Section Modulus calculation and optimization

SECTION MODULUS AND SECTION MODULUS OF HOOD

Aim

To calculate thesection modulus of the previously designed hood for analyzing its strength and also optimizing 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 peoperty for a given cross-section used in the desigen of becames or flexural members, It is also reffered to as the polerModulus or the Tortional section modulus. Other geometric proporties used in design include area for tension and shear, radious of gyration for compression, and moment of inertia and polar moment of inertia for stiffness. Any relationship between these proporties is highly dependent on the shape in quation.

The section Modulus is classified into two types:-

1. Elastic section modulus
2. Plastic section modulus

Changing the position can show the difference in bending which is becouse of the centroid distance from extream fiber end.

IN layman's terms, 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.

1) Elastic Section Modulus:

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

The formula of elastic section modulus:

S=I/Y

Where:

I= Moment of Inertia (unit mm4)

Y= Distance between neutral axis and outermost fiber (mm3)

The unit of "section modulus" is(mm3)

Steps to calculate elastic section modulus:-

• Step 1:- Find location of centroid of given cross section.
• Step 2:- Find moment of inertia about neutral axis.
• Step 3:- Find Ymax from neutral axis.
• Step 4:- Find elastic section modulus using the formula provided above.

Elastic section modulus of different sections:-

• Eastic section modulus of circle:

The elastic section modulas for circular section is,

• Elastic section modulus of rectangular section:

The elastic section modulus for rectangular section is given by,

• Elastic section modulus of hollow rectangule:

The elastic section modulus for hollow rectangule is given by,

• Elastic section modulus of Square tube:

2) Plastic section modulus :-

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

Steps to calculate plastic section modulus:

Step 1] Locate the plastic neutral axis.

At the neutral axis,the area under compression is equal to the area under tension

`Ac=At`

By using this releation, we can find the position of the plastic neutral axis.

Step 2] Find the summetion of the product of area of section undergoing compression and the distance of its CG from PNA that is `∑ AC=AT`

Step 3] Find the summation of the product of the area of cross- section undergoing tension and distance between cg of that area from PNA that is `∑AT YT.

Step4] Find the plastic section modulus using the formula.

Plastic section modulus of different sections:-

• Plastic section modulus of circle:

Plastic section modulus for a circlar section is given by.

• Plastic section modulus of rectangle:

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

First Design study

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

Moment of inertia(max)= 9.169468869x10^7 [mm^4]

Moment of inertia (min)=2.56492757x10^5 [mm^4]

Y=879.47/2= 439.735mm

Section modulus of first hood design:-

S=I/Y

S=(2.56492757X10^5)/439.735

S=583.289 mm^3

Hood design optimization

By increasing the depth of the inner panel by 0.5mm

Studys of the optimized Hood design:

Here.

Moment of inertia (max)=9.152969658x10^7

Moment of inertia (min)=2.594593964*10^5

y=879.47/2=439.735mm

S=I/Y

S=590.035 mm^3

Changing value of section moduls by optimizing the hood design:

• Section modulus of Hood before optimization =583.289 mm^3
• Section modulus of Hood after optimization =590.035 mm^3
• Incresed section modulas of hood after optimization = 6.746 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)