# Example 12.1      
IPS()
 DF   =   45.0 lbf 
 Dd   =   0.5 in 
 k = DF / Dd  ; lbf/ in 
 Fmax   =   105 lbf 
 CA1 =   0.10  
 CA2 = CA1 * Fmax / k ; in 
 Fsolid = Fmax + k * CA2  ; lbf 
# (a)      
 D1  =   1.25 in 
 d1  =   0.156 in 
 Ks   =   1.05  
 t1 = 8 * Fsolid * D1 * Ks / pi() / d1^3  ; ksi 
 Su   =   225.0 ksi 
 tsolid = 0.45 * Su   ; ksi 
 error = t1 - tsolid  ; ksi 
 Dh   =   1.5 in 
 DC = Dh  - (D1 + d1)  ; in 
# (b)      
 D2  =   1.15 in 
 d2  =   0.157 in 
 Ks   =   1.05  
 t2 = 8 * Fsolid * D2 * Ks / pi() / d2^3  ; ksi 
 Su   =   225.0 ksi 
 tsolid = 0.45 * Su   ; ksi 
 error = t2 - tsolid  ; ksi 
 Dh   =   1.5 in 
 DC = Dh  - (D2 + d2)  ; in 
# (c)      
 G2  =   11.5 Mpsi 
 N2  =   6.36  
 kp = d2^4 * G2 / 8 / D2^3 / N2  ; lbf/ in 
 error = k - kp  ; lbf/ in 
 Nt = N2 + 2   
 Ls = Nt * d2 ; in 
 Lfree = Ls + Fsolid / k ; in 
 Fstr   =   60 lbf
 Lstr = Lfree - Fstr / k ; in 
# (d)     
 Ls / Lfree   
 Lfree / D2  

# Example 12.2     
 w1   =   650.0 rpm
 N1  =   1000000.0 
 t1 = 2 * pi() *  N1 /  w1  ; hr 
 tmax_over_tmin   =   0.5 
 tmax   =   800.0 MPa
 FOS  =   1.10 
 FOSsurge   =   1.10 
 tdesign = tmax / FOS /  FOSsurge  ; MPa 
 Kw   =   1.14 
 C1   =   10.00 
 Fmax   =   600.0 N
 d1 = sqrt(8 * Fmax * C1* Kw / pi() / tdesign)  ; mm 
 d = 5.0 mm
 CKw = pi() *  tdesign * d^2 / 8 / Fmax   
 C1   =   9.40 
 D1 = C1 * d ; mm 
 DF  =   300.00 N
 Dx  =   25.00 mm
 k = DF / Dx  ; N/mm 
 G1  =   79.00 Gpa
 N1 = d * G1 / 8 / C1^3 / k 
 Ls = (N1 + 2) * d ; mm 
 CA  =   0.10 
 Fs = (1 + CA) * Fmax  ; N 
 Lf = Ls + Fs / k ; mm 
 Lf / D1  
 0.5 * N1 * d  / Lf  
 C2  =   13900.00 Hz in
 fn = C2 * d / N1 / D1^2  ; Hz 

# Example 12.3     
 w1   =   650.0 rpm
 N1  =   1000000.0 
 t1 = 2 * pi() *  N1 /  w1  ; hr 
 tmax_over_tmin   =   0.5 
 tmax   =   750.0 MPa
 FOS  =   1.13 
 FOSsurge   =   1.10 
 tdesign = tmax / FOS /  FOSsurge  ; MPa 
 Kw   =   1.14 
 C1   =   10.00 
 Fmax   =   600.0 N
 d1 = sqrt(8 * Fmax * C1* Kw / pi() / tdesign)  ; mm 
 d = 5.0 mm
 CKw = pi() *  tdesign * d^2 / 8 / Fmax  
 C1   =   9.40 
 D1 = C1 * d ; mm 
 DF  =   300.00 N
 Dx  =   25.00 mm
 k = DF / Dx  ; N/mm 
 G1  =   79.00 Gpa
 N1 = d * G1 / 8 / C1^3 / k 
 Ls = (N1 + 2) * d ; mm 
 CA  =   0.10 
 Fs = (1 + CA) * Fmax  ; N 
 Lf = Ls + Fs / k ; mm 
 Lf / D1   
 0.5 * N1 * d  / Lf   
 C2  =   13900.00 Hz in
 fn = C2 * d / N1 / D1^2  ; Hz 

# Example 12.4     
BEGIN     
 Fm   =   3000.0 N
 Fa   =   2000.0 N
 L1  =   679.8 mm
 b  =   412.2 mm
 h  =   7.0 mm
 Kf   =   1.3 
 sa = 6 * Fa * L1 * Kf / b / h^2  ; Mpa 
 sm = 6 * Fm * L1 * Kf / b / h^2  ; Mpa 
 sa / sm   
 sa_max   =   525.0 Mpa 
 k  =   30.0 N/mm 
 E  =   200.0 Gpa 
 kp = E * b * h^3 / 3 / L1^3  ; N/mm 
 err1 = sa_max - sa
 err2 = k - kp
END   
solve(err1, err2, L1, b)

# Example 12.5      
 E  =   30.0 Mpa 
 F1  =   1.0 N 
 h  =   25.0 mm 
# (a) -- Triangle      
 b  =   416.0 mm 
 L1  =   682.0 mm 
 d = 6 * F1 * L1^3 / E / b / h^3  ; mm 
 k = F1 / d  ; N/mm 
# (b) -- Triangle     
 b  =   333.0 mm
 L1  =   682.0 mm
 d = 6 * F1 * L1^3 / E / b / h^3  ; mm 
 kt = F1 / d  ; N/mm 
# (b) -- Rectangle     
 b  =   83.0 mm
 L1  =   682.0 mm
 d = 4 * F1 * L1^3 / E / b / h^3 ; mm 
 kr = F1 / d  ; N/mm 
 kb = kr + kt  ; N/mm 
 kb / k 

# Homework Problems:

TBD