DEFORMATIONOF BEAMS DUE TO BENDING 3 Determine the integral constants by boundary conditions E/(0)=Pa3+C2=0 P 6 EO(0)=-Pa2+C1=0 2 (a)=6(a):C1=D1 f(a=f(a) Ca+C2=Da+D CI=D=Pa: c2=D2===Pa 2 6
Determine the integral constants by boundary conditions 0 6 1 (0) 2 3 EIf = Pa +C = 0 2 1 (0) 1 2 EI = − Pa +C = 3 2 2 2 1 1 6 1 ; 2 1 C = D = Pa C = D = − Pa ( ) ( ) − + f a = f a ( ) ( ) − + a = a C1 = D1 C1 a +C2 = D1 a + D2 P L a x f
应用位移边界条件求积分常数 EJ(0)=:Pa+C2=0 6 E/6(0=-Pa2+C1=0 2 f (a)=6(a):C1=D1 f(a=f(a) Ca+C2=Da+D C=D2aC2≈D1 Pa 6
应用位移边界条件求积分常数 0 6 1 (0) 2 3 EIf = Pa +C = 0 2 1 (0) 1 2 EI = − Pa +C = 3 2 2 2 1 1 6 1 ; 2 1 C = D = Pa C = D = − Pa ( ) ( ) − + f a = f a ( ) ( ) − + a = a C1 = D1 C1 a +C2 = D1 a + D2 P L a x f
DEFORMATIONOF BEAMS DUE TO BENDING 4 Write out the equation of the elastic curve and plot its curve P 6FL(a-x)+3afx-a (0≤x≤a) f(x)= P a=a' (a≤x≤L) 6El s The maximum deflection and the maximum angle of rotation P Pa n=(a)= max 2EⅠ x f=f(1)=[3L-a 6EⅠ
Write out the equation of the elastic curve and plot its curve 3 2 3 2 3 ( ) 3 (0 ) 6 ( ) 3 (a ) 6 P a x a x a x a EI f x P a x a x L EI − + − = − L a EI Pa f = f L = 3 − 6 ( ) 2 max EI Pa a 2 ( ) 2 max = = The maximum deflection and the maximum angle of rotation P L a x f
④写出弹性曲线方程并画出曲线 P a=x)+3a x-a (0≤x≤a) f()-6EI P Bax-a (a≤x≤L) 6El ⑤最大挠度及最大转角 P Pa mx=6(a)= 2EⅠ x f=f(1)=[3L-a 6EⅠ
写出弹性曲线方程并画出曲线 − − + − = 3 (a ) 6 ( ) 3 (0 ) 6 ( ) 2 3 3 2 3 a x a x L EI P a x a x a x a EI P f x L a EI Pa f = f L = 3 − 6 ( ) 2 max EI Pa a 2 ( ) 2 max = = 最大挠度及最大转角 P L a x f
DEFORMATIONOF BEAMS DUE TO BENDING 86-3 METHOD OF CONJUGATE BEAM TO DETERMINE THE DEFLECTION AND THE ROTATIONAL ANGLE OF THE BEAM I Usage of the method: Determine the deflection and the rotational angle of the designated point in the beam 2> Theoretical basis of the method Similar analogy Differential equation of the deflection curve of the beam E"(x)=-M(x) Relation between the external load the M"(x)=q(x) internal force
§6-3 METHOD OF CONJUGATE BEAM TO DETERMINE THE DEFLECTION AND THE ROTATIONAL ANGLE OF THE BEAM EIf (x) = −M(x) 1、Usage of the method：Determine the deflection and the rotational angle of the designated point in the beam 2、Theoretical basis of the method：Similar analogy: M(x) = q(x) Differential equation of the deflection curve of the beam: Relation between the external load the internal force: