Friday, October 14, 2011

HARDY CROSS METHOD- Structural Analysis

My passion for Structural Engineering, I focused my sight to delve into many books for Structural Analysis and Design calculations, so most of the time given to me by God, I used to study and to research the history of this interesting major major (venus raj expression miss universe 4th runner up) subjects in civil engineering, viz.
  1. Structural Reinforced Concrete Design,
  2. Structural Steel Design,
  3. Timber Design;
  4. Foundation Analysis and Design;
  5. Engineering Mechanics;
  6. Strength of Materials (Mechanics of Materials);
  7. Soil Mechanics;
  8. Theory of structures;
  9. Hydraulics;
  10. Differential and Integral CALCULUS;
  11. Physics;
  12. Analytic Geometry;
  13. Trigonometry;
  14. Algebra.

Having a lot of experiences in life, and my passion for structural engineering, I was challenged to make research and study continuously particularly structural engineering. Fortunately, I have collected and acquired many books, design codes for civil engineers valued in USDollar, namely;
  1. ACI-2008- Manual of Concrete Practice,
  2. ACI-2004- ACI Design handbook,
  3. ACI Detailing Manual, 2004;
  4. ACI-318-2008 Building Code Requirements for Structural concrete;
  5. CRSI DESIGN HANDBOOK, 10th edition, 2008;
  6. British Steel Designer's Manual 6th edition,
  7. American Steel Construction manual 13th edition, 2005;
  8. National Structural Code of the Philippines, 2001 edition, 2010 edition, etc.
  9. Numerous Historic Reinforced Concrete Books as early 1903 to 1929.
  10. Numerous Historic Books for Structural Theory and Mechanics of Engineering; e.g. Mechanics of Materials, Newtons Mathematical Principles of Natural Philosophy, An Essay on Bridge Buildings, circa A. D. 1700  to 1929.    
ACI Design Handbook, Volume 2
Actually, since 1995, I started collecting books and studied most of the time if no projects to be supervised. In my eagerness to acquire more knowledge, I focused my mind and sight to study and research the structural analysis and design calculation methods to make works easier for civil / structural engineers and structural designers.

I have a friend having utmost desire in structural analysis and design computations, construction and claiming for cleverness and expertise in construction, this friend of mine is not really a recognized Structural Engineer by Profession Regulation Commission or by Philippine Institute of Civil Engineers (PICE), but he is just a practicing engineer; Fabian, he is used to design simple buildings, he constructed some buildings in Catarman town, but I doubted his way of designing concrete columns because he uses balance condition in concrete column design, it should be noted that the actual condition of concrete column must be used to determine the strength capacity; and he has the effrontery of criticizing other design engineers.

I had met a lot of people with different characters and personalities, the SCRUFFY, the CLEAN, the INCOMPLETE, the DEFENSIVE ones, the NONCHALANT and the BRILLIANT ones. As much as there are differences in people's character, so is there, in their works and calculations. Also, to mention, through social networking I have acquired computer software, e.g. Microsoft Excel Spreadsheets software for design, and adopted their procedures, methodology and style with some modification to suit my satisfaction and method of analysis. Further, through social networking I had learned to develop Spreadsheets for my analysis and design since 2006 up to present, I am self taught in Microsoft Excel and had developed frames and beams analysis, concrete beams, concrete columns, footings in metric versions.

I used to think that being a practicing engineer for almost two decades, I surmise myself as a Structural design engineer already, like for instance professor Besavilla who authored reviewer books, and also Gillesania also authored reviewer books, my friend Redeem Legaspi a software programmer who developed steelpro program, they are all considered structural engineer. Accordingly, in my in-depth study and research, I had learned various methods for Structural Analysis in 'Hand' or conventional method with the aid of calculator and also using computer software, namely;
  1. MS-Excel Spreadsheets software,
  2. STAAD software,
  3. PCA software,
  4. ETABS, SAP2000, SAFE design software.
In my almost 20 years of experience as practicing engineer with continuous research, study, practice solving for building frames/beams and bridge structures, I have acquired knowledge and become Structural design engineer. Henceforth, as structural designer or engineer and specialist, I prefer to use the method developed by Professor Hardy Cross the Moment Distribution.

Civil Engineer Hardy Cross, P.E.
HARDY CROSS method (innovation) is the best method (for me) for Structural Analysis and Design Calculation, developed by Professor Hardy Cross in 1924. He published the method in the proceedings of the American Society of Civil Engineers in May 1930 after having taught the subject to his students at the University of Illinois since 1924. His Paper began a new era in the Analysis of Statically indeterminate frames and gave added impetus to their use. This method can be used in complex building frames, continuous beams and simple beams and or vertical structures.

Uniformly Distributed Load:
M = W(L^2)/12 for fixed end moment

Concentrated Load or Point Load:
M = Pa(b^2)/L^2 fixed end moment
M = Pb(a^2)/L^2 fixed end moment

Prof. Hardy Cross method was a popular method and was used for the Analysis of Continuous Beams and Frames and in Structural Engineering as a "Hand Calculations method and/or Conventional Calculations method" from 1930 until 1960. Since the 1960s, however, there has been an ever increasing use of computers for the analysis of all types of structures. Computers are extremely efficient for solving the simultaneous equations that are generated by other methods of analysis. Generally, computers software used is developed from the matrix-analysis procedures. Reference: J. C. McCormac, S.E., Structural Analysis.

I developed a MS Excel spreadsheet for Continuous Span Frame Analysis using Hardy Cross method:

Distribution Factor Formula
FBD of a Beam subjected to uniformly loaded at distance L
FBD of a Beam segment at distance X
Frame diagram of  MS Excel Spreadsheet I developed
Moment distribution table of  MS excel spreadsheet I developed
Shear Diagram of my own MS Excel Spreadsheets
Moment Diagram for my own MS Excel Spreadsheet