Section Modulus calculation and optimization

OBJECTIVE:

To calculare and compare the section modulus of hood design and calculate which one as more strength.

SECTION MODULUS:

Section modulus is geometric property for given cross-section used in the design of beam or flexural members. oter geometric properties used in the design include area of tension,radius of gyration for compression,and moment of inertia for stiffness.Any relationship between these properties highly dependent on the shape in question.Equations for the section modulus of common shape are given below

The section modulus is classified into two types

1.Elastic section modulus (S) : The elastic section modulus is applicable up to the yield point of material.

It is used in most engineering applications.

2.Plastic section modulus (Z) : The plastic section modulus is generally used for material in which plastic behaviour is observed.

1.Elastic section modulus (S) :

Elastic section modulus is the ratio of moment of inertia about a neutral axis(I N.A.) and the maximum distance between the neutral axis and outermost fiber of beam (Y max).

The formula of elastic section modulus is given by,

Where,
I = Moment of inertia.
Y = Distance between neutral axes and outermost fiber.

Elastic section modulus of different sections :

A.Elastic section modulus of circle:

The elastic section modulus for circular section is,

B.Elastic section modulus of rectangular section:

The elasic section modulus for rectangular section is given by,

C.Elastic section modulus of hollow rectangle:

The elastic section modulus for hollow rectangle is given by,

2.Plastic section modulus (Z) :

The plastic section modulus is necessary to calculate plastic moment capacity of the section.

The plastic section modulus is the addition of moment of area of area under compression about PNA (plastic neutral axis) and the moment of area of area under tensile stress.

For the above cross-section, the plastic section modulus is given by,

Where,
AC = Area of cross-section under compression.
AT = Area of cross-section under tension.
YC = Distance from PNA to CG of the areas under compression.
YT = Distance from PND to CG of areas under tension.

Plastic section modulus of different sections:

A.Plastic section modulus of circle:

The plastic section modulus for a circular section is given by,

B.Plastic section modulus of rectangle:

The plastic section modulus for the rectangular section is given by,

SECTION MODULU UNITS :

The unit for section modulus is the same for the plastic section modulus and for elastic section modulus.

The unit of section modulus is given by,

In the SI system, the unit of section modulus is m³. In the FPS system, the unit of section modulus is ft³.

Section modulus can be calculated by using a 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

Section modulu analysis

Case : 1

Take a intersection of the design car hood outer and inner pannel (y axis)

Closed the car hood inner panel intersection curves

measure the moment of inertia by using section inertia analysis command in nx cad (I)

Measure the length of the neutral axis to theone of extreem end (Y)

Put all the values obtained a given formula to calculate section module

S = I/y

Moment of Inertia ( I )= 1.070693918 × 10^⁵(mm^4)

Distance between the neutral axis and the extreme end of the object (Y)

Y = 486.3986/2 = 243.20 mm

we get

S = I/y

= 440.253 (mm^3) in millimeter

S = 0.440253 (m^3) in meter

Case : 2

Offset 0.5 mm of inner panel tangent curves towards down side and Closed the hood outer and inner panel intersection curves. again applied moment of inertia by using section inertia analysis command in nx cad (I)

Put all the values obtained a given formula to calculate section module

S = I/y

Moment of Inertia ( I ) = 1.10583047 × 10^⁵(mm^4)

Distance between the neutral axis and the extreme end of the object (Y)

Y = 486.3986/2 = 243.20 mm

we get

S = I/y

= 454.70133 (mm^3) in millimeter

S = 0.45470133 (m^3) in meter

Conclusion:

Compare case :1 and case :2 the moment of innertia , section module values is more in case 2 and more strength.