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
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
|
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?