U c The objective function is a single left of x2 does not c

U. c. The objective function is a single left of x2 does not contain the maximum. value and a single variable function. d. Linear programing should be a constrained optimization. Question 2 Deflection (Rojiani 18.5)-20 Points The deflection of a simply supported beam subjected to a triangular load is given by the following equation 180 EIL where E is Young\'s modulus (ksi), I is the area moment of inertia of the beam cross section (in L is the length of the beam (in), W is the total load on the beam, x is the distance from the left support, and y(x) is the deflection at any point x along the beam. Determine the maximum deflection of the beam and the position x where this deflection occurs as a problem of root finding. The parameter values are CEE 3804 Midterm Test 2

Solution

y = -w /(180EIL^2) (3 x^5 - 10 *240^2 *x^3 + 7 * 240^4 * x) 0 < x< 240

deflection is maximum when dy/dx = 0

derivative of ( (3 x^5 - 10 *240^2 *x^3 + 7 * 240^4 * x))

=(x^4 -115200x^2 +1548288000)

f\'(x) = 0

(x^4 -115200x^2 +1548288000) = 0

x^2 = t

t^2 -115200t +1548288000 =0

t = 3840 (15 + 2*sqrt(30) = 99665 ,3840 (15 - 2*sqrt(30) = 15534 , t < 240^2

so t = 15534

x = sqrt(t) = 124.639 inch

deflection

= y(124.639) = -w /(180EIL^2) (3 x^5 - 10 *240^2 *x^3 + 7 * 240^4 * x)

-30/(180*29000*600*240^2) ( (3 x^5 - 10 *240^2 *x^3 + 7 * 240^4 * x)

=1.6629417e-13 * (1.86913225)*e12

=0.3109 inch