Sample Problem One: (40 Points) The pressure P on a 10 m high and 2 m wide struc

Question

Sample Problem One: (40 Points) The pressure P on a 10 m high and 2 m wide structure due to the wind is given by the expression 300 x 1+e where, x is measured in meters from the bottom of the structure and the pressure is in N/m2 The total force due to wind is given by the integral: F(x)- Pa) dxr 3 a) Write the MATLAB statements that develop the displayed data. disp([x' P'I) 1.2500 83.5126 2.5000 56,8936 3.7500 25.8495 5.0000 10.0393 6.2500 3.6126 7.5000 1.2438 8.7500 0.4159 10.0000 0.1362 [ s i b) Compute the force, F(x), using Trapezoidal rule for h-Ar = 1.25 c) Determine the truncation ennor for part (b). P ()3001 (1+e1)3 d) Compute the force, F(x), using Simpson's rule with 4 intervals (n=4)

Explanation / Answer

a):

x = 0:1.25:10;
P = 300*x./(1+exp(x));
disp([x' P'])

b):

h = 1.25;
x = 0:h:10;
P = 300*x./(1+exp(x));
Ib = trapz(x,P)

The result is Ib = 227.0442 N.

c):

The actual value of the integral is F(x) = 246.59. Therefore, the truncation error is 246.59-227.0442 = 19.5478

d):

h = 10/4;
x = linspace(0,10,4);
x4=0;
x2=0;
P = @(x) 300*x/(1+exp(x));
for j=2:2:4
x4 = x4 + P(x(j));
end
for k=3:2:4
x2= x2 + P(x(k));
end
Ic = (h/3)*(P(0)+ P(10) + 4*(x4)+ 2*(x2));

The result gives Ic = 119.6215

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