结构力学答案部分(2)

dv2??max.dx?v2??maxGdx??NGAsEIdx?GAN1dx?????N?EIv???sGAsv1???C132EI?v?v1?v2??f(x)?ax?bx?cx?d????62??GAs?f??(x)?ax?b??C11?f(x)?EIGAsqxf??(x)?ax436?bx2??EI??c?a?x?d2GAs??2式中由于由f(x)?24EIqxf??(x)?可得出2EIv(0)?v1??(0)?0v(l)?v1??(l)?0d1?b?0得方程组：23?ql4??EIqlalEI???c?a???l?06GAs??24EIGAs2EI??2?ql?al?0??2EI解出：a=ql2EIqx4,c?qlx3ql324EIqx2 .

?qx3ql??v(x)???????x24EI12EI2GAs?24EI2GAs??v()??2384EI8GAsl5ql4

ql22.9.题

?EIvIV?Tv???0,EIv????N?Tv?TEI2

?vIV?V???0,vIV?KV???0式中k?r??4k2T EI特征根：r1,?0,2r?3k?v?A1?Akx?Achkx?Ashkx234 ?v(0)?0??v?(0)?0?A1?A3?0???A2?A4?0?

?v??(l)?0???EIv???(l)?N(l)?Tv?(l)??A3chkl?A4shkl?0 ?? 3EIkAshkl?Achkl??p?TkA?Ashkl?Achkl?????34234?

解得：

A1??pkTthkl,A2?pkTpEIk3pkT,A?3pkTthklA,?4?pkT ?v(x)?????thkl?kx?thklchkx?shkx???thkl?1?chkx???shkx?kx???

第４章 力法

4.1题

令l?l0?2.75cm由对称性考虑一半I?I0I2?26I0 2.5??q??1???0.8?1.025?1.845吨/米2??对0，1节点列力法方程3?M0l0M1l0ql0???0??3EI6EI24EI?000?33?M0l0?M1l0?ql0??M1(0.8)l0?M2(0.8)l0?q0(0.8l0)?6EI3EI024EI03E(26I0)6E(26I0)24E(26I0)0?2??M0?M1/2?ql8即：?2??M0?2.09M1?0.2549ql2??M1?0.0817ql?1.139?t?m???2M?0.0842ql?1.175?t?m???0

4.2.题

将第一跨载荷向c支座简化M1?Q1l12,p?Q1由2节点转轴连续条件：?Q1l12?l6EI2解得?2M2l23EI2?Q2l2224EI2??M2l33EI3?I2l3?1???Il32???Ql?8?2?Ql16M2??Q1l1?Q2l2?2??8?Q1l1?若不计各跨载荷与尺度的区别则简化为M2??RA??M2l?Q16???QM2?M1?MR????B?2?ll???

2??Q84.3题

由于折曲连续梁足够长且多跨在a, b周期重复。可知各支座断面弯矩且为M 对2节点列角变形连续方程

Ma3EI?Ma6EI?qa324EI??Mb3EI?Mb6EI?qb324EI解得

2332??q?a?b?qqbaa??22 M?1????? ?a?ab?b??12?????12?a?b?12b?b????

４．４题

图4.4，对2，1节点角连续方程：

2?M?l?Ml7QlM?l/1?20????10200????I0?E3?I4E1?8I0?04EI3??6E?400?2M?l8Q?l?0??M1?l02?0???0 ??3E?4 IE6I4E18I04?????000??41?Ql?0.1242Ql?M1?解得：330??M?Ql/55?0.0182Ql?

?

4.5图令I12?I34?4I0，I23?3I0l12?l23?l34?l0,由对称考虑一半

2?M?l?Ml2Ql????10200???0??3E4IE6I4E45I?0??0???04??2M?l7Ql????M2l0Ml20?M1?l0200????? ?6E?4I0?E3?I4E1?8I0?04E（I）3E（3I） 06?00?3?解出：??M411?330Ql?0.1242Ql??M2?Ql/55?0.0182Ql4.5题

对图4.4?刚架???l02?2?13EI?l006EI0对图4.5?所示刚架考虑2，杆3，由对称性?M2l02l0M2l2?M3E（3I?6E（3I?00）0）6EI0??2?l06EI0?均可按右图示单跨梁计算。由附录表A-6（5）?l0E（4I0）21?0?2?6EI?0l?03K??1?0???21?111?3??3?3??????3636??M?2Ql0?1??2?9?41Ql0?0.1242Q?145?1136??316??330l0?????? ?M?7Ql0?1??0?1?Ql02?0.0182Q?180??1136????7??55l?0 4.6题

??2为刚节点，转角唯一（不考虑23杆） ?M2l1???Ml243EI23EI

?M2节点平衡21?M2?4?????M22

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