Presentation on theme: "Strength of Materials I EGCE201 กำลังวัสดุ 1"— Presentation transcript:
1 Strength of Materials I EGCE201 กำลังวัสดุ 1 Instructor: ดร.วรรณสิริ พันธ์อุไร (อ.ปู)ห้องทำงาน: 6391 ภาควิชาวิศวกรรมโยธาโทรศัพท์: 66(0) ต่อ 6391
2 Symmetric Bending of Beams A beam is any long structural member on which loads act perpendicular to the longitudinal axis.Learning objectivesUnderstand the theory, its limitation and its applications for strength based design and analysis of symmetric bending of beams.Develop the discipline to visualize the normal and shear stresses in symmetric bending of beams.
4 Deformation of symmetric member Under action of M and M’, the member will bend but will remain symmetric with respect to the plane containing the couples.except
5 compressed (compression) elongated (tension) There exists a surface // to the upper and lower faces of the member(see as a line on the cross-section) where no elongation and the bendingnormal stress is zero. This surface is called the neutral axis.
6 The length of arc DE for both deformed and undeformed L = rqConsider an arc some distance y above the neutral surfaceThe length of arc JK can be expressed asL’ = (r- y)q
7 The deformation d of JKd = L’-L = (r- y)q - rq = - yqThe normal strain is max when y is the largest
18 Member of several materials Assume a bar is made of two different materials bonded together. The bar will deform as previously shown.The normal strain in x direction will vary linearly with distance from the N.A.
26 Beams bending analysis Beams carry loads perpendicular to their longitudinal axis.Internal shear forces andbending moments developalong the span of a beam.In designing a beam, it is critical to determine the internalshear force (V) and bending moment distribution (M). Thisis accomplished by constructing shear and bending momentdiagrams.
27 Steps in constructing a V and M diagram In general, the load distribution across the width of thebeam is assumed to be applied uniformly. Therefore,a beam can be analyzed in 2 dimensions rather than 3.1. Determine the reactions at each support.