Section Modulus calculation and optimization
Object
To calculate section modulus of hood & optimize the design to improve section modulus. Higher section modulus of a structure more resistive it become to bending.
Section Modulus
Section modulus is defind as the ratio of the second moment of area ( moment of inertia ) & the distance fom the netural axis to given or extreme fiber. The section modulus of the crossectional shape is of significant important in design of objects. It direct measure the strength of objects. Its also indicate that the resistance towards the bending, Its a single parameter's that measures the cros-sectional strength in bending section modulus is the geometric property of the given crossection used in design. Its also refer the polar or torsional section modulus. Other the geometric property used in the design include are of Tension, shear & radius of gyration for compression.
The equation for section modulus is_
S=I / Y
Where,
S_ Section Modulus ( mm3 )
I_ Moment of Inertia (mm4 )
Y_ Distance between netural axis of fiber ( mm )
Fig-01 Centroid on beam.
Elastic section modulus
For general design, the elastic section modulus is used, applying up to the yield point for most metals and other common materials. The elastic section modulus is defined as S = I / y, where I is the second moment of area (or area moment of inertia, not to be confused with moment of inertia) and y is the distance from the neutral axis to any given fibre. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fibre, as seen in the table below. It is also often used to determine the yield moment (My) such that My = S × σy, where σy is the yield strength of the material.
Plastic section modulus
The plastic section modulus is used for materials where elastic yielding is acceptable and plastic behavior is assumed to be an acceptable limit. Designs generally strive to ultimately remain below the plastic limit to avoid permanent deformations, often comparing the plastic capacity against amplified forces or stresses. The plastic section modulus depends on the location of the plastic neutral axis (PNA). The PNA is defined as the axis that splits the cross section such that the compression force from the area in compression equals the tension force from the area in tension. So, for sections with constant yielding stress, the area above and below the PNA will be equal, but for composite sections, this is not necessarily the case.
Fig_02 Changing of section modus to their nutural fiber axis
Fig-03 Its resist the load which makes less bend amd improves the strength.
To calculate section modulus of hood By using NX_CAD software.
the sectional modulus of hood design before optimization is given below, Following image clearly shown the details in NX-Cad.
Fig_04.1 MOI Details,
Fig_04.2 MOI Details,
In fig,
Maximum Moment of inertia is ( MOI )_
Mmax=1.562288169x10^7 (mm^4)
Minimum moment of inertia is ( MOI )_
Mmin=1.481238896x10^5 (mm^4)
that is,
The distance of netural axis fiber is _
Ymax=487.4152 ( mm ) / 2 = 243.70 mm
Hence, the section modulus for the hood is given as below,
For maximum_
Smax = I / Ymax
= 1.562288169x10^7 / 243.70
= 64.103x10^3 mm3
Smax= 64.103x10^3 mm3
For minumum_
Smin = I / Ymin
= 1.481238896x10^5 / 243.70
= 0.60781x10^3 mm3
Smin= 0.60781x10^3 mm3
The given section modulus renge of hood is maximum & minimum section modulus is Smax= 64.103x10^3 mm3 & Smin= 0.60781x10^3 mm3.
Optimized Design Study
Inorder to increase the sectional modulus, cross sectional area has to be increased. So here the optmized design are given below.
Fig_05.1 MOI Details,
Fig_05.2 MOI Details,
In fig,
Maximum Moment of inertia is ( MOI )_
Mmax=1.569818024x10^7 (mm^4)
Minimum moment of inertia is ( MOI )_
Mmin=1.77585626x10^5 (mm^4)
that is,
The distance of netural axis fiber is _
Ymax=487.4152 ( mm ) / 2 = 243.70 mm
Hence, the section modulus for the hood is given as below,
For maximum_
Smax = I / Ymax
= 1.569818024x10^7 / 243.70
= 64.416x10^3 mm3
Smax= 64.146x10^3 mm3
For minumum_
Smin = I / Ymin
= 1.77585626x10^5 / 243.70
= 0.72870x10^3 mm3
Smin= 0.72870x10^3 mm3
The given section modulus renge of hood is maximum & minimum section modulus is Smax= 64.146x10^3 mm3 & Smin= 0.72870x10^3 mm3
Significance of section modulus
It is also used to determine the extreme fiber elastic strees as well as the yeild moment of elastic section.
Conclusion
Section Modulus is directly depend on the area moment of inertia & the distance of netural fiber axis, the section modulus can be improve by incerasing the moment of inertia of given section.