(a) A criterion is required for selecting a material with the lowest cost in a strength-limited design for a cylindrical tie rod. Write the objective statement. Derive the criterion and identify the material index. The length of the tie rod, L, is fixed. (1 point) (b) A criterion is also required for selecting a material with the lowest cost in a strength-limited design for a square section beam (area b2). The length of the rod, L, is fixed. Write the objective statement and derive the criterion.

look at the explanation section.

Explanation:

a) the function is cylindrical tie, the constraints is strength specified and the objective is minimum weight. To design structural elements the following elements are important:

-material properties

-the geometry

-the functional elements

solving we have the following:

objetive: minimize mass

function: tie rad. equation: mass = Area * Length * density

constraints: length must be specified; the material must have adequate fracture toughness.

b) objetive: minimize mass

function: tie rad. equation: mass = Area * Lenght * density = b² * length * density

constraint: the stiffness is

where I is the momentum of inertia, E is the Young`s modulus

the free variables are: the edge length b and the material choice

the equation is

you must select materials with low P/E^1/2, where P is the density

energy can cross the boundaries of a closed system in the form of heat and mass

explanation: