哈尔滨工程大学船舶结构力学课程习题集答案(6)

4.8 题

A1??2l?348EI?l36EI列出1节点的角变形连续方程：2?Mlvp2l??M(2l)v11?1????1??3EIl3EI2l16EI? ?v?AR?A??M1?2p???M1?p??

111???????12????2l??l?联立解出M1??311pl,v1?23pl336EI画弯矩图见右图

4.9题

１）如图所示刚架提供的

支撑柔度为A1?A2?V而由5节点?5?0得p?1

?pl?l??3E?7I?6E?7I?M5l?M5?pl2,F???pl???pl2?l?0

??3p2 由卡瓦定理：

A?V1?1p??EIM?M?Pdsp?1 ?l??l3p??3??pssds?pl?sl?sds1????2?2????1?10E?7I??022?????1p?2

1?l3???E?7I???312333?3?1?ll?l?l?s2?ds2???????0?2?4?12EI???7EI?3l1节点列出方程组求解 ２）由对称性只需对0，

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3?M0lM1lv1ql????0??3EI6EIl24EI?33?M0lM1lv1M1lM1lqlql ? ???????l24EI3EI6EI24EI?6EI3EI3???M1?M0ql?ql?lv?AR???111?????12EI??l2?2?? 联立解得：M0?11ql236,M1??ql236,v1?2v2?ql418EI

４．１０题

a)? =13?8?4,Q1?qal192, q??Q?a?ql23

k?192Eialb)Q?Q1?Q2?qal?23Q3qal2?3qal2?Q1??v中?5Q1l,?Q2?Q2l313Q5Q1l384Ei3310??7????5180Ei?228?35??5?23?????3?384Ei384EiEi?384384???5Q2lQl3?5Ql3384Ei384?,???5q???148?Q?a5?483qal15??ql3842a16?48Eial,pl?2k?Ei3 c)?al3

??148??1l48,p?p,Q?p?k?Ei?al3?48Eial3

d)令pl348Ei48p4?3?1??p=??26Ei?44?61?41???34?1???4?11p?,k848?Ei(同ac图l)

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e)??53843,??1,Q?qal2?481?4??1????9?p=?q?Q?a?

令pl5?48qal??384a2123???36p6?51623ql348Ei?3pl?11???1??6Ei?32?4?8p??6?

27?1?m????1???1??????768Ei2?2?????2

768?131m3m24768Ei??p=-???????k?37al7?122?222?l7lf)令???g)p同a)即p?7pl1?1???1?????m?26Ei2?2???l2??Q?qal2?q?pa?ql2?192Eil3?k0?x?6a?1? k???192EiA?192E(2i)l3?2??2k03l??k?k0a?192Eial3?x?6a?

4.11题

?支柱处v???0,可简化为刚性固定约束?仅考虑右半边板架

????p=1481?11?11?1????6?42?164p?1116311???????48?16??pk?48Eial?48EI0l?2EI0?4?9l0?4E9I0?6l0?03?2EI09l40u??6l0?24????12?

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?M?N??p?6l0?8p2?1?1??16p2p??6l0?81132?0.874?0.4507pl0P?0.852??0.2929p

?1?1????0.852?vm?l??vax???v?3l?4?p?6l0?3?0

?11?9?192E?I0??2??1?1??16?6?0.88996?9?3pl30EI0?0.1528pl30

EI0

4.12题

设a?l0?1mI?1.857I0,i?I0?5.833?10cmQ?q0al,54L1?l?10l026b?2.5l02q0?1kgcmE?2?10kgcm '求：中纵桁跨中及端部弯曲应力及v中解：因主向梁两端简支受均布载荷Q故其形状可设为sinc1?c3?sin1?1?6?4

?yl?y1l?sin?4?0.707c2?sin?2?1?11??12????111???3?????0.02083?44????按对称跨中求?1?11?11???1??????0.01432?6?24?164??2??i?1?1?1iciIic1I1?I1I2???3?110.707?0.02083?0.707?0.01432?1??0.0411?2?45?2???0.0411,6384?0.0130223k2?Ei?q2??2al?2?10?5.833?102?i0.01302?10q0l00.0411l0?20.0411?10??10?3?283kgcm?2Q?L24l0?3.168q0l03u?4alI1?13?10l024I04l0?10l0?1.857I0?0.0411?1.2?1?1.2??0.728, v中?q2k21?2?u??0.813,3.168?1?102832?1?u??0.774(1?0.728)?0.304?cm??1???u???

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?端?

M?h?I??t??2?q2L242?q2L122??2?1.?2I51?3q.1l0?608l1220?20?100.8?1310.833?10551?1010kgcm

?中?

??1?u?I51?3.168ql0?10l024??0.774?5110.833?105?481kgcm4.13补充题 写出下列构件的边界条件：（15分）

1）

?I?v?????A?v?0?p1?E????0 解：???EIv???0??m?????v?l ??v?l??0?0 2）

?v???1??v??0?EI??? 解：???v?0??0??0m?1????l?????v?2?l0?????v??2w?2?0时y?=?y0,a ??w=0????E?Iv??

2lm 3) 设x=0,b时两端刚性固定；y=0,a时两端自由支持 ??w?0?解：x=0时,b ??x?w=0?4) 已知：x=0,b为刚性固定边;y=0边也为刚性固定边：y=a为完全自由边

??w?0?解：x=0时,?b?x?w=0 ?y=时0w??w?y?0

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