辽宁工业大学：《材料力学》课程教学资源（PPT课件讲稿）拉压、扭转习题课

拉压、扭转习题课 小结 拉伸与压缩 扭转 外力 一一一-:一 内力 N

拉压、扭转习题课 小结： 拉伸与压缩 扭转 外力 内力 F FN A Me 1 1 x T

应力 T O max p p 强度条件、≤[a max A ≤[z] 变形 △l O EA E 刚度条件 180 max max ≤[] G p

应力 强度条件 变形 刚度条件 p I T   = p max W T  = [ ] p max   W T A FN  = [ ] N,max   A F EA F l l N  = E   = GI p Tl  = [ ] π 180 p max  max  =    GI T

(b) 2F F (c)3F 2F F +)F 2F

2-1 (a) F (b) 2F (+) F (+) (-) (+) F (c) 3F (d) 2F F (+) F (+) (-) 2F

2-3 FM=-20kN. FM =-10kN Fm=10kN 10KN F 20×10°N 100MPa , 200mm 10KN 10×103N 20KN N2 33.3MPa 300mm F310×103N n3 = 25MPa A3 400mm

2-3 FN1 = −20k N, FN 2 = −10k N, FN3 = 10k N MPa m m N A FN 100 200 20 10 2 3 1 1 1 = − −   = = MPa m m N A FN 33.3 300 10 10 2 3 2 2 2 = − −   = = MPa m m N A FN 25 400 10 10 2 3 3 3 3 =   = = 10kN (+) (-) 10kN 20kN

2-19 FN=2×(F+P)=60N A=2×4058=811.6mm2 O=2M60×103 =73.9MPa<[o] A811.6

2-19 73.9 [ ] 811.6 60 10 2 405.8 811.6 2 ( ) 60 3 2  =    = = =  = =  + = MPa A F A m m F F P k N N N

2-21 AD杆: 300×2 NI =300kN,2 2 F,300×103 A1=b:02x A1 NI =1764.7mm O 0 选择80×80×6(9397cm2)

2-21 AD杆： 80 80 6(9.397 ) 8.82 1764.7 170 300 10 [ ] 300 ,2 2 300 2 2 2 1 2 3 1 1 1 cm A cm m m F A F k N N N   = =  = = =  = 选择 

AB杆: F=2×300=600kN F600×10 242=M2 =15294mm O 170 A1=1765cm2 选择100×100×10(19261cm2)

AB杆： 100 100 10(19.261 ) 17.65 1529.4 170 600 10 [ ] 2 2 300 600 2 2 1 2 3 2 2 1 cm A cm m m F A F k N N N   = =  = = =  = 选择 

第3次作业: 2-7 F F F 1F23 n3 3 △= EA EA EA F Fl F Fl Fl BEA 3EA3EA 3EA D △Z → 3EA

第3次作业： 2-7 F F F EA Fl EA Fl EA Fl EA Fl EA l F EA l F EA l F l N N N 3 3 3 3 3 3 3 1 2 3 + = − = +  = + + ( ) 3 =  = → EA Fl u l D

2-12 NI 10kNV.F,=0 2 10×103×1000 △l,=△ 0.467mm EA210×103×100 x 0.467mm以 ),a,=0.467mm()

2-12 m m EA F l l l k N F F F F N N N N 0.467 210 10 100 10 10 1000 10 , 0 2 3 3 1 1 2 1 2 3 =      =  = = = = = = = 0.467mm(→), = 0.467mm()  Cx  Cy

2-15 d(x)=a1+ X 2 X fAx d(△)= E(1+2,1x) 4F7 △Z=d(△O) nEd,d

2-15 1 2 0 2 1 2 1 2 1 2 1 2 1 1 4 ( ) ( ) 4 ( ) ( ) 4 ( ) ( ) Ed d Fl l d l x l d d E d Fdx d l x l d d A x d x l d d d x d l     =  = − +  = − = + − = + 