Section Modulus calculation and optimization
Section Modulus calculation and optimization
Aim: To create the section for hood and calculate Section Modulus and optimiz the Section Modulus.
Introduction: Section properties involve the mathematical properties of structural shapes. They are of great use in structural analysis and design. Note that these properties have nothing to do with the strength of the material, but are only based on the shape of the section. Those properties are
centre of area (or centroid)
second moment of area or moment of inertia (I)
section modulus (S)
radius of gyration (r)
Though generally section modulus is calculated for the extreme tensile or compressive fibres in a bending beam, often compression is the most critical case due to onset of flexural torsional buckling. Generally tensile extreme fibres have a higher allowable stress or capacity than compressive fibres.
centre of area (or centroid): The centroid of a section is important in structural design and is like the centre of gravity of the shape. Many other simple shapes are symmetrical about the x-x and y-y axes and the centroid can easily be seen
second moment of area or moment of inertia (I): The second moment of area is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The second moment of area is typically denoted with either an I
The second moment of area is also known as the moment of inertia of a shape. It is directly related to the area of material in the cross-section and the displacement of that area from the centroid. Once the centroid is located, the more important structural properties of the shape can be calculated. The axis that determines the centroid is also known as the neutral axis (N/A). The second moment of area is a measure of the 'efficiency' of a shape to resist bending caused by loading. A beam tends to change its shape when loaded. The second moment of area is a measure of a shape's resistance to change.
Certain shapes are better than others at resisting bending as demonstrated in the diagram. Clearly, the orientation of the shape also influences bending.
Calculating the moment of inertia (I):
For simple shapes such as squares, rectangles and circles, simple formulas have been worked out and the values must be calculated for each case.
A standard method of denoting moment of inertia is to write the value mm4.
section modulus (S): The section modulus of the cross-sectional shape is of significant importance in designing beams. It is a direct measure of the strength of the beam. A beam that has a larger section modulus than another will be stronger and capable of supporting greater loads.
section modulus is denoted by S. To calculate S, the distance (y) to the extreme fibres from the centroid (or neutral axis) must be found as that is where the maximum stress could cause failure.
Calculating the section modulus by S = I/y
where I = moment of inertia, y = distance from centroid to top.
For symmetrical sections the value of S is the same above or below the centroid. For asymmetrical sections, two values are found: S max and S min.
radius of gyration (r): This is another property of a section and is also a function of the second moment of area. Put in general terms, the radius of gyration can be considered to be an indication of the stiffness of a section based on the shape of the cross-section when used as a compression member.
The diagram indicates that this member will bend in the thinnest plane.
The radius of gyration is used to compare how various structural shapes will behave under compression along an axis. It is used to predict buckling in a compression member or beam.
The formula for the radius of gyration r is:
`r = sqrt(I/A)` in mm
where I = second moment of area
A = area of material in the cross section
Procedure:
1. Create Intersection: Create intersection for outer and inner panel by using Intersection tool
Where the first element is the element you want to cut and the second element is the cutting element or plane. in the fig 1.1 shown the intersection for outer and inner panel.
Fig0.1: Intersection
2. Boundary for Cross sectional area: In order to calculate Moment of Inertia, we have to create 2D cross section plane, for creating
a. select outer most intersection line of outer panel and inner most intersection line of inner panel.
b. Fill in gaps by using Spline and make sure that there is no any gap or discontinuity.
c. Join all the lines and create a surface by using Fill. shown in the fig.
3. Calculating the section modulus: To calculate section modulus by S = I/y. where I = moment of inertia, y = distance from centroid to top.
We need I = moment of inertia, y = distance from centroid to top
Moment of Inertia: by using measure inertia tools we can find the Moment of Inertia of any shape of 2D geometry.
From the fig. we have Min and Max of I which is M1 and M2.
M1 = 1.54 X 10^6 mm^4
M2 = 5.357 X 10^8 mm^4
y = distance between the neutral axis and the extreme end of the object = 438.4355mm
So
S1 = I/y
= 1.54 X 10^6 mm^4 / 438.4355mm
S1 = 3512.48 mm^3
S2 = 5.357 X 10^8 / 438.4355
S2 = 1.221844 X 10^6 mm^3
Similarly by changing the section area.
offset inner panel side curve by 0.5mm out side and create close loop and 2d surface.
rom the fig. we have Min and Max of I which is M1 and M2.
M1 = 1.637 X 10^6 mm^4
M2 = 5.656 X 10^8 mm^4
y = distance between the neutral axis and the extreme end of the object = 438.4355mm
So
S1 = I/y
= 1.637 X 10^6 mm^4 / 438.4355mm
S1 = 3733.73 mm^3
S2 = 5.656 X 10^8 / 438.4355
S2 = 1.290041 X 10^6 mm^3
1. As we knew larger section modulus than another will be stronger and capable of supporting greater loads. so frome the above we can see that 2nd case has more section modulus so by increasing area we can get more stronger and capable of supporting greater loads
2. So by changing section area, we can change the strength of hood, so depending on the feedback from the CAE team we can change strength.
3. Hood should design in such a way that it should absorb all maximum loads when a crash happens. So while designing we have design in such a way that it should not be more stiffer and not more weeker
Result: section for hood and calculate Section Modulus is done and results were discussed.