Prob. 4.16 Define angle, stress, strain, compliance as functions of time Theta: =t - gamma(t)*l/r; 6:=1→Y a/(2*Pi★x^2*b); unprotect(gamma): gamma: =t ->J(t)*sigma Y:=t→J(1) >J:=t→>(.75+.15*1og10(t)+.018*(1og10(t))^2)/1e9; J:=1→.7510°+.1510log10(1)+.1810log10(t) Set values of numerical parameters > Digits:=4:1:=2;x:=.04/2; Gamma:=8;b:=.002; (1) Compute angle after 20 hrs at 20C >I Theta(deg)'=evalf((180/Pi)*Theta(20*3600))i (2)Compute effective time and angle for 60C >a60:=.001;t60:=20*3600/a60; >I Theta(deg)'=evalf((180/Pi)*Theta(t 60))i e(deg)=27 ()Compute effective time and twist for two-step temperature program >teff:=19.75*3600+(.25*3600)/a60; >Theta(deg)'=evalf((180/Pi)*Theta(t eff))i
Prob. 4.16 Define angle, stress, strain, compliance as functions of time: > Theta:=t -> gamma(t)*l/r; γ( )tl Θ := t → r > sigma:=Gamma/(2*Pi*r^2*b); 1 Γ σ := 2 π r 2 b > unprotect(gamma):gamma:=t -> J(t)*sigma; γ := t → J () t σ > J:=t -> (.75+.15*log10(t)+.018*(log10(t))^2)/1e9; J := t → .75 10-9 + .15 10-9 log10 ( ) + .18 10-10 t log10 ( )t 2 Set values of numerical parameters: > Digits:=4:l:=2;r:=.04/2;Gamma:=8;b:=.002; (1) Compute angle after 20 hrs at 20C: > 'Theta(deg)'=evalf((180/Pi)*Theta(20*3600)); Θ( deg) = 17.36 (2) Compute effective time and angle for 60C: > a_60:=.001;t_60:=20*3600/a_60; > 'Theta(deg)'=evalf((180/Pi)*Theta(t_60)); Θ( deg) = 27.72 (3) Compute effective time and twist for two-step temperature program: > t_eff:=19.75*3600+(.25*3600)/a_60; > 'Theta(deg)'=evalf((180/Pi)*Theta(t_eff)); Θ( deg) = 20.91 Page 1
