Section Modulus calculation and optimization

OBJECTIVE :-

To Calculate the section modulus for the previously designed hood and optimized hood.
To Come up with the new section that has improved section modulus of the previous section.

INTRODUCTION :-

WHAT IS SECTION MODULUS :-

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.

Types of section modulus:

Elastic section modulus(S).
Plastic section modulus(Z).

ELASTIC SECTION MODULUS :-

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

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 yeild strength of the material.

Section modulus equations

Cross-sectional shape	Figure	Equation	Comment
Rectangle			Solid arrow represents neutral axis
doubly symmetric I-section (major axis)		,	NA indicates neutral axis
doubly symmetric I-section (minor axis)			NA indicates neutral axis
Circle			Solid arrow represents neutral axis
Circular hollow section			Solid arrow represents neutral axis
Rectangular hollow section			NA indicates neutral axis
Diamond			NA indicates neutral axis
C-channel			NA indicates neutral axis

PLASTIC SECTION MODULUS :-

The plastic section modulus is used for materials where elastic yielding is acceptable and plastic behavior is assumed to be an acceptable limit. Designs generally strive to ultimately remain below the plastic limit to avoid permanent deformations, often comparing the plastic capacity against amplified forces or stresses.

The plastic section modulus depends on the location of the plastic neutral axis (PNA). The PNA is defined as the axis that splits the cross section such that the compression force from the area in compression equals the tension force from the area in tension. So, for sections with constant yielding stress, the area above and below the PNA will be equal, but for composite sections, this is not necessarily the case.

The plastic section modulus is the sum of the areas of the cross section on each side of the PNA (which may or may not be equal) multiplied by the distance from the local centroids of the two areas to the PNA:

the Plastic Section Modulus can also be called the 'First moment of area'

Description	Figure	Equation	Comment
Rectangular section
Rectangular hollow section			where: b=width, h=height, t=wall thickness
For the two flanges of an I-beam with the web excluded			where: b1,b2 =width, =thickness, are the distances from the neutral axis to the centroids of the flanges respectively
For an I Beam including the web
For an I Beam (weak axis)			d = Full height of the I Beam
Solid Circle
Circular hollow section

The plastic section modulus is used to calculate the plastic moment, M_p, or full capacity of a cross-section. The two terms are related by the yield strength of the material in question, F_y, by M_p=F_y*Z. Plastic section modulus and elastic section modulus are related by a shape factor which can be denoted by 'k', used for an indication of capacity beyond elastic limit of material. This could be shown mathematically with the formula :-

FOR HOOD DESIGN THE GIVEN SECTION MODULUS FORMULA IS :-

S = I/y

Where :-

S = Section Modulus

I = Moment of Inertia

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

FEATURE TREE :-

CALCULATION OF SECTION MODULUS :-

FOR SECTION 1 :-

Moment of inertia :-

Y value :-

CALCULATION OF SECTION MODULUS :-

S= I/Y

y= 480.474/2

=240.237mm

I value :-

M1 = 3.665e^-007 m^4

= 3.342e^-6 m^4

Then

S1=

=0.008283/240.237

= 3.448257e^-5 mm^3

And

S2= ?

M2= 1.227e^-004 m^4

= 2.24732e^-5 mm^4

Then

S2 =

= 2.24732e^-5/240.237

= 6.3030e^-5 mm^3

SECTION 2 :-

This is the improved section , in this section incresed the gap between outer panel and inner panel.

Moment of inertia :-

Y value :-

CALCULATION OF SECTION MODULUS :-

S= I/Y

y= 480.474/2

=240.237mm

I value :-

M1 = 3.925e^-007 m^4

= 0.003579 m^4

= 3.57913e^-6 mm^4

= 0.008871 mm^4

Then

S1=

=0.008871/240.237

= 3.6929e^-5 mm^3

And

S2= ?

M2= 1.277e^-004 m^4

= 0.023389 m^4

= 2.33890e^-5 mm^4

= 0.01575938 mm^4

Then

S2 =

= 0.01575938/240.237

= 6.559930 e^-5 mm^3

CONCLUSION :-

These calculation is necessary to know the design actual withstand capability of product. As we increase sectional area, the moment of inertia & section modulus increases it means capacity of material also increases.