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2. A W200X22 wide flanged beam made from A992 steel (E 200GPa) is loaded as show

ID: 2086115 • Letter: 2

Question

2. A W200X22 wide flanged beam made from A992 steel (E 200GPa) is loaded as shown. Utilize MATLAB to determine the following: 100 N 400 N/m (m) 0 1.5 2.5 3. 4. a) b) c) Plot the elastic curve (show the deflection in units of mm). Determine the maximum upward and downward deflections of the beam and their locations. If the maximum allowed deflection (up or down) is limited to 1.0 mm, determine the maximum value of the concentrated load (currently set at 100 N) that will result in not exceeding the allowed deflection Note: You may hand-write a problem statement then present your solution attaching your MATLAB code and the elastic curve. You should explicitly tell me your answers, or in other words, I should not have to read through the output of your code to determine or interpret the answer.

Explanation / Answer

a) The following code plots deflection of beam in mm along the length of the beam (The equations are derived using Discontinuity functioin method) b) It gives the minimum, maximum deflections of the beam and the locations of min. and max. deflectioins of the beam c) The maximum value of concentrated load that allows min. and max. deflections of beam as -1.023mm and +1.023mm is P=743N upwards..below 1.023mm is not possible, i.e. If you want the min. deflection of beam below -1mm the max. deflection of beam is going above +1.023mm and vice versa

     If you want the discription of the Discontinuity function method, comment below

clc,clear,clf

E=200*10^9; I=(200*(22^3)*10^(-12))/12;

P=100; %Here P=100N means point load acting downwards at a distance of 2.5m

%P=-747; %Here P=-747N means point load acting upwards at a distance of 2.5m

x1=[0:0.01:1.5];

y1=1/(E*I)*((-50/3*x1.^4)+(((2700+P)/36)*x1.^3)-(((759.375+(0.7292*P))/3)*x1))*10^3;

plot (x1,y1)

hold on

x2=[1.5:.01:2.5];

y2=1/(E*I)*((-50/3*x2.^4)+(50/3*(x2-1.5).^4)+(((2700+P)/36)*x2.^3)-(((759.375+(0.7292*P))/3)*x2))*10^3;

plot (x2,y2)

hold on

x3=[2.5:.01:4];

y3=1/(E*I)*((-50/3*x3.^4)+(50/3*(x3-1.5).^4)-(P/6*(x3-2.5).^3)+(((2700+P)/36)*x3.^3)-(((759.375+(0.7292*P))/3)*x3))*10^3;

plot (x3,y3)

title('Deflection of beam in mm')

grid on

axis on

a=min(y1);

b=max(y2);

c=max(y3);

p=[x1;y1]';

q=[x2;y2]';

r=[x3;y3]';

for i=1:151

if (abs(p(i,2))-abs(a))==0

fprintf(' Minimum deflection in mm of the beam is = ')

fprintf('%d',a )

fprintf(' Location in metres of minimum deflection of the beam is = ')

fprintf('%0.2f',x1(i))

end

if (c > b)

if(abs(r(i,2))-abs(c))==0

fprintf(' Maximum deflection in mm of the beam is = ')

fprintf('%d',c)

fprintf(' Location in metres of maximum deflection of the beam is = ')

fprintf('%d ',x3(i))

end

end

end

for i=1:101

if (b > c)

if (abs(q(i,2))-abs(b))==0

fprintf(' Maximum deflection in mm of the beam is = ')

fprintf('%d',b)

fprintf(' Location in metres of maximum deflection of the beam is = ')

fprintf('%d ',x2(i))

end

end

end