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Homework 3

# Homework 3 - ENME400 HW 3...

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%%% ENME400 HW 3 d1=40;E1=25;v1=.45;d2=5.5;E2=200;v2=.3; Pmax=250; %%%%%%%%%%%%%%%%%%%%%%%%%%A%%%%%%%%%%%%%%%% %%%%%%%%%% syms F a=(3/8)^(1/3)*(((1-.3^2)/200E9+(1-.45^2)/25E9)/(1/.0055+1/.04))^(1/3)*F^(1/3) %% a = 5966547068436287/147573952589676412928*F^(1/3) P=(3/(2*pi))*F/a^2 %% P = 10398263182555662570885145012543462309888/35599683919865650465503378346 369*F^(1/3) solve('250E6=10398263182555662570885145012543462309888/355996839198656504 65503378346369*F^(1/3)') %% ans = .62701226480921619556637799283516 ****answer in Newtons **** %%%%%%%%%%%%%%%%%%%%%%%%%%BBBBBBBBB%%%%%%%%% %%%%%%%%%%%%%%%%% %% -sig/pmax .... x=z/a syms x sig1_pmax=((1-abs(x)*atan(1/abs(x)))*(1+v1)-1/(2*(1+(x)^2))) sig3_pmax=1/(1+x^2) ezplot(sig1_pmax) hold on ezplot(sig3_pmax) axis([0 3 0 1.3]) Tm=-(sig1_pmax-sig3_pmax)/2 dTm=diff(Tm) %%dTm = 29/40*abs(1,x)*atan(1/abs(x))-29/40/abs(x)*abs(1,x)/(1+1/abs(x)^2)-2/ (2+2*x^2)^2*x-1/(1+x^2)^2*x z_a=solve('29/40*abs(1,x)*atan(1/abs(x))-29/40/abs(x)*abs(1,x)/(1+1/abs(x)^2)-2/ (2+2*x^2)^2*x-1/(1+x^2)^2*x=0')

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%%z_a = -.53096581852222696575032898666891 ***x=z/a=.5309*** %%sig1 at z_a 29/20-29/20*abs(z_a)*atan(1/abs(z_a))-1/(2+2*z_a^2) %%ans = .22640258002107872450109030971985 %%sig3 at z_a 1/(1+z_a^2) %%ans =.78007701985737773119502932627011 solve('P*(.78007701985737773119502932627011-.226402580021078724501090309719 85)/2=.5*250') %%ans = 451.52888053477008302914544303507 MPa %% solve equation Pmax=3*F/(2*pi*a^2) for F(max) ((2*pi/3)*451.52888053477008302914544303507*5966547068436287/1475739525896 76412928)^(3/2) %%ans = 0.0075 Newtons =F for shear failure %%%%%%%%%%%%%%%%%%%%%%%%%%C%%%%%%%%%%%%%%%%

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Homework 3 - ENME400 HW 3...

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