Respuesta :
Answer:
For uniaxial tension the objective is to minimize cost:
C = mCm= ALrCm where m is mass, A is the cross-section area, r is density, and Cm is cost per unit mass. For strength limited design: F/A ≤sy, and A ≥ F/sy To minimize C = (F/sy) LrCm= (FL)(rCm/sy), minimize the quantity (rCm/sy). Maximize the material index,M =sy/(rCm)
b. The objective is to minimize cost C = mCm= b2LrCm, where A = b2 is the cross-section for strength limited design. It is necessary to eliminate the variable b from the equation.
Now if A= b2
Then b=A/2
Therefore cost C= mCm=A/2.2LrCm
= ALrCm
Answer:
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
[tex]s =\frac{CEI}{L^{3} }[/tex]
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
[tex]m=(\frac{125L^{5} }{C} )^{1/2} (\frac{P}{E^{1/2} } )[/tex]
you must select materials with low P/E^1/2, where P is the density
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