东南大学：《建筑力学 Architectural Mechanics》课程教学课件（英文讲稿）A08 Introduction to MoM

Introductionmi@see.cn

Introduction mi@seu.edu.cn

Contents·ABriefHistory（学科简史）·ContentDescription（课程描述）·ClassificationofSolidBodies（固体的分类）·StructuresComposedofPrismaticBars（杆系结构）·Loads（荷载）·RestraintsandReactions（约束与支反力）Spacevs.Free-bodyDiagram（真实系统与受力简图）·AssumptionsofStrengthofMaterials（材料力学基本假设）·GeometricCharacteristicsofPrismaticBars（杆件的几何特征）·FormsofDeformationofPrismaticBars（杆件基本变形形式）·RequirementsofaStructuralElement（构件基本要求）·Fatigue（疲劳）·CourseObjectives（课程目标）·Topics Covered（主要议题）2

Contents • A Brief History（学科简史） • Content Description（课程描述） • Classification of Solid Bodies（固体的分类） • Structures Composed of Prismatic Bars（杆系结构） • Loads（荷载） • Restraints and Reactions（约束与支反力） • Space vs. Free-body Diagram（真实系统与受力简图） • Assumptions of Strength of Materials（材料力学基本假设） • Geometric Characteristics of Prismatic Bars（杆件的几何特征） • Forms of Deformation of Prismatic Bars（杆件基本变形形式） • Requirements of a Structural Element（构件基本要求） • Fatigue（疲劳） • Course Objectives（课程目标） • Topics Covered（主要议题） 2

History of Strength of Materials‘From the earliest times when people started tobuild, it was found necessary to have informationregarding the strength of structural materials sothat rules for determining safe dimensions ofmembers could be drawn up.HISTORYOFSTRENGTHOFMATERIALSSTEPHENPTIMOSHENKO3

“From the earliest times when people started to build, it was found necessary to have information regarding the strength of structural materials so that rules for determining safe dimensions of members could be drawn up.” 3 History of Strength of Materials

Old Kingdom of EgyptPyramids at Giza, Egypt ~ 2500 B. C.4

Old Kingdom of Egypt Pyramids at Giza, Egypt ~ 2500 B. C. 4

Technology of Ancient Egypt? Solar Calendar: Accurate Surveying Techniques: Mathematics and Spatial Concepts:Volumes (truncated pyramid),Slopes, Angles, Weight of Stones(Density), Multiplication &Division, Decimal System, π→3.16. Simple Machines: Lever, Inclinedplane, Leveling with water, Nopulleys, No wheeled carts, Verylittle timber5

• Solar Calendar • Accurate Surveying Techniques • Mathematics and Spatial Concepts: Volumes (truncated pyramid), Slopes, Angles, Weight of Stones (Density), Multiplication & Division, Decimal System, π→3.16 • Simple Machines: Lever, Inclined plane, Leveling with water, No pulleys, No wheeled carts, Very little timber 5 Technology of Ancient Egypt

Progression of Pyramid DesignStep PyramidBent PyramidKhufu's Pyramid: 147m in height, 51.90.Built in stages,. Poor foundation,subsidenceexpanded later: Granite beamsInward leaningblocks.Internal structural: Facing stones fittedcollapse·Graniteroofbeamwith a tolerance of less· Below ground chambers · Reduced angle by 10°than 1 mm: Stress relieving: Corbelled ceilingschambers6

Step Pyramid 6 Progression of Pyramid Design • Built in stages, expanded later • Inward leaning blocks • Granite roof beam • Below ground chambers Bent Pyramid • Poor foundation, subsidence • Internal structural collapse • Reduced angle by 10° • Corbelled ceilings • 147 m in height, 51.90 , • Granite beams • Facing stones fitted with a tolerance of less than 1 mm • Stress relieving chambers Khufu’s Pyramid

Lessons Learned by Trial and Error? Site must be solid rock (no shifting sand): Foundation must be strong enough to support thestructure above it, but not be crushed or dislodged: Precise Measurements: to maintain shape and verticalplumb: Masonry Courses: placed horizontally to distribute loads. Strength of Materials Knowledge: Limestone vs. Granite> Limestone: readily available, soft - easy to work with, cut byhand, limited strength ( Granite: used for large beams in interior chambers because ofits superior strength7

Lessons Learned by Trial and Error • Site must be solid rock (no shifting sand) • Foundation must be strong enough to support the structure above it, but not be crushed or dislodged. • Precise Measurements: to maintain shape and vertical plumb • Masonry Courses: placed horizontally to distribute loads • Strength of Materials Knowledge: Limestone vs. Granite  Limestone: readily available, soft – easy to work with, cut by hand, limited strength (< 3 m beams)  Granite: used for large beams in interior chambers because of its superior strength 7

Archimedes (287-212 BC)·唯一与现代科学相通的天才. The Law ofLever: “Magnitudes are in equilibriumat distances reciprocally proportional to theirweights." Said to have discovered Archimedes'principle"while bathing and subsequently ran naked throughthe streets of Syracuse shouting ‘Eureka!"EUREKAI8

8 • 唯一与现代科学相通的天才 • The Law of Lever: “Magnitudes are in equilibrium at distances reciprocally proportional to their weights.” • Said to have discovered “Archimedes’ principle” while bathing and subsequently ran naked through the streets of Syracuse shouting “Eureka!”. Archimedes (287-212 BC)

Archimedes (287-212 BC): Most known for geometric proofs andmay have invented calculus: Invented the pulley, screw, and catapult;definedthe law oflevers. Outlined methods for finding the center ofArchimedes portrait ingravity of bodies.Fields Medal0SunMirrotArchimedesHeatMirrorRayMirrorArchimedes'Heat Ray“On the Sphere &Cylinder""Archimedes'Screw

Archimedes (287-212 BC) “On the Sphere & Cylinder” Archimedes’ Screw Archimedes’ Heat Ray Archimedes portrait in Fields Medal • Most known for geometric proofs and may have invented calculus. • Invented the pulley, screw, and catapult; defined the law of levers. • Outlined methods for finding the center of gravity of bodies

Roman Empire. Archimedes killed by Romansoldiers while doing research. The Romans did not understandstrength of materials, so theybuilt semi-circular arches ofsmall span.· E is “Flexural Rigidity":Romans used large E and I.. Modern materials: when E islarge I does not have to be large10

Roman Empire 10 • Archimedes killed by Roman soldiers while doing research. • The Romans did not understand strength of materials, so they built semi-circular arches of small span. • EI is “Flexural Rigidity”: Romans used large E and I. • Modern materials: when E is large I does not have to be large