辽宁工业大学：《材料力学》课程教学资源（作业试题）第7次作业弯曲应力

弯曲应力 第7次作业 4-1(b) 2 F4=5×==2kN,F=3kN F= F,=2kN, M,=F, x3=6kN.m Fs2=-FB=-3,M2=F4×3=6kNm 4-1(g) FA=FB=×(20×2+10×4)=40kN Fs1=40-10×1=30kN,M1=-80+40×1-×10×1×1=-45kNm Fs2=40-20-10×2=0,M2=-80+40×2-20×1-×10×2×2=-40kNm 2(b) BC:Fs(x)=30+15x,M(x)=-30x--x CA:F(x)=45,M(x)=-30(1+x)-15(0.5+x) 45kN 剪力图 1275kN 弯矩图 2(c) FA=FB=×(3×8+75)=495kN AC F5(x)=49.5-3x M(x)=495x~3x2

弯曲应力 第 7 次作业 4-1 (b) F F M F kN m F F kN M F kN m F kN F kN S B A S A A A B 3, 3 6 . 2 , 3 6 . 2 , 3 5 2 5 2 2 1 1 = − = − =  = = = =  = =  = = 4-1(g) F M k N m F k N M k N m F F k N S S A B 10 2 2 40 . 2 1 40 20 10 2 0, 80 40 2 20 1 10 1 1 45 . 2 1 40 10 1 30 , 80 40 1 (20 2 10 4) 40 2 1 2 2 1 1 = − −  = = − +  −  −    = − = −  = = − +  −    = − = =   +  = 4-2(b) : ( ) 45, ( ) 30(1 ) 15(0.5 ) 2 15 : ( ) 30 15 , ( ) 30 2 CA F x M x x x BC F x x M x x x S S = = − + − + = + = − − 4-2(c) 2 3 ( ) 49.5 ( ) 49.5 3 : (3 8 75) 49.5 2 1 2 x M x x F x x AC F F k N S A B = − = − = =   + = 45kN 剪力图 127.5kN.m 弯矩图

N 49.5kN 174kN. m 第8次作业 4-3(b) 15kN 25kN 10kN. m 4-3(h F=FB=280kN 280kN 280kN 45kN m

第 8 次作业 4-3(b) 4-3(h) FA = FB = 280kN 49.5kN 49.5kN 174kN.m 15kN 25kN.m 10kN.m 280kN 280kN 545kN.m

FR FA=0,M,=9a 4-15(a) lOkN l OkN. m 10kN 轴力图 剪力图 弯矩图 4-l8(b) FN()=-Fsin Fs()=Fcos o M()=FRsin 剪力图 轴力图 弯矩图

4-4(a) 2 0, 2 2 qa F M F qa Ay A B = = = 4-15(a) 4-18(b)       ( ) sin ( ) cos ( ) sin M FR F F F F S N = = = − qa qa qa2 qa2 /2 (+) 10kN 20kN.m 20kN (-) (+) 10kN 80kN.m 轴力图 剪力图 弯矩图 (+) (-) 剪力图 轴力图 弯矩图

第9次作业 m-m截面 M.=20kN m M1y1_20×10×(-150 =-741MPa 180×1503 =494MPa,c=0,0D=741MPa n-n截面 M.=-22kNm a,=M1y=-25×10×(-150) 9.26MPa 80×150 =-681MPa,ac=0,0D=-926MPa 4-31 M=4F kNm W=2×340.328cm3=680.656cm3 M mx=≤[o] F]=x170×680656 =289×102N=28.9kN 4000 4-36 5F,q×6 3-F×2-F×1 q =202.5kN W=2×6597=13194cm M202.5×10° 13194×10 =1535MPa<[]满足强度条件 M=3.5kNm bh h h≥ 8M 18×3.5×10° =185mm,b=-=62mm

第 9 次作业 4-25 MPa MPa MPa I M y M k N m m m B C D A 4.94 , 0, 7.41 7.41 12 180 150 20 10 ( 150) 20 . 3 6 1 1 1 = = = = −    − = = = −     截面 MPa MPa MPa I M y M k N m n n B C D A 6.81 , 0, 9.26 9.26 12 180 150 25 10 ( 150) 22 . 3 6 1 1 2 = − = = − =  −   − = = = − −     截面 4-31 N k N W F W M W cm cm M F k N m z z z 28.9 10 28.9 4000 170 680656 4 [ ] [ ] [ ] 2 340.328 680.656 4 . 2 max max 3 3 max =  =  =  = =  =  = =    4-36 153.5 [ ],满足强度条件 1319.4 10 202.5 10 2 659.7 1319.4 202.5 . 2 3 3 2 1 2 6 2 5 3 6 max max 3 2 max  =     = = =  = =   −  −  −       = + MPa W M W cm k N m q F F F q M z z 4-38 mm h mm b M h bh h W M k N m z 62 3 185 , 10 18 3.5 10 [ ] 18 6 18 3.5 . 3 6 3 max 2 3 max = = =    = = = = 

第10次作业 4-46 5×75 =18.75kN 3Fm3×18.75×1 =0.52MPa≤[r] A2×300×180 4-52 Fl F F=40kN. M =10kN m 、h2 h 69 9×10×106 mEx =208mmb、2×208 =139mm 3FSm_3×40000 =207MPa<[z b=139mm,h=208mm

第 10 次作业 4-46 0.52 [ ] 2 300 180 3 18.75 10 2 3 18.75 2 5 7.5 3 .max max .max  =       = = =  = MPa A F F k N S S 4-52 b mm h mm MPa A F mm b mm M h bh h W k N m Fl F F k N M S z S 139 , 208 2.07 [ ] 2 208 139 3 40000 2 3 139 3 2 208 208 , 10 9 10 10 [ ] 9 6 9 10 . 4 40 , .max max 3 6 3 max 2 3 .max max = = =     = = =  = =    = = = = = = =   