Section Modulus calculation and optimization
AIM : To calculate the Section Modulus Using the Section from your Hood design
S = I/y
Where,
S = Section Modulus
I = Moment of Inertia
y = distance between the neutral axis and the extreme end of the object
To Come up with a new section that has an improved Section Modulus compared to the previous one and mention what changes you made which resulted in the increased strength.
Section Modulus :
Section Modulus is defined as the ratio between moment of Inertia of a section about the Neutral Axis to the distance of the outermost layer from the neutral axis .
It is denoted by Z or S .
Z= I/Ymax
where I=Moment of Inertia about Neutral Axis
Ymax= Distance of Outermost layer from the neutral axis
Note :
1. The neutral axis of a section always passes through its centroid.
2. In case of symmetrical sections such as circular, square or rectangular, the neutral axis passes through its geometrical centre and
the distance of extreme fibre from the neutral axis is
y = d / 2,
where 'd ' is the diameter in case of circular section or depth in case of square or rectangular section.
3. In case of unsymmetrical sections such as L-section or T-section, the neutral axis does not pass through its geometrical centre.
In such cases, first of all the centroid of the section is calculated and then the distance of the extreme fibres for both lower and upper side of the
section is obtained. Out of these two values, the bigger value is used in bending equation.
Bending Equation :
σ/y=M/I=E/R
Where M= Bending moment acting at the given section
σ=Bending stress
I= Moment of Inertia of the crossection about the Neutral Axis
E= Young's Modulus of the material of the beam
R= Radius of curvature of the beam
Let 'M' be the Maximum bending Moment (or moment of resistance offered by the section) then
M=σ*Z
Where σ=permissible bending stress which occurs at the point most distance from the neutal axis i.e at Y maximum
Hence Moment of resistance offered by the section is Maximum when Section modulus Z is Maximum . Hence Section Modulus represents the strength of the section .
CALCULATIONS & OPTIMIZATION :
Before Optimization :
Taking a section of Hood using " Intersection Curve " command and then performing "Section Inertial Analysis " to know the Strength based on section modulus calculation
From the above Section Inertial Analysis ,
Imax= 9.043*10^7 mm^4
Imin= 2.920*10^5 mm^4
Y=Total Length/2
Y= 881.54/2 = 440.77 mm
i) Now taking Imin to check minimum value for which it fails
S= Imin/Y = 9.043*10^7/440.77 = 205163.6908 mm^3
After Optimization :
To Come up with a new section that has an improved Section Modulus compared to the previous one
In order to increase the Sectional Modulus, cross sectional area has to be increased . Hence ,By increasing the depth of the inner panel by 0.5 mm the final optimized design is
From the above Section Inertial Analysis ,
Imax= 9.054*10^7 mm^4
Imin= 2.964*10^5 mm^4
Y=Total Length/2
Y= 881.54/2 = 440.77 mm
i) Now taking Imin to check minimum value for which it fails
S= Imin/Y = 9.054*10^7/440.77 = 205413.2541 mm^3