Reinforced Concrete Design

Reinforced Concrete Design.  My blog which I used most of my time, research, writing about concrete design calculations….!!!

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Reinforced Concrete Design

What makes Unique of RC…?

It is a COMPOSITE MATERIAL…

  • It requires APPLICATION of more involved Principles of Mechanics…
  • Structural Design is iterative requiring both ANALYSIS and DESIGN DECISIONS aided by judgment and EXPERIENCE.
  • ACI 318 -the model code in the United States of America for guiding the design of RC members, look at Chapter 8.
  • NSCP Code -the code in the Philippines..conforms to the provisions of ACI 318 Code!!!

Important Material Properties…

Concrete Strength and Steel Strength…

  • 28-day Compressive Strength, f’c: ACI 318 Code 2011 edition, Chapter 5.
  • Modulus of Elasticity of Concrete, Ec: ACI 318 Code 2011 edition, Chapter 8.5
  • Strength property or yield strength, fy..
  • Modulus of Elasticity of Steel, Es: 29,000,000 psi –ACI 318 Code 2011 edition.

1. –Procedures on how to Design Reinforced Concrete Beams!!!

Concrete Beam Sizing..!

Beam Section Diagram

Beam Section Diagram

Determination of Beam Size (b x h)—USE Spreadsheet or Hand Calculation!!!

Concrete Beam Size (b x h) or (b x d), FORMULA:

Beam Size Formula

Beam Size Formula

Beam Section, Strain and Force Diagram

Beam Section, Strain and Force Diagram

Equilibrium Equation orm Neutral Axis Distance, c --- Quadratic Equation for c

Equilibrium Equation orm Neutral Axis Distance, c — Quadratic Equation for c

Rebars Determination..

Area of Steel (As) determination!!!

Strength Formula

Strength Formula

As

Rho

The ACI Code 10.3.3 to 10.3.5 limits on the Steel Ratio (rho):

1.1 Minimum Beam Size for which Deflections are NOT LIKELY to be a Problem.

1.1.1 Set Neutral Axis distance, c = 0.375cb….

Beam Size NOT LIKELY TO HAVE DEFLECTIONS

Smallest Beam Size NOT LIKELY TO HAVE DEFLECTION PROBLEM

1.2 Arrangement of Rebars, Splicing points and splice length, development length, hooks requirement, and required Stirrups.

Stirrup Spacing Requirements per ACI

Stirrup Spacing Requirements per ACI

Stirrup Maximum Spacing

Stirrup Maximum Spacing

ACI Bottom Bar Splice Requirements

ACI Bottom Bar Splice Requirements

ACI Standards for Top and Bottom Splice Requirements

ACI Standards for Top and Bottom Splice Requirements

ACI Standards for Beams Reinforcements

ACI Standards for Beams Reinforcements

2. –Procedures on how to Design Reinforced Concrete Columns!!!

Tie Design Standards

Tie Design Standards

ACI Standards Columns Bars Details

ACI Standards Columns Bars Details

ACI Column Splice Details

ACI Column Splice Details

ACI Bar Bending Details

ACI Bar Bending Details

ACI Bar Bending Details

ACI Bar Bending Details

ACI Column Ties Requirements

ACI Column Ties Requirements

2.A. –Structural Design for column using Interaction Diagram!!!

Interaction Diagram

Interaction Diagram plot using Column design software and MS Excel Spreadsheet

 2.B. –Example of ACI Interaction Diagram.

Interaction Diagram-Rectangular Section-Courtesy of ACI

Interaction Diagram-Rectangular Section-Courtesy of ACI

Interaction Diagram-Spiral Column-Courtesy of ACI

Interaction Diagram-Spiral Column-Courtesy of ACI

2.C. –Summary of Column Design Requirements!!!

Column Design Requirements

Column Design Requirements

2.1 Strength Reduction Factor, phi =0.70 -applicable up through ACI 318-1999; they have been changed to phi =0.65, for compression controlled members (columns and beams under compression controls) beginning with ACI 318-2002 Code, and continuing with the ACI 318-05 and 2008 up to present.

3.–Example: Design of Concrete Members, i.e. Frame Analysis, Beams, Columns, Footings using MS Spreadsheet.

FRAME ANALYSIS-My own Spreadsheet Program

FRAME ANALYSIS-My own Spreadsheet Program

MS Excel Spreadsheet for Column

MS Excel Spreadsheet for Column

Column Excel Spreadsheet

Column Excel Spreadsheet

RC BEAMS

RC BEAMS

1-Footing

RC FOOTING1

 

RC FOOTING2

RC FOOTING2

REFERENCES:

  1. Design of Reinforced Concrete by Jack. C. McCormc, 3rd edition-1993, 7th edition-2005, 9th edition-2011;
  2. Design of Concrete Structures by Arthur H. Nilson, 12th edition -1997, International edition;
  3. Design of Concrete Structures by Arthur H. Nilson, 14th edition -2010, International edition;
  4. Reinforced Concrete (A Fundamental Approach), by Edward G. Nawy, 6th edition -2008,
  5. Reinforced Concrete, Mechanics and Design, by James K. Wight and  James G. MacGregor, 6th edition -2012,

History of Reinforced Concrete and Structural Design

Engineer's Outlook

The average person thinks that concrete has been in common use for many centuries, but such is not the case. Although the Romans made cement – called Pozzolana – before Christ by mixing slaked lime with a volcanic ash from Mount Vesuvius and used it to make concrete for building, the art was lost during the Dark Ages 5th century -15th century A.D. and was not revived until eighteenth and nineteenth centuries (A. D.). Marcus Vitruvius Pollio, Vitruvius, an Architect/Engineer during the golden age of Caesar Augustus (around 25 BC). In his writings around 25 BC in Ten Books on Architecture distinguished types of aggregate appropriate for the preparations of lime mortars. For the use of structural members, he recommended pozzolana, which were volcanic sand from the sandlike beds of Puteoli, brownish-yellow-gray in color near Naples and reddish brown at Rome. He specifies 1 part lime to 3 parts…

View original post 1,867 more words

History of Structural Analysis

Engineer's Outlook

STRUCTURAL ANALYSIS as we know it today evolved over several thousand years. During this time many types of structures such as beams, arches, trusses and frames were used in construction for Hundred or even thousand of years before satisfactory methods of analysis were developed for them.

While ancient engineers showed some understanding of structural behavior (as evidenced by their successful construction of bridges, cathedrals), real progress with the theory of structural analysis occurred only in the past 150 years.

The EGYPTIANS and other ancient builders surely had some kinds of empirical rules drawn from previous experiences for determining sizes of structural members. There is, However, NO EVIDENCE that they had developed any THEORY of STRUCTURAL ANALYSIS. The Egyptian Imhotep built the great PYRAMID of Saqqara, the Step Pyramid of Djoser Egypt’s first pyramid, built during the third dynasty of the old kingdom in circa 2630 B.C. sometimes is referred to…

View original post 2,496 more words

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.

History of Reinforced Concrete and Structural Design

The average person thinks that concrete has been in common use for many centuries, but such is not the case. Although the Romans made cement – called Pozzolana – before Christ by mixing slaked lime with a volcanic ash from Mount Vesuvius and used it to make concrete for building, the art was lost during the Dark Ages 5th century -15th century A.D. and was not revived until eighteenth and nineteenth centuries (A. D.). Marcus Vitruvius Pollio, Vitruvius, an Architect/Engineer during the golden age of Caesar Augustus (around 25 BC). In his writings around 25 BC in Ten Books on Architecture distinguished types of aggregate appropriate for the preparations of lime mortars. For the use of structural members, he recommended pozzolana, which were volcanic sand from the sandlike beds of Puteoli, brownish-yellow-gray in color near Naples and reddish brown at Rome. He specifies 1 part lime to 3 parts pozzolana for cements use in buildings. In his textbook, quite humbly titled “On the Origin of all Things”, Vitruvius held forth on the fundamental behavior of building materials, and then presented his views about the nature of theory versus practice, Vitruvius suggestion that design engineers should have more construction experience, and vice versa.

Vitruvius expressed his feelings and complained that:

“The WORKMEN are in a HURRY, the UNEDUCATED rather than the educated are in HIGHER FAVOR” and “ARCHITECTURE and ENGINEERING are professed by men, who have no knowledge even of carpenter’s trade.”

He wrote the textbook De Architectura libri decem (Ten books on Architecture), the only complete treatise on architecture to survive from classical antiquity. It influenced deeply from the Early Renaissance onward artist, thinkers and architects, engineers, among them Leonardo Da Vinci (1452-1519), Michelangelo (1475-1564).

Basilica at Fano design by Vitruvius -19 BC

In the mid-1800s, Joseph Lambot in France constructed a small boat and received a patent in 1855. Another Frenchman, Francois Coignet, published a book in 1861 describing many applications and uses of reinforced concrete.

Francois Coignet House, First House in reinforced concrete, built in 1853

Francois Coignet House, 1853

F. Coignet Reinforced Concrete System

Joseph Monier, the owner of an important nursery in Paris, generally deserves the credit for making the first practical use of reinforced concrete in 1849 to 1867. He acquired first French patent in 1867 for iron reinforced concrete tubs, then followed by his pipes, tanks in 1868, flat plates in 1869, bridges in 1873, stairways in 1875. He apparently had NO QUANTITATIVE KNOWLEDGE regarding its behavior or ANY METHOD of making design CALCULATIONS.

Chazelet Bridge design-built by Joseph Monier, 1875 – Photo by Dr. Sid French

Reinforced Concrete – Monier System 1867

Reinforced Concrete details -Monier System 1867

In the United States, the pioneering were made by Thaddeus Hyatt, who conducted experiments on reinforced concrete beams in 1850s. However, Hyatt’s experiments were unknown until 1877 when published his work privately. Ernest L. Ransome was the first to use and patent in 1884 the deformed (twisted) bar. In 1890, Ransome built the Leland Stanford Jr. Museum in San Francisco, a reinforced concrete building two stories high and 312ft (95m) long. Since that time, development of reinforced concrete in the United States has been rapid.

Ernest L. Ransome System

Photo by Jacques Mossot, thru  Structurae

Bridge designed by F. Hannebique -1899-1900, Photo by Jacques Mossot

Dragon Bridge design by Prof. Josef Melan-1901

Larimer Ave. Bridge, USA -Josef Melan system 1912

GA Wayss and Prof. Emil Morsch Test of Beam

G.A. Wayss and Prof. Emil Morsch Test of Beam

During 1891-1894, various investigators in Europe published theories and test results; among them were, Professor Moller system (Germany), Robert Wunsch, 1884 (Hungary -builder), Josef Melan 1892, (Austria -professor/engineer, the inventor of Melan system (dragon bridge), the German G. A. Wayss the first engineer who made theory, and then furnish formulas and methods for design; Francois Hannebique 1892 (France -contracting engineer), received patent in Brussels in 1892, and he first used reinforced concrete in 1879, in this he demonstrates the utility of stirrups to reinforce beams against SHEAR, Hannebique who was probably the first to use stirrups and bent-up bars, and then F. von Emperger (Hungary- professor/engineer), but practical use was less extensive than in United States, like C.A.P. Turner, Arthur Talbot at the University of Illinois, W.A. Slater, Morton O. Withey and Federick Turneaure at the University of Wisconsin.

Concrete-Steel Rod Detailing, Hannebique System – 1892

Continuous Beams, Hannebique System – 1892

Typical Arrangement of Reinforcement for Beams and Columns- Hannebique System

Professor Moller System (Germany) – 1894

Professor Talbot Test of Reinforced Concrete Beam

Throughout the entire period 1850 -1900, relatively little was published, as the engineers working in the reinforced concrete field considered construction and computational methods as trade secrets.

Photo by: Jacques  Mossot

Bridge at Menier, by Armand Consider built in 1906- Photo Jacques Mossot

One of the first publications that might be classified as a textbook was that of Armand Considere in 1899.

In 1903, with the formation in the United States of a joint committee of representatives of all organizations interested in reinforced concrete, uniform applications of knowledge to design were initiated.

Principles of Reinforced concrete construction, by F.E. Turneaure

The earliest textbook in English was that of Frederick E. Turneaure and Maurer published in 1907 entitled “Principles of Reinforced Concrete Construction”.  In the first decade of the twentieth century, progress in reinforced concrete was rapid. Extensive testing to determine beam behavior, compressive strength of concrete, and modulus of elasticity was conducted by Arthur N. Talbot at the University of Illinois, by Frederick E. Turneaure and Morton O. Withey at the University of Wisconsin, and by Bach in Germany, C.A.P Turner US, among others. Ernest L. Ransome (1852-1917) engineer -architect an early innovator of reinforced concrete and was the first to use twisted bars.  In 1912 Ernest L. Ransome and Alexis Saurbrey co-authored Reinforced Concrete Buildings.  

First reinforced concrete skyscraper, 1903 by E. L. Ransome

M. Withey Test of Concrete Beams

Turner System

Test of Beam conducted by Prof. Talbot

In 1906 major earthquake struck San Francisco, California (magnitude is 7.9), hence, engineers had conducted research extensively and revised the method of designs.

San Francisco Earthquake, magnitude -7.9, 1906

1906 San Francisco Earthquake

From about 1916 to the mid – 1930s, research centered on axially loaded column behavior. In the late 1930s and 1940s, eccentrically loaded columns, footings, and the Ultimate Strength of beams received special attention.

With the interest in and understanding of the elastic methods of analysis in the early 1900s, the elastic Working Stress method(also called Allowable-Stress Design or straight-line design) was adopted almost universally by codes as the best for design.

Historic Working Stress Design Formula, ACI, Prof. Taylor -1907

Historic WSD Formula, ACI, Prof. Taylor -1907

Historic formula by F. Turneaure 1907 #1

Historic Formula by F. Turneaure and Maurer 1907 -#2

Historic Formula for Ultimate Loads by Turneaure 1907 #3

Historic Formula by F. Turneaure and Maurer, 1907 -#4

Historic Formula by Turneaure and Maurer, 1907 – #5

Turneaure and Maurer, 1907 -#6

Historic Formula by Charles Whitney, 1921

Historic WSD Formula-Charles Whitney, 1921

The first modification of the elastic Working Stress method resulted from the study of axially loaded columns in the early 1930s. By 1940s, the design of axially loaded columns was based on Ultimate Strength.

Charles S. Whitney Rectangular Stress Block

In the 1930s, Charles S. Whitney an american civil engineer graduated from Cornell University in 1915 proposed the use of a rectangular compressive stress distribution to replace that an average stress of 0.85f’c is used with a rectangle of depth a = β1 x, determine so that a/2 = k x. In 1942 Charles S. Whitney ;  his image , presented a paper emphasizing this fact and showing how a probable stress-strain curve with reasonable accuracy, a parabola be replaced with an artificial rectangular stress block.

Charles S. Whitney stress block “a” and “c”

With the rectangular stress block simplification, the 1956 ACI-318 code added an appendix permitting Ultimate Strength Design (USD) as an alternate to Working Stress Design (WSD). The 1963 ACI-318 Code gave both methods equal standing.

Strength Design Stress

Flexure Formula, Beam Design

Beam Analysis -1

Beam Analysis -2

Beam Analysis-3

Since the mid-1950s, reinforced concrete design practice has made the transition from that based on elastic methods to the one based on strength.

Hence, my viewpoint, reinforced concrete design has been continuously studied for one hundred fifty (150) years and/or one and one half century already since it was invented by Joseph Monier in 1849 and patented in 1867. Therefore, It is ridiculous to say that working and drafting proposed projects in short period of time would suffice them to pretend they know the processes, methods of design.  If the manager, however, does not know something about THEORY of DESIGN, then the owner is taking a great chances. The man in charge should be an engineer.

References – All Books below are on the Shelves of my Private/Personal Library for additional sources of information:

  1. American Concrete Institute (ACI) Manual of Concrete Practice, six (6) volumes, 2004 and 2008;
  2. American Concrete Institute -ACI DESIGN HANDBOOK, Special Publication (SP-17), circa 1997 and reapproved 2004;
  3. Building Code Requirements for Structural Concrete -2002, 2005, 2008;
  4. Building Code Requirements for Reinforced Concrete -1977;
  5. Building Code Requirements for Reinforced Concrete -1963;
  6. A Treatise on Concrete Plain and Reinforced by Frederick W. Taylor Sanford Thompson, 1st edition -1905, 2nd edition -1912, 3rd edition -1916;
  7. Cyclopedia of Civil Engineering -American Technical School, 8 Volumes -1908;
  8. Cyclopedia of Construction (Radford’s) – (Carpentry, Building and Architecture, based on the practical experience of a large staff of experts in actual construction works), volumes 1 to 12 -1909;
  9. Cassell’s Reinforced Concrete by Bernard E. Jones -1913;
  10. Concrete Engineer’s Handbook by George Hool -1918;
  11. Concrete Designers Manual by Charles Whitney and George Hool -1921;
  12. Concrete-Steel by W. N. Twelvetrees -1905;
  13. Concrete Steel Buildings by W. N. Twelvetrees -1905;
  14. Concrete and Reinforced Concrete by W. N. Twelvetrees -1922;
  15. Concrete and Reinforced Concrete Construction by Homer Reid -1907 and 1908;
  16. Concrete and Reinforced Concrete by Walter Loring Webb and W. Herbert Gibson -1919;
  17. Concrete-Steel Construction by Prof. Emil Morsch and translated by E. P. Goodrich, 3rd edition -1909;
  18. Concrete-Steel Construction by C. A. Turner and Henry Eddy, 1st edition -1909, 2nd edition -1914, 3rd edition -1919;
  19. Engineers Pocketbook of Reinforced Concrete by E. Lee Heidenreich -1908;
  20. Experimental Research on Reinforced Concrete by Armand Considere -1903;
  21. Elementary Reinforced Concrete Building Design by Leonard C. Urquhart -1915;
  22. Handbook of Cost and Data for Contractors and Engineers by Halbert P. Gillette, member ASCE, 1,888 pages, 2nd edition -1920;
  23. Handbook of Building Construction volumes 1 and 2, by George A. Hool, 2nd edition -1929;
  24. Handbook on Reinforced Concrete by F. D. Warren -1906;
  25. Plain and Reinforced Concrete Arches by Josef Melan, 1st edition-1915, 2nd edition -1917;
  26. Practical Reinforced Concrete Standards by Hiram B. Andrews -1908;
  27. Principles of Reinforced Concrete by Frederick E. Turneaure and Edward R. Maurer, 1st edition -1907, 2nd edition -1909, 3rd edition -1919;
  28. Reinforced Concrete by Charles F. Marsh -1904;
  29. Reinforced Concrete by A. W. Buel and C. S. Hill -1904;
  30. Reinforced Concrete in Europe by Albert L. Colby, 1909;
  31. Reinforced Concrete by Frederick Rings -1910;
  32. Reinforced Concrete by John P. Brooks -1911;
  33. Reinforced Concrete Design, volume 1-Theory, by Oscar Faber and P. G. Bowie- 1st edition-1912, 2nd edition-1919;
  34. Reinforced Concrete Design, volume 2-Practice, by Oscar Faber and P. G. Bowie -1920;
  35. Reinforced Concrete -A Manual of Practice by Ernset McCullough, 1908;
  36. Reinforced Concrete Construction -Fundamental Principles, volume 1, by George A. Hool -1912;
  37. Reinforced Concrete Construction -Retaining Walls and BUILDINGS, volume 2, by George A. Hool -1913;
  38. Reinforced Concrete Construction -BRIDGES and CULVERTS, volume 3, by George A. Hool -1916;
  39. Reinforced Concrete and Construction by Henry Adams and Ernest R. Matthews -1911 and 1920;
  40. Reinforced Concrete for Buildings by Ernest L. Ransome and Alexis Saurbrey -1912;
  41. Mechanics of Building Construction by Henry Adams -1912;
  42. Steel and Reinforced Concrete in building by Edward Godfrey -1911;
  43. Structural Engineering -Concrete, Book 2, by Edward Godfrey -1908;
  44. Structural Engineering -Steel Designing, Book 3, by Edward Godfrey -1913;
  45. Test of Reinforced Concrete Beams by Arthur Talbot, Bul. No. 1-1904;
  46. Test of Reinforced Concrete Columns by Arthut Talbot and Arthur A. Lord, Bul. No. 56 -1912;
  47. Test of Reinforced Concrete Buildings under load by Arthur Talbot and W. A. Slater, Bulletin No.64 -1913;
  48. Test of Reinforced Concrete Flat Slab Structures by Arthur Talbot and W. A. Slater -1912;
  49. Reinforced Concrete Wall Footings and Column Footings, Bulletin No.67, by Arthur N. Talbot -1913;
  50. Moments and Stresses -Proceedings of the American Concrete Institute, volume 17 by H. M. Westergaard and W. A. Slater -1921;
  51. Kahn System of Reinforced Concrete by Trussed Concrete Steel Company 5th edition-1913;
  52. Johnson’s Materials of Construction by John B. Johnson, 1st edition, 2nd edition, 3rd edition, 4th edition-1907;
  53. Johnson’s Materials of Construction by F.E. Turneaure, M.O. Withey, Aston -5th edition-1919
  54. History of Architectural Development-volume 1, 2  and 3, by F. M. Simpson -1913;
  55. Manual of Structural Design by Jack Singleton, 3rd edition -1947;
  56. Design of Reinforced Concrete by Jack C. McCormac, 3rd edition -1993;
  57. Reinforced Concrete Fundamentals by P. Ferguson, J. Breen, J. Jirsa, 5th edition -1988;
  58. Design of Concrete Structures by Arthur H. Nilson, 12th edition -1997
  59. Design of Prestressed Concrete by Arthur H. Nilson, 2nd edition -1987;
  60. Reinforced Concrete Design by C. K. Wang and Charles G. Salmon 6th edition-1997;
  61. Building Design and Construction Handbook by Frederick S. Merritt and Jonathan t. Ricketts, 6th edition -2002;
  62. Foundation Analysis and Design, 4th edition by Joseph E. Bowles -1988.

Relevant Web Sites: the following external links open in new window, Engineer’s outlook is not responsible their contents nor endorses it. Charles WhitneyReinforced Concrete analysis, Historic Civil Engineering Landmarks, History of Concrete and cement. Luzon Philippines Earthquake, Philippine Earthquake and tsunami, Marcus Vitruvius. Vituvius 46-30BC. Vitruvius Book6, WaterHistoryqanat. History of concrete, Bridgehunter. Structurae.en.

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

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