Question
Asked Oct 12, 2019
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A transmission tower is held by three guy wires attached to a pin at A and anchored by bolts at B, C, and D. If the tension in wire AB is 840N, determine the vertical force P exerted by the tower on the pin at A.

4 m
20 m
5 m
14.8 m
4 m
12 m
3.6 m
Fig. P2.111 and P2.112
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4 m 20 m 5 m 14.8 m 4 m 12 m 3.6 m Fig. P2.111 and P2.112

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Expert Answer

Step 1

The free body diagram of the tower with three guy wires is shown below.

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У ТАв, 20 m AB Тло AD /Г АС 4 m 5 m В' 14.8 m 4 m 3.6 m 12 m С Z х

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Step 2

The position vectors of cables are calculated as,

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AB 4i 20j+5k AB-4)+(20)+(5 = 21 AC 12i 20j+3.6k AC=12+(20) (3.6 =23.6 AD = 4i 20j-14.8k AD4(20)(-14.8) = 25.2

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Step 3

The tension in cable AB ...

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АВ Т. —Т, AB Plugging values AB AB АВ -4i+20j+5k (840 N Тдв 21 TAB 160i800j +200k

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Civil Engineering

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