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本帖最后由 十年一梦 于 2012-3-5 05:17 编辑
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这是一道有意思的力学题，选自《Advanced stress and stability analysis: worked examples》一书，苏联人写的，又译成了英语，网上可找到下载。书中有209道力学习题和解答。本题是第3题。. F5 O0 J( @5 V, M
: v- b2 A$ n; t) z0 N7 J原题：3. An absolutely rigid slab has a hole. An elastic bolt is inserted into this hole and is tightened with the force of preliminary tension Nt. The force P is applied to the nut after the tightening (Fig. 3). What change in the force accounting for the bolt will occur under this condition?
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. ?4 L0 X) ~9 {+ ^: F: U+ D试译：一个绝对刚性板上有一个孔，把弹性螺栓插入此孔，预紧力为Nt。螺母拧紧后施以力P，如图3所示。问: （施加力P后），螺栓的受力会发生什么变化？
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6 |1 }' A w" B解答：As the slab is rigid, the length AB of the strained bolt remains unchanged up to opening of contacts. And so the internal tensile force remains unchanged also. In the case, where force P is greater than the force of preliminary tension, the contact between the slab and lower bracket will be opened. Then internal tensile force in the bolt will be equal to P .
! ?2 u" P5 s4 E2 J Consequently, under P <=Nt the internal tensile force in the bolt is equal to N = Nt and under P >＝ Nt it will be N = P.
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由于板是刚性的，在板和螺母脱离接触前，螺栓受拉段AB的长度保持不变，其内部拉力也不变。如果力P大于预紧力Nt, 板和螺母将脱离接触，螺栓内部拉力将等于P。（A和B原图中没有注明，我认为应该是螺栓头到螺母间的一段。）
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$ u) y; @3 n0 d5 u* H因此，P <=Nt 时，螺栓内部拉力为N=Nt；P>＝Nt时，螺栓内部拉力为N= P
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# Q- z8 r1 X `7 O+ ] v, \（此图对应是下面这段话。）
* D7 ^1 L6 e U% P. _% z" OThe validity of the obtained result is well illustrated with the following simple example. Imagine a spring balance of a steelyard, the upper ring of which we put on a nail and the lower hook after tension hitch up by some rigid ledge, for example, up a table edge as shown in Fig. 188. The balance after this will indicate some value, for example, 4 Kg-wt. Let us liken this
. C3 Q2 U5 M. K# U L C5 ~balance to the strained bolt. Now let us hang weights to the lower hook of the strained balance. Until the weight of the load remains less than the specified tension force, balance will permanently indicate four kilograms. And only when a load hanged on the hook will be greater than four kilograms then the indicator will move from its place and indicate the corresponding weight.
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所得结果的有效性可用以下简单的例子说明。想象一只弹簧秤，上环勾在一只钉子上，下边的钩子勾在一个刚性架，如桌子的边缘上，如图188所示。弹簧秤稳定后显示为，比如是4公斤。我们可以把这个弹簧秤看成图3中张紧的螺栓。现在，在下面的钩上挂上重物。如果重物重量小于弹簧秤的预拉力，弹簧秤就一直显示为4公斤。只到钩上的重量超过4公斤时，秤的指针才会移动位置，并显示此时相应的重量。
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（有意思吗？）) O; @4 X! H9 q) d( |9 J
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另：从本周起，本人每星期发三个主题贴，一贴设计，一贴分析，一贴为分享一本中文或英文专业书。但愿能为社区做点贡献。
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1 O3 | m! o8 e4 O" t- j 此为第一周第一贴，所以标号为1A。0 F: v4 ?& e& |
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发表于 2012-3-5 04:27:37
