A cable supports three vertical loads as shown inIf the maximum tension in the cable is 50 kN,determineThe length L of the cable.3 m4 m5m3 mYnBS kN12 kN15 kN

Answered: A cable supports three vertical loads…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Related questions

Question

A cable supports three vertical loads as shown in
If the maximum tension in the cable is 50 kN,
determine
The length L of the cable.
3 m
4 m
5m
3 m
Yn
B
S kN
12 kN
15 kN

Expert Solution

Step 1 To determine the vertical distances of the cable:

To determine the length of the cable, first we will have to calculate the vertical distances $y_{B,} y_{C}, y_{D}$ .

To determine the values of $y_{B,} y_{C}, y_{D}$ , lets calculate the reactions at support A.

Taking moments about E, we get

$(v_{A} \times 15) - (12 \times 12) - (15 \times 8) - (5 \times 3) = 0 \Rightarrow v_{A} = 18.6 k N$

Now, the maximum tension in the cable = 50 kN

Maximum tension occurs where slope is maximum, and chord AB of the cable has maximum slope.

Therefore,

$\sqrt{{V_{A}}^{2} + {H_{A}}^{2}} = T_{m a x} \Rightarrow \sqrt{18 . 6^{2} + {H_{A}}^{2}} = 50 \Rightarrow H_{A} = 46.41 k N$

Now, consider the FBD of AB, we get

$\sum_{}^{} M_{B} = 0 V_{A} \times 3 - H \times y_{B} = 0 18.6 \times 3 - 46.41 \times y_{B} = 0 \Rightarrow 46.41 \times y_{B} = 55.8 o r y_{B} = 1.20 m$

Consider the FBD of ABC, we get

$\sum_{}^{} M_{C} = 0 V_{A} \times 7 - H \times y_{C} - 12 \times 4 = 0 18.6 \times 7 - 46.41 \times y_{C} - 48 = 0 \Rightarrow 46.41 \times y_{C} = 82.2 o r y_{C} = 1.77 m$

Consider the FBD of ABCD, we get

$\sum_{}^{} M_{D} = 0 V_{A} \times 12 - H \times y_{D} - 12 \times 9 - 15 \times 5 = 0 18.6 \times 12 - 46.41 \times y_{D} - 108 - 75 = 0 \Rightarrow 46.41 \times y_{D} = 40.2 o r y_{D} = 0.866 m$