I have this question for some uni work and its really troubling me!
If anyone can help it will be greatly appreciated!
Suppose that you are asked to design a column to support a compressive load P. The column has a cross section shaped as a thin-walled pipe. The design variables are the pipe mean diameter, d, and the wall thinness, t. The cost of the pipe is computed by
Cost: J = f(t,d) = c1*W+c2*d
where c1 = 4 and c2 = 2 are cost factors and W is the weight of pipe.
W = pi*d*t*H*density (W = dtHp?)
where density = density of pipe material = 0.0025kg/cm^3
The column must support the load under compressive stress and not buckle. Therefore,
Actual stress (s) = maximum compressive yield stress = sy = 550 kg/cm^2
Actual stress (s) = buckling stress
The actual stress is given by: s = P/A = P/p*d*t
The buckling stress is: sb = p*E*I/H^2*d*tp
Where E=modulus of elasticity.
I = second moment of the area of the cross section:
I = (p/8)*dt(d^2+t^2)
Finally, diameters of available pipes are between d1 and d2 and thickness between t1 and t2. Develop a MATLAB program (use command