Suppose that the breaking load of the cables used to support the weight in Problem 8.15 is 1500 lb. The factor of safety is defined as 1500 lb divided by the maximum tensile force in any of the three cables. Write a MATLAB program to vary d from 0 to 15 feet, in 0.1-foot intervals. For each value of d, calculate the factor of safety. Plot the factor of safety versus d. What value of d produces the highest factor of safety?

Problem 8.15

A 1000-lb weight is supported by three cables, as shown in Figure P8.15. Note that cable 3 is attached along the y-axis, at a distance of d in feet from the origin O. Using concepts of vector analysis and particle equilibrium (usually taught in statics classes), three simultaneous equations can be formulated. The tensile forces in the three cables, T1, T2, and T3, (in pounds) are the independent variables:

Write a MATLAB program to solve for the three tensile forces if d is equal to:

a. 0 feet

b. 5 feet

c. 10 feet