Section Modulus calculation and optimization
Section Modulus calculation and optimization
what is section modulus:
Section modulus is the property of the cross-section that is used while the design of beams.
The section modulus is classified into two types:-
1, Elastic section modulus:- The elastic section modulus is applicable up to the yield point of material. It is used in most engineering applications.
2, Plastic section modulus:- The plastic section modulus is generally used for material in which plastic behavior is observed.
Let’s know about each of them in detail.
Elastic section modulus is the ratio of moment of inertia about a neutral axis(IN.A.IN.A.) and the maximum distance between the neutral axis and the outermost fiber of the beam (YmaxYmax).
The formula of elastic section modulus is given by,
S=IN.A.YmaxS=IN.A.Ymax
Where,
I = Moment of inertia (m4m4)
Y = Distance between neutral axes and outermost fiber (m)
Briefly Explain the Section Modulus :
it is the ratio of the moment of inertia of a section about the neutral axis to the distance of the outermost layer from the neutral axis
The elastic section modulus is defined as S = I / y, where I is the second moment of area (or moment of inertia) and y is the distance from the neutral axis to any given fiber. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fiber, as seen in the table below.
is denoted by S:
Formula: S=I/Y
where,
S = Section modulus
I= Moment of Inertia (Unit mm 4)
Y= Distance from the Neutral axis to the extreme end (unit mm)
The Unit of a “section modulus” is (mm3)
Steps to calculate elastic section modulus:-
- Step 1:- Find the location of the centroid of the given cross-section.
- Step 2:- Find the moment of inertia about a neutral axis (INAINA)
- Step 3:- Find YmaxYmax from the neutral axis.
- Step 4:- Find elastic section modulus using the formula provided above.
Elastic section modulus of different sections:-
1, Elastic section modulus of the circle:-
The moment of inertia about Neutral axes for a circular section is,
IN.A.IN.A.=πD464πD464
The YmaxYmax is given by,
YmaxYmax=D2D2
The elastic section modulus for the circular section is,
S = INAYmaxINAYmax=π.D464D2π.D464D2=π.D332π.D332
SCircle S Circle =π.D332
2, Elastic section modulus of rectangular section:-
The moment of inertia about N.A. is given by,
INAINA =bd312
The YmaxYmax is given by,
YmaxYmax =d2d2
The elastic section modulus for the rectangular section is given by,
S = INAYmaxINAYmax=bd312d2bd312d2=bd26bd26
S = bd26
3, Elastic section modulus of hollow rectangle:-
The Moment of inertia about a neutral axis is given by,
INAINA =BD312BD312-bd312bd312
The YmaxYmax is given by,
YmaxYmax =D2D2
The elastic section modulus for a hollow rectangle is given by,
S = INAYmaxINAYmax=BD312−bd312D2BD312-bd312D2
S =BD26−bd36DBD26-bd36D
SHollow rectangleshallow rectangle = BD26−bd36D
4, Elastic section modulus of square tube:-
The moment of inertia about the neutral axis is given by,
IN.A.IN.A.=a412a412-(a−2t)412(a-2t)412
YmaxYmax is given by,
YmaxYmax = a2a2
Now the section modulus for the square tube is given by,
S =IN.A.YmaxIN.A.Ymax=a412−(a−2t)412a2a412-(a-2t)412a2
SSquare tubeS Square tube = a36a36-(a−2t)46a
Use the Section from your Hood design and calculate the Section Modulus using the formula
SECTION #1
- I have taken my design hood, for the calculation.
- To calculate the moment of inertia, I have taken the hood section along the length of the hood & find the inertia using the 'section inertia analysis' tool in NX CAD.
- Then, the section modulus is calculated using the given formula i.e.
S = I/y
Where,
S = Section Modulus
I min = moment of inertia(min.) = 7.1134*10^3 mm^4
Y = distance from neutral axis to extreme end =(L/2)=486.8 /2 = 243.4 mm
S= 7.1134*10^3mm^4/243.4
Hence, S = 29.22mm^3
(fig) the total distance of the Hood section
From the above image, we find the total distance of the section
Optimization of the section Area
I have optimized the hood section Area by offsetting downward 0.5mm of the hood inner panel for the calculation to get
more strengthen the hood panel.
SECTION #2 (Optimaization)
- I have taken my design hood, for the optimized calculation.
- To calculate the moment of inertia, I have taken the hood section along the length of the hood & find the inertia using the 'section inertia analysis' tool in NX CAD.
- Then, the section modulus is calculated using the given formula i.e.
S = I/y
Where,
S = Section Modulus
I min = moment of inertia(min.) = 7.334*10^3 mm^4
Y = distance from neutral axis to extreme end =(L/2)=486.8 /2 = 243.4 mm
S= 7.334*10^3mm^4/243.4
Hence, S = 30.13mm^3
Conclusion:
Hence when comparing section#1 & section#2,
1. The section modulus value of section#2 is higher than section#1
2. after we have increased the section area by 0.5mm, the moment of inertia & section modulus values increase. which means strength and load material also increase.