A simply supported beam is loaded as shown. Using singularity functions, the she

Question

A simply supported beam is loaded as shown. Using singularity functions, the shear, bending moment, slope, and displacement along the beam can be expressed by the following equations: V (x) = 20 [(x - 0)^1 - (x - 5)^1] - 15 (x - 8)^0 - 57 M (x) = - 10 [(x - 0)^2 - (x - 5)^2] + 15 (x - 8)^1 + 150 (i - 7)^0 + 57x EI times S (x) = -10/3 [(x - 0)^3 - (x - 5)^3] + 15/2 (x - 8)^2 + 150 (x - 7)^1 + 57/2 x^2 - 238.25 EI times D (x) = -1/6 [(x - 0)^4 - (x - 5)^4] + 15/6 (x - 8)^3 + 75 (x - 7)^2 + 57/6 x^3 - 238.25x By definition, the singularity function can be expressed as follows: (x - a)^n = {(x - a)^n when x > a 0 when x lessthanorequalto a Plot the shear, bending moment, slope, and displacement as a function of x on 4 subplots (Assume El = 10000 kips.ft^2). Show how to find the points where each of them equals zero. Determine the maximum deflection and its location. (x - a)^n = (x > a). * (x - a). ^n

Explanation / Answer

* create an M-File that gives singularity function as follows:

function s = sing(x,a,n)

if x > a

s = (x-a).^n;

else

s=0;

end

* write the following M-file to obtain the plot displacement Vs distance

function beam(x)

y = linspace(0,x);

n= length (y);

for i=1:n

uy(i) = -5/6. * (sing(y(i),0,4)-sing(y(i),5,4));

uy(i)= uy(i) + 15/6. * Sing (y(i),8,3) + 75* sing(y(i),7,2);

uy(i)=uy(i)+57/6.*y(i)^3 - 238.25.* y(i);

end

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