课堂测试(7)
课堂测试（7） X1 X2 X4 MF X3 M1 M2 M3 M4
课堂测试(7)
课堂测试（7） X1 X2 TF X3 T1 T2 T3 T4
课堂测试(7) M,·M TE x El M,Mdx≠0[元,d=0△≠0JM,Mx=0J7=0=61=0 2Mdx=0「72Tdx=042F=0 0∫7,dr=0 M,·Mdx=0T,Tdx=062=6,=0 0|73·Tdx=0△3=0 ∫,M,dx≠0「T,Tx=06=6≠0 M4Mdx≠0「7Tdx=0△≠0(M2,Mdx=0J元,7dx=062=62=0 MMdx=0「77dx=06=61=0 M T T2 T
课堂测试（7） d d i F i F iF l l p M M T T x x EI GI = + d d i j i j ij l l p M M T T x x EI GI = + 1 2 M M x = d 0 1 d 0 M M x F M T 1 d 0 T T x F = 1 0 F 2 d 0 M M x F = 2 d 0 T T x F = 2 0 = F 3 d 0 M M x F = 3 d 0 T T x F = 3 0 = F 1 2 T T x = d 0 12 21 = =0 1 3 M M x = d 0 1 3 T T x d =0 13 31 = =0 2 3 M M x = d 0 2 3 T T x = d 0 23 32 = =0 M1 M2 M4 MF T1 T2 T4 TF T3 M3 4 d 0 M M x F 4 d 0 T T x F = 4 0 F 1 4 M M x d 0 1 4 T T x d =0 14 41 = 0 2 4 TTx = d 0 24 42 = =0 3 4 M M x = d 0 3 4 T T x = d 0 34 43 = =0 2 4 M M x = d 0
课堂测试(7 M,·M TE x El M,Mdx≠0[元,d=0△≠0JM,Mx=0J7=0=61=0 2Mdx=0「72Tdx=042F=0 0∫7,dr=0 M,·Mdx=0T,Tdx=062=6,=0 0|73·Tdx=0△3=0 M,Mdr≠0JT,rd=06:=6,≠0 M4Mdx≠0「7Tdx=0△≠0(M2,Mdx=0「,dx=06,=6=0 M, Mdx=0 t3 1X1+612X2+O3X3+O14X4+△1F=0 1X1+614X4+△F=0 X1+a2X2+a2x3+24X4+△2=0→ 6X=0 X2=0 1xX1+O32X2+O3x3+o344+△3F=0 4X1+4X4+△4F=0 61X1+62X2+O43X3+4X4+△4F=0 X1≠0,x2=0,X3=0,X4≠0 对称结构的对称截面上的对称内力为0,反对称内力不为0 对称结构上作用了反对称载荷→二次超静定问题
31 1 32 2 33 3 34 4 3 X X X X + + + + = F 0 21 1 22 2 23 3 24 4 2 X X X X + + + + = F 0 11 1 12 2 13 3 14 4 1 + 0 X X X X + + + = F 33 3 X = 0 22 2 X = 0 11 1 14 4 1 0 X X + + = F 1 2 3 4 X X X X = = 0, 0, 0, 0 对称结构的对称截面上的对称内力为0，反对称内力不为0 对称结构上作用了反对称载荷 二次超静定问题 课堂测试（7） d d i F i F iF l l p M M T T x x EI GI = + d d i j i j ij l l p M M T T x x EI GI = + 1 2 M M x = d 0 1 d 0 M M x F 1 d 0 T T x F = 1 0 F 2 d 0 M M x F = 2 d 0 T T x F = 2 0 = F 3 d 0 M M x F = 3 d 0 T T x F = 3 0 = F 1 2 T T x = d 0 12 21 = =0 1 3 M M x = d 0 1 3 T T x d =0 13 31 = =0 2 3 M M x = d 0 2 3 T T x = d 0 23 32 = =0 4 d 0 T T x F = 1 4 M M x d 0 1 4 T T x d =0 14 41 = 0 2 4 M M x = d 0 2 4 TTx = d 0 24 42 = =0 3 4 M M x = d 0 3 4 T T x = d 0 34 43 = =0 41 1 42 2 43 3 44 4 4 0 X X X X + + + + = F 41 1 44 4 4 + + 0 X X = F 4 d 0 M M x F 4 0 F
课堂测试(7) M M TF T1 ,0≤x1≤L/2 0,0≤x1≤L/2 M1(x) 0.0≤x1≤L/2 M1(x) F2,0≤x2≤2L x2,0≤x2≤2L MAx)- 1.0≤x,<2L T(x)=0 0,0≤x1≤L/2 T 几10≤xsL/2 7(x)=1,05x2s2L T(x) 0,0≤x2≤2L 16FL 3EI q、4FL F E
课堂测试（7） 3 2 2 2 1 0 16 2 d 3 L F Fx x FL x EI EI = − = − M T M1 M4 MF T1 T4 TF 1 2 2 0,0 / 2 ( ) ,0 2 F x L M x Fx x L = ( ) 0 T x F = 1 1 1 2 2 ,0 / 2 ( ) ,0 2 x x L M x x x L = 1 1 2 0,0 / 2 ( ) ,0 2 2 x L T x L x L = 1 4 2 0,0 / 2 ( ) 1,0 2 x L M x x L = 1 4 2 1,0 / 2 ( ) 0,0 2 x L T x x L = 2 2 2 4 0 4 2 d L F Fx FL x EI EI = =