Section Modulus calculation and optimization

OBJECTIVE:-

To increase the Section Modulus of the hood by necessary changes using NX Cad.

Moment of Inertia:-

The second moment of area or second area moment,or quadratic of area and also known as area moment of inertia,is geometrical property of an area which reflects how its oints are distributed with regard to an arbitrary axis.the second moment of area is typically denoted with I (for axis that lies in the plane of area)or with J (For an axis perpendicular to the plane)

In stuctural engineering,The second moment of area of the beam is an important property used in the calculation of the beams deflection and in the calculation of stress caused by a moment applied to the beam.In order to maximize the second moment of area,a large fraction of cross-sectional area of an I-beam is located at maximum possible distance from the centriod of the i-beam cross section.

SECTION MODULUS:-

Its termed as ratio of the second moment of area and distance from N.A.(Neutral axis)to the extreme fiber.Also,it is measure of the strength of the given memeber.The stress in the outermost section of the beam is computed with the help of section modulus.Its indicated by S.

Section modulus is indicated as follows:-

S=I/Y

Here,I is "moment of inetia"and y is the distance from the "neutral axis" to the top or bottom of fiber.

The Unit of a "Section modulus"is in.3(3mm).

Section modulus depends only on the cross-section shape of the structure.For symmetric sections,the value of "section modulus"is for both above and below of the centriod of the fiber.An asymmetric section has two values for top and bottom fiber due to the different distance from the centriod to the top and bottom of the material,the maximum "section modulus"is S max and the minimum section modulus is S min.

Importance:-

• Its significant for beam and flexural member design.
• More the section modulus,the more the member is resistant to the bending of the beam.
• It is easier to calculate stresses in the beam and an exact measure of strength of the steel.
• If two beams are made of the same material and comparing the "section modulus"of two beams,the beam with bigger section modulus will be tougher and more capable to withstand larger loads.

Section Modulus calculation of the Hood Design:-

case1:-Initial hood Design.

Area Moment of inertia:-I(min)

MOI(MIN):2.800083590e+05mm^4

Y distance:-439.94mm

S=I/Y

S=2.800083590e+05mm^4/439.94mm(2.800083590*10^5)

S=636.46mm^3.

CASE2:-Optimized Hood Design

Aim:-Our Aim here is to increase the I(min)

Optimization:-

The distance bitween inner and outer curve is increased by offsetting the inner curve by 0.5mm and then the curve also added in the sketch inthe modified sketch.

Y distance:439.94mm

S=I/Y

S=3.080776819e+05mm^4/439.94mm(3.80776819*10^5)

S=865.52mm^3.

Final Result:-

Thus the stiffness of the car hood has been increased by increasing its area moment of inertia.

Conclusion:-

Section modulus is ditectly dependent on the area moment of inertia and the distance from the neutral axis.Hence,to improve the geometry of the carry more bending load,the section modulus can be improved by increasing the area MOI of a given section.We can increase the section modulus just increasing the gap between the outer and inner panel.