Section Modulus calculation and optimization

A REPORT ON SECTION MODULUS CALCULATION AND OPTIMIZATION

INTRODUCTION

The section modulus of the cross-sectional shape is of significant importance in designing beams. It is a direct measure of the strength of the beam. A beam that has a larger section modulus than another will be stronger and capable of supporting greater loads.

Sectional Modulus (Z): It is the ratio of Moment of Inertia (I) of the beam cross-section about the neutral axis to the distance (ymax) of extreme fiber from the neutral axis. For a circular section, the section modulus:

Z = I /y max.

Where

I = Moment of Inertia.

Y max=Distance from NA to extreme layer.

Section modulus is depends on the value of moment of Inertia. The three main types of the moment of force are the mass moment of inertia, the area moment of inertia, and the polar moment of inertia.

QUESTION

Use the Section from your Hood design and calculate the Section Modulus using the formula

S = I/y

Where,

S = Section Modulus

I = Moment of Inertia

Y = distance between the neutral axis and the extreme end of the object

EXPLANATION

For checking the strength(Section Modulus ) here we use two condition

Case 1 =Exact Value

Here,

Minimum Moment of Inertia=1.4270x10⁴ mm⁴

Here,

Total Distance =877.0067mm

So, ymax= 438.5033mm

Section Modulus Calculation

Given Data ,

I=1.4270x10⁴ mm⁴

ymax= 438.5033mm

Then,

S=I/ymax

= 1.4270x10⁴/438.5033

=32.54

So,

S=32.54mm³

Case 2 Area Extend

The Hood inner panel curve is offset by 0.5mm outwards and section inertia analysis is done again in a similar way.

Here,

Minimum Moment of Inertia=1.4681x10⁴

Here,

Total Distance =877.0067mm

So, ymax= 438.5033mm

Section Modulus Calculation

Given Data ,

I=1.4681x10⁴

ymax= 438.5033

Then,

S=I/ymax

= 1.4681x10⁴ /438.5033

=33.45

So,

S=33.45mm³

CONCLUSION:

It was observed that the value of Section Modulus (S) obtained in case 1 was S = 32.54mm3 and the value of Section Modulus (S) obtained in case 2 was S=33.45mm3

I.e. The Section Modulus value obtained in case 2 was greater

When the Hood inner panel curve is offset by 0.5mm outwards the cross section value of the section increases which in turn increases the strength of the section.

It can be concluded that when the cross-section increase the Section Modulus also increases which in turn improves the strength i.e. Higher the section modulus of a structure, higher is he strength and the more resistive it becomes to bending.