Galile0 Galilei (1564-1642): Fracture occurs at the point B, serving as thefulcrum for the lever BC: The resistance (stress) is uniformlydistributed along AB.. Predicted a value three times larger than thecorrect resisting moment at the built-in. Thesame is true for the breaking load at C. For beams with b>h. the ratio b:h holdsbetween breaking loads along breadth anddepth.. The bending moment at the built-in, due togravity, increases as the square of beam(6)(c)(a)length.. The resisting moment increases as the cubeof the radius of a circular beam16
16 • Fracture occurs at the point B, serving as the fulcrum for the lever BC. • The resistance (stress) is uniformly distributed along AB. • Predicted a value three times larger than the correct resisting moment at the built-in. The same is true for the breaking load at C. • For beams with b>h, the ratio b:h holds between breaking loads along breadth and depth. • The bending moment at the built-in, due to gravity, increases as the square of beam length. • The resisting moment increases as the cube of the radius of a circular beam. Galileo Galilei (1564-1642)
Galile0 Galilei (1564-1642) End-supported beams are mostsensitive to loads applied at themiddle of the span; Bendingmoment is proportional to ab: Thecross-sections near supports can bereasonably reduced Gave a complete derivation of acantilever beam of equal strength:五EEC:AC-(EF)2 :(AB) 2(b)(a): Hollow beams are employed in artand still more often in nature (bonesofbirds, stems of straw
• End-supported beams are most sensitive to loads applied at the middle of the span; Bending moment is proportional to ab; The cross-sections near supports can be reasonably reduced. • Gave a complete derivation of a cantilever beam of equal strength: EC:AC=(EF) 2 :(AB) 2 • Hollow beams are employed in art and still more often in nature (bones of birds, stems of straw.) Galileo Galilei (1564-1642)
Robert Hooke (1635-1703)·English mechanic and experimenterROBERTHOOK70. Thought that light was composed of waves.: Contemporary and frequent adversary ofNewton.·First to study solids microscopically.《显微术》，1665.. First to study the elastic properties of materials.foundation of further developments ofmechanics of elastic bodies: Considered the deformation of longitudinalfibers of beams: the fibers on the convex(concave) side are extended (compressed)during bending.18
18 Robert Hooke (1635-1703) • English mechanic and experimenter • Thought that light was composed of waves. • Contemporary and frequent adversary of Newton. • First to study solids microscopically.《显微 术》，1665. • First to study the elastic properties of materials, foundation of further developments of mechanics of elastic bodies. • Considered the deformation of longitudinal fibers of beams: the fibers on the convex (concave) side are extended (compressed) during bending