材料力学附录A答案

材料力学附录材料力学附录A A答案答案 A 1确定下列图形C形心的位置 ayycyczyzzcCChbDO a b 解 a 32322 61312 6121213 132312 612bh1312 3121322122222222abbhabhhbbhabhhbbhhahaabhh aabhhbhaahabhabbhaabahabhabyc 3 2abzc b 0 cy ASAzdAzyAc 320232023xx232coscos2cossin2sincossin22RdRd RR dRRdzzRzzdASRAy 3 3 22413223DRRRASzy c yycyczczcCCO c d 303030250300140100N O 22aN O 16 c 0 cy 2 68 15725168 42122205 172 2516 1108 4212 cz d 0 cy mmzc683 127140220 xx50100300210140220 225200 250 50 100300 A 2图示扇形 证明图形面积A D2 4及形心位置y Dsin2 2 3 22DRdA SSS 证42220R 21zzz 2323111cossin121cos sin32cos32sincosDRRRRyAScz d 3333023cos2sin121sin 32sincos222DRRyzdyydASRRAz 3 3 sinsincossi n4sin121cossin1212223323DDDDDASyzc A 3图示切去1 4的边 长b的正方体 求形心C的坐标 bbzy122 解bbbbbbbb125431632144341223322 A 4试求图示 平面图形对x轴和y轴的惯性矩 解641243dbhIx 12321283 2d2481283 2283 28128322422422224bdb ddbdbdddbddddIy 2 半 圆6166412123212821232243343bdbddhbbdbdhbIy A 5计算题A 1各图形的对形心轴yc的惯性矩及惯性半径iyc ayycyczyzzcCChbDO a b yCyzzc O D 2yzbCbb 2b 2 yxbh dO解 a 366123221362332CabhhbbhabbhbhAzIIyyc 186122 36bh612223abhabhhbbhAIiyy b 128 3 1281828442242 CDDDDDAzIIyyc 2222218449 416118812888128 DDDDDDAIiyy yycyczczcCCO c d 303030250300140100N O 22aN O 16 c 16号槽钢44 831cmIcy mmzc5 171 21162 25cmA 22a 号工字钢43400cmIcy mmzc1102 22128 42cmA 4242434 604 4260068 1572205 172 2516104 8368 1571108 4212103400mmIcy mmAIiyy78 948 42122 251634 60442600 d 42323237 607055853683 1272102xx0122xx0683 127225250 xx2250 xx 83 1275010030012100300mmIcy mmAIiyy1 1112 xx0 xx501003007 607055853 A 6求 1 边长为a的正方形及 2 边长为a b的矩形 对于各自对角线的惯性矩 4aIIzy 0 yzI 11IIzy 解 a 121224aIIzy b 123abIy 123baIz 0 yzI 22cosbaa 22sinbab 223322232223 22 1612122 sinsincosbab abab babaa abIIIIyzzyy 22 44222322232211212122 sincossinbaababbaa babab abIIIIyzzyz A 7计算下列图示图形对于的轴y和轴z的惯性积 cyzyzyzChbROOO50101050 a c b y z R222解 a c 2423242c32431218128242461236384c646b26 64b28 28624822222222232232232332222322322232232222244223322 2222223222220232222023200021bhcbbbhbbbbbcbcbbhhcbbbchbbbchc bbhcbcbchcbbhcbbbchcbbbcbhdycyhhbyyhbdycbyhdychybydycbyhdy zdzydy zdzyyzdAyzdAyzdAIbcbcbbcbcbbcbcybhcbcbhyAAAyz b 4222225010 10010050012250060000625 002102105025021021mmdy zdzydy zdzyyzdAyzdAyzdAIAAAyz c 84242 sin21sincos4402030203RRd d d d yzdAIRRAyz A 8求图中各图形对形心轴z的 惯性矩 zC52z2020 a b 801xx0 xx050 40 a 7637333521080 xx2080 5280120 xx120202323 zI b 734654875044026440212 xx202243 zI A 9用转轴公式求图示矩形对轴y1和z1的惯性矩和惯性积 yzz1y1baC123baIy 123abIz 0 yzI 22cosbab 22sinbaa 223322232223221612122 sinsincosbab abaa abbab baII IIyzzyy 2244222322232 2 11212122 sincossinbabaabbab abbaa baIIIIyzzyz A 10确定倒T字形图形的形心主轴的方 向及形心主惯性矩 130 xx10030 解14 52130 xx03095 cz 43 128009529514 52130 xx130 xx14 523010012301002323 cyI67 2586666 12xx0121003033 czI A 11图示角钢形截面 1 确定通过O的主轴及相应的惯性矩 2 确定形心主轴及相应的形心主惯性矩 解 1 确定通过O的主轴及相应的惯性矩36800005060 xx60 xxxx0123xx02 23 yI116800001060 xx206060 xx012120202323 zI 204000042020804xx022222 yzI4232 01168000036800002 040000 2220 zyyzIIItg 47 110 或 51 1030 11 3xx22 2 sin2 cos2202 yzzyzyyIIIIIII10030 xx0O80120zy2020 C03 121701672 sin2 cos2201 yzzyzyzIIIIIII 2 确定形心主轴及相应的形心主惯性矩33 2360 xx0205060 xx1202 0 cz33 4360 xx0 xx60206012020 2c cy172056033 23360036800002 yycAzII492104033 4336001168000022c