# Example 10.1  
IPS(deg)      
 tpi  =   5.0 /in   
 p = 1/ tpi ; in 
 L1 = 2 * p ; in 
 dth = p/2 ; in 
 d  =   1.0 in   
 dm = d - p/2  ; in 
 len = atan(L1 / pi() / dm)  ; deg   
 f  =   0.12    
 fstart = (4/3) * f    
 fc = f  
 a   =   14.5 deg
 an = atan(tan(a) * cos(len)) ; deg 
 W1  =   1000.0 lbf
 # dc = d - p/2  
 dc = 1.5 in
 T_up1 = (W1 * dm / 2) * (fstart * pi() * dm + L1 * cos(an)) / \
        (pi() * dm * cos(an) - fstart * L1) + W1 * fc * dc / 2 ; lbf in 
 T_down1 = (W1 * dm / 2) * (fstart * pi() *  dm - L1 * cos(an)) / \
        (pi() * dm * cos(an) + fstart * L1) + W1 * fc * dc / 2 ; lbf in 

# DYNAMIC     
 tpi  =   5.0 /in
 p = 1/ tpi ; in 
 L1 = 2 * p ; in 
 dth = p/2 ; in 
 d  =   1.0 in
 dm = d - p/2  ; in 
 len = atan(L1 / pi() /  dm)  ; deg 
 f  = 0.09 
 fstart = (4/3) * f  
 fc = f  
 a   =   14.5 deg
 an = atan(tan(a) * cos(len)); deg 
 W1  =   1000.0 lbf
 # dc = d - p/2  
 dc = 1.5 in
 T_up2 = (W1 * dm / 2) * (fstart * pi() * dm + L1 * cos(an)) / \
     (pi() * dm * cos(an) - fstart * L1) + W1 * fc * dc / 2 ; lbf in 
 T_down2 = (W1 * dm / 2) * (fstart * pi() *  dm - L1 * cos(an)) / \
    (pi() * dm * cos(an) + fstart * L1) + W1 * fc * dc / 2 ; lbf in 

# NO FRICTION     
 tpi  =   5.0 /in
 p = 1/ tpi ; in 
 L1 = 2 * p ; in 
 dth = p/2 ; in 
 d  =   1.0 in
 dm = d - p/2  ; in 
 len = atan(L1 / pi() /  dm)  ; deg
 f  = 0.0
 fstart = (4/3) * f  
 fc = f  
 a   =   14.5 deg
 an = atan(tan(a) * cos(len)); deg
 W1  =   1000.0 lbf
 # dc = d - p/2  
 dc = 1.5 in
 T_up3 = (W1 * dm / 2) * (fstart * pi() * dm + L1 * cos(an)) / \
     (pi() * dm * cos(an) - fstart * L1) + W1 * fc * dc / 2 ; lbf in 
 T_down2 = (W1 * dm / 2) * (fstart * pi() *  dm - L1 * cos(an)) / \
    (pi() * dm * cos(an) + fstart * L1) + W1 * fc * dc / 2 ; lbf in 

err = T_up3 / T_up2

# Example 10.2     
 Sp   =   380.0 Mpa
 F1   =   4.5 kN
 FOS  =   4.0 
 Fdesign = F1 * FOS ; kN 
 A1 = Fdesign / Sp  ; mm^2 
 dM10X15   =   10.0 mm 
 AM10X15   =   58.0 mm^2
 Fi = 0.9 * AM10X15 * Sp  ; kN 
 T1 = 0.2 * Fi * dM10X15  ; N m 

# Example 10.3     
 Sp   =   85.0 ksi
 Sy   =   92.0 ksi
 d  =   0.5000 in 
 A1  =   0.1419 in^2
 Fi_rough = A1 * Sp  ; lbf 
 FOSFi   =   1.59 
 Fi = A1 * Sp / FOSFi  ; lbf 
 m1  =   0.4000 
 Ff = m1 * Fi  ; lbf 
 F1 = 2 * Ff  ; lbf 
 Fshear = 2 * (0.58 * Sy) * pi() *  d^2 / 4 ; lbf 

# Example 10.4      
BEGIN      
 FOS  =   6.0  
 F1  =   24.0 kN 
 Fdesign = FOS * F1  ; kN 
 FD   =   87.3 kN 
 FE = FD / 4   ; kN
 xF   =   500.0 mm 
 xE   =   100.0 mm 
 xD   =   400.0 mm 
 SumM = xF * Fdesign - xE * FE - 2 * xD * FD  ; kN mm 
 Sp   =   650.0 Mpa 
 At = FD / Sp  ; mm^2 
END     
Solve(SumM, FD)

# Example 10.5     
BEGIN     
 A1  =   100 mm^2
 F1   =   87.3 kN
 V1   =   81.5 kN
 s1 = F1 / A1 ; Mpa 
 t = V1 / A1 ; Mpa 
 se = (s1^2 + 3 * t^2)^(1/2)  ; Mpa 
 Sp   =   650.0 Mpa
 error = se - Sp  ; Mpa 
 d = (4 * A1 / pi())^(1/2)  ; mm  
END  
solve(error, A1)

# Example 10.6 
IPS(deg)    
BEGIN     
# (a)     
 Fmax   =   3000 lbf 
 Kf   =   3.8  
 At   =   0.1419 in^2 
 sa = Fmax * Kf / 2 / At  ; ksi 
 sm = sa
 Sp   =   37.0 ksi 
 error1 = sa - Sp  ; ksi 
# (b)      
 Sp   =   85.0 ksi 
 At   =   0.1419 in^2 
 Fi = Sp * At  ; lbf 
 d  =   0.5000 in  
 Ab = pi() *  d^2 / 4  ; in^2 
 q  =   30 deg 
 gg  =   2 in  
 Ac = (pi() / 16) * \
    (5 * d^2 + 6 * d * gg * tan(q) + gg^2 * tan(q)^2) ; in^2 
 r = Ab / (Ab + Ac)  
# (c)     
 Fp = 0.07 * Fmax  ; lbf 
 sa = Fp * Kf / At  ; ksi 
END  
solve(error1, Fmax)

# Example 10.7     
 n  =   12 
 d  =   250 mm
 pmax   =   5.0 Mpa
 Fc = pmax * pi() *  d^2 / 4  ; kN 
 F1 = Fc / n ; kN 
 gg  =   1 mm
 Ab   =   1 mm^2
 E1   =   100 Mpa
 L1 = gg / 2 ; mm 
 A1 = 5 * Ab  ; mm^2 
 k1 = A1 * E1 / L1  ; kN/mm 
 E2   =   70 Mpa
 L2 = gg / 2 ; mm 
 A2 = 5 * Ab  ; mm^2 
 k2 = A2 * E2 / L2  ; kN/mm 
 kc = k1 * k2 / (k1 + k2) ; kN/mm 
 Eb   =   200 Mpa
 Lb = gg  ; mm 
 kb = Ab * Eb / Lb  ; kN/mm 
 DF = kb * F1 / (kb + kc)  ; kN 
 Fa = DF / 2 ; kN
 Sy   =   69.0 MPa
 At = Fa / Sy  ; mm^2 
 Aact   =   58.0 mm^2
 Sp   =   0.6 GPa
 Fc = 0.55 * Sp * Aact ; kN 
 Fp = Fc - (F1 - DF) ; kN

# Homework Problems:

TBD