# Example 8.1     
 Su   =   150 ksi
 Sy   =   120 ksi
 d  =   1 in
 SN = 0.75 * Su  ; ksi 
 SpN = 0.5 * Su  ; ksi 
 CL   =   1.0 
 CG   =   0.9 
 CT   =   1.0 
 CR   =   1.0 
 CS   =   0.9 
 Sn = SpN * CL * CG * CS * CT * CR  ; ksi 
 S10e5 = SN - (2/3) * (SN - Sn)  ; ksi 
 S10e4 = SN - (1/3) * (SN - Sn)  ; ksi 

# Example 8.2   
IPS()  
BEGIN     
 Su   =   150.0 ksi
 Sy   =   120.0 ksi
 d  =   0.366 in
 A1 = pi() * d^2 / 4 ; in^2 
 Fmin   =   1000 lbf
 Fmax   =   5000 lbf
 Fm = (Fmin + Fmax) / 2 ; lbf 
 Fa = (Fmax - Fmin) / 2 ; lbf 
 SF  =   2.00  
 sm = SF * Fm / A1 ; ksi 
 sa = SF * Fa / A1 ; ksi 
 sa / sm    
 sa1   =   38.0 ksi # from Fig 8.22
 error1 = sa1 - sa  ; ksi 
 sa2   =   48.0 ksi # from Fig 8.22
 error2 = sa2 - sa  ; ksi 
END      
solve(error1, d)
solve(error2, d)

# Example 8.3 
MKS(mm)     
BEGIN      
 Su   =   1.2 Gpa 
 Sy   =   1.0 Gpa 
 Tm   =   1000.00 N m 
 Ta   =   250.00 N m 
 FOS  =   2.00  
 D_over_d  =   1.20  
 r_over_d  =   0.05  
 d  =   29.689 mm 
 Kt   =   1.57  
 q  =   0.95  
 Kf = 1 + (Kt - 1) * q  
 tm = 16 * FOS * Tm * Kf / (pi() *  d^3)  ; MPa 
 ta = 16 * FOS * Ta * Kf / (pi() * d^3)  ; MPa 
 ta / tm    
# Case 1      
 ta1 =   116.0 MPa  # from Fig 8.27  
 err1 = ta1 - ta  ; MPa 
# Case 2      
 ta2   =   150.0 MPa # from Fig 8.27
 err2 =  ta2 - ta  ; MPa 
END   
solve(err1, d)
solve(err2, d)

# Example 8.4      
 Su   =   900 Mpa 
 Sy   =   750 Mpa 
 ro   =   100 mm 
 T1  =   12 N m 
 m1  =   0.6  
 Ft = T1 / ro  ; N 
 Fn = Ft / m1  ; N 
 xt   =   50 mm 
 Mt = Ft * xt  ; N m 
 xn   =   100 mm 
 Mn = Fn * xn  ; N m 
 M = sqrt(Mn^2 + Mt^2)  ; N m 
 q  =   0.95 
 Kt_t   =   1.10 
 q  =   0.93 
 Kf_t = 1 + (Kt_t - 1) * q  
 Kt_a   =   1.28 
 q  =   0.91 
 Kf_a = 1 + (Kt_a - 1) * q  
 Kt_b   =   1.28 
 q  =   0.91 
 Kf_b = 1 + (Kt_b - 1) * q  
 d  =   16 mm
 t = 16 * T1 * Kf_t / pi() / d^3  ; Mpa 
 s_a = 4 * Fn * Kf_a / pi() / d^2  ; Mpa 
 s_b = 32 * M * Kf_b / pi() / d^3  ; Mpa 
 sem = s_a / 2 + sqrt(t^2 + s_a^2 / 4)  ; Mpa 
 sea = s_b  ; Mpa 
 FOS  =   4

# Example 8.5     
 S1   =   80.0 ksi
 n1   =   5.0 
 N1   =   1.00E+05 
 S2   =   90.0 ksi
 n2   =   2.0 
 N2   =   3.80E+04 
 S3   =   100.0 ksi
 n3   =   1.0 
 N3   =   1.60E+04 
 fL = n1 / N1 + n2 / N2 + n3 / N3   
 n = 1 / fL   
 t  =   20.0 s
 L1 = n * t ; hr 

# Example 8.6     
 Sa   =   120.0 Mpa
 na   =   2.0 
 na_over_NA = 0
 Sb   =   150.0 Mpa
 nb   =   4.0 
 Nb   =   3.50E+06 
 Sc   =   310.0 Mpa
 nc   =   2.0 
 Nc   =   2.00E+04 
 Sd   =   380.0 Mpa
 nd   =   1.0 
 Nd   =   2.50E+03 
 fL = na_over_NA + nb / Nb + nc / Nc + nd/ Nd   
 n = 1 / fL   
 t  =   6.0 s
 L1 = n * t ; hr 

# Example 8.7     
BEGIN     
 Y0   =   0.9 
 a1   =   0.2 
 I1 = (-1 / a1 - 4 * ln(a1) + 6 * a1 - 2 * a1^2 + a1^3 / 3) / Y0^4   
 a2   =   0.5 
 I2 = (-1 / a2 - 4 * ln(a2) + 6 * a2 - 2 * a2^2 + a2^3 / 3) / Y0^4   
 I = I2 - I1  
 w  =   30.0 mm
 dc_over_dN  =   1.00E-06 mm
 DK0   =   5.0 Mpa m^/2
 Ds   =   40.0 Mpa 
 n  =   4.0  
 DN12   =   1.19E+06  
 Ip  = (DN12 / w) * dc_over_dN * (Ds * (pi() * w)^(1/2) / DK0)^n   
END 
solve(Ip, n)   

# Homework Problems:

TBD