The area moment of inertia I_x of a rectangle about the axis x_0 passing through

Question

The area moment of inertia I_x of a rectangle about the axis x_0 passing through its centroid is I_x = 1/12 bh^3. The moment of inertia about an axis x that is parallel to x_0 is h given by I_x = I_x_0 + Ad^2_x, where A is the area of the rectangle, and d_x is the distance between the two axes. Write a MATLAB user-defined function that determines the area moment of inertia I_x of a "I" beam about the axis that passes through its centroid (see drawing). For the function name and arguments use Ixc = IxcBeam (w, h, d, t) where the input arguments w, h, d, and t are the dimensions shown in the figure and the output argument Ixc is I_x. For finding the coordinate y_c of the of the centroid, use the user-defined function centroidI from the previous problem as a subfunction inside IxcBeam. (The moment of inertia of a composite area is obtained by dividing the area into parts and adding the moments of inertia of the parts) Use the function to determine the moment of inertia of for a beam with w = 10 in., h = 8 in., d = 6 in., and t = 0.5 in.

Explanation / Answer

clear all; clc; close all; %% PART I. display('What is the cross section of the beam?') disp('To see an example #1 (rectangular X-section), hit enter') disp('If circular X-section, enter 1; If square, enter 2;') disp('If rectangle, enter 3; ') disp('If your beam"s X-section is not listed here, enter 4') disp('To see an example #2 (rectangular X-section), enter 5') disp('To use specific beam"s X-section including, E, Ix, Ro, enter 6 ') CS=input(' Enter your choice: '); if isempty(CS) || CS==0 disp('Example #1. Rectangular X-section Aluminum beam') disp('Length=0.321 [m], Width=0.05 [m], Thickness=0.006 [m];') disp('E=69.9*1e9 [Pa]; Ro=2770 [kg/m^3]') L=.321; W=.05; Th=.006; A=W*Th; V=L*W*Th; Ix=(1/12)*W*Th^3; %Iy=(1/12)*(W^3)*Th; E=69.9*1e+9; Ro=2770; elseif CS==1 R=input('Enter Radius of the X-section= '); L=input('Enter Length= '); Ix=(1/4)*pi*R^4; %Iy=Ix; A=pi*R^2; disp('Material proprties of the beam'); E=input('Enter Young"s modulus in [Pa]= '); Ro=input('Enter material density in [kg/m^3]= '); elseif CS==2 W=input('Enter Width of the X-section: '); L=input('Enter Length: '); Ix=(1/12)*W^4; %Iy=Ix; A=W^2; disp('Material proprties of the beam'); E=input('Enter Young"s modulus in [Pa]= '); Ro=input('Enter material density in [kg/m^3]= '); elseif CS==3 W=input('Enter Width of the X-section= '); Th=input('Enter Thickness of the X-section= '); L=input('Enter Length= '); Ix=(1/12)*W*Th^3; %Iy=(1/12)*(W^3)*Th; A=W*Th; disp('Material proprties of the beam'); E=input('Enter Young"s modulus in [Pa]= '); Ro=input('Enter material density in [kg/m^3]= '); elseif CS==4 display('Note: you need to compute Ix (area moment of inertia along x axis) and X-sectional area') L=input('Enter Length: '); Ix=('Enter Ix in [m^4]: '); A=('Enter X-sectional area in [m^2]: '); disp('Material proprties of the beam'); E=input('Enter Young"s modulus in [Pa]= '); Ro=input('Enter material density in [kg/m^3]= '); elseif CS==5 display('Given example data are used for evaluations.'); display('Given Example is rectangular X-section Al. beam '); L=.3; W=.005; Th=.0005; A=W*Th; V=L*W*Th; Ix=(1/12)*W*Th^3; Iy=(1/12)*(W^3)*Th; E=70*1e+9; Ro=2.7*1e+3; else F=warndlg('It is not clear what your choice of X-section of a beam is. Re-run the script and enter your beam"s X-section !!!!!!','!! Warning !!'); waitfor(F) display('Type in:>> FF_endBEAM') pause(3) return end %% PART II. % display('How many modes and mode shapes would you like to evaluate ?'); HMMS=input('Enter the number of modes and mode shapes to be computed: '); if HMMS>=7 disp(' ') warning('NOTE: Up to 6 mode shapes (plots) are displayed via the script. Yet, using evaluated data (Xnx) of the script, more mode shapes can be plotted'); disp(' ') end Nm=4*HMMS; jj=4; while jj

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