Section Modulus calculation and optimization
AIM : To Use the Section from Hood design and calculate the Section Modulus using the Euler's and Bernouli's 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.
Area moment of Inertia:
The area moment of inertia of a beams cross sectional area measures the beam ability to resist bending. The larger the moment of inertia less will be the bend.
Where,
M = Bending moment.
I = Area moment of Inertia.
E = Youngs modulus.
R = Radius of gyration.
Neutral axis: When beam is subjected to pure bending the top most fibres of the beam are subjected to maximum compression, while the bottom most fibres of the beams are subjected to maximum tension.
PROCEDURE:
The data are collected from taking the master section using the mid plane.
Front crash first design
Front crash Second design
Side Crash First design
Side Crash Second design
SECTION VIEW
OBSERVATION
| SECTION MODULUS DATA | FRONT CRASH F.D | FRONT CRASH S.D | SIDE CRASH F.D | SIDE CRASH S.D |
| I min(in meters) | 1.881*10^6 | 2.29*10^6 | 8.164*10^6 | 9.901*10^6 |
| I max(in meters) | 6.662*10^8 | 7.909*10^8 | 1.299*10^8 | 1.526*10^8 |
| I min(in mm) | 1881000 | 2290000 | 8164000 | 9901000 |
| I max(in mm) | 666200000 | 790900000 | 129900000 | 1526000000 |
| Total distance(in mm) | 878.496 | 878.144 | 485.339 | 485.339 |
| Y=Total dis/2 (in mm) | 439.248 | 439.072 | 242.6695 | 242.6695 |
| S min= I min/y(in mm) | 4282.318 | 5215.545 | 33,642.464 | 40,800.347 |
| S max= I max/y (in mm) | 1516683.06 | 1801299.1 | 535,295.947 | 628,838.811 |
| S avg=(Smin+Smax)/2(in mm) | 760,482.689 | 903,257.322 | 284,469.205 | 334,819.579 |
SAMPLE CALCULATION
CASE1) FRONT CRASH first design
Imin (in Meters)=1.881*10^6
Imax(in Meters)=6.662*10^8 m
Imin (in mm)=1881000 mm
Imax (in mm)=666200000 mm
Total Dist=878.496 mm
Y=Total Dist./2 = 439.248 mm
S=I/Y
Smin=Imin/Y ; Smax=Imax/Y
Smin=1881000/439.248 => 4282.318 mm
Smax=666200000/439.248 => 1516683.06
Savg=(4282.318+1516683.06)/2 => 760,482.689 mm
CASE2) FRONT CRASH Second design
Imin (in Meters)=2.29*10^6
Imax(in Meters)=7.909*10^8
Imin (in mm)=2290000
Imax (in mm)=790900000
Total Dist=878.144
Y=Total Dist./2 = 439.072
S=I/Y
Smin=Imin/Y ; Smax=Imax/Y
Smin= 2290000/439.072 => 5215.545
Smax=790900000/439.072 =>1801299.1
Savg=(5215.545+1801299.1)/2 => 903,257.322 mm
By Comparing both the cases,
Front Crash
760,482.689 mm < 903,257.322 mm
Side Crash
284,469.205 mm < 334,819.579 mm
CONCLUSION
The inner pannel strength is increased, while changing the geomentrical property of the emboss. By considering the above calculation the section modulus value for the design was increased. This results in, that the hood will resist more stress when the external stress increases. While Comparing with first hood design, second hood design will resist more bending stress.