A 20-kg crate is suspended as shown below. Each rope can withstand a maximum force of 910 N before it breaks. Note that AB always remains horizontal. YA A B D The equations of equilibrium are: FAB – FAC Cos 0 = 0 FAC sin 0 – 196.2 = 0 1-A) 1-B) Analytically, with FAB = 500 N, calculate 0 (in degree) and Fac- Write down a general formula that calculates 0 from FaB, and another formula that calculates FAc from 0 and FaB- Use MATLAB to calculate 0 (in degree) and FAc as the applied FAB is varied from 100 N to 900 N (with 100 N steps). Tabulate your findings neatly. 1-C)
A 20-kg crate is suspended as shown below. Each rope can withstand a maximum force of 910 N before it breaks. Note that AB always remains horizontal. YA A B D The equations of equilibrium are: FAB – FAC Cos 0 = 0 FAC sin 0 – 196.2 = 0 1-A) 1-B) Analytically, with FAB = 500 N, calculate 0 (in degree) and Fac- Write down a general formula that calculates 0 from FaB, and another formula that calculates FAc from 0 and FaB- Use MATLAB to calculate 0 (in degree) and FAc as the applied FAB is varied from 100 N to 900 N (with 100 N steps). Tabulate your findings neatly. 1-C)
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Task 1
A 20-kg crate is suspended as shown below. Each rope can withstand a maximum force of 910 N before it breaks.
Note that AB always remains horizontal.
YA
В
The equations of equilibrium are:
FAB – FAC Cos 0 = 0
FAC sin 0 – 196.2 = 0
1-A) Analytically, with FAB = 500 N, calculate 0 (in degree) and Fac-
1-B) Write down a general formula that calculates 0 from FAB, and another formula that calculates FAc from 0
and FAB.
1-C) Use MATLAB to calculate 0 (in degree) and Fac as the applied FAB is varied from 100 N to 900 N (with
100 N steps). Tabulate your findings neatly.
1-D) Based on the results above, does any of the forces exceed the 910-N rope max withstanding?
1-E) Analytically, calculate the minimum 0 (in degree) so that none of the ropes break (Hint: Fac breaks before
FAB).
1-F)
At maximum withstanding condition, what is the height YA (assuming the rope AC has a length of 20 cm)?
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