Section Modulus calculation and optimization

Section Modulus Calculation and Optimization

Aim:

To calculate section modulus of hood and optimize the designto have improved section modulus.

Section Modulus:

Section Modulus is defined as it is direct measure of strength of any cross sectional area of any object about an reference axis.

(OR) I may be defined as the geometric property for a given cross section used in the design of beams, flextural members, other geometric properties used in design including area of tension, shear and radius of gyration etc.

It is mainly done for the purpose of measuring Stiffeness.

Units for section modulus is mm^3.

the formula of section modulus is given as

s=I/Y

Where,

I=Moment of inertia

Y=Distance between neutral axes and outermost fiber(mm)

Steps to calculate 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 and Ymin from neutral axis.
• Step-4:- Find elastic section modulus using the formula provided above.

Moment of inertia is defined as the resistance against the moment, bending or twisting. So higher the moment of inertia will be its resistance to deform is higher.

Here the section modulus of hood design before & after optimization is calculated out by using NX-CAD software.

case-1: Section modulus of hood design before optimisation:-

Imax = 9.039599236x10^5(mm^4)

Imin = 2.766104952x10^3(mm^4)

Total Length = 880.0507 mm

s=Imin/Y

Y = Total length/2

= 880.0507/2

= 440.02535 mm

section modulus for min = 2.76610492x10^3/440.02535

= 0.00628623x10^3 mm^3

Optimized design:

In order to increase the sectional modulus, cross sectional area has to be increased. So here the optimized designis as follows:

case-2: Section modulus of hood design after optimisation:-

Imax = 9.163425087x10^5(mm^4)

Imin = 2.876458262x10^3(mm^4)

Total Length = 880.0602 mm

s=Imin/Y

Y = Total length/2

= 880.0602/2

= 440.0301 mm

section modulus for min = 2.876458262x10^3/440.0301

= 0.006536957x10^3 mm^3

Therefore % increase sectional modulus of hood before and after optimization is as follows

= [(0.006536957x10^3)-(0.00628623x10^3)/0.00628623x10^3] x 100

=3.9885%

Conclusion:

Strength of material is directly proportional to moment of inertia, thus increasing sectional area increases the strength of component.

Therefore % increase in sectional modulus is 3.9885%.

Thus sectional modulus for hood design is calculated and optimized design is also done to increase the section modulus of the hood.