12 m4 m5 mBW2Fig. P6.88, P6.896.89 The cable of length 15 m supports the forces Wi = W2 = W at B and C(a) Derive the simultaneous equations for B, B2, and B3. (b) Show that the solution to these equations is B = 41.0°, B2 = 9.8°, and B3the force in each segment in terms of W50.5°. (c) Compute6 m

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Asked Oct 9, 2019
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12 m
4 m
5 m
B
W2
Fig. P6.88, P6.89
6.89 The cable of length 15 m supports the forces Wi = W2 = W at B and C
(a) Derive the simultaneous equations for B, B2, and B3. (b) Show that the solu
tion to these equations is B = 41.0°, B2 = 9.8°, and B3
the force in each segment in terms of W
50.5°. (c) Compute
6 m
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12 m 4 m 5 m B W2 Fig. P6.88, P6.89 6.89 The cable of length 15 m supports the forces Wi = W2 = W at B and C (a) Derive the simultaneous equations for B, B2, and B3. (b) Show that the solu tion to these equations is B = 41.0°, B2 = 9.8°, and B3 the force in each segment in terms of W 50.5°. (c) Compute 6 m

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Expert Answer

Step 1

From geometry resolve the length of cable in vertical and horizontal direction;

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6 sin A-5 sin B-4 sin B 0 ) ...1) --2) 6 cosB5 cos +4 cos B 12.

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Step 2

Express the total number of independent equilibrium Equation for a cable with n segments as follows:

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T, (tan -tan )w..

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Step 3

Apply Equation (3) in Joint B and C.

...
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To(tan -tan )=W 4 T(tan B- tan(-A)) = .. To (tan e-tan e) =W To(tan -tan A)W.... (5)

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