Section Modulus calculation and optimization

Optimizing and Calculation of section Modulus of the Front Hood of a Car using NX-Cad to improve results

Objective

The objective of this project is to find the section modulus of front hood and optimizing it to achieve best results by using some modifications by explaining detailed comparison.

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 for stiffness. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below. 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 Inertia (or area moment of inertia, not to be confused with moment of inertia) and

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 (M_y) such that

M_y = S × σ_y

where σ_y is the yield strength of the material.

My is Yield moment

σ_{y for Stainless steel is 520 MPA.}

Calculation of Section Modulus

To get better results in optimizing some modifications have been done on Hood. Then these two results are compared to get detailed conclusion.

Before Optimization

By using the command Section Inertia Analysis these results like Max & Min Moment of Inertia, principal length, Section length & Area using NX-Cad has been obtained.

Before Optimizing Results:

Moment of Inertia(Max) = 4.862336416*10^6 [mm^4]

Moment of Inertia(Min) = 1.570647864 *10^4 [mm^4]

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

For MOI max,

S= (4.862336416*10^6 [mm^4])/(440 mm)

S= 11,045.45 mm^3

For MOI min,

S= (1.570647864 *10^4 [mm^4])/(440 mm)

S= 35.68 mm^3

M_y = S × σ _y

(35.68 mm^3)*(520*10^6* N/mm^2)

M_y = 18,553.6 *10^6*Nmm

After Optimization

For getting better results the hood inner panel width was increased to 0.50 mm than achieved below values as results.

Optimized Results:

Moment of Inertia(Max) = 7.096309913 *10^6 [mm^4]

Moment of Inertia(Min) = 2.442917872 *10^4 [mm^4]

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

For MOI max,

S= (7.096309913 *10^6 [mm^4])/(440 mm)

S= 16,127.27 mm^3

For MOI min,

S= (2.442917872 *10^4 [mm^4])/(440 mm)

S= 55.5 mm^3

M_y = S × σ _y

(55.5 mm^3)*(520*10^6* N/mm^2)

M_y = 28,860*10^6*Nmm

Detailed Comparison:

Conclusion

Thus, the section modulus of front hood was calculated and compared with optimized value for finding the better result. Hence the result I would like to conclude is when the sectional area of hood increases the strength and bending moment of hood also will increases.