压杆稳定(BucklingofColumns)$9-2P两端绞支细长压杆的临界压力(The Critical Load for a straight, uniformaxially loaded, pin-ended columns)xFM(x)=-FwmmmmWXXBIB
(Buckling of Columns) §9-2 两端绞支细长压杆的临界压力 (The Critical Load for a straight, uniform, axially loaded, pin-ended columns) m m F m x m w B x y l M(x)=-Fw F x y B
压杆稳定(Bucklingof Columns压杆任一x截面沿y方向的位移w=f(x）该截面的弯矩M(x) =-Fw杆的挠曲线近似微分方程FElw"= M(x)=-Fw (a)M(x)=-FwmmFk2-x今yBIEI得w"+kw=0(b)(b)式的通解为w=Asinkx+Bcoskx(c)（A、B为积分常数）
(Buckling of Columns) 该截面的弯矩 杆的挠曲线近似微分方程 压杆任一 x 截面沿 y 方向的位移 w = f (x) M(x) = −Fw EIw = M(x) = −Fw '' （a) 令 EI F k = 2 (b)式的通解为 w = Asinkx + Bcoskx (c) （A、B为积分常数） 0 '' 2 得 w + k w = (b) m m x y B F M(x)=-Fw
压杆稳定(Buckling of Columns)边界条件W=0x=0,PW=0x=l,由公式(c)Asin0+Bcos0=0B=0mm=0wAsinkl=0xBsinkl=01讨论：若A=0,W=0则必须sinkl=0kl=n元(n=0,1,2,.)
(Buckling of Columns) 边界条件 由公式(c) 讨论： x = 0, w = 0 x = l, w = 0 Asin0 + Bcos0 = 0 → B = 0 Asinkl = 0 A = 0 sin kl = 0 若 A = 0,w 0 m x m w B x y l F 则必须 sin kl = 0 kl = nπ(n = 0,1,2, )
压杆稳定(Buckling of Columns)Fkl = n元(n = 0,1,2,...)EIPn元EIF(n= 0,1,2,...)1?元EIF令n=1得cr12mm这就是两端铰支等截面细长受压直杆临wx界力的计算公式（欧拉公式）：BV08sinkx挠曲线方程为W=klsin2元X当kl=元时，w=Ssin曲线为半波正弦曲线7
(Buckling of Columns) 这就是两端铰支等截面细长受压直杆临 界力的计算公式（欧拉公式）. π( 0,1,2, ) 2 = kl = n n = EI F k ( 0,1,2, ) π 2 2 2 = n = l n EI F 令 n = 1, 得 = 2 cr 2 EI F l 当kl = π 时， kx kl w sin 2 sin 挠曲线方程为 = 挠曲线为半波正弦曲线. m x m w B x y l F l x w π = sin
压杆稳定(Buckling of Columns作业：习题9-2/4/9
(Buckling of Columns) 作业：习题9-2/4/9