1) The diving board shown below has cross-section of 600 x 45 mm with E 10.3 GPa

Question

1) The diving board shown below has cross-section of 600 x 45 mm with E 10.3 GPa Determine maximum bending stress and tip deflection when a 300 lb person is standing at the center of the width at the free end 0.7 m MAX MPa MAX 2) Write a MATLAB m-file to plot vertical deflection of the diving board in Problem 1) as a function of position along the beam. The plot should be fully annotated with meaningful labels, titles, and legends as appropriate. The MATLAB code provided below shows two ways to implement beam functions. Attach copy of your plot and your MATLAB code % hol-demo-m-demonstration code for ME 360 HO! % HJSill, 17.08.21 % constants L 10 a 4 % fill column vector from 0 to L with step 0.5 x (0:0.5:L) % number of elements in x n length(x); % beam o-a> function using for-loop and if-statement for i 1 n, if x(i) a, beam1 (i) = 1 + 2*x(i)-2.5*(x(i)-a); se beam1() 1 2*x(); end end % beam o-a-function using conditional-test and dot-multiply beam21 2x-2.5*(x-a).*(>-a); % plot both figure( 1) clf plot(x,beam1,r, xbeam2,go) xlabel('x[inches] ylabel('beam1 and beam2 inches title( Sample plot for beam function) legend('if-else,'conditional-test) % bottom of hol-demo

Explanation / Answer

clear all; clc; close all; display('What is the X-section of the beam to be computed ?') disp('If circle, 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 example #1, hit ENTER or enter 0') disp('To see example #2, enter 5') 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=69.90e+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 properties of the beam') display('Do you know your beam"s material properties, viz. Young"s modulus and density ?') YA=input('Enter 1, if you do; enter 0, if you don"t '); if YA==1 E=input('Enter Young"s modulus in [Pa]: '); Ro=input('Enter material density in [kg/m^3]: '); else display('Steel: E=2.1e+11 [Pa]; Ro=7850 [Kg/m^3]') display('Copper: E=1.2e+11 [Pa]; Ro=8933 [Kg/m^3]') display('Aluminum: E=0.69e+11 [Pa]; Ro=2700 [Kg/m^3]') E=input('Enter Young"s modulus in [Pa]: '); Ro=input('Enter material density in [kg/m^3]: '); end elseif CS==2 W=input('Enter Width of the X-section in [m]: '); L=input('Enter Length in [m]: '); Ix=(1/12)*W^4; A=W^2; disp('Material properties of the beam'); disp('Do you know your beam"s material properties, viz. Young"s modulus and density ?') YA=input('Enter 1, if you do; enter 0, if you don"t: '); if YA==1 E=input('Enter Young"s modulus in [Pa]: '); Ro=input('Enter material density in [kg/m^3]: '); else display('Steel: E=2.1e+11 [Pa]; Ro=7850 [Kg/m^3]') display('Copper: E=1.2e+11 [Pa]; Ro=8933 [Kg/m^3]') display('Aluminum: E=0.69e+11 [Pa]; Ro=2700 [Kg/m^3]') E=input('Enter Young"s modulus in [Pa]: '); Ro=input('Enter material density in [kg/m^3]: '); end elseif CS==3 W=input('Enter Width of the X-section in [m]: '); Th=input('Enter Thickness of the X-section in [m]:'); L=input('Enter Length in [m]: '); Ix=(1/12)*W*Th^3; Iy=(1/12)*(W^3)*Th; A=W*Th; disp('Material properties of the beam') disp('Do you know your beam"s material properties, viz. Young"s modulus and density ?') YA=input('Enter 1, if you do; enter 0, if you don"t: '); if YA==1 E=input('Enter Young"s modulus in [Pa]: '); Ro=input('Enter material density in [kg/m^3]: '); else display('Steel: E=2.1e+11 [Pa]; Ro=7850 [Kg/m^3] ') display('Copper: E=1.2e+11 [Pa]; Ro=8933 [Kg/m^3] ') display('Aluminum: E=0.69e+11 [Pa]; Ro=2700 [Kg/m^3] ') E=input('Enter Young"s modulus in [Pa]: '); Ro=input('Enter material density in [kg/m^3]: '); end elseif CS==4 display('Note: you need to compute Ix (area moment of inertia along x axis) and X-sectional area') L=input('Enter Lengthin [m]: '); Ix=('Enter Ix in [m^4]: '); A=('Enter X-sectional area in [m^2]: '); disp('Material proprties of the beam') disp('Do you know your beam"s material properties, viz. Young"s modulus and density ?') YA=input('Enter 1, if you do; enter 0, if you don"t '); if YA==1 E=input('Enter Young"s modulus in [Pa]: '); Ro=input('Enter material density in [kg/m^3]: '); else display('Steel: E=2.1e+11 Pa; Ro=7850 Kg/m^3 ') display('Copper: E=1.2e+11 Pa; Ro=8933 Kg/m^3 ') display('Aluminum: E=0.69e+11 Pa; Ro=2700 Kg/m^3 ') E=input('Enter Young"s modulus in [Pa]: '); Ro=input('Enter material density in [kg/m^3]: '); end elseif CS==5 display('Example #2') display('This is a rectangular X-sectional steel beam ') display('Length=0.45 m; Width=0.04 m; Thickness=0.003 m;') L=.45; W=.04; Th=.003; A=W*Th; Ix=(1/12)*W*Th^3; E=2.1*1e11; Ro=7.85*1e3; 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:>> Cbeam') pause(3) return end display('How many modes and mode shapes would you like to evaluate ?') HMMS=input('Enter the number of modes and mode shapes to 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=3*HMMS; jj=1; while jj

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