FINAL INDEPENDENT PROJECT

Objective:

The structure of the aircraft wing is a cantilever Beam. To determine the reaction forces, shear force and bending moment of an aircraft wing

Consider a simple cantilever Beam used to calculate the reaction forces and Plot the Shear forces & bending moment diagram of a Beam

Procedure:

L=length of the beam

F=Point force acting at free end of th beam

RAx = Reaction force at A in x direction

Ray = Reaction force at A in Y direction

Let us consider a variable length x at a disatnce from the free end

Shear force calculations:

Sum of horizontal reaction forces on beam

RAx=0

Sum of Vertical reaction forces on beam

Ray=F

Beanding moment calculatiosn:

Taking moment about point A

BMA+F*L=0 (Clock wise direction)

BMA =-F*L

Find the BM at a distance ‘x’ from the free end

Bmx=-F*x

Step by step procedure of a code:

1.length of the beam = 10m

2.Force acting at the end of the beam= 1 KN

3.linspace is used to extarct the intermediate points between length of the beam

4.Figure() is used to save the 2D plot

5.axis() is used to scale the x and y axis

6.xlabel and ylabel is used to labelling the 2D plot

7.patch() is used to fill the 2D surface plot.To plot the patch we used the x and Y co-ordinates are

a=[0 L L 0],b=[ 0 0 SF SF] respectively.These are the x & y co-ordinates of the plot vertices

8.gtext() is used to add text to graph using mouse to locate the point

9.annotation() This command is used to display shapes,text box and arrows in the plot.

 clear all
close all
clc

% Shear force and Bending Moment diagram of a cantilever Beam

% Inputs
L=10 % length of the beam in m
F=1 % point load at the end of the beam in KN
x1=[0.5 0.7];  %x-coordinates used for locating the annotation
y1=[0.3,0.7];  %y-coordinates used for loacting the annotation

x=linspace(0,10,100); % Discritization of the length of the beam

% Shear force calculations
RA=F;
SF=F;

% Bending Moment Calculaions
%Bending at a ponit x from the free end of the beam

BM=-F*L;
M=-F*(L-x);
figure(1)
hold on
plot([0 10],[0 0],'color','k','linewidth',3)
a1=[0 L L 0]    % x coordinate to plot the patch
b1=[0 0 SF SF] % y coordinate to plot the patch
patch(a1,b1,'green')
gtext("Max SF is 1 N")
xlabel("Length of the Beam in m")
ylabel("Shear Force (N)")
title("Shear force Diagram")
figure(2)
a=[0 0 L]; % x coordinate to plot the patch
b=[0 BM 0] % y coordinate to plot the patch
patch(a,b,'red')
gtext("Max BM is 10KNm")
xlabel("Length of the Beam in m")
ylabel("Bending Moment (KN-m)")
title("Bending Moment Diagram")
figure(3)
plot(x,M,'r')
gtext("Max BM is 10KNm")
annotation('textarrow',x1,y1,"string",'Bending momemt')
xlabel("Length of the Beam in m")
ylabel("Bending Moment (KN-m)")
title("Bending Moment Diagram")

Results:

In Aircraft Wing structure,The bending moment is more at the fixed end,that can be found in above Bending Moment Graph