Section Modulus calculation and optimization
MOMENT OF INERTIA:
Area moment of inertia also known as second area moment or 2nd moment of area is a property of a two-dimensional plane shape where it shows how its points are dispersed in an arbitrary axis in the cross-sectional plane. This property basically characterizes the deflection of the plane shape under some load.
Area moment of inertia is usually denoted by the letter I for an axis in a plane. It is also denoted as J when the axis lies perpendicular to the plane. The dimension unit of second area moment is Length to the power of four which is given as L4. If we take the International System of Units, its unit of dimension is meter to the power of four or m4. If we take the Imperial System of Units it can be inches to the fourth power, in4.
We will come across this concept in the field of structural engineering often. Here the area moment of inertia is said to be the measure of the flexural stiffness of a beam. It is an important property that is used to measure the resistance offered by a beam to bending or in calculating a beam deflection. Here we have to look at two cases.
- First, a beam’s resistance to bending can be easily described or defined by the planar second moment of area where the force lies perpendicular to the neutral axis.
- Secondly, the polar second moment of area can be used to determine the beam’s resistance when the applied moment is parallel to its cross-section. It is basically the beams ability to resist torsion.
AREA OF MOMENT OF INERTIA FORMULAS
If we consider the second moment of area for the x-axis then it is given as;
Meanwhile, the “product” moment of area is defined by
- Section modulus is a direct measure of strength of any sectional area of an object about an reference axis(neutral axis).
- Strength is nothing but, capable of supporting greater loads, so higher the strength it has a high capable of supporting greater loads.
- This strength can measured directly from Section modulus formula, and defined by below 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
The change of the position of the flank it varie the change of moment of inertia
FORMULAS FOR DIFFRENT CROSS SECTION:
1 ST DESIGN STUDY:
MAXIMUM VALUE MOI:8.202716896e+07(mm4)
MINIMUM VALUE MOI:2.798367954e+05(mm4)
area y = 874.5248 mm/2 =437.2624mm
S=2.79836*10^5/437.2624
S=639.972702 MM4
MODIFIED SECTION STUDY:
MAXIMUM VALUE=4.7586800e+0.06 mm4
MINIMUM VALUE=1.474454568e+0.04 mm4
area y = 874.5248 mm/2 =437.2624mm
S=1.474454*10^4/437.2624
S=33.7201 MM3
CONCLUSION:
The differnece between the two section of area momenta of inertia is Calculated