Section Modulus calculation and optimization

Report On Section Modulus Calculation and Optimization Of Hood

Aim:

To calculate the section modulus of the previously designed hood for analyzing its strength and also optimizing the design to see the difference in the bending strength of the hood.Higher the section modulus of a structure , the more the resistive it becomes to bending.

Section Modulus:

Section modulus is a geometric property for a given cross section used in the design of beams or flexural members , it is also referred to as the polar modulus or the Torsional Sectional Modulus.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.There are two types of section modulus,the elastic section modulus and the plastic section modulus.

S=l/y

Here,

S= Section of modulus

i=Moment of inertia(unit mm4)

Y= Distance from neutral axis to the extreme end(unit mm)

The Unit of a " section modulus " is (mm3).

Elastic section modulus :

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

The elastic section modulus is defined as S=l/y where l 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 most extreme fibre , as seen in the table below .it is also often used to determine the yeild moment (My)

such that My = S*sigma y where sigma y is the yeild strength of the material.

Plastic section modulus:

The plastic section modulus is used for materials where elastic yielding is acceptable and plastic behaviour 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 of stresses.the plastic section modulus depands on the location of the plastic neural axis. the plastic neural axis is defined as the axis that splits the cross section such that the compression force from the area in compression equals the tension force.

The plastic section modulus is the sum of the areas of the cross section on each side of the plastic neural axis multiplied by the distance from the local centroids of the two areas to the plastic neural axis.

K=Z/S

where k is shape factor andZ is plastic modulus amd S is section modulus.

shape factor for a rectangular section is 1.5.

so here we are calculating elastic section modulus.

First design study:(SECTION 1)

The intersection of the design was taken and then section inertia Analysis was done.

Moment of inertia (max)=8.660*10^5*mm^4

Moment of inertia (min) = 8.743*10^3*mm^4

Y=483.90/2=241.95

s=m/y

s=36.13mm^3

SECTION 2

Hood design optimization: In this section modulus to increase of inner panel distance from the previous section 1 offset of inner panel 3mm.

Moment of inertia (max) :8.534*10^5*mm^4

Moment of inertia (min) : 1.0476*10^4*mm^4

y=241.95mm

s=m/y

=1.0476*10^4/241.95

=43.29mm^3

Conclusion:

Different section ,as shown above ,were tried in order to acheive a higher moment of inertia.It is observed that increasing the gap between the inner and outer panel has resulted to improve the section modulus .hence it is best to add more geometric features to the master section to more stiffness of section .however this could result in an increase in manufacturing cost.