Chapt 5 Stress due o bending5章受力弯曲.pptVIP

????? ????? Chapt 5. Stress due to bending ????? ????? 5.1 introduction Stress distribution the resultant what about bending? 5.2 Geometry of deformation Considering a straight beam with the sym. cross-section of homogeneous material under pure bending 5.3 stress distribution equil. requirements For a line element // the long. axis, using Hooke’s law like a tensile bar ? comp. for ?y tension for y requirements are Ex 5.2) Ex 5.3) (a) 5.4 stress in symmetric elastic beams with variable bending moment Even for non-pure bending , (?1)~(?3) are still good approx. for slender sym. beams Ex 5.4) ?) Ex 5.5) Ex 5.6) Ex 5.7) Ex 5.8) Ex 5.9) ?section modulus For given load, we can select the cross section on the basis of S Ex 5.10) 5.6 Shear stress distribution in symmetric beams with variable bending moment variable M ? shear force ? shear stress on the section cf) normal stress given by (?3) Ex 5.12) P=1500lb ?? B? ???? ?? ??? shear stress?(neglect the weight) Ex 5.13) Ex 5.14) ?circular cross- section Assuming uniform distribution through b Ex 5.15) ?for beams of arbitrary cross-section 5.6 Built-up beams Ex) Ex 5.16) Ex 5.17) Ex 5.16)? ?? ?? Ex 5.18) ?) ?? t=50mm? ?? using MOMENT OF INERTIA Using BENDING OF BEAMS(see Fig. 5.23 24) ? M=-173.1KNm at x=10m M=97.38KNm at x=3.75m If t=70mm max. compressive max. tensile a= b= ?) FBD R ???? (?3) dependent on geometry only ?) Not good! OK Moment force equil. ? Fig 5.32 ? Fig 5.33 ?? For A1 For total A -(?4) In a case of a rectangular beam (?4)? ??? ?? ???? 3/2? At the neutral surface ?) “V? ?? ??” ??? ?? ?? ??? ?? oak ?) 15 6 ?) Slenderness 1/10 A ?? ?? But you must consider the free surface-effect! for a thin hollow shaft For the same material length,weight Ex) I-beam * Geometry of deform. ?strain?stress Radius of curvature -(?1) Sym. of ABED BCFE ?plane surfaces long. axis remai