Section Modulus calculation and optimization

Objective:

     To find the section modulus of the hood and optimize the design to improve the section modulus. 

Section Modulus:

     Section modulus is the measure of the strength of a cross-section with respect to a particular axis. It is a geometric property of cross-section used to design beams.

     It is defined as the ratio of the total moment resisted by the section to the stress in the extreme fiber, which is equal to the yield strength. 

     Therefore, the formula of Section Modulus (S) is:

       S = I/y

       Where, S = Section Modulus

                  I = Moment of Inertia (mm^4)

                  y = distance between the neutral axis and the extreme end of the object (mm)

Finding the Moment of Inertia:

• The moment of inertia for the Hood is found using the NX Cad software. 
• A neutral datum plane is created along the "Z-Axis", right in the center of the hood. By this, we are about to find the section modulus for the frontal impact. 

• Create an intersection curve with respect to the datum plane created and the outer surface of the hood outer panel and the outer surface of the hood inner panel as boundaries.

• Create a sketch and project the intersection curve on the new sketch. 
• Close the sketch using the "Line" command and "Studio Spline" command. 

• Use the "Section Inertia Analysis" command with respect to the curve and enter the hollow thickness as 0.75 mm, which is the thickness of the panel, to find the Moment of Inertia of the curve which is denoted as MOI in the PMI notes. We always consider the value of the MOI (min) for the consideration of the Factor of Safety. 

• Thus the Moment of inertia value is obtained. 

 

Finding the Y (distance between the neutral axis and the extreme end of the object):

• In the above-created sketch, measure the distance between two horizontal extremes of the sketch.

• Divide the measured distance by 2, since the neutral axis will be in the middle of the sketch. 

Calculation of Section Modulus:

i. Case 1 - The Actual Hood Design:

     For the cross-section of our actual design, the following values have been obtained using NX Cad software. 

   Thus obtained Value of the Moment of Inertia (I) is

        MOI (Min): 2.671041368 e+05 (mm^4)

                        I : 2.671 x 10^5 (mm^4)

   

    Thus, the distance between the neutral axis and the extreme end of the object (y) is

                y = Total distance / 2

                   = 877.0067 / 2

                y = 438.50 mm

   Section Modulus, S = I/y

                               = 2.671*10^5 / 438.50

                             S = 609.122 mm^3

     Thus, the Section Modulus of the actual hood design is 609.122 mm^3.

ii. Case 2 - Optimised Hood Design:

    Optimization:

          The cross-section of the design is increased by offsetting the outer wall of the inner panel by 0.5mm,  and a new closed sketch is created. 

          For the cross-section of the optimized Curve, the following values have been obtained using NX Cad software.

Thus obtained Value of the Moment of Inertia (I) is

        MOI (Min):  2.705752122 e+05 (mm^4)

                        I :  2.7 x 10^5 (mm^4)

Thus, the distance between the neutral axis and the extreme end of the object (y) is

                y = Total distance / 2

                   = 877.0067 / 2

                y = 438.50 mm

   Section Modulus, S = I/y

                               = 2.7 x 10^5 / 438.50

                             S =  615.735 mm^3

     Thus, the Section Modulus of the optimized hood design is  615.74 mm^3.

Conclusion:

• By our calculations, we have found that the increase in cross-section results in an increase of Moment of Inertia which in turn increases the Section Modulus of the design. 
• The Strength of the Design is directly proportional to the Cross-section of the design and so we can optimize the cross-section for the best output.