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单击此处编辑母版标题样式,*,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,材料力学,习题解答,(,六,),P86,46,-,1,F,C,F,B,l,C,A,0.5,l,B,M,x,=,F,C,F,B,=,m,= 0,l,M,M,(,x,),=,(,l,-,x,),l,M,弯矩方程,挠曲线近似微分方程,EI,=,(,x,-,l,),d,x,2,d,2,y,l,M,积分,EI,q,=,(,x,-,l,),2,+,C,2,l,M,EIy,=,(,x,-,l,),3,+,C,x,+,D,6,l,M,边界条件,x,= 0,y,= 0,：,x,=,l,y,= 0,：,D,=,Ml,2,6,1,挠曲线方程,y,(,x,),=,(,x,-,l,),3,-,l,2,x,+,l,3,6,EIl,M,转角方程,q,(,x,),=,3,(,x,-,l,),2,-,l,2,6,EIl,M,A,处挠度,y,A,=,16,EI,Ml,2,x,=,：,2,l,B,处转角,x,=,l,：,q,B,=,-,6,EI,Ml,y,max,3,1,x,=,(,1,-,),l,讨论：,q,= 0,：,令,y,max,=,9,EI,Ml,2,3,0.0625,0.06415,误差,2.6,C,=,-,Ml,6,1,3,l,1,-,积分法,坐标,P86,46,-,2,(,b,),A,C,a,M,B,l,x,弯矩方程,AC,BC,M,1,(,x,),=,-,M,M,2,(,x,),=,0,挠曲线近似微分方程,EI,=,M,d,x,2,d,2,y,1,EI,=,0,d,x,2,d,2,y,2,EI,=,Mx,+,C,1,d,x,d,y,1,EI,=,C,2,d,x,d,y,2,AC,BC,EIy,1,=,Mx,2,+,C,1,x,+,D,1,2,1,EIy,2,=,C,2,x,+,D,2,边界条件,x,= 0,q,1,= 0,：,C,1,=,0,x,= 0,y,1,= 0,：,D,1,=,0,q,2,(,x,),=,EI,Ma,2,EI,Ma,y,2,(,x,),=,(,2,x,-,a,),连续条件,=,q,C,=,y,C,x,=,a,q,2,=,q,1,x,=,a,y,2,=,y,1,=,EI,Ma,2,EI,Ma,2,=,C,2,=,Ma,D,2,=,-,Ma,2,2,1,q,B,=,EI,Ma,2,EI,Ma,y,B,=,(,2,l,-,a,),积分,q,1,(,x,),=,EI,Mx,2,EI,Mx,2,y,1,(,x,),=,P87,46,-,4,F,A,a,A,C,a,F,B,D,B,a,q,x,F,A,=,qa,F,B,=,qa,m,A,= 0,F,y,= 0,4,3,4,9,弯矩方程,AB,BC,M,1,(,x,),=,qax,-,qx,2,2,1,4,3,M,2,(,x,),=,-,(,3,a,-,x,),2,2,q,挠曲线近似微分方程,EI,=,qx,2,-,qax,d,x,2,d,2,y,1,2,1,4,3,EI,=,(,3,a,-,x,),2,d,x,2,d,2,y,2,2,q,EI,=,qx,3,-,qax,2,+,C,1,d,x,d,y,1,6,1,8,3,EI,=,-,(,3,a,-,x,),3,+,C,2,d,x,d,y,2,6,q,EIy,1,=,qx,4,-,qax,3,+,C,1,x,+,D,1,24,1,24,3,EIy,2,=,(,3,a,-,x,),4,+,C,2,x,+,D,2,24,q,边界条件,x,= 0,y,1,= 0,：,D,1,=,0,x,=2,a,y,1,= 0,：,q,1,(,x,),=,(,4,x,3,-,9,ax,2,+,4,a,3,),24,EI,q,24,EI,q,y,1,(,x,),=,(,x,4,-,3,ax,3,+,4,a,3,x,),连续条件,=,q,B,x,=2a,q,2,=,q,1,x,=2a,y,2,=,y,B,=,0,：,=,0,：,C,2,=,qa,3,6,1,D,2,=,-,qa,4,8,3,q,2,(,x,),=,a,3,-,(,3,a,-,x,),3,6,EI,q,24,EI,q,y,2,(,x,),=,(,3,a,-,x,),4,+,4,a,3,x,-,9,a,4,C,1,=,6,qa,3,q,A,=,6,EI,qa,3,12,EI,qa,4,y,D,=,q,B,=,0,8,EI,qa,4,y,C,=,P88,47,-,1,(,b,),B,M,(,qa,2,),C,F,(,qa,),q,A,a,a,P224,表,19,-,1,序号,1,2,EI,M,(,2,a,),2,y,CM,=,-,q,CM,=,-,EI,M,(,2,a,),EI,2,qa,4,=,-,=,-,EI,2,qa,3,P224,表,19,-,1,序号,3,6,EI,5,qa,4,=,=,2,EI,qa,3,y,CF,=,y,BF,+,q,BF,a,q,CF,=,q,BF,=,2,EI,Fa,2,3,EI,Fa,3,=,+,q,BF,a,P224,表,19,-,1,序号,5,24,EI,7,qa,4,=,y,Cq,=,y,Bq,+,q,Bq,a,q,Cq,=,q,Bq,=,6,EI,qa,3,8,EI,qa,4,=,+,q,Bq,a,y,C,=,y,CM,+,y,CF,+,y,Cq,q,C,=,q,CM,+,q,CF,+,q,Cq,8,EI,7,qa,4,=,-,3,EI,4,qa,3,=,-,P88,47,-,2,(,a,),A,C,0.5,l,B,0.5,l,M,(,F,l,),F,P225,表,19,-,1,序号,8,y,CM,=,0,q,AM,=,-,24,EI,Ml,P225,表,19,-,1,序号,9,48,EI,Fl,3,y,CF,=,q,AF,=,16,EI,Fl,2,y,C,=,y,CM,+,y,CF,q,A,=,q,AM,+,q,AF,=,q,BM,=,-,q,BF,48,EI,5,Fl,2,=,-,q,B,=,q,BM,+,q,BF,48,EI,Fl,2,=,48,EI,Fl,3,=,=,-,24,EI,Fl,2,F,P89,47,-,3,(,c,),A,B,C,q,F,(,qa,),a,a,P225,表,19,-,1,序号,11,y,Cq,=,q,Bq,a,q,Cq,=,q,Bq,P226,表,19,-,1,序号,12,3,EI,2,qa,4,y,CF,=,q,CF,=,6,EI,5,qa,3,y,C,=,y,Cq,+,y,CF,q,C,=,q,Cq,+,q,CF,24,EI,qa,3,=,-,24,EI,19,qa,3,=,8,EI,5,qa,4,=,=,-,24,EI,qa,4,P90,48,-,1,A,B,l,q,b,h,1,2,ql,2,M,图,M,max,1,2,= ql,2,= 45 kN,m,W,z,=,6,bh,2,=,12,h,3,s,max,=,W,z,M,max,s,= 16.5 cm,h,3,s,12,M,max,I,=,12,bh,3,=,24,h,4,y,max,=,8,EI,ql,4,查表：,=,8,EI,ql,3,y,max,l,f,l,= 17.8 cm,h,4,E,3,ql,3,f,l,取,b,=,8.9 cm,其中,：,h,=,17.8 cm,变形协调条件,：,变形几何方程,：,P91,48,-,3,A,C,B,q,l,l,F,A,F,B,F,C,5,8,ql,3,8,ql,F,S,图,5,8,ql,3,8,ql,1,8,ql,2,16,1,ql,2,M,图,9,128,ql,2,F,C,静定基,y,CF,=,-,48,EI,F,C,(,2,l,),3,查表：,补充方程：,多余约束力,：,y,C,= 0,y,Cq,=,384,EI,5,q,(,2,l,),4,48,EI,F,C,(,2,l,),3,-,= 0,384,EI,5,q,(,2,l,),4,F,C,=,ql,5,4,平衡：,F,A,=,F,B,=,ql,3,8,y,Cq,+,y,CF,= 0,（,简便方法,）,P92,49,-,1,3,T,0,2,T,0,T,0,F,F,T,0,T,0,F,t,max,=,W,P,M,n,s,s,=,A,F,M,n,=,2,T,0,W,P,=,16,p,d,3,M,n,=,T,0,W,P,=,16,p,d,3,t,max,=,W,P,M,n,s,=,A,F,N,t,s,B,t,A,C,C,B,A,F,N,=,F,危险截面,(,内力分布,),危险点,(,应力分布,),横截面位置,应力方向,P92,49,-,2,(,a,),30,50 MPa,20 MPa,30 MPa,s,x,=,30 MPa,s,y,=,50 MPa,t,x,=,-,20 MPa,a,=,30,2,s,x,+,s,y,s,a,=,+,cos2,a,t,x,sin2,a,2,s,x,-,s,y,t,a,=,sin2,a,+,t,x,cos,2,a,2,s,x,-,s,y,=,52.32 MPa,=,-,18.66 MPa,18.66,52.32,应力表示,(,方向 数值,),P92,49,-,2,(,b,),30,20 MPa,40 MPa,s,x,=,-,40 MPa,s,y,=,0,t,x,=,20 MPa,a,=,60,2,s,x,+,s,y,s,a,=,+,cos2,a,t,x,sin2,a,2,s,x,-,s,y,t,a,=,sin2,a,+,t,x,cos,2,a,2,s,x,-,s,y,=,-,27.32 MPa,=,-,27.32 MPa,27.32,27.32,P93,49,-,3,(,a,),30,20 MPa,50 MPa,s,x,=,50 MPa,s,y,=,0,t,x,=,-,20 MPa,a,=,30,2,s,x,+,s,y,s,a,=,+,cos2,a,t,x,sin2,a,2,s,x,-,s,y,t,a,=,sin2,a,+,t,x,cos2,a,2,s,x,-,s,y,=,54.82 MPa,=,11.65 MPa,11.65,54.82,tan2,a,0,=,-,2,t,x,s,x,-,s,y,a,0,= 19.33,a,0,= 109.33,2,s,x,+,s,y,s,=,2,s,x,-,s,y,+,t,x,2,( ),2,maxmin,=,57.02 MPa,-,7.02 MPa,= 0.8,s,1,=,57.02 MPa,s,2,=,0,s,3,=,-,7.02 MPa,t,=,2,s,x,-,s,y,+,t,x,2,( ),2,maxmin,=,32.02 MPa,-,32.02 MPa,tan2,a,1,=,2,t,x,s,x,-,s,y,= 1.25,a,1,= 64.33,a,1,=,-,25.67,=,25 MPa,2,s,x,+,s,y,s,a,1,=,19.33,64.33,57.02 MPa,7.02 MPa,32.02 MPa,25 MPa,解析法,P93,49,-,3,(,e,),30 MPa,20 MPa,20 MPa,30,s,x,=,-,20 MPa,s,y,=,30 MPa,t,x,=,20 MPa,a,=,-,30,2,s,x,+,s,y,s,a,=,+,cos2,a,t,x,sin2,a,2,s,x,-,s,y,t,a,=,sin2,a,+,t,x,cos2,a,2,s,x,-,s,y,=,9.82 MPa,=,31.65 MPa,9.82,31.65,tan2,a,0,=,-,2,t,x,s,x,-,s,y,a,0,= 19.33,a,0,= 109.33,2,s,x,+,s,y,s,=,2,s,x,-,s,y,+,t,x,2,( ),2,maxmin,=,37.02 MPa,-,27.02 MPa,= 0.8,s,1,=,37.02 MPa,s,2,=,0,s,3,=,-,27.02 MPa,t,=,2,s,max,+,s,min,( ),maxmin,=,32.02 MPa,-,32.02 MPa,a,1,=,a,0,+ 45,a,1,=,-,25.61,=,5 MPa,2,s,x,+,s,y,s,a,1,=,= 64.33,19.33,27.02 MPa,37.02 MPa,64.33,5 MPa,32.02 MPa,P93,49,-,4,a,s,=,100 MPa,c,t,=,22.5 MPa,s,=,50 MPa,d,s,=,100 MPa,b,t,=,30 MPa,h,/,2,h,/,4,F,S,M,a,b,c,d,M,= 10 kN,m,W,z,=,6,bh,2,= 100 cm,3,s,max,=,W,z,M,= 100 MPa,F,S,=,120,kN,I,z,=,12,bh,3,= 500 cm,4,S,z,max,*,= 75 cm,3,S,z,3,*,= 56.25 cm,3,= 30 MPa,= 22.5 MPa,t,max,=,F,S,S,z,max,I,z,b,*,t,c,=,F,S,S,z,3,I,z,b,*,=,s,d,=,-,s,a,=,2,s,c,s,1,=,s,2,=,0,s,3,=,-,100 MPa,s,2,=,0,s,1,=,30 MPa,=,-,s,3,s,1,= 58.6 MPa,s,2,= 0,s,3,=,-,8.6 MPa,s,2,=,s,3,=,0,s,1,=,100 MPa,=,t,b,2,s,x,+,s,y,s,=,2,s,x,-,s,y,+,t,x,2,( ),2,max,min,P94,50,-,1,(,b,),45,25 MPa,s,x,=,0,=,s,y,t,x,=,25 MPa,a,=,45,25,s,t,O,D,x,D,y,A,D,0,B,C,D,a,2,a,25 MPa,s,C,=,0,R,=,25 MPa,t,a,=,0,s,a,=,-,25 MPa,s,1,=,25 MPa,s,3,=,-,25 MPa,s,2,=,0,t,max,=,25 MPa,2,a,0,a,0,=,45,a,1,=,0,s,a,1,=,s,C,=,0,45,25 MPa,25 MPa,25 MPa,图解法,几何关系,对应关系,P94,50,-,1,(,d,),30,80 MPa,20 MPa,s,x,=,0,s,y,=,-,80 MPa,t,x,=,20 MPa,a,=,60,24.64,77.32,31.72,84.72 MPa,4.72 MPa,40 MPa,44.72 MPa,s,t,O,D,x,D,y,A,D,0,B,C,D,a,2,a,20 MPa,R,=,44.72 MPa,s,a,=,-,77.32 MPa,=,4.72 MPa,=,-,84.72 MPa,s,2,=,0,2,a,0,2,a,1,s,a,1,=,s,C,13.28,s,C,=,-,40 MPa,tan2,a,0,=,-,1,2,a,0,=,-,13.28,33.44,t,a,=,24.64 MPa,s,1,=,s,C,+,R,s,3,=,s,C,-,R,=,44.72 MPa,t,max,=,R,=,-,40 MPa,a,1,=,31.72,
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