Section Modulus calculation and optimization

Section Modulus

AIM :To generate the report on finding the section modulus for the hood design and improving it by based on the input and increasing the strength of the hood by using the software NX-CAD.

Objective:Use the Section from Hood design and calculating the Section Modulus using the 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

INTRODUCTION TO SECTION MODULUS:

It is a geometric property for a given cross-section used in the design of beams or flexural members. 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. Any relationship between these properties is highly dependent on the shape.

The formula of elastic section modulus is given by,

S=I/Y ;

Where,
I = Moment of inertia (mm^4)
Y = Distance between neutral axes and outermost fiber (m)

The section modulus is defined as S = I / y, where I is the second moment 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 (M_y) such that M_y = S ⋅ σ_y, where σ_y is the yield srength of the material.

section modulus equations:

Cross-sectional shape	Figure	Equation	Comment
Rectangle			Solid arrow represents neutral axis
doubly symmetric I-section (major axis)		,	NA indicates neutral axis
doubly symmetricI-section (minor axis)			NA indicates neutral axis
Circle			Solid arrow represents neutral axis
Circular hollow section			Solid arrow represents neutral axis
Rectangular hollow section			NA indicates neutral axis
Diamond			NA indicates neutral axis
C-channel			NA indicates neutral axis

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.

First objective design to find section modulus:

Maximum moment of inertia = 8.247889546e+05[mm^4]

Minimum moment of inertia = 6.44292486e+03[mm^4]

The total distance of the hood Y =484.5mm

Distance between the neutral axis to the extreme end is y/2 = (484.5/2) = 242.25mm

To find section modulus, we have to calculate:

S=I[minimum]/y

S= 6.44292486*10^4/242.25

S=26.596 mm

Second objective design to find section modulus:

To change the optimization of section modulus we should change the position of the curve of the

inner panel to somehow 0.5 mm distance so that section modulus will increase thus the bending stress

will be more and the panel get strengthned.

Maximum moment of inertia = 8.223640091e+05[mm^4]

Minimum moment of inertia = 6.672348327e+03[mm^4]

The total distance of the hood Y =484.5mm

Distance between the neutral axis to the extreme end is y/2 = (484.5/2) = 242.25mm

To find section modulus, we have to calculate:

S=I[minimum]/y

S= 6.672348327*10^4/242.25

S=27.543 mm

Conclusion :

In first objective the sectiom modulus is;

S1= 26.59 mm

In second objective the section moduls is;

S2 = 27.543 mm

Thus the second objective design selected to perform the manufacturing process so the strength of hood will increase..