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1、习题解答习题解答组合变形组合变形P96P96 51- -1Fl bA l h z zy yCBFa aj jb bFy = Fcosj jFz = Fsinj j= 9.66 kN= 2.59 kN14Mz = Fy2l = 7.24 kNm14My = Fz2l = 1.94 kNm I Iz z = = 1212bhbh3 3= 1104 cm4 I Iy y = = 1212hbhb3 3= 5625 cm4s s = - - - - y - - - - z IzMzIyMy( (1) )s s = 0 令令tana a =z0y0=Iy MzIz My= tanj jbh2( )= 0
2、.476a a = 25.5WWz z = = 6 6bhbh2 2= 1103 cm3WWy y = = 6 6hbhb2 2= 750 cm3= + +WzMzWyMys st max = s sc max= 9.83 MPa( (2) )Fy( (2l) )348EIzfy =Fz( (2l) )348EIyfz = 5.43 mm= 2.59 mmf = = fy2 + + fz 2= 6.02 mmtanb b =fyfz= tana a b b = a a = 25.5f跨中截面跨中截面跨中截面跨中截面: :中性轴中性轴中性轴中性轴 s s s st t maxmaxs s s s
3、c c maxmax中性轴中性轴拉压区拉压区P96P96 51- -2F lA lCBF z zy ya a查表查表查表查表: b = 20 cmz0 = 5.69 cmIz = 4554.55 cm4 Iy = 1180.04 cm4 L L L L 200200 2020z z0 0s st max 在在B点点:危险截面危险截面: 跨中跨中Fy = Fz22= F = 17.68 kNMy =1 14 4Mz = F Fy y 2 2l l = 17.68 kNms s = - - - - y - - - - z IzMzIyMys s = 0 令令tana a =z0y0= 3.86a
4、a = 75.5zB = - - z02yB = 0= - - 80.47 mms sB = 120.6 MPas sA = - - - - 146.2 MPas sc max 在在A点点:= 60.95 mmzA = b- - z0222= 141.4 mmyA = b22中性轴中性轴中性轴中性轴 弯曲中心弯曲中心弯曲中心弯曲中心 形心形心形心形心主惯性平面主惯性平面主惯性平面主惯性平面 P97P97 51- -3zyx2FA AB BC CD DlMMz z MMy y FN = 2F = 20 kN23h2Mz = Fl - - 2F 12My = Fl + + 2F b2= 7.46
5、kNm= 5.6 kNmA A = bh= bh = 72 cm2s s = + + + + y + + z IzMzIyMyAFNs sA = 2.78 + + 51.81 + + 77.78s sB = 2.78 + + 51.81 - - 77.78s sC = 2.78 - - 51.81 - - 77.78s sD = 2.78 - - 51.81 + + 77.78= 132.4 MPa= - - - - 23.2 MPa= - - - - 126.8 MPa= 28.8 MPaWWz z = = 6 6bhbh2 2= 144 cm3WWy y = = 6 6hbhb2 2= 7
6、2 cm3 斜弯曲斜弯曲偏心受压偏心受压F FN NF3030s s角点角点角点角点 = + + + + + + + + WzMzWyMyAFN- - - - - - -P97P97 51- -4FFeez zy y50250横截面为横截面为横截面为横截面为 50502 250 mm50 mm2 2FN = FA = bhM = FeWz = 6bh2s s = IzMzAFNmax+- -min= ( (1 ) ) h6ebhF+- -e e 左左 = Es s s sminmine e 右右 = Es s s smanman= ( (1- - ) ) h6eEbhF= ( (1+ + )
7、) h6eEbhFF = ( ( e e左左 + + e e右右 ) ) Ebh2e = h6e e右右 + + e e左左e e右右 - - e e左左= 625 kN= 25 mm讨论讨论:( (1) )s smax 0s smin 0 0( ( e 0 0 0- - - - 整个截面整个截面:s s s s 0 0- - - - 0 0( ( e ) )h6- - 虎克定律虎克定律偏心受拉偏心受拉P98P98 52- -2hbD风压力的合力风压力的合力:底截面底截面:14F = p p pD2 M = F h Mn = F b = 314 Nm= 235.6 Nms sr3 = = M2
8、 + + Mn2W1= = h2 + + b2d3( (1- -a a4) )8pD21- -a a4a a 0.3086- - d d = = ( (1- -a a ) )d2 2 2.64 mm- - 取取圆杆内径圆杆内径圆杆内径圆杆内径: : 54.6 mm 54.6 mm- - - - 弯扭组合弯扭组合( (圆杆圆杆) ) WW = = 3232p p p pd d3 3( ( ( (1 1- - - -a a a a4 4) ) ) )- - s s 危险截面危险截面d d = 2.7 mmP99P99 52- -3lllABCDx xy yz zF3F4F1F24.09 kN4.0
9、9 kN15.91 kN15.91 kN7.96 kN7.96 kN0.68 kN0.68 kNMMe eMMe eMn 图图0.204 kN0.204 kNmm1 kN1 kNmm1.227 kN1.227 kNmm3 kN3 kNmm1.092 kN1.092 kNmmMy 图图Mz 图图反力反力 内力图内力图危险截面危险截面B:Mz= 1.092 kNmMy= 3 kNmM M = = = = MMz z2 2 + + + + MMy y2 2s sr4 = = M2 + + 0.75Mn2W1= 3.193 kN= 3.193 kNmmMMn n= = - - - - 1 kN 1 k
10、Nmm弯扭组合弯扭组合- - s s M2 + + 0.75Mn2 s s - - M2 + + 0.75Mn2 s s 323p p= 69.6 mm取取F4F1内力图内力图= = 3232p p p pd d3 3WW = = WWz z 弯扭组合弯扭组合( (圆轴圆轴) ):d = 7.0 cmP99P99 52- -4T T M M 4545A At ts sA As s = WMW = 32p pd3t t = WPTWP = 16p pd3e e 00 = Es ss s = Ee e 0 虎克定律虎克定律虎克定律虎克定律:M = Ws s = 105 MPa= 278 Nm2s ss sa a = + + cos2a a ( t t ) sin2a a2s s2s ss s 4545 = + + t t2s ss s - -4545 = - - t t1Ee e 4545 = ( (s s4545 - - nsns- -4545 ) ) 广义虎克定律广义虎克定律广义虎克定律广义虎克定律: :1 - -n n2= e e00 + t t 1 + +n nE1 - -n n2t t = ( (e e4545 - - e e00 ) )1 + +n nE= 40.4 MPaT = WPt t = 214 Nm
