# Example 4.1     
 Zstraight   =   6 
 ro_over_ri    =   3 
 e_over_h = 1 - 1 / ln(ro_over_ri)   
 Z_minus = (0.5 - e_over_h) / ((e_over_h) * 0.5) 
 Z_plus = (0.5 + e_over_h) / ((e_over_h) * 1.5) 
 Ki = Z_minus / Zstraight  
 Ko = Z_plus / Zstraight  

# Example 4.2     
 V1  =   40000 N
 I  =   1840000 mm^4
 b  =   60 mm
 ylo   =   30 mm
 yhi   =   40 mm
 b0   =   60 mm
 t1 = (V1 / (I * b)) * b0 * (yhi^2 - ylo^2) / 2 ; Mpa 
 V1  =   40000 N
 I  =   1840000 mm^4
 b  =   20 mm
 ylo   =   30 mm
 yhi   =   40 mm
 b0   =   60 mm
 t2 = (V1 / (I * b)) * b0 * (yhi^2 - ylo^2) / 2 ; Mpa 
 V1  =   40000 N
 I  =   1840000 mm^4
 b  =   20 mm
 ylo   =   0 mm
 yhi   =   30 mm
 b0   =   20 mm
 t3 = (V1 / (I * b)) * b0 * (yhi^2 - ylo^2) / 2 ; Mpa 
 t4 = t2 + t3  ; Mpa 
 d  =   100 mm
 M = V1 * d ; N m 
 c  =   40 mm
 s1 = M * c / I ; MPa 

# Example 4.3     
 I1  =   0.0490 in^4
 J1  =   0.0980 in^4
 c1  =   0.50 in
 M1  =   4000.0 in lbf
 r1  =   0.50 in
 T1  =   6000.0 in lbf
 s1 = M1 * c1 / I1 ; ksi 
 t1 = T1 * r1 / J1 ; ksi 

# Example 4.4     
 a1  =   7.00E-06  / degF
 DT   =   400.0 degFdiff
 e1 = a1 * DT  
 L1  =   10.0 in
 DL = e1 * L1  ; in 
 dmeas   =   0.0080 in
 dcons = DL - dmeas  ; in 
 A1  =   1.0 in^2
 E1  =   3.00E+07 psi
 P = dcons * A1 * E1 / L1 ; lbf 

# Homework Problems:

TBD