Section Modulus calculation and optimization

Report on section modulus calculation of hood design

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 secion 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 its also refered to as the polar modulus or the torsional section 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 modulus Elastic and Plastic section modulus.

S=I/Y

Here,

S-Section 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 design the 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(My)Such that My=S x `sigma`Y,where `sigma`Y is the yield strength of the material.

Plastic section modulus:

The plastic section modulus is used for materials where the 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 avoide perment deformations,often comparing the plastic capacity amplified forces or stresses.

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 diatnce from the local centroids of the two areas to the PNA.

The plastic section modulus can also be called the 'First moment of area`

The plastic section modulus is used to calculate the plastic moment,MP or full capacity of a cross section ,The two terms are related by the yield stregth of the material in question,FY by MP=FY*z,Plastic section modulus and elastic section modulud are related by a shape factor which can be denoted by K used for an indiacation of capacity beyond elastic limit of material.This could be shown mathematically with the formula.

Shape factor for a rectangular section is 1.5

so we can calculate elastic section modulus

First design study:

The intersection of the design was taken and then section inertia analysis was done:

`Moment of inertia Max-9.10497x10^7xmm4`

`Moment of inertia Min-2.79939x10^5xmm4`

Y=877/2 = 438.5mm

S=I/Y

S=279939/438.5 =638.41mm^3

Hood design optimization:

By increasing the depth of the inner panel by 0.5mm

Here,

`Moment of inertia Max=9.088239x10^7xmm^`

`Moment of inertia Min=2.834866x10^5xmm`

Y=877/2 = 438.5mm

S=I/Y

S=283486/438.5 =647.17mm^3

Conclusion:

so here the difference can be seen in the moment of inertia and the change in the section modulus can be seen by the change in the design(depth)