Question

EMT 101- Engineering Programming Homework 3 Deflection of an I-Beam(100 %) You are to develop a program that calculates and plots the vertical deflection of a beam subjected to a force acting on it as given in Figure 1. The I-Beam has length, L 2m with its left end fixed at the wall (no deflection at wall) The right end of the beam is applied with a vertical load force P with a vertical deflection function (3L -a) EI wherer 0, L and I(is the moment of inertia of the cross section about its neutral axis(second moment of inertia) defined as I(x) 12 The beam has a cross-sectional diagram in Figure 2 and has the following properties ·u, = 150mm for 0 < x < L/2: w = 90mm for L/2 < x L Assume that the Young's Modulus (the inherent 'strength' of the beam) E 7 × 1010P and that the load at the tip P 3kN. Your code should have the tollowing 1. A function or subroutine to compute the second moment of inertia Ix) 2. A function or subroutine to compute the overall deflection v(x) of the beain. 3. A function or subroutine to plot the deflection u(z) over /0.L]

Answer 1

I assumed you asked to write a MATLAB programme. So here is the matlab programme for the given question

%==================Here is the matlab code==================

clear all
close all
clc

P=3e3; %in N
E=7e10; % in N/m^2
h=100e-3; % in m
b=5e-3; % in m
t=8e-3; % in m
L=2; %in m

x=0:0.1:L;

for i=1:length(x)

l=x(i);

% calculating the I(x) using the subroutine
Ix=MI(h,b,t,l,L);

% calculating the deflection
vx=(P*x.^2.*(3*L-x))/(E*Ix);

end

% plotting the deflection
plot(x,vx)
xlabel('length in m')
ylabel('deflection in m')

%=============== a subroutine to calculate the moment of inertia==================

function Ix=MI(h,b,t,l,L)

if (l>=0&&l<L/2)
  
w=150e-3;
else
w=90e-3;
end
Ix=(w*h^3-(h-2*t)^3*(w-b))/12;

end

%===============End of the matlab code=============================