d848f6ed-d544-46b1-9c22-9607509d8462 3 2 5 false false 0 decimal

Equations a and b are simplified versions of maximum deflection in a beam under different loading conditions. All variables are known except for x, the length of the beam. I would like to superimpose these equations, but combining the 3rd order and 4th order polynomials seems only to result in errors. Equation c is a deflection limit which is also based on x. The ultimate goal of this worksheet is to find the longest beam where maximum deflection is less than/equal to the deflection limit: the first intersection (greater than zero) where c and d intersect.

a 0.00018 x 3^* ft 2^/ :

b 7.28197 105 -^* x 4^* ft 3^/ :

c x 600 / :

d 7.28197 105 -^* x 4^* ft 3^/ 0.00018 x 3^* ft 2^/ + :

Following the example in Mkraska's reference book for FindRoot, I am getting a weird error: the solution is equal to the guess, which is visibly incorrect. Why?

a b c d a b + 5 1 sys

f 1 el a :

f 2 el c :

f Unknowns x 11 mat

You can see that the X-Y plot graphs functions a, b, and c, but not d or a+b. Why?

f 1 ft * FindRoot 1 ft *

I also tried using the Maxima Solve function, which does provide a correct x value, but it only works with symbolic operation and the process for handing the vector solution appears is beyond me.

a c ≡ x Solve x 5 ft * 10 sqrt * 32 nthroot 3^/ - ≡ x 5 ft * 10 sqrt * 32 nthroot 3^/ ≡ x 0 ≡ 31 sys

5 ft * 10 sqrt * 32 nthroot (3^/ 3.04 ft *

x.max a c ≡ x Solve 2 el # # @ = :

Finally, if I try combining a and b to get a superimposed deflection value, I get the same error for FindRoot (guess is returned as solution) but Solve doesn't work at all. Why?

f 1 el d :

f 2 el c :

a d ≡ x Solve x 0 ≡

f Unknowns x 11 mat

f 1 ft * FindRoot 1 ft *