Consider the jib crane shown here where it is supported by a pin at C and rod AB.The maximum tension allowed in the rod is 60 kN and the maximum rated force in the pin C is 80 kN. The load has a mass of 2000 Kgwith its center of mass located atG. Answer the following questions
![](data:image/png;base64,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)
1. Apply equilibrium conditions and expressFCand FABas functions of x (the distance shown on the figure). Note:FCis the overall force in pin C which isobtained by first findingCXand CY.
CX= 6131.25X
CY= 4598.43X - 19620
FC= √((?6131.25X)?^2+?(4598.43X - 19620)?^2 )
FAB= 7664x
2. Use Excel to form a table with the headingsshown. Then have Excel calculate and plot FAB and FC for distances x from 4.5 m to 10 m, which is the crane's length. Increment every 1 meter.Make sure your plot is well labeled.
|
FAB (kN)
|
CX (kN)
|
CY (kN)
|
FC (kN)
|
4.5
|
34488
|
27590.63
|
1072.935
|
27611.48
|
5.5
|
42152
|
33721.88
|
5671.365
|
34195.46
|
6.5
|
49816
|
39853.13
|
10269.8
|
41155.08
|
7.5
|
57480
|
45984.38
|
14868.23
|
48328.32
|
8.5
|
65144
|
52115.63
|
19466.66
|
55632.63
|
9.5
|
72808
|
58246.88
|
24065.09
|
63022.43
|
10
|
76640
|
61312.5
|
26364.3
|
66740.53
|
![1434_plot FAB.png](https://secure.tutorsglobe.com/CMSImages/1434_plot%20FAB.png)
3. Based on your simulation results, and the given rated forces (on the rod and the pin C) how close to the tip of the crane (i.e. 10 m), will you allow the load to go?Why?