Giza Pyramid: Evidence of Ancient Machining


History of Structural Analysis

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 as the world’s first Structural Engineer and master builder. The pyramid of Khufu at about circa 2550 B.C., height 147 meters built by Egyptian’s Hemiunu, Pharaoh Khufu’s master builder; the largest pyramid ever built, it incorporates about 2.3 million tones blocks. No doubt the Egyptians and ancient builders had formulated empirical rules based on their previous experience to guide them in planning a new structure, but there is NO EVIDENCE that they had developed even the beginning of a theory of structural behavior.

How did they do it? A question made by Dr. Craig Smith in his November 2004 issue of Civil Engineering (American Society of Civil Engineering magazine), Craig B. Smith, Ph.D., P. E.

He profoundly explained this as follows:

Unfortunately, no plans, no drawings, or no written records regarding construction of Khufu’s pyramid have ever been discovered; it is clear from surviving and from examination of structures at Giza and before the Giza pyramids that the ancient Egyptians understood the principles of the lever and inclined plane; calculations of volumes, slopes and angles, they knew how to survey, that they devised a sound system of measurements based on cubit, a unit of length approximately equal to half a meter; they had no PULLEYS. Clearly ramps were employed by the pyramid’s builders in some fashion. The ramp is constructed by about 158 linear meters against the base of pyramid and the ramp construction proceeds hand in hand with pyramid construction Dr. Smith concluded. Only One other structure built in the Old kingdom can compete with Khufu’s pyramid in terms of size, grandeur, and engineering complexity – the system of ramps that was erected to build the pyramid itself. Regrettably, this remarkable example of Fourth Dynasty ingenuity and skill was obliterated as the final measure before Khufu’s stair-steps to the gods was consecrated.

Aerial View of the Pyramids at Giza

Geat Pyramid of Giza (Pyramid Khufu and Cheofs to the Greeks, circa 2550 B.C.)

Diagram of the Great Pyramid at Giza -Pharaoh Khufu showing the inside view of  structure -from wikipedia

First Theory of Ramp Construction used to construct the Pyramids at Giza

Second Theory of Ramp Construction used to construct the Pyramids at Giza

The ruined pyramid of Djedefre at Abu Rawash-wikipedia

Although the Greeks built some magnificent structures, their contributions to structural theory were few and far between. Apparently, evidence showed that Greeks had Little KNOWLEDGE about Structural Analysis.

Ruins of Parthenon -Ancient Greece built by Iktinos- 447 to 438 BC

Ruins of Parthenon -Ancient Greece built by Iktinos – 447 to 438 BC

Remains of the west gate in the Roman Forum, Greece athens -146 -12 BC

Ruins of the theater and of the Temple of Apollo at Delphi-Greece built on 4th century BC

Pythagoras (about 570 -475 B.C.), a Greek mathematician, who is said to have originated the word mathematics, is famous for the right angle theorem that bears his name the Pythagorean theorem, Pythagoras (569 -475). Archimedes(287-212 B.C.) Greek mathematician developed some fundamental principles of static and introduced the term center of gravity.

Pythagorean theorem

The Romans were outstanding builders and were very competent in using certain structural forms such as semicircular masonry arches. As did the Greeks, they, too had Little KNOWLEDGE of Structural Analysis and made even less Scientific progress in Structural Theory. They probably designed most of their beautiful buildings from an ARTISTIC VIEWPOINT. Perhaps their great bridges , Roman bridge and aqueducts , Roman aqueduct in France were proportioned with some RULES OF THUMBS, however, if these methods of design resulted in proportions that were insufficient, the structures collapsed and no Historical records were kept. Only their successes endured. Readers of this site are suggested to link to relevant web site below.

Most of the knowledge that the Romans accumulated concerning structural engineering was lost during the Middle Ages A. D. 476 to 1492 century, and has been recovered only since the Renaissance.

Verona Italy, Ponte Pietra or Stone bridge -100 BC

Ruins of Roman Aqueduct, Asia Minor Turkey, Circa 300 AD to 363 AD

Ruins of Roman stone Bridge, designer roman engineers , Iran -260 -270 AD

Ancient Roman Bridge that collapsed -142 BC

Collapsed Roman Bridge -30 BC to 14 AD

One of the greatest and most noteworthy contribution to structural analysis, as well as to all other scientific fields, was the development of the Hindu-Arabic system of numbers. Unknown Hindu mathematician in the second and third centuries B.C. originated numbering system of One to Nine (1 to 9). In about 600 A.D. the Hindus invented the symbol SUNYA (meaning empty). which we call ZERO. (The Mayan Indians of Central America, However, had apparently developed the concept zero about 300 years earlier).

In the 8th century A.D. the Arabs learned this numbering system from scientific writings of the Hindus. in the following century, a Persian mathematician wrote a book that include the system, his book was translated into Latin some years later and brought to Europe. In around 1000 A.D. Pope Sylvester II decreed that the Hindu- Arabic numbers were to be used by Christians.

In the Renaissance period 14th to 17th century, Leonardo da Vinci (1452 -1519) was not only the leading artist of his time but was also a great scientist and engineer. The work of da Vinci appears to be the real beginning of the development of structural theory. Galileo Galilei (1564 -1642) is properly acknowledged to be not only founder of modern science but also the originator of the mechanics of materials.

In the 17th Century A.D., Sir Isaac Newton (1642-1727), invented the fundamental principles of Structural Analysis, an English mathematician and physicist, and one of the Greatest Scientists in history who ever lived. His discoveries and theories laid the foundation for much of the progress in the science. For, in his last publication, “Two New Sciences,” completed in 1636 and published in 1638.

Sir Isaac Newton was one of the inventors of the branch of mathematics called DIFFERENTIAL and INTEGRAL CALCULUS (The other was German mathematician Gottfried Wilhelm Leibniz). Newton also formulated 3 laws of motion, and from them the universal law of Gravitation. To develop his Theory of Gravitation, Newton had to develop the Science of FORCES and MOTION called MECHANICS.

elastic collision -head-on collision of carts

Newton’s Law of Universal Gravitation

Starting about 1665, at the age of 23, newton enunciated (pronounce, speak) the principles of mechanics, formulated the law of Gravitation; viz.

Newton developed the Laws of Inertia and motion which become the fundamental principles used in Structural Analysis.

  1. The first law of motion; an object at rest tends to remain at rest; an object in motion tends to in motion in a straight line unless acted upon by an outside force. The development of physics owes much to Newton’s Law of motion, notably;
  2. the second law…… “the force acting on an object is equal to the mass of the object multiplied by the acceleration”, F = ma;
  3. and the third Law of motion; for every action there is an equal and opposite reaction.

By the middle of the 19th century, much progress had been made in this area. A French physicist Charles Augustine Coulomb (1736-1806) and a French engineer-mathematician Louis Marie Henri Navier (1785-1836), are said to have founded the science of mechanics of materials, and often considered to be the founder of modern structural analysis.

Andrea Palladio (1518-1580), an Italian architect, is thought to have been the first person to use modern trusses. He may have revived some old Romans designs and probably sized the members by some RULES of THUMB (perhaps revivals of old Romans rules). After his time trusses were forgotten for 200 years, until they were reintroduced by Swiss designer.

Montagnana building designed by Andrea Palladio

Tesina Stone Bridge, designed by Palladio-1569

It was actually in 1847, the first rational method of analyzing jointed trusses was introduced by Squire Whipple (1804 -1888) of United States. Squire Whipple was a civil engineer, born in Hardwick, Massachusetts, USA. This was the first significant American contribution to structural theory. Several excellent methods for calculating deflections were published in the 1860s and 1870s which further accelerated the rate of structural analysis development. He has become known as the father of Iron Bridge building in America.

Squire Whipple’s Bridge, Norman’s Kill, Schenectady, NY, USA – 1867

Bridge -NY-mohawk design by Squire Whipple, students, observers on top of the bridge

Among the important investigators and accomplishments were: James Clerk Maxwell (1831-1879) of Scotland, for the Reciprocal Deflection theorem in 1864; Otto Mohr (1835-1918) of Germany for Elastic Weights in 1870; Alberto Castigliano of Italy for Least Work theorem in 1873; Charles E. Green of the United States for the Area Moment theorems in 1873; B.P.E Clapeyron of France for the Three-Moment theorem in 1857.

Prof. Hardy Cross

In the United States of America two great developments in Statistically Indeterminate Structure Analysis were made by GEORGE A. MANEY (1888-1947) and HARDY CROSS (1885-1959). See reference link.

GEORGE A. MANEY introduced Slope Deflection method in 1915 at University of Minnesota engineering publication. In Germany, BENDIXEN introduced Slope Deflection in 1914. For nearly 15 years, until the introduction of Moment Distribution, Slope Deflection was the popular method used for the Analysis of continuous beams and frames in the United States of America.

A very common method used for the approximate analysis of continuous concrete structures, was the Moment and Shear Coefficient developed by the H. M. Westergaard and W. A. Slater a member of the American Concrete Institute in 1926-1929. Also, prior to this, moments and stresses in slabs was published by Westergaard and Slater in a Proceedings of American Concrete Institute in 1921.

Another most common approximate method of analyzing building frames for LATERAL LOADS such as winds, earthquake (seismic) is the PORTAL method which was presented by Albert Smith in the Journal of the Western Society of Engineers in 1915. Another simple method of analyzing building frames for Lateral Loads is the Cantilever method presented by A.C. Wilson in engineering record, 1908. These methods are said to be satisfactory for buildings with height not in excess of 25 to 35 stories.

In the first half of the 20th century A.D., many complex structural problems were expressed in mathematical form, but sufficient computing power was not available for practically Solving the resulting EQUATIONS and/or FORMULAS. This situation continued in the 1940s, when much work was done with MATRICES for analyzing aircraft structures. Fortunately, the development of digital computers made practical the use of equations and FORMULAS for these and many other types of Structures, including High rise Buildings.

Jack C. McCormac, Professor at the Clemson University engineering department has stated it eloquently as follows:

All of us, unfortunately, have the weakness of making exasperating mistakes, and the best that can be done is to keep them to the absolute minimum.

The best structural designer is not necessarily the one who makes the fewest mistakes initially, but probably is the one who discovers the largest percentage of his or her mistakes and corrects them.1

Hence, in my research and study for almost two decades, it is seems IRONIC that the COLLEGE Student of TODAY can LEARN in a FEW MONTHS the Theories and Principles of STRUCTURAL ANALYSIS that took HUMANKIND several THOUSAND YEARS to DEVELOP.

  • Member: American Concrete Institute (ACI)
  • Member: American Society of Civil Engineers (ASCE)
  • Member: Phil. Institute of Civil Engineer (PICE)

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

  1. Structural Analysis by Jack C. McCormac and J.K. Nelson Jr. -1997;
  2. Civil Engineering magazine by American Society of Civil Engineers (ASCE), Soaring toward the Heavens (Great pyramid at Giza), by Craig B. Smith, Ph.D., PE, Volume 74, No. 11, Nov. 2004;
  3. Design of Concrete Structures by Arthur H. Nilson -1997;
  4. Structural Design Data and Specifications by Abelardo Carrillo, 6th edition -1980;
  5. Engineering Mechanics by Ferdinand L. Singer, 3rd edition -1976;
  6. Elementary Theory of Structures by Chu-Kia Wang and Clarence I. Eckel -1957;
  7. Elementary Structural Analysis by C. H. Norris, J. B. Wilbur and S. Utku, 3rd edition -1976;
  8. The Theory of Plates and Shells by Professor S. Timoshenko and S. Woinowsky -Kreiger, 2nd edition -1959;
  9. Cyclopedia of Civil Engineering -American Technical School, by Frederick E. Turneaure, volumes 1 to 8 -1908;
  10. Mechanics’ and Engineers’ -Mechanics, Mathematics and Physics by Chas H. Haswell, 1079 pages, 78th edition -1930;
  11. Applied Mechanics for Engineers by J. Duncan -1926;
  12. Applied Mechanics (Strength and Elasticity of Materials, Theory and Design of Structures) by David Allan Low -1909;
  13. Applied Mechanics (general introduction to the theory of structures and machines) by James H. Cotterill, 1st edition -1884, 6th edition -1906;
  14. Analytical Mechanics for Engineers by Fred B. Seely and Newton E. Ensign -1921;
  15. Structural Mechanics by Charles E. Greene, 1st, 2nd and 3rd editions -1897 to 1909;
  16. Graphics for Engineers, Architects and Builders- Trusses and Arches by Charles E. Greene, Parts 1, 2 and 3 – 1878;
  17. An Elementary and Practical Treatise on BRIDGE BUILDING by Squire Whipple, C.E., (Inventor of Whipple Bridge), 2nd edition -1872 and 1873;
  18. General Theory of Bridge Construction by Professor Herman Haupt, C.E., 1st edition -1851, 1865 and 1878;
  19. A Treatise on Bridge Architecture by Thomas Pope -1811;
  20. Engineering Construction in STEEL and TIMBER by William Henry Warren, 2nd edition -1910;
  21. The Mathematical Principles of Natural Philosophy by ISAAC NEWTON -Translated into English by Andrew Motte, volume 2 -1803;
  22. The Mathematical Principles of Natural Philosophy by ISAAC NEWTON -by Andrew Motte -1843;
  23. Mechanics of Engineering volume 1, 2 and 3 by Irving P. Church, C. E., 8th edition-1893, 1894, 1895; 9th edition-1905, 1908 and 1911;
  24. Mechanics of Engineering volume 2- (The Strsses in Framed structures, Strength of Materials and Theory of Flexure), by A. Jay Dubois, C.E., PhD., 1st edition -1902;
  25. Mechanics of Materials by George Young, Jr. and Hubert E. Baxter -1927;
  26. Strength of Materials by Arthur Morley, 3rd edition -1913, 4th edition -1916;
  27. The Elements of Mechanics of Materials by Charles E. Houghton, 1st edition -1909, 2nd edition -1915;
  28. Mechanics of Materials by Mansfield Merriman, 10th edition -1910, 11th edition -1914 and 1916;
  29. A Text-Book on Roof and Bridges by Mansfield Merriman and Henry S. Jacoby, parts 1, 2, 3 and 4, 5th edition -1903;
  30. A Tex-Book on the Mechanics of Materials (Beams, Columns and Shafts) by Mansfield Merriman, 1st edition -1885, 4th edition -1892, 8th edition -1899;
  31. Principles of Mechanics by William Emerson, 3rd edition -1773;
  32. The Principles of Structural Mechanics by Percy J. Waldram -1912;
  33. Mechanics of Building Construction by Henry Adams -1912;
  34. The first, second, third and fourth book of Architecture by Andrea Palladio, 1755;
  35. The Elements of Civil Architecture -Andrea Palladio and Vitruvius by Henry Aldrich -1824;
  36. The Builders Director or Bench Mate -Andrea Palladio by Batty Langley, July 14, 1746;
  37. History of Architectural Development volumes 1, 2 and 3, by F. M. Simpson -1913;
  38. Theory of Structures and Strength of Materials by Henry Bovey, 1st edition -1893, 2nd edition-1896, 884 pages, 3rd edition-1900;
  39. Theory of Structures by Charles M. Spofford -1911;
  40. Theory of Structures by Arthur Morley, 5th edition -1912;
  41. The Elements of Structures by George A. Hool, 1st edition -1912;
  42. Bridge and Structural Design W. Chase Thomson -1905;
  43. Manual of Structural Design by Jack Singleton, 3rd edition -1947;
  44. Practical Structural Design, by Ernest McCullough, 2nd edition -1921;
  45. Principles of Structural Engineering, by C. K. Smoley -1928;
  46. Structural Designer’s Handbook by William Fry Scott -1904;
  47. Specifications Standards by John Ostrup -1910;
  48. Structural Engineering by A. W. Brightmore -1908;
  49. Structural Engineering J. Husband and W. Harby -1911;
  50. Structural Design Horace R. Thayer, volume 1 -1912;
  51. Structural Engineering by John E. Kirkham, 1st edition -1914;
  52. Structural Engineering -Steel Designing, book 3, by Edward Godfrey -1913;
  53. Structural Engineering – Strength of Materials by George F. Swain, volume 1 -1924;
  54. Structural Engineering -Fundamental Properties of Materials by George F. Swain, volume 2-1924;
  55. Structural Engineering -Stresses, Graphical Statics and Masonry by George F. Swain, volume 3, 1st edition-1924.

Relevant Web Sites: the following external links opens new window. engineer’s outlook is not responsible for their contents nor endorses it.

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.

A serious killing, greed for power and wealth

In my standpoint, killings done by ruthless and reprobate people are the works of evil, EVIL who entices people to do beyond the limits of their sanity and senses and the freewill, freedom to choose given by God to us. To do what is bad in the eyes of God, because the worldly desires are severe, the desire for power, for fame, and greed for money even to the extent of killing people, being a false witness.  To name God’s commandments, viz: 

  1. Thou shall not kill;
  2. Thou shall not steal;
  3. Thou shall not make false witness against your fellowman;

Here are signs of greed for power, selfishness, enviousness, political killings and transgressions of the law of God:

People in power are not satisfied with their honor and fame; victorious political party have used their powers for political persecution against the people who supported their political rival and other political party (I am a victim of political persecution, bickering and jeering). In some instant implementation of infrastructures (the method of design and construction); instead of listening to the suggestion and complaints of their subordinates, employees they said “don’t interfere.!” The worst is the insidious evil attitude of few individuals, who are selfish flatterer of the politicians (false witness). 

The killing of late Mayor of Catubig Ceasar Vicencio son of late congressman Romy Vicencio, Father Cecelio Lucero the brother of former Congressman Wilmar Lucero, Manolo Daza brother of Congressman Raul Daza, and killing of 10 policemen in Catarman, ambushed of 10 soldiers in Las Navas town, Northern Samar, Philippines.

The difference between good acts and evil and bad acts: 

The good acts are; people in power and few politicians have powers to choose and appoint for appointive positions in government, and have influence to recommend for employment and promotions; while the bad acts are; they may block and oppose employment and promotions by calling the heads of agencies and visiting the office of the head of offices in the government; with due respect to good and clean politicians, “I salute them.!”

In my standpoint, people in power want professional people (like teachers, architects, doctors and even lawyers, accountants) to bend knees, bow down and implore to them just to ask favor from them for employment, begging for projects or infra (I knew for a fact that they are powerful being a politicians it’s clear as SUN SHINES at the East and as fresh water running at the Spring! I know fully well!). In Philippine history they were described as ilustrados elite!” but these elite people I described as ilustrados elite!”, in earlier time their status were the same as we are in the “middle class!” It’s only their feelings that they are elite! My Auntie Ligaya in Catarman N. Samar, said those people who claimed that they are wealthy, are not actually wealthy class people before, she compared to my/our society status she said! I quote! “Boy your father has vast landholdings compared to them, they have only fighting spirit (their capitalization is COURAGE “TAPANG”) without giving consideration to other people and without principles and conscience.”

Also some unscrupulous contractors have deceived their works by reducing the cement factors, quantity of materials, used substandard materials to show that they are more clever and have knacks compared to other contractors and engineers. While they are using their influence (on the part of contractors), powers (on the part of politicians) to amass wealth or fortune through kickbacks from supply of goods, infrastructure projects, obviously, these are abuse of power and/or authority and corruptions in government. Lying, deceptions, and corruptions are just normal to them.

Government appointed officials used their positions to get money by demanding percentage as kickbacks, ranging from 1.5% to 10% of the total cost; if papers pass through their hands being one of signatories for the supply of goods and infrastructure projects, this is an obvious red tapes; although Anti-Red tape law (RA 9485) had been enacted into law by congress of the Republic of the Philippines. Law is not deterrence instead law is being used as an instrument in asking many documents before they sign the contracts and documents papers.  

During the time, when I was working in a multi-million projects owned by the government I observed that all signatories personnel assigned in the project had asked percentage from the savings in all item of works that were not put in the project. 

In our town, the engineer embedded in the detailed estimate of the program of works the assistance to the engineer a five (5%) per cent of the project cost.  In my 20 years’ experience as practicing engineer, and having worked with government projects, this assistance to the engineers in general item requirements of the detailed estimates is only applicable to a foreign assisted projects and/or foreign funded projects, e.g. Philippine Japan Highway Loan (PJHL), Philippine Australian Development Assistance Project- Samar Integrated Rural Development Project (PADAP-SIRDP), Help for Catubig Agricultural Advancement Program (HCAAP) to name a few.  Wherein, the consultants for the foreign assisted and/or foreign funded projects should come from the countries (Government of Japan) who grant loans to developing countries like the Philippines and it is being stipulated in the Memorandum of Agreement (MOA). The HCAAP program is being funded by Japan International Cooperation Agency (JICA) to alleviate poverty in the Philippines in my knowledge because I worked in this program, the construction of diversion DAM and Irrigation canals, drainage canals, so I can attest to the fact that there is no assistance to the engineer included in the detailed estimates and program of works..  

Corruptions in government; abuse of authority by those who are in power, abuses and injustices done by few law enforcement authorities and/or people with guns, land grabbing, preponderance of poverty; these are the reasons why many individuals had urged to act for themselves, and had goaded to join the rebel groups like e.g. New People’s Army (NPA), MILF, MNLF these are the groups with ideology. Others became thieves, robbers it’s because of poverty, starvation, lack of basic education. 

Hungry people are now 4.1 million people (20%) of the low income people and/or living below poverty level in the Philippines as per the latest survey by Social Weather Station (SWS). The national government of the Philippines are now very serious to eradicate corruptions in government, but corruptions are deeply rooted in the government because of the main reasons “to get back or recoup all their expenses…” what they have spent in the elections. Politicians (President, Senators, governors, congressmen, Mayors) are spending millions of pesos to buy votes to ensure their victory. 

Few of the government agencies, law enforcement authorities deliberately neglect to act. The reason why they do not act, and why they do not interfere and/or intrude the business of those corrupt officials, grabbers, evildoers, insidious evil, it’s because of the following;  

  1. Fear to people in power;
  2. Fear to get killed and lose their lives;
  3. Fear of losing their jobs;
  4. Fear that they might be charged and be sued for something;
  5. Fear of the threat that he would be transferred to another place of assignment, e.g. Jolo, Basilan, Cotabato, Maguindanao, Mindanao, Leyte; obviously fear of being far from their family;

Hence, what are they going to do? What have they done? They done nothing; they better closed their eyes and become deaf and mute of what they have heard and seen.

Let EVIL ACTS be stopped by witchcraft:

A methodology being suggested by my friend; here it goes: One of the methods to avenge is to ask help from witchery (Mangkukulam…in local Filipino term for witches) to avoid law enforcement authorities and justice. Witch uses doll as a substitute of the person to be made powerless and crippled, instead of the real person. And the witch could do harm the subject person using needle and pierce the doll. In the island of Samar there is/are place having these witch particularly in Eastern Samar, Northern Samar.  I advice her/him, (If I were the witch), that he should pierce the needle in the eyes, in the brain, through the heart, lung and liver of the doll, so that the subject person would be paralyzed swiftly and promptly; or she/he must cut the throat and lower limb of the doll so that he would be (subject person) killed instantly.

To wait for the divine intervention to give justice and punishment to these evildoers in our society:

As Christian we do not wish for the death of the people we felt hatred, we felt dislike, but instead we let God bring punishment for them. When time comes, ailments have affected them we suddenly say “it’s karma because he is bad, greedy, selfish, and envious (AWAON…. in local waray-waray Filipino dialect)…”  Many of us especially those who have money, fortune and power do not believe in karma. Karma a (Buddhism and Hinduism word) belief for punishment after death, the sum total of the acts done in one stage of a person’s existence.  The holy bible says “For the wages of sin is death.”  However, punishment and/or judgment do not come only after death as being said and claim by many of us.  Believe me, my dearest friends out there, punishment would come and beset, even if these people are still alive.  Alive but suffering from sicknesses, ailments like CANCER, LIVER SEROSAES, DIABETES, KIDNEY MALFUNCTION which need DIALYSIS for lifetime and then death comes to them.

Therefore, in my simple sense and discernment, happy are those having fear in God and has observed his commandments. The bible says “Man must live, not on bread alone, but on every word coming forth through God’s mouth, Matthew 4:4.” ” Return evil for evil to no one… book of Romans 12:17″

In my fervent prayer to my God almighty for almost 2 decades (1993 – 2012), from the time I resigned from my work in 1995 until now, I perceived that God has answered most of my prayers to punish those arrogant people who maligned, besmirched and trampled my reputations, dignity, being a simple person, most of them had died already, if DEATH has not come to those persons, his/her husband or wife died and received punishment from God almighty.

I will not name names, only God almighty knows who are these people?