Week 1 Challenge - Introduction to MATLAB and Basics of Structural Engineering

CHALLENGE 1

HOWE TRUSS:

a)Howe truss is created with 2 hinge supports and links is shown below.

Assumptions:

All line members have to uniform cross sections.

Joints are rigid.

Hinges can lock horizontal and vertical movements.

b) Model definitions:

No. of links (m)=21

No. of joints (j)=12

Hinge links*2=> r=4

Here, m+r=25 and 2j=24

m+r>2j.

c) Structure is Internally indeterminate. By force method equation, the truss is Indeterminate.

Indeterminate:

One in which the number of unknown forces and reactions exceeds the number of equilibrium equations.

d)Externally stable:

Yes, the Truss member shown above is externally stable. It has 2 hinge supports that prevent external motions.

e)Internally stable:

No, by force equations (m+r>2j).

f)Structure is indeterminate.

Kinematic degree of indeterminacy :3j-r-m => 3(12)-4-21 => 11

Static degree of indeterminacy :m+r-2j=>21+4-2(12)=>1

g) Does your answers to the above questions remain the same for the below given coplanar truss:

No, this structure is unstable.

No. of links (m)=6

No. of joints (j)=5

Hinge links+roller support=> r=3

Therefore,

m+r=9

2j=10

m+r<2j

The structure is unstable.

MATLAB PROGRAM:

2.Create a Matlab script and assume variables a,b,c. Assign random numbers for variables a,b,c. Perform mathematical operations as listed below and list the answers.

a=2; 
b=4;
c=3;
%Mathematical operations
A1=a*b^c;
A2=(a*b)^c;
A3=a-b^c;
A4=a^b-c;
A5=a^b\c;
A6=a^b/c;

3.Perform Matlab script operations to create a row vector and perform the following:

%Understanding vector algebra
Col_Algebra=(1:2:3:4:5:6); %list
LinSpace=linspace(1,100,10); %Linspace
Length=length(LinSpace); %Length to find no. of elements
Size=size(LinSpace); %list row and column value 
Specific_Element=LinSpace(5); %Specific element in list
Specific_Range=LinSpace(2:8); %Get elements for specified range
Transpose=LinSpace' %Transpose matrix

4.Create a matrix with m rows and n columns A and B and perform the following commands

%Matrix Operations
Mat_A=rand(3)
Mat_B=rand(3)

Ma_Multiply=Mat_A*Mat_B %Cross multiplication for matrix
Ma_Divide=Mat_A/Mat_B  %Matrix divide
Ma_Mod=Mat_A\Mat_B %Matrix inverse and divide
Square=Mat_A^2  %Perform Mat_A cross multiplication
Val=Mat_A^2-Mat_A*Mat_A %Justifies '^' operator perform cross multiplication
Dot_Product=Mat_A.^2
Val2=Mat_A.^2-Mat_A^2 %Proof that dot product and cross product are different

5.Create a Matlab script to understand the standard commands to create standard matrices

%Creating Matrices
A=ones(3)       %Creating matix with 1 for given range
B=zeros(3)      %Creating matrix with 0 for given range
C=eye(3)        %Creating diagonal matrix
D=diag(rand(3)) %Creating diagonal values as matrix.

6.create a Matlab script to perform selecting and changing parts of matrices:

%Accessing elements in matrix
B1=rand(3)
i=input('Enter row for access and replace (1~3)') %Input from user to select row
j=input('Enter column for access and replace less than (1~3)') %Input from user to select column.
%If user inputted value greater or lesser than permissible value.
if i<1|i>3
    i=3
end
if j<1|j>3
    j=3
end
Row_Elements=B1(i,:) %User selected row will be assigned to Row_Elements
Column_Elements=B1(:,j) %User selected Column will be assigned to Column_Elements

%Changing elements 
I_Matrix=round(rand(3)*10) %Temp matrix
Row_Change=B1 %B1 matrix assigned to Row_Change
Row_Change(i,:)=I_Matrix(1,:) %Row values are changed.
Column_Change=B1 %B1 Matrix assigned to Column_Change
Column_Change(:,j)=I_Matrix(:,2) %Column value changed.

CONCLUSION:

Matlab codes are created for a given tasks and outputs are verified.