工程科學應力應變題 Ex3 ?

Question

Acceleration due to gravity = 10 ms-2;

Calculation steps should be clearly shown;

Answers correct to two decimal places.

3. A uniform beam AB, 30m long and weighing 20kgf, carries loads of 100kg at A and 80kg at B. It is supported horizontally at two points C and D, C being 10m from A. Determine the position of D when the reactions on the two supports are equal. What minimum load must be added at A to cause the beam to tip up?

Answer 1

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圖片參考：http://hk.geocities.com/namsm4e/P74.jpg

如圖成為平衡，則

FC + FD = 2F = (100 + 80 + 20)x10 = 2000

FC = FD = F = 1000N

若以 A 為轉軸，則

1000*10 + 1000x = 20*10*15 + 80*10*30

10000 + 1000x = 27000

x = 17.0m (距 A 點 17.0m)

所以使 AB 升起，則在加一重物 m，則

AB 會離開 D 點，使 FD = 0

若以C 點為轉軸

(100 + m)*10 = 20*10*5 + 80*10*20

10(100 + m) = 1000 + 16000

100 + m = 170

m = 70kg