Section Modulus calculation and optimization
AIM
To calculate the section modulus from the hood design using the formula S=I/y.
SECTION MODULUS
Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. It does not represent anything physically.
The section modulus is defined as the ratio of moment of inertia to distance from the neutral axis.
Formula
S=I/y
where
S - Section modulus (mm^3)
I - Moment of inertia (mm^4)
y - Distance from neutral axis (mm)
AREA MOMENT OF INERIA
Area moment of inertia 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.
NEUTRAL AXIS
Neutral axis is the axis shown in cross-section where bending stress is zero.
CALCULATION
CASE 1: BEFORE OPTIMISATION
The hood which was already designed is imported and section inertia analysis is done.
We have to make sure that the curve obtained is a single closed/open curve.
Fig 1.1
Fig 1.2
MOI (Max) = 9.146137426e+07[mm^4]
MOI (Min) = 2.821255212e+05[mm^4]
As per section inertia equation,
S=I/y
I = MOI (Min) value is considered
= 2.821255212e+05[mm^4]
y = Total distance/2
= 880.86/2
= 440.43 mm
Therefore,
S = I/y
= 282125.521/440.43
S = 640.5683 mm^3
CASE 2 : AFTER OPTIMIZATION
The hood inner panel's curve is offseted 0.5mm outwards and section inertia analysis is done.
Fig 2.1
MOI (Max) = 9.129377541e+07[mm^4]
MOI (Min) = 2.860926506e+05[mm^4]
As per section modulus equation,
S = I/y
I = MOI (Min) value is considered
= 286092.6506mm^4
y = Total distance / 2
= 880.86/2
= 440.43mm
Therefore,
S = 286092.6506/440.43
S = 649.57mm^3
CONCLUSION
When comparing with case 1 and case 2, increasing the area moment leads to increase in section modulus which means strenght and load capacity of design increases.