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 subjects in civil engineering; 

  1. Structural Reinforced Concrete Design;
  2. Structural Steel Design;
  3. Timber Design;
  4. Engineering Mechanics;
  5. Strength of Materials (Mechanics of Materials),
  6. Theory of Structures;
  7. Hydraulics;
  8. Transportation Engineering;
  9. Soil Mechanics and Foundation Design;
  10. Differential and Integral Calculus;
  11. Physics;
  12. Analytic Geometry;
  13. Plane Trigonometry;
  14. Advance Algebra.

Having a lot of experiences in life, and my passion for structural engineering, I was challenged to research and study continuously particularly structural engineering. Fortunately, I have collected and acquired many books, design codes for civil engineers valued in US Dollars, namely;

  1. ACI Manual of Concrete Practice, 2008 -American Concrete Institute;
  2. ACI Design handbook, 2004 -American Concrete Institute;
  3. ACI 318-Building Code Requirements for Structural concrete, 2011 edition,
  4. DETAILING MANUAL 2004 edition,
  5. PCI Design Handbook, Precast and Prestressed Concrete-7th edition,
  6. CRSI Design Handbook, 2008 edition,
  7. ASCE 7 Standard-Minimum Design Loads for Buildings and other Vertical Structures,
  8. Uniform Building Code (UBC),
  9. British Steel Designer’s Manual 6th edition,
  10. American Steel Construction manual 13th edition,
  11. National Structural Code of the Philippines 2001 edition, etc.
  12. Numerous Historic Books in Civil Engineering, e.g. Theory of Structures, Reinforced Concrete, Mechanics of Materials, Mechanics of Engineering dated 1750 A.D. to 1930 A.D.
ACI 2008 -MANUAL OF CONCRETE PRACTICE
ACI 2008 MANUAL OF CONCRETE PRACTICE

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 who has the desire in structural analysis and design computations and construction, this friend of mine is not really a recognized Structural Engineer by Professional Regulation Commission or by Philippine Institute of Civil Engineers (PICE), but he is just a practicing engineer; Fabian, he used to design simple buildings, he constructed some buildings in Catarman town, I doubted the method of calculations he used because he uses the balance condition in concrete designs. The method he used was erroneous it should be actual condition of the concrete columns. 

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 more than 22 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 design engineer and specialist, I prefer to use the method developed by Professor Hardy Cross the Moment Distribution.

Prof. Hardy Cross

HARDY CROSS method (innovation), to me it’s the best method 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. 


Formula:

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 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

Frame diagram for moment distribution

Moment Distribution screen shot of my MS Spreadsheet

Shear Diagram screen shot of MS excel Spreadsheet I developed

Moment Diagram-screen shot of MS Excel spreadsheets, which I have developed

Relevant Web Sites: This external links open a new window, any of their contents the engineersoutlook is not responsible nor endorses it. Hardy Cross, Biography, Hardy Cross School.

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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 subjects (venus raj expression miss universe 4th runner up) in civil engineering.

  1. structural reinforced concrete design;
  2. structural steel design;
  3. timber design;
  4. engineering mechanics;
  5. mechanics of materials;
  6. theory of structures;
  7. Hydraulics.
  8. Soil Mechanics;
  9. Foundation Design;
  10. Differential and Integral CALCULUS;
  11. Analytic Geometry;
  12. Trigonometry;
  13. Algebra.

Having a lot of experiences in life, and my passion for structural engineering, I was challenged to research and study continuously particularly structural engineering. Fortunately, I have collected and acquired many books, design codes for civil engineers valued in US Dollars, namely;

  1. ACI 2008- Manual of Concrete Practice,
  2. ACI Design handbook 2004,
  3. ACI 318 Building Code Requirements for Structural concrete 2011 edition,
  4. Detailing Manual, ACI 2004 edition,
  5. ASCE 7 Standards-Minimum Design Loads for Buildings and other Vertical Structures,
  6. British Steel Designer’s Manual 6th edition,
  7. American Steel Construction manual 13th edition,
  8. National Structural Code of the Philippines 2001 edition- volume 1 and 2, etc.
  9. Numerous Historic books for Reinforced Concrete and Structural Analysis, Mechanics of Engineering dated circa 1750 A.D. to 1930 A.D.;
ACI 2008 -MANUAL OF CONCRETE PRACTICE
ACI 2008 MANUAL OF CONCRETE PRACTICE

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 whose expertise is structural analysis and design computations and 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; Fabs, he used to design simple buildings, he constructed some buildings in catarman town, I doubted the method of calculations he used, because he uses the balance condition of the concrete column designs, in my viewpoint this method is erroneous! It should be the actual condition of the structural members; I have a Hard Copy of his Design Calculations. So, I can’t fathom his way of design, indeed he show off himself to be all knowing and criticized me about my design of the CFIC building for using a 50 psf dormitory dwelling and not good in design.

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 more than 22 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 design engineer and specialist, I prefer to use the method developed by Professor Hardy Cross the Moment Distribution.

Prof. Hardy Cross

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. 


Formula:

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 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

Frame diagram for moment distribution

Moment Distribution screen shot of my MS Spreadsheet

Shear Diagram screen shot of MS excel Spreadsheet I developed

Moment Diagram-screen shot of MS Excel spreadsheets I have I developed

Relevant Web Sites: This external links open a new window, any of their contents the engineersoutlook is not responsible nor endorses it. Hardy CrossHardy Cross School.