[每周三貼1A]　螺栓內部拉力分析　

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十年一夢

電梯直達

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發表于 2012-3-5 04:27:37 | 只看該作者 |倒序瀏覽 |閱讀模式

本帖最后由十年一夢于 2012-3-5 05:17 編輯

這是一道有意思的力學題，選自《Advanced stress and stability analysis: worked examples》一書，蘇聯人寫的，又譯成了英語，網上可找到下載。書中有209道力學習題和解答。本題是第3題。

原題：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?　

試譯：一個絕對剛性板上有一個孔，把彈性螺栓插入此孔，預緊力為Nt。螺母擰緊后施以力P，如圖3所示。問: （施加力P后），螺栓的受力會發生什么變化？

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 .
　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.

由于板是剛性的，在板和螺母脫離接觸前，螺栓受拉段AB的長度保持不變，其內部拉力也不變。如果力P大于預緊力Nt, 板和螺母將脫離接觸，螺栓內部拉力將等于P。（A和B原圖中沒有注明，我認為應該是螺栓頭到螺母間的一段。）

因此，P <=Nt 時，螺栓內部拉力為N=Nt；P>＝Nt時，螺栓內部拉力為N= P

（此圖對應是下面這段話。）
The 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
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.

所得結果的有效性可用以下簡單的例子說明。想象一只彈簧秤，上環勾在一只釘子上，下邊的鉤子勾在一個剛性架，如桌子的邊緣上，如圖188所示。彈簧秤穩定后顯示為，比如是4公斤。我們可以把這個彈簧秤看成圖3中張緊的螺栓?，F在，在下面的鉤上掛上重物。如果重物重量小于彈簧秤的預拉力，彈簧秤就一直顯示為4公斤。只到鉤上的重量超過4公斤時，秤的指針才會移動位置，并顯示此時相應的重量。

（有意思嗎？）

另：從本周起，本人每星期發三個主題貼，一貼設計，一貼分析，一貼為分享一本中文或英文專業書。但愿能為社區做點貢獻。

　此為第一周第一貼，所以標號為1A。

force, 螺栓, accounting, examples, elastic