Section Modulus calculation and optimization

SECTION MODULUS CALCULATION AND OPTIMIZATION

AIM:

In this report we are going to calculate the section modulus for hood which was designed previously under certain design considerations. Now we are going to make modifications on the hood without affecting its design parameters in order to improve the value of section modulus for hood.

SECTION MODULUS (S)

Section Modulus is the geometric value obtained by dividing MOMENT OF INERTIA of a section to its LENGTH OF THE SECTION from its centre axis to extreme end point.

S= I / Y

Where ,

S= section modulus

I= Moment of inertia

Y= Distance between the neutral axis and extreme end of the object.

unit, S= I / Y = mm^3

MOMENT OF INERTIA

Moment of inertia,in physics, quantitative measure of the rotational inertia of a body. i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of a torque. Generaly is denoted by (I),

TYPES OF SECTION MODULUS

There are two types of section modulus

1. Elastic sectiopn modulus
2. plastic section modulus

1. ELASTIC SECTION MODULUS

Elastic section modulus is calculated when we are use to the material behaviour till the yield point.For general design purpose we are use elastic section modulus.

Elastic section modulus of different section:

1. Rectangular section

I= bd^3/12

And distance from the neutral axis,

Ymax=d/2

section modulus of Rectangular section Z=bd^2/6

2. Hollow Rectangular Section

section modulus of hollow rectangular section z=(BD^3-bd^3 )/ 6D

3. Solid Circular Section

section modulus of solid circular section z=(π/32)*d^3

4. Hollow circular section

section modulus of hollow circular section z=π/32 * {(D^4 - d^4)/D}

5. Symetric I and C section

section modulus of I and C section z={BD^3 - (B-b)d^3}/6D

2.PLASTIC SECTION MODULUS

The plastic section modulus is used for materials where the elastic is yield is acceptable and the plastic behavior is considered to be an accetable range. A plastic section modulus is geometric property for a cross section of an object generallly used in material in which plastic behaviour can be observed. This is only one of the two different types of plastic section modulus is used in engineering and design. Plastic section modulus is the more uncommon form of plastic section modulus, and most general designs by engineers do not used in their calculations.

DISTANCE BETWEEN THE NEUTRAL AXIS TO THE OUTSIDE OF THE BEAM (L)

FIG: CALCULATION OF THE LENGTH

Here we need neutral axis to the outside edge of the beam y= L/2

Y=874.1/2

Y=437.05mm

CASE 1: BEFORE OPTIMIZING THE DESIGN

In this initial case,

MOI (Max) :9.130707137e+07[mm^4]

MOI (Min) : 3.097948281e+05[mm^4]

we already know the length of the section is L=437.05mm

Therefore section modulus is S=I/y

(Here am going to take the minimum moment of inertia)

S=MOI(Min)/y

S=3.097948281e+05[mm^4] / 437.05mm

S=8.43253685638mm^3

CASE 2: AFTER OPTIMIZING THE DESIGN

In this case,

MOI (Max) :1.224822168e+08[mm^4]

MOI (Min) : 4.372011765e+05[mm^4]

we already know the length of the section is L=437.05mm

Therefore section modulus is S=I/y

(Here am going to take the minimum moment of inertia)

S=MOI(Min)/y

S=4.372011765e+05[mm^4] / 437.05mm

S=11.8958004732mm^3

NOTE:

Here am adding the additional embosses and increases the thickness of the inner panel from 0.75mm to 1mm it will improves the inertia of the section. If the area inertia is increases the section modulus is also increased.

fig:- AFTER OPTIMIZING DESIGN

TABULATION FOR BOTH CASES:

PROPERTIES OF THE SECTION		BEFORE OPTIMIZATION	AFTER OPTIMIZATIOMN
MOI(Max)		9.130707137e+07[mm^4]	1.224822168e+08[mm^4]
MOI(Min)		3.097948281e+05[mm^4]	4.372011765e+05[mm^4]
SECTION MODULUS(S)		S=8.43253685638mm^3	S=11.8958004732mm^3

CONCLUSION:

The section modulus of the hood section is calculated. The optimization of hood is done by the increases area of the section.From this we can conclude that increase in area of the cross secion keeping it's length constant, also improves moment of inertia which is proportional to section modulus.