Section Modulus calculation and optimization

Report on section modulus

Calculation of hood

Aim

To calculate the section modulus of the previously designed hood for analysing its strength and also optimizing the design the design to see the deference 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.

There are two types of section moduli, the elastic section modulus and plastic section modulus.

S=I/Y

Here,

S = section modulus

I = moment of inertia (unit mm 4)

Y = distance from natural axis to the extreme end (unit mm)

The unit of a “section modulus” is (mm3)

 

Charging the position can show the difference in bending which is because of the centroid distance from extreme fibre end.

In layman’s design in this position there is more material from axis to the specific direction, to resist the load which makes less bend and improves the strength.

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.

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 or stresses.

The plastic section modulus depends on the location of the plastic neutral axis (PNA). The PNA is defined as axis that splits the cross section such that the compression forces from the area on compression equals the tension. So, for sections with constant yielding stress, the area above and below the PNA will be equal, but for composite sections, that 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 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 strength of the material in question, Fy, by Mp= Fy*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: -

                                                                             

Shape factor for a rectangular section is 1.5.

So here we are calculating elastic section modulus

First design study

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

 

 

Moment of inertia(max) = 8.39286*10^5*mm^4

Moment of inertia(min) = 4.35750*10^3*mm^4

Y = 486.7599/2 = 243.37 mm

s = I/Y

s =4.35750*10^3/243.37 = 17.9 mm^3

hood design optimization

By increasing the depth of the inner panel by 0.5mm

 

 

Here,

Moment of inertia(max) = 8.37345*10^5*mm^4

Moment of inertia(min) = 4.53042*10^3*mm^4

Y = 486.7599/2 = 243.37 mm

s = I/Y

s =4.53042*10^3/243.37 = 18.61 mm^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).