Cantilever Deflection of beams with different cross section.
12 views (last 30 days)
Show older comments
hello everyone,
Script not solving deflection and max deflection for different beam cross section
while trying to calulate cantilever deflection for different type of beam section, my result produces just one deflection graph and i don't know what else to add. i included moment of inertia formula for different cross section in my script.
%Maximum Deflection and Deflection at any point X on a cantilever beam
disp('inputs your given parameters and input "0"2 for ungiven parameters')
W1=input('W1-Uniform Distributed load, N/mm ?');
W2=input('W2-Triangular Distributed load, N/mm ?');
P1=input('P1-End Point load, N ?');
P2=input('P2-Intermediate Point load, N ?');
L=input('Beam length, mm ?');
b=input('Beam diameter/breadth, m2 ?');
bo =input('Beam breadth inside mm ?');
h=input('Beam depth outside, mm ?');
ho= input('Beam depth inside, mm ?');
k= input ('I flange, mm ?');
a=input('Distance of point load from cantilever (a), mm ?');
Mo=input('MO-End moment, Nmm ?');
disp(' P1 Deflection of a Cantilever beam with End Point load')
disp(' P2 Deflection of a Cantilever beam with Intermediate load')
disp(' UDL Deflection of a Cantilever beam with Uniform Distributed loadings')
disp(' TDL Deflection of a Cantilever beam with Triangular Distributed loadings')
disp(' Mo Deflection of a Cantilever beam with End Moment')
Moment_of_inertias = zeros(5);
Circular = (pi*(b/2)^4/4); %Circular cross section;
Rectangular = (b*h^3/12); %Rectangular cross section;
square = (b^4/12); %square cross section;
I_symmetrical = (k^3 *h)/12 + (b^3 *(h^3-ho^3))/12; % I-cross section symmetrical;
hollow_cylindrical = (pi * (b^4-bo^4)/64); % hollow cylindrical cross section;
Moment_of_inertias(1) = Circular
Moment_of_inertias(2) = Rectangular
Moment_of_inertias(3) = square
Moment_of_inertias(4) = I_symmetrical
Moment_of_inertias(5) = hollow_cylindrical
for m=1:5
I = Moment_of_inertias(m);
end
E=2*10^5; %young modulus N/mm2
x = 0:0.1*L:L;
Deflection = zeros(11);
P1_Max = P1*L^3/ 3*E*I;
P2_Max = P2*a^2*(3*L-a)/ 6*E*I;
UDL_Max = W1*L^4 / 8*E*I;
TDL_Max = W2*L^4/ 30*E*I;
MO_Max = Mo* L^2/2*E*I;
for i = 1:11
P1_Def(i) = -(P1*x(i)^2*(3*L- x(i))/6*E*I);
P2_Def(i) = -(P2*x(i)^2*(3*a-x(i))/6*E*I);%for 0<x<a range
P22_Def(i) = -(P2*a^2*(3*x(i)-a)/6*E*I);%for a<x<L range
UDL_Def(i) = -(W1*x(i)^2*((x(i)^2)+(6*L^2)-(4*L*x(i)))/24*E*I);
TDL_Def(i) = -(W2*x(i)^2*((10*L^3)-(10*L^2*x(i))+(5*L*x(i)^2)-(x(i)^3))/(120*L*E*I));
MO_Def(i) = -(Mo* x(i)^2/2*E*I);
end
Loading = input('Enter 1 for P1 +, 2 for P2 +, 3 for UDL +, 4 for TDL +, 5 for Mo +, = ');
if (Loading == 1);
double_loadings = input('Enter 1 for P1, 2 for P1+P2, 3 for P1+UDL, 4 for P1+TDL, 5 for P1+Mo =');
if(double_loadings == 1);% for a single point Point load at the end of the cantilever beam
Deflection = P1_Def;
Max_Deflection = P1_Max
elseif(double_loadings == 2);% for both end Point load and intermediate load.
Range_across_beam_length = input('Enter 1 for 0<x<a range, Enter 2 for a<x<L range = ');
if (Range_across_beam_length == 1); %for both end Point load and intermediate load 0<x<a range
Deflection = P1_Def + P2_Def
elseif (Range_across_beam_length == 2); %for both end Point load and intermediate load a<x<L range
Deflection = P1_Def + P22_Def;
end
Max_Deflection = P1_Max + P2_Max
elseif (double_loadings == 3);% for both end Point load and UDL load.
Deflection = P1_Def + UDL_Def;
Max_Deflection = P1_Max + UDL_Max
elseif (double_loadings == 4); % for both end Point load and TDL load.
Deflection = P1_Def + TDL_Def;
Max_Deflection = P1_Max + TDL_Max
elseif (double_loadings == 5);% for both end Point load and Mo.
Deflection = P1_Def + MO_Def;
Max_Deflection = P1_Max + MO_Max
end
elseif (Loading == 2); %intermediate loading
double_loadings = input('Enter 1 for P2, 2 for P2+UDL, 3 for P2+TDL, 4 for P2+Mo =')
if(double_loadings == 1); % a single intermediate load(P2)
Range_across_beam_length = input('Enter 1 for 0<x<a range, Enter 2 for a<x<L range = ');
if (Range_across_beam_length == 1); % a single intermediate load(P2)
Deflection = P2_Def;
elseif (Range_across_beam_length == 2); % a single intermediate load(P2)
Deflection = P22_Def;
end
Max_Deflection = P2_Max
elseif(double_loadings == 2); % both intermediate(P2) load and UDL
Range_across_beam_length = input('Enter 1 for 0<x<a range, Enter 2 for a<x<L range = ');
if (Range_across_beam_length == 1);% both intermediate(P2) load and UDL 0<x<a range
Deflection = P2_Def + UDL_Def;
elseif (Range_across_beam_length == 2); % both intermediate(P2) load and UDL a<x<L range
Deflection = P22_Def + UDL_Def;
end
Max_Deflection = P2_Max + UDL_Max
elseif(double_loadings == 3) % both intermediate load(P2) and TDL
Range_across_beam_length = input('Enter 1 for 0<x<a range, Enter 2 for a<x<L range = ');
if (Range_across_beam_length == 1);
Deflection = P2_Def + TDL_Def;
elseif Range_across_beam_length == 2
Deflection = P22_Def + TDL_Def;
end
Max_Deflection = P2_Max + TDL_Max
elseif(double_loadings == 4);
Range_across_beam_length = input('Enter 1 for 0<x<a range, Enter 2 for a<x<L range = ');
if (Range_across_beam_length == 1); % both intermediate(P2) load and MO
Deflection = P2_Def + MO_Def;
elseif Range_across_beam_length == 2 % both intermediate(P22) load and MO
Deflection = P22_Def + MO_Def;
end
Max_Deflection = P2_Max + MO_Max
end
elseif (Loading == 3); % UDL on Cantilever beam
double_loadings = input('Enter 1 for UDL, 2 for UDL+TDL, 3 for UDL+Mo =')
if(double_loadings == 1);% for a UDL the cantilever beam
Deflection = UDL_Def;
Max_Deflection = UDL_Max
elseif (double_loadings == 2);% for both UDL and TDL on the cantilever beam
Deflection = UDL_Def + TDL_Def;
Max_Deflection = UDL_Max + TDL_Max
elseif (double_loadings == 2);% for both UDL and MO on the cantilever beam
Deflection = UDL_Def + MO_Def;
Max_Deflection = UDL_Max + MO_Max
end
elseif (Loading == 4); %TDL on a cantilever beam
double_loadings = input('Enter 1 for TDL, 2 for TDL+MO, =')
if(double_loadings == 1);% for a TDL on the cantilever beam
Deflection = TDL_Def;
Max_Deflection = TDL_Max
elseif(double_loadings == 2);% for both TDL and MO on the cantilever beam
Deflection = TDL_Def + MO_Def;
Max_Deflection = TDL_Max + MO_Max
end
elseif (Loading == 5); % moment(MO) on a cantilever beam
Deflection = MO_Def;
Max_Deflection = MO_Max
end
Deflection_Circular = Deflection(1);
Max_Deflection_Circular = Max_Deflection(1);
Deflection_rectangular = Deflection(2);
Max_Deflection_rectangular = Max_Deflection(2);
Deflection_square = Deflection(3);
Max_Deflection_square = Max_Deflection(3);
Deflection_I_Section = Deflection(4);
Max_Deflection_I_Section = Max_Deflection(4);
Deflection_Hollow_cylindrical = Deflection(5);
Max_Deflection_Hollow_cylindrical = Max_Deflection(5);
plot(x, Deflection(1), x, Deflection(2), x, Deflection(3),x, Deflection(4), x, Deflection(5));grid
legend({'y=Deflection(1)','y=Deflection(2)','y=Deflection(3)','y=Deflection(4)','y=Deflection(5)'},'Location','southwest')
xlabel('X Length along the beam (mm)')
ylabel('Deflection(mm), Slope (rad)')
title('Cantilever Beam Deflection ')
0 Comments
Answers (0)
See Also
Categories
Find more on Vibration Analysis in Help Center and File Exchange
Products
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!