1. This powerful software in my possession can be verified by any structural mechanics
expert or any visual basic computer expert. A sample of this software is shown below for
comparison with available software using approximate methods. The program was done
using Microsoft Excel and the analytical equations for reinforced concrete columns were
entered in the cells to determine the minimum yield capacity of a given circular and
rectangular section. There were hundreds of equations involved that were eventually
published years later by Universal Publishers of Boca Raton, Florida in 2004. The title of
the book is “Analytical Method in Reinforced Concrete”.
The output of this software will give the envelope of the minimum yield capacity of a
reinforced circular or rectangular column section. It tabulates the numerical values every
inch of the section as well as the standard key points and graphs the envelope where the
axial load is represented by the vertical axis and the bending moment on the horizontal
axis. The current method is in error because the correct free body diagram was not drawn
to include all variable parameters. You can easily see this fact because rotation of XYZ
axes were not done as well as the coordinates of every reinforcing bars by the current
method. The user have 3 selections available – concrete capacity, bar force capacity or
the combined yield capacity of the given reinforced concrete rectangular or circular
column section. He can print these graphs for future use or he can change the numbers as
he/she pleases.
Any structural engineer can have different factor of safety from others in his/her design
as the external load in a particular locality is plotted on this graph. The user can easily
notice that as he/she plots the external load, the column section will define itself as a
short or long column.
It is indeed inconceivable that experts will continue copying others or existing literature
in this age of electronic digital computers where basic mathematics and physics can
easily be applied to derive applicable equations in structural mechanics. Basic
mathematics include algebra, trigonometry, analytic geometry and differential and
integral calculus among others in order to derive applicable equations where verification
for authenticity by Microsoft Excel is done in no time even for hundreds of equations.
A new exact paradigm is therefore required in structural mechanics so that modelling and
interpretation of laboratory data can reconcile with the analytical equations derived by the
researcher. To continue in deliberate ignorance is not advisable since digital computers
with basic mathematics can easily expose incorrect analysis.
Instructions:
(1) Circular – You can enter any variable number in the sample boxes below as well
as follow the instructions stated herein.
2. (2) Rectangular – Again you may enter any number that applies to your specific
problem and follow the instructions to enter and to proceed to next.
3. This software was based on the analytical equations published by Universal
Publishers of Boca Raton, Florida in 2004, years after the software was created
and ignored globally by experts. Hence, an example from this software is shown
below for experts to dispute the numbers indicated as minimum yield capacity of
a given column rectangular section according to Euler’s, Hooke’s Law and
Pythagorean Theorem.
………………………………………………………………………………………………
*
Column software using the parabolic stress method and 2 pivot points. The
Microsoft Excel program was prepared by William R. Mulford of Port Washington,
New York and assisted by Ramon V. Jarquio, P.E. in entering all the hundreds of
derived equations in their respective cells. This software was registered in the
Library of Congress and Bill submitted the technical details of this software as
required by the Library of Congress.
An example of this software is shown here to show the power of this software
which was advertised in ASCE magazine 2 decades ago. All declared experts
then ignored this analytical approach and did not admit the mistake of using only
1 pivot point and the rotation of XYZ axes in a 3D structural analysis invoking the
established Euler’s, Hooke’s Law and Pythagorean Theorem. Even today
approximate methods with finite-element are being copied and implemented
globally. A new paradigm of exactitude using electronic digital computers should
be employed with basic mathematics to derive the required structural solutions in
any problem. This software for reinforced concrete sections in highway and
building column components should be utilized by all agencies.
Figure1: Minimum Yield Capacity
4.
5. Table 1: Key Points of the Minimum Yield Capacity Curve
RECTANGULAR COLUMN INTERACTION CURVE { 30x20 in. WITH 18 - 1in. BARS }
DESIGN SAFETY FACTOR 1 COLUMN CAPACITY AXIS 0.588 RADIANS
C M steel P steel M concrete P concrete M P e=M / P Mz z
Q= 67.305 817 765 -817 2878 0 3643 .000 5708 1.567
R= 36.056 2404 538 3880 2490 6284 3028 2.076 706 .233
S= 31.896 2757 470 5898 2237 8655 2707 3.197 -1439 -.532
T= 19.664 4889 60 8824 1164 13713 1224 11.201 -4997 -4.081
U= 18.877 5024 24 8664 1092 13688 1116 12.268 -4938 -4.426
V= 9.147 3657 -283 3655 283 7312 0 82611.706 -1755 -19823.852
Q=Theoretical maximum axial load
R=Full section in compression
S=Zero tension in rebar
T=Max moment capacity of section
U=Balanced loading condition
V=Beam condition
6. Table 2: User Input / Output Information
RECTANGULAR COLUMN INTERACTION CURVE { 30x20 in. WITH 18 - 1in. BARS }
LENGTH of RECTANGLE 30 in. BARS ALONG LENGTH 5
WIDTH of RECTANGLE 20 in. BARS ALONG WIDTH 6
CLEARANCE BAR CENTER to FACE 3.00 in. TOTAL BARS in COLUMN 18
REBAR DIAMETER 1.000 in. NUMBER of BUNDLES 0
STEEL STRENGTH 60.00 kips/sq. in. Space Between BARS, Along Length 5.000 in.
CONCRETE STRENGTH 5.00 kips/sq. in. Space Between BARS, Along Width 1.800 in.
DESIGN SAFETY FACTOR 1.00 BARS on CENTER, ALONG LENGTH 6.000 in.
% of STEEL to CONCRETE 2.36% BARS on CENTER,ALONG WIDTH 2.800 in.
RADIANS .58800 CONCRETE STRAIN .0030
MODULUS of ELASTICITY Es 29000 kips/sq. in. EQUIVALENT DIAMETER
VOLUME of CONCRETE WEIGHT of STEEL REBARS
cu. yd. per ft. of COLUMN .1542 lbs. per ft. of COLUMN 48.11
