Great Deal! Get Instant $10 FREE in Account on First Order + 10% Cashback on Every Order Order Now

See two files. Need by 7am (Central time) on March 28th in formats listed in assignment.

1 answer below »
See two files. Need by 7am (Central time) on March 28th in formats listed in assignment.
Answered Same Day Mar 26, 2021

Solution

Kshitij answered on Apr 01 2021
170 Votes
Problem 2.zip
Problem 2/BeamAssemble.m
function y = BeamAssemble(K,k,i,j)
%This function assembles the element stiffness
% matrix k of the beam element with nodes
% i and j into the global stiffness matrix K.
% This function returns the global stiffness matrix K
% after the element stiffness matrix k is assembled.
K(2*i-1,2*i-1) = K(2*i-1,2*i-1) + k(1,1) ;
K(2*i-1,2*i) = K(2*i-1,2*i) + k(1,2) ;
K(2*i-1,2*j-1) = K(2*i-1,2*j-1) + k(1,3) ;
K(2*i-1,2*j) = K(2*i-1,2*j) + k(1,4) ;
K(2*i,2*i-1) = K(2*i,2*i-1) + k(2,1) ;
K(2*i,2*i) = K(2*i,2*i) + k(2,2) ;
K(2*i,2*j-1) = K(2*i,2*j-1) + k(2,3) ;
K(2*i,2*j) = K(2*i,2*j) + k(2,4) ;
K(2*j-1,2*i-1) = K(2*j-1,2*i-1) + k(3,1) ;
K(2*j-1,2*i) = K(2*j-1,2*i) + k(3,2) ;
K(2*j-1,2*j-1) = K(2*j-1,2*j-1) + k(3,3) ;
K(2*j-1,2*j) = K(2*j-1,2*j) + k(3,4) ;
K(2*j,2*i-1) = K(2*j,2*i-1) + k(4,1) ;
K(2*j,2*i) = K(2*j,2*i) + k(4,2) ;
K(2*j,2*j-1) = K(2*j,2*j-1) + k(4,3) ;
K(2*j,2*j) = K(2*j,2*j) + k(4,4) ;
y=K;
Problem 2/BeamElementForces.m
function y = BeamElementForces(k,u)
%This function returns the element nodal force
% vector given the element stiffness matrix k
% and the element nodal displacement vector u.
y=k*u;
Problem 2/BeamElementStiffness.m
function y = BeamElementStiffness(E,I,L)
%BeamElementStiffness This function returns the element
% stiffness matrix for a beam
% element with modulus of elasticity E,
% moment of inertia I, and length L.
% The size of the element stiffness matrix is 4x4.
y = E*I/(L*L*L) * [12 6*L -12 6*L ; 6*L 4*L*L -6*L 2*L*L ; -12 -6*L 12 -6*L ; 6*L 2*L*L -6*L 4*L*L];
Problem 2/Data_Input_Output_Table.xlsx
Input_Data
            Number of nodes in the slab                                    6
            # Element             Node                         Element length L, ft            Height of the slab section in element, in            Modulus of the elasticity for the element material, psi            Density of the element material, l
ft^3
                        i            j
            1            1            2            5            8            4.50E+06            145
            2            2            3            5            6            4.50E+06            145
            3            3            4            5            4            4.50E+06            145
            4            4            5            5            6            4.50E+06            145
            5            5            6            5            8            4.50E+06            145
Problem 2/Problem_2.m
% Length of each element (in):
L_1=xlsread('Data_Input_Output_Table.xlsx','Input_Data','D5')*12;
L_2=xlsread('Data_Input_Output_Table.xlsx','Input_Data','D6')*12;
L_3=xlsread('Data_Input_Output_Table.xlsx','Input_Data','D7')*12;
L_4=xlsread('Data_Input_Output_Table.xlsx','Input_Data','D8')*12;
L_5=xlsread('Data_Input_Output_Table.xlsx','Input_Data','D9')*12;
%Height of the slab section in each element, in
H_1=xlsread('Data_Input_Output_Table.xlsx','Input_Data','E5');
H_2=xlsread('Data_Input_Output_Table.xlsx','Input_Data','E6');
H_3=xlsread('Data_Input_Output_Table.xlsx','Input_Data','E7');
H_4=xlsread('Data_Input_Output_Table.xlsx','Input_Data','E8');
H_5=xlsread('Data_Input_Output_Table.xlsx','Input_Data','E9');
% Modulus of the elasticity for material of each element (psi)
E_1=xlsread('Data_Input_Output_Table.xlsx','Input_Data','F5');
E_2=xlsread('Data_Input_Output_Table.xlsx','Input_Data','F6');
E_3=xlsread('Data_Input_Output_Table.xlsx','Input_Data','F7');
E_4=xlsread('Data_Input_Output_Table.xlsx','Input_Data','F8');
E_5=xlsread('Data_Input_Output_Table.xlsx','Input_Data','F9');
% Unit width of the slab in Z direction
UW=12;
%The second-area moment of the beam section of each element about the Z axis, in^4:
J_Z_1=Rectangular_Area_Moment(UW,H_1);
J_Z_2=Rectangular_Area_Moment(UW,H_2);
J_Z_3=Rectangular_Area_Moment(UW,H_3);
J_Z_4=Rectangular_Area_Moment(UW,H_4);
J_Z_5=Rectangular_Area_Moment(UW,H_5);
%Stiffness matrices for each element:
Km_1=BeamElementStiffness(E_1,J_Z_1,L_1);
Km_2=BeamElementStiffness(E_2,J_Z_2,L_2);
Km_3=BeamElementStiffness(E_3,J_Z_3,L_3);
Km_4=BeamElementStiffness(E_4,J_Z_4,L_4);
Km_5=BeamElementStiffness(E_5,J_Z_5,L_5);
% Global Stiffness Matrix
GM=zeros(2*(xlsread('Data_Input_Output_Table.xlsx','Input_Data','D1')),2*(xlsread('Data_Input_Output_Table.xlsx','Input_Data','D1')));
GM=BeamAssemble(GM,Km_1,xlsread('Data_Input_Output_Table.xlsx','Input_Data','B5'),xlsread('Data_Input_Output_Table.xlsx','Input_Data','C5'));
GM=BeamAssemble(GM,Km_2,xlsread('Data_Input_Output_Table.xlsx','Input_Data','B6'),xlsread('Data_Input_Output_Table.xlsx','Input_Data','C6'));
GM=BeamAssemble(GM,Km_3,xlsread('Data_Input_Output_Table.xlsx','Input_Data','B7'),xlsread('Data_Input_Output_Table.xlsx','Input_Data','C7'));
GM=BeamAssemble(GM,Km_4,xlsread('Data_Input_Output_Table.xlsx','Input_Data','B8'),xlsread('Data_Input_Output_Table.xlsx','Input_Data','C8'));
GM=BeamAssemble(GM,Km_5,xlsread('Data_Input_Output_Table.xlsx','Input_Data','B9'),xlsread('Data_Input_Output_Table.xlsx','Input_Data','C9'));
%GM(1,1) GM(1,2) GM(1,3) GM(1,4) GM(1,5) GM(1,6) GM(1,7) GM(1,8) GM(1,9) GM(1,10) GM(1,11) GM(1,12) U_1_y F_1_y
%GM(2,1) GM(2,2) GM(2,3) GM(2,4) GM(2,5) GM(2,6) GM(2,7) GM(2,8) GM(2,9) GM(2,10) GM(2,11) GM(2,12) Phi_1 M_1
%GM(3,1) GM(3,2) GM(3,3) GM(3,4) GM(3,5) GM(3,6) GM(3,7) GM(3,8) GM(3,9) GM(3,10) GM(3,11) GM(3,12) U_2_y F_2_y
%GM(4,1) GM(4,2) GM(4,3) GM(4,4) GM(4,5) GM(4,6) GM(4,7) GM(4,8) GM(4,9) GM(4,10) GM(4,11) GM(4,12) x Phi_2 = M_2
%GM(5,1) GM(5,2) GM(5,3) GM(5,4) GM(5,5) GM(5,6) GM(5,7) GM(5,8) GM(5,9) GM(5,10) GM(5,11) GM(5,12) U_3_y F_3_y
%GM(6,1) GM(6,2) GM(6,3) GM(6,4) GM(6,5) GM(6,6) GM(6,7) GM(6,8) GM(6,9) GM(6,10) ...
SOLUTION.PDF

Answer To This Question Is Available To Download

Related Questions & Answers

More Questions »

Submit New Assignment

Copy and Paste Your Assignment Here