We are using python. Thanks!
2. (35 points) One important part of the airplane design process is: Choose the size of the wing spar (main structural beam) so that the wing is strong enough to survive the forces imposed on it. The following shows an extremely over-simplified example of wing spar stress calculation: X=0 (root) X= Length Omax = Mroot Wing Lift Force Lift (x) Z - section moculus (based on beam size) Mrost - bending moment at the root Mroot = S x. Lift(x) dx max - Bending stress at the root- mora Mroot " Chength The figure shows that for a given lift force function (Lift(x)), wing length ( Length ) and wing spar section modulus ( z ), the maximum stress in the wing (max ) can be calculated. This process can be viewed as a Stress Analysis" problem stated as: Knowing the loads and the geometry, calculate the stress. The wing spar design problem can be stated as: Choose the spar section modulus (2) so that Omax = design stress The design stress is the maximum safe wing stress, generally based on material properties and factors of safety. Note: for the purpose of this exam, the lift force function is: Lift(x) = 1.5 * cos(x/Length) and the wing length is: Length = 320. Assume that all units are compatible and no unit conversions are needed. Write a Python program that defines and calls the following three functions: a) def SigmaMax(z) z: the wing section modulus The function calculates and returns: the maximum bending stress at the root of the wing (max), calculated using the given value of z and the procedure shown on the previous page. It uses the lift force function and the wing length given at the bottom of the previous page. You must use your Simpson function to perform the required integration. b) def Design TheSpar(DesignStress): Design Stress: the maximum allowable (safe) wing stress. The function calculates and returns: the section modulus ( z ) required for a wing to safely survive the wing loading given on the previous page. Hint: this is the design problem described on the previous page. It must use a root-finding method to find the value of section modulus that causes: SigmaMax( z) = DesignStress or SigmaMax(z) - DesignStress = 0) You must use your Secant function so solve for value of z that makes this equation true. c) def main(): main() has no arguments and no return value. main() does the following: a) calls SigmaMax (3.5) to calculate the stress for a value of z = 3.5. Print the value of z and the value of wing stress, each formatted with one decimal place, using nice text labeling. b) calls SigmaMax (1.5) to calculate the stress for a value of z = 1.5. Print the value of z and the value of wing stress, each formatted with one decimal place, using nice text labeling. c) calls Design TheSpar (25000) to calculate the section modulus needed if the design stress is 25000. Print the value of Design Stress and the value of wing section modulus, each formatted with two decimal place, using nice text labeling, 2. (35 points) One important part of the airplane design process is: Choose the size of the wing spar (main structural beam) so that the wing is strong enough to survive the forces imposed on it. The following shows an extremely over-simplified example of wing spar stress calculation: X=0 (root) X= Length Omax = Mroot Wing Lift Force Lift (x) Z - section moculus (based on beam size) Mrost - bending moment at the root Mroot = S x. Lift(x) dx max - Bending stress at the root- mora Mroot " Chength The figure shows that for a given lift force function (Lift(x)), wing length ( Length ) and wing spar section modulus ( z ), the maximum stress in the wing (max ) can be calculated. This process can be viewed as a Stress Analysis" problem stated as: Knowing the loads and the geometry, calculate the stress. The wing spar design problem can be stated as: Choose the spar section modulus (2) so that Omax = design stress The design stress is the maximum safe wing stress, generally based on material properties and factors of safety. Note: for the purpose of this exam, the lift force function is: Lift(x) = 1.5 * cos(x/Length) and the wing length is: Length = 320. Assume that all units are compatible and no unit conversions are needed. Write a Python program that defines and calls the following three functions: a) def SigmaMax(z) z: the wing section modulus The function calculates and returns: the maximum bending stress at the root of the wing (max), calculated using the given value of z and the procedure shown on the previous page. It uses the lift force function and the wing length given at the bottom of the previous page. You must use your Simpson function to perform the required integration. b) def Design TheSpar(DesignStress): Design Stress: the maximum allowable (safe) wing stress. The function calculates and returns: the section modulus ( z ) required for a wing to safely survive the wing loading given on the previous page. Hint: this is the design problem described on the previous page. It must use a root-finding method to find the value of section modulus that causes: SigmaMax( z) = DesignStress or SigmaMax(z) - DesignStress = 0) You must use your Secant function so solve for value of z that makes this equation true. c) def main(): main() has no arguments and no return value. main() does the following: a) calls SigmaMax (3.5) to calculate the stress for a value of z = 3.5. Print the value of z and the value of wing stress, each formatted with one decimal place, using nice text labeling. b) calls SigmaMax (1.5) to calculate the stress for a value of z = 1.5. Print the value of z and the value of wing stress, each formatted with one decimal place, using nice text labeling. c) calls Design TheSpar (25000) to calculate the section modulus needed if the design stress is 25000. Print the value of Design Stress and the value of wing section modulus, each formatted with two decimal place, using nice text labeling
