Section Modulus calculation and optimization

AIM

To increase the section modulus of a given hood by necessary changes

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 in question. Equations for the section moduli of common shapes are given below.

S=I/Y

where, 'I'moment of inertia

'Y' is the distance from the reference line(neutral axis) to one of the extreme end of an object.

For general design, the elastic section modulus is used, applying up to the yield point for most metals and other common materials.

Elastic section modulus

The elastic section modulus is defined as S = I / y, where I is the second moment of area (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, as seen in the table below. 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

Case 1:-

Section Modulus of the Initial Hood Design

Moment of the Inertia of the Hood cross section is found using a command called “section Inertia Analysis” In NX 11.

From the above analysis, following minimum and maximum moment of the inertia are obtained

I_max = 4.613307583 e⁺⁰⁶ mm⁴

I_min = 1.4020563792 e⁺⁰⁴ mm⁴

^“Y^” for Length of Hood 1 = 433.54 mm

S_max = I_max/Y =4.613307583 e⁺⁰⁶ / 433.54

= 10641.01 mm³

S_min = I_min/Y = 1.4020563792 e⁺⁰⁴ / 433.54

= 32.33 mm³

So the strength of an hood varies from 10641.01 mm³ to 32.33 mm³

Case 2:-

From the above equation it can be observed that the section modulus of the body is directly proportional to the sectional area of the body

So in this cross section of the hood , the distance between outer panel and inner panel increased by 1mm and embosses are incorporated

From the above analysis, following minimum and maximum moment of the inertia are obtained

I_max = 5.353345383 e⁺⁰⁶ mm⁴

I_min = 1.868451069 e⁺⁰⁴ mm⁴

^“Y^” for length of Hood 1 = 453.63 mm

S_max = I_max/Y =5.353345383 e⁺⁰⁶ / 453.63

= 11801.12 mm³

S_min = I_min/Y = 1.868451069 e⁺⁰⁴ / 453.63

= 41.18 mm

So the strength of an hood varies from 11801.12 mm³ to 41.18 mm³

When compared section values in case 1 and case 2, when increase in cross sectional area there will be increase in minimum strength or maximum strength

Conclusion:-

The strength of the material is directly proportional to the moment of inertia, hence increase in sectional area there is have increase in overall mass of an object ,hence have increase in strength