弯曲内力doulan.pptVIP

4-6　刚架和曲杆的内力图及叠加法 刚架和曲杆可看作折线或曲线的梁，内力的计算和剪力 弯矩图的作法原理上与横梁相同。剪力的正负仍以外法线为 基准判断，弯矩图画在受压一侧。 例4-5 作下列刚架和曲杆的内力图 F a a 2a A B C D 解：支反力 M图 N图 + - Q图 + - RA y RB y RA x R F － Q图 F ＋ M图 FR ＋ N图 F N M Q F 作业 4-2（f, i） 4-3（d, e） * * Section 4 Internal Forces for Bend on Beam 4 -1 Background of Engineering Character of loading：direction of forces and couples is perpendicular to the axis of the beam. Character of drformation ：The axis-line of beam becomes to curve. Bended menbers are called beam. M M F RA RB Planar constructure 3 unknown constrained reactions can be found from statics equations. Overhanging beam Simple supported beam Types of loadoings 3 equilibium equations Multi-span continued beam 3 basic types of statically determinate beam Concentrated forces Concentrated couples distributing forces Cantalever beam 4-2 Internal forces of beam and the Sign Convention Shear force perpandicular to normal of section equal magnitude , directe toward opposition, the same deformations Bending moment direction perpandicular to normal of section x l F x n’ Q’ M’ R m Q M n F x Q = F M = Fx Q = Q? M = M? Planar constructure The sign convention： The direction of out-normal clockwise rotated 90? is the positive shear forces; The positive ben- ding moment causes the compression at the top of horizontal beam．． The functions of shear and moment Q = Q ( x )，M = M ( x ) Exam 4.1 Determine the fuctions of shear and moment and drawing shear and moment diagrams of the beam shown. Q(x) M(x) x n q l Q M 4-3 The equations of Shear and Bending Moment and Diagrams of Shear and Bending Moment Solution: Draw the free segment diagram Write the equilibium equations Draw shear and moment diagram Q(x) M(x) x n M q l RA RB Q Solution: Find supported reactions RA RB F Q M Q(x’) M(x’) n’ RB Q(x) M(x) x n RA Q(x) M(x) F RA n Solution: Find supported reactions Loading zone Q M m RA RB Q(x) M(x) x n RA Q(x) M(x) m RA n Solution: Find supporte