Section Modulus calculation and optimization
AIM- To calculate the Section modulus (MOI-Moment of Inertia) of the Hood of a car.
SUBJECT-
* Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members.There are two types of section moduli, the Elastic Section Modulus and the Plastic Section Modulus. For general design, the Elastic Section Modulus is used, applying up to the Yield Point for most metals and other common materials.
* Section modulus is the important factor for design of beam and flexural member design. More the section modulus, more the member is resistant to bending of the beam.
* Below mentioned are the formula by which the MOI of various cross section can be calculated.
PROCEDURE- To calculate the increase in Section modulus of the Hood as comapred to the variation done in the curvature of theb cross section Hood and to proceed we will consider three case scenario.
Case 1 : Initial cross-section of the hood
Case 2 : Offset of 0.5mm of the curvature
* Since, the total width if the Inner and Outer panel cannot exceed 25mm hence, this cross section is only considered for theroetical calculation and not practically.
Case 3 : Adding extra area on the curvature
CALCULATION-
1) PERCENTAGE IN SECTION MODULUS WITH RESPECT TO CASE 1 AND CASE 2 :
Section Modulus- S=I/Y
where, S=Section Modulus of the structure
I=Moment of Inertia (Imin)
Y=Total lenght of the cross section/2= L/2
For Case 1-
Imin=2.563 x 10^5 mm^4
For Case 2-
Imin=3.88 c 10^5 mm^4
Hence, % increase in the Section of Modulus, S= ((Imin for case 2 - Imin for case1) / Imin for case 1) * 100
Therefore, % increase in the Section of Modulus, S= ((3.88 x 10^5 - 2.563 x 10^5) / 2.563 x 10^5 ) * 100
= 51.38 %
1) PERCENTAGE IN SECTION MODULUS WITH RESPECT TO CASE 1 AND CASE 3 :
Section Modulus- S=I/Y
where, S=Section Modulus of the structure
I=Moment of Inertia (Imin)
Y=Total lenght of the cross section/2= L/2
For Case 1-
Imin=2.563 x 10^5 mm^4
For Case 3-
Imin=2.574 x 10^5 mm^4
Hence, % increase in the Section of Modulus, S= ((Imin for case 3 - Imin for case1) / Imin for case 1) * 100
Therefore, % increase in the Section of Modulus, S= ((2.574 x 10^5 - 2.563 x 10^5) / 2.563 x 10^5 ) * 100
= 0.4 %
RESULT-
1) % increase in the Section of Modulus for Case 1 and Case 2, S=51.38 %
2) % increase in the Section of Modulus for Case 1 and Case 3, S=0.4 %