材料力學(xué)第五版附錄I截面的幾何性質(zhì)+習(xí)題答案

.附錄I(a)(b)(c)Ayc(4020)(2010)24000(mm3)Ayc(20Ayc(2065)2(d)SxAycmm)xdSxdAy(xddx)yxddxxsinx2sindxd'..x00rx2dx003[x][cos]0333r[(cos333cos]2r333因?yàn)镾xAyc，所以2r1r2ycyc4r3323(a)4YciAiYcic4AiLi*BiYc=∑AiYci/∑Ai習(xí)題I-3(b):求L形截面的形心位置矩形LiBiAiYciAiYciYcXciAiXciXc下16080128000左900545002500575002313250053Ai=Li*BiYc=∑AiYci/∑AiXc=∑AiXci/∑Ai'..習(xí)題I-3(c):求槽形與L形組合截面的形心位置Ai(cm2Yci(cmAiYci(cm3Yc(cmXci(cmAiXci(cm3Xc(cm)))))))槽鋼2032.83710328.37-1.95-64.03等邊角鋼15.1262.3535.5462.3535.54647.963363.927.6-28.49-0.6xdIxy2dAy2(xddx)x2sin2xddxx3sin2dxd 4r{1[sin2]0/2}48224r4'..4r4dAIyr0xdxr2r202x2r1x(r202221r22224]0x4]0444224r4)44r48Idmm的圓形截面，在其上、下對(duì)稱地切去兩個(gè)高為20mm的弓形，試用積分法求余下陰影部分對(duì)其對(duì)稱軸x的慣性矩。xx如圖，作兩條平行x軸的、相距為dy線段，截圓構(gòu)成微分面積，微分面積為：rsinIxrsin2y2r2y2dyy2y282r22y2rrrsin4r(1sin4)4244r(4sin4)482x12x'..10020603arctan453.1300.927(rad)34Ix100(40.927sin212.520)3.963107(mm4)8[習(xí)題I-6]試求圖示正方形對(duì)其對(duì)角線的慣性矩。解：正方形四條邊的直線方程如圖所示(設(shè)水平坐標(biāo)軸為z，豎坐標(biāo)軸為y)。02yA20z2dz20z2dz222[022ay3222za22zza22a2202za2dz22y2dyza22222a220z0z022aa22a220yyz30z32222dz]020232232=34a4aa2a)3d(z22a)222222(0z2a)3d(z2a)]222a)4244a40232a22(z22222404a4'..4a4164124D(142)13.141754[1(150)4]21177368(mm4)1753313390449999(mm4)試求圖示三角形截面對(duì)通過(guò)頂點(diǎn)A并平行于底邊BC的軸的慣性矩。'..的半圓形截面對(duì)于軸的慣性矩，其中軸與半圓形的底邊理，得截面對(duì)軸的慣性矩[習(xí)題I-10]試求圖示組合截面對(duì)于形心軸x的慣性矩。截面的形心，因此下面兩個(gè)圓的圓心，到形心軸'.dd.上面一個(gè)圓的圓心到軸的距離是236習(xí)題I-11]試求圖示各組合截面對(duì)其對(duì)稱軸的慣性矩。解：(a)22a號(hào)工字鋼對(duì)其對(duì)稱軸的慣性矩是。利用平行軸定理得組合截面對(duì)軸的慣性矩Iz3.4107(1120103115212010)265760000(mm4)12(b)等邊角鋼的截面積是，其形心距外邊緣的距離是28.4習(xí)題I-11(b)圖圖形bhIxcaAIx0000上矩形250102083333333下矩形250102083333333左上L形271.61926143869495右上L形271.61926143869495左下L形271.61926143869495右下L形271.61926143869495IxIxc2aA2a1220644645'..[習(xí)題I-12]試求習(xí)題I-3a圖所示截面對(duì)其水平形心軸的慣性矩。關(guān)于形心位置，可利[習(xí)題I-12]試求圖示各截面對(duì)其形心軸x的慣性矩。13i0ciI(a)iYcic'.1iI-13(b)cicic2圖形圖形矩形半圓全圖.ycyhir4r/3iYciAiYci7YcIxc(mm4)83330202791r4/88r4/9aiIx(mm4)15933321369827599i15ciiYcic06042699342699514[習(xí)題I-14]在直徑D8a圓截面中，開(kāi)了一個(gè)2a4a的矩形孔，如圖所示。試求截面軸形心的慣性矩IxIy。的位置截面圖形對(duì)形心軸的靜矩(面積矩)等于零：(y軸向下為正)(組合圖形對(duì)過(guò)圓心軸x1的慣性矩)'..(組合圖形對(duì)形心軸x的慣性矩)b(a)h(a)r(a)Ai(a2)Yci(a)AiYciYc(a)IxcaiIx(a4)矩42-8.001-82.6671.189314.0形圓450.2700201.062-0.1893202.942.27-8-0.1893188.9yychir43i0習(xí)題I-15YciAiYciYc79-30936536906351024r8r4xc89xx346422a'..4a44r4844844a200Iyr8I16]圖示由兩個(gè)若欲使截面對(duì)兩對(duì)稱軸的慣性矩Ix和的慣性矩是。根據(jù)慣性矩定義和平行軸定理，組合截面對(duì)；若即等式兩邊同除以2，然后代入數(shù)據(jù)，得'..[習(xí)題I-17]試求圖示截面的慣性積2241221224hhb[習(xí)題I-18]圖示截面由兩個(gè)125mm125mm0010mm的等邊角鋼及綴板(圖中虛線)組合而成。試求該截面的最大慣性矩Imax和最小慣性矩Imax。解：從圖中可知，該截面的形心C位于兩綴板共同的形心上。'..直線為yc軸向上為正。把xccyc坐標(biāo)繞C點(diǎn)逆時(shí)針轉(zhuǎn)045xy2'42'4a2z02222573.891148(cm4).952cm(注：綴板用虛線畫出，表示其面積可忽略不計(jì))4a4a124IIxII2cos2224a4'..IIxII2cos22aa2004a4112Ixysin2112(a)13400402Ix[20040(134004021222Iy[40200(Iy[40200()20040]2122222222Ixy(2)(259200000)22222Ixy(2)(259200000)tan20020arctan1.31645247'0002624'001120(400332020240)3575146666.5(mm4)'..2122Iy)224Ixy解：以20號(hào)槽鋼(圖I)的下邊緣為x軸，左邊緣為y軸，建立坐標(biāo)系。8號(hào)槽鋼編號(hào)習(xí)題I-20(b)長(zhǎng)度