature
including me when I was still active in the profession. I had no choice at
the time but I vowed to find the truth myself if I can.
The derived equations are all in this
book and Microsoft Excel can be used to do all the numerical calculations
required by the equations. When you can program in Microsoft Excel, you may
easily duplicate my spreadsheets mentioned at the back of my 3rd book
published by
Xlibris Corporation April, 2012.
Comment
Before you became an engineer, you have a working
knowledge of basic mathematics and physics in your college years. Now
that almost everyone has a personal computer, the truth can now be
exposed using basics and the power of the computer to do the numerical
calculations required by the equations you derived for a particular
problem in your profession. A new paradigm from the approximate to the
exact method is now possible because of the availability of personal
computers. You do not have to copy the works of others without knowing
the veracity of what you are copying. You do not have to blame others
for any mistakes because you can prove whether what you are copying is
true or not using your basic knowledge and the computer.
There is no more justification to use approximate
method because we have computers now to do all the numerical
calculations in no time after all the equations are entered and verified
in the computer. The computer remembers all the equations required in
the solution of a problem. To get a different answer we can vary any or
all of the variables involved in our solution. We can use Microsoft
Excel or any mathematical program we are familiar with.
If we have the talent and patience in basic
mathematics and physics, we can derive all the equations required in a
problem. We can find many truths in our profession if these 3 tools of
math, physics and computer are employed in any problem encountered. Our
conclusions will be tempered by the truths that we can discover by going
back to basics that we learned in school. If you want to find out how
the analytical method is applied you may consult my books.
To Whom It May Concern
There are no more justifications to use approximate methods in our
structural analysis because of the availability of personal computers.
Microsoft Excel or other mathematical program in the computer can now
perform the numerical calculations required by the equations we derived
for any problem encountered in practice using basic math and physics.
Any truth can now be exposed using basic principles we learned in
school.
“Slide rule” and “finite element”
approximations are no longer valid and thus existing literature and well
intentioned authors and professors should now apply the analytical
method in any analysis. We can do the right approach by urging all
engineers to use basic principles of math and physics harnessing the
power of computers for all numerical calculations required.
We can now do the updating of all
information related to engineering using the exact method in our
analysis. Our educational system should emphasize basic mathematics and
physics for all students. It may take time to adopt a new paradigm from
the approximate to the exact method because we have been buried for many
years using the approximate methods. Computers are now readily available
and are all over the place that it is relatively easy to harness the
power of computers to do all the numerical calculations required in our
equations for a particular problem.