bruce mayer, pe licensed electrical & mechanical engineer [email protected]
DESCRIPTION
Engineering 36. Lab-19 Chp07 Beam VM Diagrams By Calculus. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected]. Calculus Relations. MATLAB V&M Diagrams. MatLab Code - 1a. % Bruce Mayer, PE * 31Jul07 % ENGR36 * problem 10.1.28 % file = Prob10_1_28_VM_Plot.m - PowerPoint PPT PresentationTRANSCRIPT
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt1
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
Bruce Mayer, PELicensed Electrical & Mechanical Engineer
Engineering 36
Lab-19 Chp07
Beam VM Diagrams
By Calculus
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt2
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
Calculus Relations
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V
V
V
dxxwVVdVD
C
D
C
KnowMust curve LOADunder area
1
knowMust
curve SHEARunder area
1
C
x
xCD
M
M
M
dxxVMMdMD
C
D
C
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt3
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt4
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt5
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt6
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt7
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt8
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt9
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt10
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt11
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt12
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt13
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt14
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt15
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
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t-lbs
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P10.1.28 Vertically Loaded Beam
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x (ft)
V (l
bs)
P10.1.28 Vertically Loaded Beam
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt16
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
MATLAB V&M Diagrams
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ENGR-36_Lab-23_Fa07_Lec-Notes.ppt17
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
MatLab Code - 1a% Bruce Mayer, PE * 31Jul07% ENGR36 * problem 10.1.28% file = Prob10_1_28_VM_Plot.m% % Find V & M functions by calculus% Plot Using this File%%%clear % clears memory%% Calculate PieceWise Shear-Force Functionsx1 = 0:.1:4;v1= -12.5*x1.^2+246.67;x2 = 4:0.1:8;v2 = -100*x2+446.67;x3 = 8:0.1:10;v3 = -353.3*(x3./x3)x4 = 10:0.1:12;v4 = 300*(x4./x4);x5 = 12.01; v5 = 0;%% Combine the pieces by appendingxv = [x1 x2 x3 x4 x5];v = [v1 v2 v3 v4 v5];% plot v(x); use formating tools to adjust appearanceplot(xv,v) ,xlabel('x (ft)'),ylabel('V (lbs)'), title('P10.1.28 Vertically Loaded Beam'), griddisplay('Shear-force plot complete; hit any key to continue')pause%
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt18
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
MatLab Code – 1b% Calculate PieceWise Bending-Moment Functionsm1 = -25*x1.^3/6 + 246.67*x1;m2 = -50*x2.^2 + 446.67*x2 - 266.67;m3 = -353.3*x3 + 2933;m4 = 300*x4-3600;% Combine the pieces by appendingxm = [x1 x2 x3 x4];m = [m1 m2 m3 m4];% plot v(x); use formating tools to adjust appearanceplot(xm,m) ,xlabel('x (ft)'),ylabel('M (ft-lbs)'), title('P10.1.28 Vertically Loaded Beam'), grid
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt19
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
MatLab Code - 2a% Bruce Mayer, PE * 30Nov10% ENGR36 * S&T problem 10.1.28% file = Prob10_1_28_VM_AREA_AnonFcn_1211.m% % Find V & M functions by calculus% Plot Using this File%% Set V Break-PointsV0 = 246+2/3V4 = V0 - 200V8 = V0 - 600V10 = 300%% Define V functionsV04x = @(x) -12.5*x.^2 + V0V48x = @(x) -100*x + V0 + 200V810x = @(x) 0*x + V8V1012x = @(x) 0*x + V10%% Set x, Calc V(x)x0m = -.001V0m = 0x04 = linspace(0,4);V04 = V04x(x04);x48 = linspace(4,8);V48 = V48x(x48);x810 = linspace(8,10);V810 = V810x(x810);x1012 = linspace(10,12);V1012 = V1012x(x1012);x12p = 12.001;V12p = 0;%% make solid line on x-Axisxax = linspace(-2,14);Vax = 0*xax;%
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt20
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
MatLab Code – 2b% concatenate x & V(x) vectorsxAll = [x0m,x04,x48,x810,x1012,x12p];Vall = [V0m, V04,V48, V810, V1012,V12p];%% plotplot(xax, Vax, xAll,Vall, 'LineWidth', 3),xlabel('x (ft)'),ylabel('V (lbs)'),... title('P10.1.28 Vertically Loaded Beam'), griddisplay('Shear-force plot complete; hit any key to continue')pause%% Set M Break-PointsM0 = 0;M4 = 720;M8 = 106 + 2/3;M10 = -600;%% Define M functionsM04x = @(x) (-12.5/3)*x.^3 + V0*x;M48x = @(x) (-100/2)*x.^2 + (V0+200)*x - 200*(1+1/3);M810x = @(x) V8*(x-8) + M8;M1012x = @(x) V10*x - V10*10 + M10;%% calc M(x) using previous x vectorsM0m = 0;M04 = M04x(x04);M48 = M48x(x48);M810 = M810x(x810);M1012 = M1012x(x1012);M12p = 0%% concatenate M(x) vectorsMall = [M0m, M04,M48, M810, M1012, M12p];%
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt21
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
MatLab Code – 2c%plot(xax, Vax, xAll,Mall, 'LineWidth', 3),xlabel('x (ft)'),ylabel('M (ft-lbs)'),... title('P10.1.28 Vertically Loaded Beam'), griddisplay('Bending-Moment plot complete; hit any key to continue')pause%%subplot(2,1,1)area(xAll,Vall),,ylabel('V (lbs)'),title('P10.1.28 Vertically Loaded Beam'), gridsubplot(2,1,2)area(xAll,Mall),xlabel('x (ft)'),ylabel('M (ft-lbs)'),grid
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt22
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt23
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
0 2 4 6 8 10 12-400
-300
-200
-100
0
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V (l
bs)
P10.1.28 Vertically Loaded Beam
0 2 4 6 8 10 12-800
-600
-400
-200
0
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x (ft)
M (f
t-lbs
)
ENGR-36_Lab-23_Fa07_Lec-Notes.ppt24
Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics
0 2 4 6 8 10 12-600
-400
-200
0
200
400
600
800
x (ft)
M (f
t-lbs
)
P10.1.28 Vertically Loaded Beam
0 2 4 6 8 10 12-400
-300
-200
-100
0
100
200
300
x (ft)
V (l
bs)
P10.1.28 Vertically Loaded Beam