CALCULATING THE SECTION MODULUS OF THE FRONT HOOD OF A CAR AND OPTIMIZING IT FOR BETTER RESULTS

OBJECTIVE

The objective of the project is to find the section modulus of the designed front hood and optimizing it to get an improved section modulus compared to the previous section.

INTRODUCTION

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and moment of inertia and polar moment of inertia for stiffness. Any relationship between these properties is highly dependent on the shape. There are two types of section moduli, the elastic section modulus and the plastic section modulus.

The elastic section modulus is defined as,

                                                                 S = I / y

Where,

• S is the Section Modulus
• I is the second moment of area (or area moment of inertia, not to be confused with moment of inertia)
• y is the distance from the neutral axis to any given fibre. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fibre.

It is also often used to determine the yield moment (My) such that,

                                                              My = S × σy

Where, σy is the yield strength of the material.

The neutral axis is an axis in the cross section of a beam (a member resisting bending) or shaft along which there are no longitudinal stresses or strains. If the section is symmetric, isotropic and is not curved before a bend occurs, then the neutral axis is at the geometric centroid. All fibers on one side of the neutral axis are in a state of tension, while those on the opposite side are in compression.

SECTION MODULUS CALCULATION

For finding the better results I have analyzed two sections and considered it as case 1 and case 2 and again the two sections were optimized and analyzed and then compared to get better results.

CASE 1

For case 1 the below section were considered parallel to x-coordinate for calculating the section modulus.

 

BEFORE OPTIMIZATION

By using the Section Inertia Analysis in Siemens NX the below shown results were achieved.

Moment of Inertia (MAX) = 4.868895354 x 10^6 [mm^4]

Moment of Inertia (MIN) = 1.484837056 x 10^4 [mm^4]

Section Modulus, S = Moment of Inertia (MOI) / Distance between the neutral axis and the extreme end of the object (y)

For MOI max,

                      S = (4.868895354 x 10^6 [mm^4])÷(440 mm)

                      S = 11065.6713 mm^3

For MOI min,

                      S = (1.484837056 x 10^4 [mm^4])÷(440 mm)

                      S = 33.7462967 mm^3

AFTER OPTIMIZATION

The hood inner panel width was increased to 0.50 mm than the original one and achieved the below shown results in Siemens Nx,

Moment of Inertia (MAX) = 4.859738545 x 10^6 [mm^4]

Moment of Inertia (MIN) = 1.501847196 x 10^4 [mm^4]

Section Modulus, S = Moment of Inertia (MOI) / Distance between the neutral axis and the extreme end of the object (y)

For MOI max,

                     S = (4.859738545 x 10^6 [mm^4])÷(440 mm)

                     S = 11044.8603 mm^3

For MOI min,

                     S = (1.501847196 x 10^4 [mm^4])÷(440 mm)

                     S = 34.1328908 mm^3

CASE 2

For case 1 the below section were considered parallel to x-coordinate for calculating the section modulus.

BEFORE OPTIMIZATION

By using the Section Inertia Analysis in Siemens NX the below shown results were achieved.

Moment of Inertia (MAX) = 8.366235185 x 10^5 [mm^4]

Moment of Inertia (MIN) = 5.367065048 x 10^3 [mm^4]

Section Modulus, S = Moment of Inertia (MOI) / Distance between the neutral axis and the extreme end of the object (y)

For MOI max,

                      S = (8.366235185 x 10^5 [mm^4])÷(239 mm)

                      S = 3500.51681 mm^3

For MOI min,

                      S = (5.367065048 x 10^3 [mm^4])÷(239mm)

                      S = 22.4563391 mm^3

AFTER OPTIMIZATION

The hood inner panel width was increased to 0.50 mm than the original one and achieved the below shown results in Siemens Nx,

Moment of Inertia (MAX) = 8.346664414 x 10^5 [mm^4]

Moment of Inertia (MIN) = 5.556807509 x 10^3 [mm^4]

Section Modulus, S = Moment of Inertia (MOI) / Distance between the neutral axis and the extreme end of the object (y)

For MOI max,

                     S = (8.346664414 x 10^5 [mm^4])÷(239 mm)

                     S = 3492.32821 mm^3

For MOI min,

                     S = (5.556807509 x 10^3 [mm^4])÷(239 mm)

                     S = 23.2502406 mm^3

COMPARING THE CASE 1 AND 2 TO FIND THE BETTER RESULT

 
From the comparison table we have achieved the section modulus result and for maximum moment of inertia the section modulus value decreases after optimization but for minimum moment of inertia the value increases. 

• But the minimum limit of deformation of the hood needs to be analyzed so we’ll go with the minimum moment of inertia.
• After increasing the sectional area to 0.5 mm from the original the Section Modulus value increased which shows that the load carrying capacity and resistance of the hood will also be increased simultaneously.

CONCLUSION

Thus the section modulus of the Front Hood of a car was calculated and compared with the optimized hood and found the better result. Hence I’m concluding that when the sectional area of the hood increases the stiffness and resistance of the hood will also be increased.