赵州桥，600A.D.，隋朝·横跨河北省赵县液河，由著名匠师李春设计和建造。? Small circular arc (84°)? Reduced building materials. Water currents not disturbed bybridge supports? Bridge abutments protected? Preserving the water channel: 45°span angle from abutmentsdistributes load vertically andhorizontally11
赵 州 桥 ，600 A.D.，隋朝 11 •横跨河北省赵县洨河，由著名 匠师李春设计和建造。 • Small circular arc (84 ° ) • Reduced building materials • Water currents not disturbed by bridge supports • Bridge abutments protected • Preserving the water channel • 45°span angle from abutments distributes load vertically and horizontally
The Middle Ages. “Most of the knowledge that Greeks and Romansaccumulated in the way of structural engineering waslost during the Middle Ages and only since theRenaissance has it been recovered.: Fortunately, Arabians served as the knowledge keeper.Europe-Middle AgesFEUDALISMKingClergyNoblesLordsKnightsVassalsPeasantsSerfs12
• “Most of the knowledge that Greeks and Romans accumulated in the way of structural engineering was lost during the Middle Ages and only since the Renaissance has it been recovered.” • Fortunately, Arabians served as the knowledge keeper. 12 The Middle Ages
Le0nardo da Vinci (1452-1519). Italian artist and scientist: A true Renaissance man who studiedarchitecture, astronomy and anatomy.. Conducted tensile tests on wires andrelated the measured displacement tothe wire strength.: Attempted to analyze columns,beams, and trusses“Mechanics is the paradise ofOQmathematical science because herewe come to the fruits of mathematics.13
13 Leonardo da Vinci (1452-1519) • Italian artist and scientist. • A true Renaissance man who studied architecture, astronomy and anatomy. • Conducted tensile tests on wires and related the measured displacement to the wire strength. • Attempted to analyze columns , beams, and trusses. • “Mechanics is the paradise of mathematical science because here we come to the fruits of mathematics
Leonardo da Vinci (1452-1519)? Load-carrying ability of columns:linearly proportional to diameter butinversely proportional to length. Load-carrying ability of beams:> Varying inversely as length and directly as widthfor both end-supported and cantilever beams.> The part that is farthest from the two supports willbend the most.> The effect of beam depth was not discussed: These important results were unfortunately buried inda Vinci's notes. Engineers of the 15th and 16thcenturies still relied on experience and judgment14
14 • Load-carrying ability of columns: linearly proportional to diameter but inversely proportional to length. • Load-carrying ability of beams: Varying inversely as length and directly as width for both end-supported and cantilever beams. The part that is farthest from the two supports will bend the most. The effect of beam depth was not discussed. Leonardo da Vinci (1452-1519) • These important results were unfortunately buried in da Vinci’s notes. Engineers of the 15th and 16th centuries still relied on experience and judgment
Galile0 Galilei (1564-1642)· Another true Renaissance man whois most known for his work indynamics and astronomy.· Performed the leaning Tower of Pisaexperiment in (1589).· “Two New Sciences" (1638)DISCORSIrepresents the beginning of theDIMOSTRAZIONIMATEMATICHEscience of strength of materialsintornod duenone fCienztAttenenti allMECANICA&IMOVIMENTI LOCALI,delSigma. Studied the tensile strength of bars.GALILEO GALILEILINCEO,FilofofoeMatdel SerenilinGrand Duca di Tofcanand found that this strength (absoluteAppemdicrdelemrdigraitidalcemisalidiRresistance to fracture) is proportionalto cross-sectional area, butindependent of lengthINLEIDAApprello gliEllfeviri, M. D, c, xx15
15 Galileo Galilei (1564 -1642) • Another true Renaissance man who is most known for his work in dynamics and astronomy. • Performed the leaning Tower of Pisa experiment in (1589). • “Two New Sciences” (1638) represents the beginning of the science of strength of materials . • Studied the tensile strength of bars, and found that this strength (absolute resistance to fracture) is proportional to cross -sectional area, but independent of length