Section Modulus calculation and optimization
SECTION MODULUS
Introduction
Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members.
The section modulus of the cross-sectional shape is of significant importance in designing structures. It is a direct measure of the strength of the structures. A structures that has a larger section modulus than another will be stronger and capable of supporting greater loads.
Sectional Modulus (S): It is the ratio of Moment of Inertia (I) of the beam cross-section about the neutral axis to the distance (y max) of extreme fiber from the neutral axis.
The Area Moment Of Inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. It is also known as the second moment of area or second moment of inertia.
The Section Modulus is defined as
S = I/y,
S = Section modulus, mm3
I = Moment of Inertia, MOI – mm4
y = Distance from Neutral axis to the extreme end, mm
Section Inertia Analysis
The cross section of the Hood is taken by creating an intersection curve in a plane halfway of the hood.
The Section inertia analysis is done and the MOI values are taken.
The y value is measured by taking half of the distance value between extreme ends.
Moment of inertia (max) = 4923063.038 mm4
Moment of inertia (min) = 14566.60147 mm4
y = 882.6839 / 2
y = 441.342 mm
S max = 4923063.038 / 441.342
S max = 11154.76 mm3
S min = 14566.60147 / 441.342
S min = 33.01 mm3
Optimization
The edges mentioned in the image by blue curves are the new edges 1 mm offsetted from the original edges on both sides of the hood CS. Then the Section Modulus is calculated for this new section.
Moment of inertia (max) = 5281963.5 mm4
Moment of inertia (min) = 16438.52439 mm4
y = 441.342 mm
S max = 5281963.5 / 441.342
S max = 11697.96 mm3
S min = 16438.52439 / 441.342
S min = 37.25 mm3
Conclusion
Thus the Section Modulus is increased in the new section which has increased CS area away from its neutral axis.