Section Modulus calculation and optimization
SECTION MODULATION AND OPTIMIZATION
AIM
To calculate the section modulus of the hood section and optimising the hood for strength improvement.
SECTION MODULUS (S)
Section modulus is the geometric property of a cross section used in the design of beams or other flexural members that will experience due to an applied bending moment.The unit of the section modulus is m^3. Its denoted by (S).
There are two types of section moduli
1) elastic section modulus is referred to as simply section modulus.
2) Plastic section modulus.
The general formula for section modulus is ,
S=I/Y
Here, S -> section modulus.
I-> moment of inertia.
Y-> the distance between the neutral axix to the outside edge of the beam.
FIG:- SECTION MODULUS AT DIFFERENT SHAPE SECTIONS
PLASTIC SECTION MODULUS
A plastic section modulus is geometric property for a cross section of an object generallly used in material in which plastic behaviour can be observed. This is only one of the two different types of plastic section modulus is used in engineering and design. Plastic section modulus is the more uncommon form of plastic section modulus, and most general designs by engineers do not used in their calculations.
MOMENT OF INERTIA (I)
The tendency of rigid body to resist angular rotation is called moment of inertia. It is a quantity that depends on the shape of body, mass distribution and orientation of the rotational axis. Generally its denoted by (I).
FIG:- MOMENT OF INERTIA FOR DIFFERENT SECTION
DISTANCE BETWEEN THE NEUTRAL AXIX TO THE OUTSIDE EDGE OF THE BEAM (L)
FIG :- CALCULATION OF THE LENGTH
Here we need neutreal axis to the outside edge of the beam Y = L/2
Y= 876.4/2
Y= 438.2 mm
CASE 1 : ( BEFORE OPTIMISING THE DESIGN)
FIG :- BEFORE OPTIMISING THE DESIGN
In this initial case ,
MOI (Max) = 8.920239400e+07[mm^4]
MOI (Min) = 2.635476954e+05 [mm^4]
we already know the length of the section is (L)= 438.2MM
Therefore modulus of the section is S=I/Y
( Here im going to take the minimum range of the inertia )
S=MOI(Min)/y
S=2.635476954e+05[mm^4]/438.2
S=7.1753794283mm^3
CASE 2 : (AFTER OPTIMISING THE DESIGN)
FIG:- AFTER OPTIMISING THE DESIGN
In this case ,
MOI(Max)=1.198274738e+09[mm^4]
MOI(Min)=3.348564027e+05[mm^4]
Already we know the length of th section is (L)=438.2mm
Therefore the section modulus is (S) = MOI(Min)/Y
S=3.3485664027e+05[mm^4]/438.2
S=9.1137575188mm^3
NOTE
Adding the additional embosses on the inner pannel and improving the thickness of the inner pannel from 0.75mm to 1.0mm it will improves the inertia of the section.If the area inertia is increases the section modulus of the section is also increased.
FIG:- CASE1 ( BEFORE OPTIMISING)
FIG:- CASE 2 ( AFTER OPTIMISING)
TABULATION FOR THE BOTH CASES
| PROPERTIES OF THE SECTION | BEFORE OPTIMIZATION | AFTER OPTIMIZATION |
| MOI(Max) | 8.920239400e+07[mm^4] | 1.198274738e+09[mm^4] |
| MOI(Min) | 2.635476954e+05[mm^4] | 3.3488564027e+05[mm^4] |
| SECTION MODULUS (S) | 7.1753794283mm^3 | 9.1137575188mm^3 |
CONCLUSION
- The section modulus of the hood section is calculated.
- Optimisation of the hood is done by increase the area of the section.