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 (with evidenced of their successful construction of bridges, cathedrals, etc.), 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) in circa 2630 B.C. sometimes is referred to as the world's first Structural Engineer and master builder. The Khufu's pyramid at about circa 2550 B. C., height 147 meters built by Egyptian Hemiunu, Pharaoh khufu's master builder; the largest pyramid ever built, it incorporates about 2.3 millions tone blocks. No doubt the Egyptians and other ancient builders had formulated empirical rules on their previous experience to guide them in planning a new structure, but then again there is NO EVIDENCE that they had developed even the beginnings of a Theory of structural behavior.

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

He profoundly explained this as follows:

Although the Greeks built some magnificent structures, their contributions to structural theory were few and far between. The Secrets of the Parthenon link to youtube

Pythagoras (about 582 -500 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. Archimedes (287-212 B.C.) Greek mathematician developed some fundamental principles of static and introduced the term center of gravity.

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 and aqueducts 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.

Most of the knowledge that the Greeks and Romans accumulated concerning structural engineering was lost during the Middle Ages between A.D. 476 and 1492, and has been recovered only since the Renaissance (beginning of Renaissance period -the fall of Muslim Granada in Spain and the voyage of Christopher Columbus to America).

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. Galileo Galilei (1564-1642) is properly acknowledged to be not only the 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.

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.

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

Andrea Palladio (1518-1580), an Italian architect, is thought to have been the first person to use modern trusses, although his is not rational. He may have revived some ancient types of Roman structures and their empirical rules for proportioning them and probably sized the members by RULES of THUMB, but after his time trusses were forgotten for 200 years, until they were reintroduced by Swiss designer Ulric Grubermann.

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 the father of iron Bridge building in America.

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 Moment-Area theorems in 1873; B.P.E Clapeyron of France for the Three-Moment theorem in 1857.

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).

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, particularly method 2 in ACI 318-1963. In 1921 Westergaard and Slater published the "Moments and Stresses in Slab."

In 1929 H. Marcus a German Engineer developed Method 3 of 1963 ACI Code moment coefficient based on elastic analysis, but also account for inelastic redistribution, and widely used in Europe, it was introduced in the United States by P. Rogers in 1944 (Two -way Reinforced concrete Slab).

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 has stated it eloquently as follows:

While ancient engineers showed some understanding of structural behavior (with evidenced of their successful construction of bridges, cathedrals, etc.), 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) in circa 2630 B.C. sometimes is referred to as the world's first Structural Engineer and master builder. The Khufu's pyramid at about circa 2550 B. C., height 147 meters built by Egyptian Hemiunu, Pharaoh khufu's master builder; the largest pyramid ever built, it incorporates about 2.3 millions tone blocks. No doubt the Egyptians and other ancient builders had formulated empirical rules on their previous experience to guide them in planning a new structure, but then again there is NO EVIDENCE that they had developed even the beginnings of a Theory of structural behavior.

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

He profoundly explained this as follows:

Unfortunately, no plans, no drawings, or no written records regarding the construction of Khufu's pyramid have ever been discovered; It is clear from surviving records and from examination of structures built at Giza and before the Giza pyramids that the ancient Egyptians understood the principles of the lever and inclined plane; calculate the volumes, slopes, and angles, they knew how to survey, that they devised a sound system of measurements based on cubit, a unit of length equal to approximately half a meter; they had no pulleys. Clearly ramps were employed by the pyramids' builders in some fashion. The ramp is constructed by about 158 m against the base of the pyramid and the ramp construction proceeds hand in hand with pyramid construction Dr. Craig 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.

Great Pyramid of Giza (Pharaoh Khufu or Cheops to the Greeks) - circa 2550 B. C. |

Aerial View of the Great Pyramids of Giza -circa 2550 B.C. |

Diagram of Great Pyramid of Giza -Pharaoh Khufu showing the inside view of structure |

First Theory of Ramp Construction, Source: Public Domain via Wikimedia commons |

Second Theory of Ramp Construction, Source: Public Domain via Wikimedia commons |

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. The Secrets of the Parthenon link to youtube

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

Remains of the west gate Roman Forum, Greece Athens - 146 to 12 BC |

Pythagoras (about 582 -500 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. Archimedes (287-212 B.C.) Greek mathematician developed some fundamental principles of static and introduced the term center of gravity.

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 and aqueducts 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.

Most of the knowledge that the Greeks and Romans accumulated concerning structural engineering was lost during the Middle Ages between A.D. 476 and 1492, and has been recovered only since the Renaissance (beginning of Renaissance period -the fall of Muslim Granada in Spain and the voyage of Christopher Columbus to America).

Roman Bridge, 134 AD |

Ponte Pietra Stone Bridge -100 BC |

Roman Bridge -Circa 102-106AD |

Ruin of Roman Bridge, 30 BC - 14AD |

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

Ruins of Roman Bridge -142 BC |

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. Galileo Galilei (1564-1642) is properly acknowledged to be not only the 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.

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.

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

Newton's Law of Universal Gravitation |

Newton developed the Laws of Inertia and Motion which become the fundamental principles used in structural analysis.

- 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 the

- second law...... "the force acting on an object is equal to the mass of the object multiplied by the acceleration", F = m*a ;
- and the third Law of motion; for every action there is an equal and opposite reaction.

Andrea Palladio (1518-1580), an Italian architect, is thought to have been the first person to use modern trusses, although his is not rational. He may have revived some ancient types of Roman structures and their empirical rules for proportioning them and probably sized the members by RULES of THUMB, but after his time trusses were forgotten for 200 years, until they were reintroduced by Swiss designer Ulric Grubermann.

Designed by Andrea Palladio |

Squire Whipple Bridge -Tourist, students on top of bridge |

Squire Whipple's Bridge, Normans kill, Schenectady, NY, USA -1867 |

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 Moment-Area theorems in 1873; B.P.E Clapeyron of France for the Three-Moment theorem in 1857.

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).

Civil Engineer Hardy Cross, P. E. |

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, particularly method 2 in ACI 318-1963. In 1921 Westergaard and Slater published the "Moments and Stresses in Slab."

In 1929 H. Marcus a German Engineer developed Method 3 of 1963 ACI Code moment coefficient based on elastic analysis, but also account for inelastic redistribution, and widely used in Europe, it was introduced in the United States by P. Rogers in 1944 (Two -way Reinforced concrete Slab).

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 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.

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.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

- Member: American Concrete Institute (ACI)
- Member: American Society of Civil Engineers (ASCE)
- Member: Philippine Institute of Civil Engineers (PICE)

**References - All books below are on the shelves in my Personal Library for additional sources of background information**:

- Structural Analysis by Jack C. McCormac and J. K. Nelson Jr., 1997;
- Civil Engineering Magazine of ASCE, Soaring Toward the Heavens (Great Pyramid at Giza) by Craig B. Smith, Ph.D. Volume 74, No. 11, November 2004;
- Design of Concrete Structures by Arthur H. Nilson, 1997;
- Structural Design Data and Specifications by Abelardo B. Carrillo 6th edition -1980;
- Elementary Structural Analysis by C. H. Norris, J. B.Wilbur and S. Utku, 3rd edition -1976;
- Engineering Mechanics by Ferdinand L. Singer, 3rd edition-1975;
- Elementary Theory of Structures by Chu-Kia Wang and Clarence l. Eckel -1957;
- Theory of Plates and Shells by Professor S. Timoshenko and S. Woinowsky-Krieger, 2nd edition -1959;
- Cyclopedia of Civil Engineering -American Technical School by Frederick E. Turneaure, 8 volumes -1928;
- Mechanics' and Engineers' -Mechanics, Mathematics and Physics by Chas H. Haswell, 1079 pages-Seventy Eight Edition-1930;
- Applied Mechanics for Engineers by J. Duncan -1926;
- Applied Mechanics (Strength and Elasticity of Materials, Theory of Structures) by David Allan Low -1909;
- Applied Mechanics (general introduction to the theory of Structures and Machines) by James H. Cotterill, 1st edition -1884, 6th edition -1906;
- Analytical Mechanics for Engineers by Fred B. Seely and Newton E. Ensign -1921;
- Structural Mechanics by Charles E. Greene, 1st, 2nd, 3rd editions-1897 to 1909;
- Graphics for Engineers, Architects, Builders-Trusses and Arches, Part 1, 2 and 3 by Charles E. Greene, 1878;
- An Elementary and Practical Treatise on BRIDGE BUILDING by SQUIRE WHIPPLE, C. E. (Inventor of Whipple Bridge) -2nd edition -1872 and 1873;
- General Theory of BRIDGE CONSTRUCTION by Prof. HERMAN HAUPT, C. E., 1st edition-1851, 1865, 1878;
- A Treatise on BRIDGE Architecture by Thomas Pope -1811;
- Engineering Construction in STEEL and TIMBER by William Henry Warren, 2nd edition -1910;
- The Mathematical Principles of Natural Philosophy by ISAAC NEWTON-Translated into English by Andrew Motte, 1st edition -1846;
- The Mathematical Principles of Natural Philosophy by ISAAC NEWTON-Andrew Motte, volume 2-1803;
- Mechanics of Engineering volume 1, 2 and 3, by Irving P. Church, C.E., 8th edition-1893, 1894, 1895; 9th edition -1905 and 1908 and 1911;
- Mechanics of Engineering volume 2 -(The Stresses in Framed Structures, Strength of Materials and Theory of Flexure), by A. Jay Dubois, C.E., PhD, 1st edition -1902;
- Mechanics of Materials by George Young, Jr. and Hubert E. Baxter -1927;
- Strength of Materials by Arthur Morley, 3rd edition -1913, 4th edition -1916;
- The Elements of Mechanics of Materials by Charles E. Houghton, 1st edition -1909, 2nd edition -1915;
- Mechanics of Materials by Mansfield Merriman, 10th edition -1910, 11th edition -1914 and 1916;
- A text-Book on the Mechanics of Materials (Beams, Columns and Shafts) by Mansfield Merriman, 1st edition -1885, 4th edition -1892, 8th edition -1899, 9th edition -1903;
- A text-Book on Roof and Bridges by Mansfield Merriman and Henry S. Jacoby, Parts 1, 2, 3 and 4, 5th edition -1903;
- The Principles of Mechanics by William Emerson, 3rd edition -1773;
- The Principles of Structural Mechanics by Percy J. Waldram, 1912;
- Mechanics of Building Construction by Henry Adams -1912;
- The first, second, third and fourthbook of Architecture by Andrea Palladio, 1755;
- The elements of Civil Architecture-Andrea Palladio-Vitruvius by Henry Aldrich -1824;
- The Builder's Director or Bench Mate -Andrea Palladio, by Batty Langley, July 14, 1746;
- History of Architectural Development, volumes 1, 2 and 3, by F. M. Simpson -1913;
- Theory of Structures and Strength of Materials by Henry Bovey, 1st edition-1893, second edition-1896, 884 pages-3rd edition-1900;
- The Theory of Structures by Charles M. Spofford-1911;
- Theory of Structures by Arthur Morley 5th edition -1912;
- The Elements of Structures by George A. Hool, 1st edition-1912;
- Bridge and Structural Design by W. Chase Thompson -1905;
- Practical Structural Design by Ernest McCullough, 2nd edition -1921;
- Manual of Structural Design by Jack Singleton, 3rd edition -1947;
- Principles of Structural Engineering C. K. Smoley -1928
- Structural Designer's Handbook by William Fry Scott -1904;
- Structural Design by Horace R. Thayer, volume 1-1912;
- Structural Engineers' Handbook: Data for the Design and Construction of Steel Bridges and Buildings by Milo S. Ketchum, 1st edition -1914; 2nd edition -1918, 3rd edition -1924;
- Specification Standards by John Ostrup-1910;
- Structural Engineering by A. W. Brightmore -1908;
- Structural Engineering by J. Husband and W. Harby-1911;
- Structural Engineering by John Edward Kirkham, 1st edition-1914;
- Structural Engineering -Steel Designing, Book 3, by Edward Godfrey -1913;
- Structural Engineering -Strength of Materials by George F. Swain, volume 1, 1st edition-1924;
- Structural Engineering -Fundamental Properties of Materials by George F. Swain, volume 2,1st edition-1924;
- Structural Engineering -Stresses, Graphical Statics and Masonry by George F. Swain, volume 3-1924;

- Library of Congress,
- Squire Whipple,
- Squire Whipple's link,
- Isaac Newton biography,
- Philippine Earthquake and Tsunami,
- Smeatonian Society,
- Dr. Hawass, the Secret Doors Inside the Great Pyramid
- Egypt the Pyramids of Giza,
- The Pyramids,
- AncientWorldWonders,
- The Pyramids of Giza.
- The Great Pyramid of Khufu
- The Guardians