# Example 5.1     
 e0   =   -0.000750 m/m
 e120   =   0.000400 m/m
 e240   =   0.001850 m/m

 e1 = (e0 + e120 + e240) / 3 + ((2 *e0 - e120 - e240)^2 / 9 \
     + (e120 - e240)^2 / 3)^(1/2); m/m 
 e2 = (e0 + e120 + e240) / 3 - ((2* e0 - e120 - e240)^2 / 9 \
     + (e120 - e240)^2 / 3)^(1/2); m/m 

 a = (1/2) * atan(3^(1/2) * (e120 - e240) /  \
    (2* e0 - e120 - e240)) ; deg 

# Example 5.2     
 e0   =   2600 micron / m
 e45   =   -200 micron / m
 e90   =   450 micron / m
 e1 = (e0 + e90 ) / 2 + ((e0 - e45)^2 / 2 + \
     (e45 - e90)^2 / 2)^(1/2) ; micron / m 
 e2 = (e0 + e90 ) / 2 - ((e0 - e45)^2 / 2 \
      + (e45 - e90)^2 / 2)^(1/2) ; micron / m 
 a = (1/2) * atan( (e0 - 2 * e45 + e90) / (e0 - e90)) ; deg 

# Example 5.4     
 x1  =   5 in
 P1  =   100 lbf
 M1 = P1 * x1 / 2 ; lbf in 
 V1 = P1 / 2 ; lbf 
 L1 = 2 * x1 ; in 
 E1  =   30 Mpsi
 I1  =   1 in^4
 G1  =   10 psi
 A1  =   1 in^2
 U1 = P1^2 * L1^3 / (96 * E1 * I1) + 3 * P1^2 * L1 / (20 * G1 * A1) ; J 
 d1 = P1 * L1^3 / (48 * E1 * I1) + 3 * P1 * L1 / (10 * G1 * A1 ); in

# Example 5.5     
 L1  =   400 mm
 x = L1 / 2 ; mm 
 P  =   5000 N
 E  =   2.07E+11 Pa
 b  =   25 mm
 h  =   50 mm
 I = b * h^3 / 12 ; mm^4 
 G1  =   8.00E+10 Pa
 A1 = b * h ; mm^2
 d = P * L1^3 / (48 * E * I) + 3 * P * L1 / (10 * G1 * A1) ; mm 

# Example 5.6     
 L1  =   400 mm
 P  =   5000 N
 E  =   2.07E+11 Pa
 h  =   50 mm
 I  =   2000 mm^4
 d = P * h * L1^2 / (2 * E * I)  ; mm

# Example 5.7     
 R  =   400 mm
 F1  =   5000 N
 E  =   2.07E+11 Pa
 G1  =   8.00E+10 Pa
 I  =   2000 mm^4
 A1  =   100 mm^2
 d = 3 * pi() * F1 * R^3 / (E* I) \ 
    + pi()  * F1 * R / (E * A1) \
    + 6 * pi() * F1*  R / (5 * G1 * A1) ; mm

# Example 5.8     
 R  =   2 in
 F1  =   1 lbf
 E  =   18.00 Mpsi
 G1  =   7.00 Mpsi
 b  =   0.2 in
 h  =   0.3 in
 I = b * h^3 / 12 ; in^4 
 A1 = b * h ; in^2 
 d = 3 * pi() * F1 * R^3 / (E * I) \
     + pi() * F1 * R / (E * A1) \
     + 6 * pi() * F1 * R / (5 * G1 * A1) ; in 

# Example 5.9     
BEGIN     
 m1  =   500 kg
 Fm = m1 * grav()  ; N 
 xm   =   1.20 m
 Mm = Fm * xm  ; N m 
 F1  =   2942 kg * grav()
 y  =   1 m
 a  =   3 m
 M = Mm - F1 * y ; N m 
 E  =   30 Mpsi 
 I  =   0.001 in^4 
 U = (1/(2* E* I)) * ( Mm^2 * a - F1 * M * a^2  + F1^2 * a^3 / 3)   ; J 
 d = (2 * a^3 * F1 / 3 - a^2 * Mm) / (2 * E* I)  ; m 
END 
solve(M, F1)

# Example 5.10      
BEGIN      
 M0   =   0.12 N m 
 b  =   1 m 
 P  =   1 N 
 E  =   30 Mpsi 
 I  =   0.001 in^4 
 E * I ; lbf in^2 
 G1  =   7 Mpsi 
 a  =   1 m 
 Kp  =   0.1 m^4
 y1 =  2 / (E * I) * (M0 * b / 2 - P * b^2 / 16) 
 y2 = 2 * M0 * a / (G1 * Kp)
 
 q = y1 + y2 ; deg 
 Z = b^2 * G1 * Kp / (8 * (b * G1* Kp + 2 * a * E * I))  
 z1 =   P/ (E * I) * (Z^2 * b - Z * b^2 / 4 + b^3 / 48)
 z2 = P * a^3 / (6 *E *I)
 z3 = 2 * P * Z^2 * a / (G1 * Kp)
 d = z1 + z2 + z3 ; m 
END 
solve(q, M0)

# Example 5.11      
BEGIN      
 Sf   =   2.5  
 Sy   =   689 Mpa 
 E  =   203 Gpa 
 L1  =   1 m 
 F1  =   80000 N 
 D1  =   0.0378 m 
 A1 = pi() * D1^2 / 4 ; m^2 
 r = D1 / 4 ; m 
 P = Sf * F1 ; N 
 SR = L1 / r   
 err = P / A1 - pi()^2 * E / (L1 / r)^2  ; Mpa 
END  
solve(err,D1) 

# Example 5.12      
BEGIN      
 Sf   =   2.50  
 Sy   =   496.00 Mpa 
 E  =   71.00 Gpa 
 L1  =   200.00 mm 
 F1  =   80000 N 
 D1  =   25.0 mm 
 A1 = pi() * D1^2 / 4 ; mm^2 
 r = D1 / 4 ; mm 
 P = Sf * F1 ; N 
 SR = L1 / r   
 err1 = P / A1 - pi()^2 * E / (L1 / r)^2  ; Mpa 
 err2 = P / A1 - Sy + Sy^2 * (L1 / r)^ 2  / (4 * pi()^2 * E) ; Mpa 
END     
solve(err1, P1)
solve(err2, L1)

# Homework Problems:

TBD