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《结构力学习题集及答案》(下)-3a

《结构力学习题集及答案》(下)-3a
《结构力学习题集及答案》(下)-3a

第十章 结构弹性稳定计算

一、判断题:

1、稳定方程即是根据稳定平衡状态建立的平衡方程。

2、压弯杆件和承受非结点荷载作用的刚架丧失稳定都属于第一类失稳。

3、在稳定分析中,有n 个稳定自由度的结构具有n 个临界荷载。

4、两类稳定问题的主要区别是:荷载—位移曲线上是否出现分支点。

5、静力法确定临界荷载的依据是结构失稳时的静力平衡条件。

6、能量法确定临界荷载的依据是势能驻值原理。

二、计算题:

7、用静力法推导求临界荷载cr P 的稳定方程。

8、写出图示体系失稳时的特征方程。

9、求刚架在反对称失稳时的稳定方程。 n 为常数。

10、求图示完善体系的临界荷载cr P 。转动刚度kl k r 2=,k 为弹簧刚度。

11、求图示刚架的临界荷载cr P 。已知弹簧刚度l EI k 33= 。

12、求图示中心受压杆的临界荷载cr P 。

13、用静力法求图示结构的临界荷载cr P ,欲使B 铰不发生水平移动,求弹性支承的最小刚度k 值。

14、用静力法确定图示具有下端固定铰,上端滑动支承压杆的临界荷载cr P 。

15、用能量法求图示结构的临界荷载参数cr P 。设失稳时两柱的变形曲线均为余弦曲线:y x h =-δπ(cos ).12提示:cos d sin22u u u u a b a b

?=+??????214。 16、用能量法求中心受压杆的临界荷载cr P 与计算长度,BC 段为刚性杆,AB 段失稳

时变形曲线设为:()y x a x x l

=-().3

2 17、用能量法求图示体系的临界荷载cr P 。

18、用能量法求图示中心压杆的临界荷载cr P ,设变形曲线为正弦曲线。提示:

Sin d Sin22u u u u a b a b

?=-??????214 19、设y Ax l x =-22(),用能量法求临界荷载cr P 。

第十章 结构弹性稳定计算

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6、( O )

7、()21-=?cos sin .αααl l l

8、1α?P k k P -?? ???sin αl +

kl P -?? ???1 cos αl = 0 9、n l l l n EI k p k l r r

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6= = tg =?=αααααα 10、kl P kl P 414.3,586.02cr 1cr ==

11、 l EI l k P r 2cr 6==

12、()l EI P cr 22

2π=

13、32min 22 ,l EI K kl l EI ππ=

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π224。 15、 322cr h EI P π=

16、l l l 01581987==π

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