Section Modulus calculation and optimization

AIM: Calculate the section modulus of the Hood.

OBJECTIVES:

1. Calculate the section modulus of the Hood using the formula
   `S=I/y`
   Where,
   S= Section Modulus
   I = Moment of Inertia
   y= Distance between the neutral axis and the extreme end of the object.
2. Find the Maximum and Minimum Moment of Inertia for the Hood.
3. Make the Section Inertia Analysis Chart.

THEORY:

Section Modulus:

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area for tension and shear, Radius of Gyration for compression, and Moment od Inertia and Polar Moment of Inertia for stiffness.

For general design, the Section modulus is used, applying up to the yield point for most metals and other common materials.

The Section modulus is defined as S = I / y, where I is the Moment of Inertia and y is the distance from the neutral axis to the one end of the material. 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 (M_y) such that M_y = S ⋅ σ_y, where σ_y is the Yield Strength of the material.

NOTE: We are calculating the section modulus to minimize the bending moment of the material.By using the formula,
`M/I=σ/y=E/R`

From this Equation we can get,
`S=I/y`

Steps to calculate the section modulus:

1. Make the Datum Plane at the half section of the hood such as it is perpadicular to the External Force.
   
2. Select the Intersection Curve in the Curve tab.
   
3. Select the Datum plane for "Select Face (1)" and Outer surface of Outer Panel and Outer surface of Inner Panel for "Select Face (2)"
   
4. Press OK and the curve is created parallel to the Datum Plane.
   
   
   
5. Now Hide complete body of the Hood.
   
   
   
6. Now Select Sketch on the Datum Plane and project the same curve on the datum plane.
   
   
   
7. Trim an internal curves of the Hood. Connect outer curve and inner curve by Spline and end the sketch.
   
8. The moment of inertia of the closed area is calculated by using Section Inertia Analysis.
   
   
   
   The minimum and maximum Moment of Inertia of the closed curve of the Hood are 4.915211e+06 mm^4 and 1.479498e+04 mm^4 and Sectional Area is 73.542295 mm^2. An end to end length of an intersection curve is 885.1332 mm. But we have to consider half of it that is 442.5666 mm.
   
   Now the Section Modulus of the Hood is,
   Smax = Imax/y = 4.915211e+06/442.5666 = 1.1106e+4 mm^3.
   Smin = Imin/y = 1.479498e+04/442.5666 = 33.4299 mm^3.
   
   
9. For high strength of the material we have to calculate for high moment of inertia, so after offsetting the curve by 0.75mm close to the outer surface of the inner panel, we get the Moment of Inertia as shown in below,
   
   
   The minimum and maximum Moment of Inertia of the closed curve of the Hood are 9.192498e+07 mm^4 and 2.8436826e+05 mm^4 and Sectional Area is 1.3777412e+03 mm^2. An end to end length of an intersection curve is 885.1332 mm. But we have to consider half of it that is 442.5666 mm.
   
   Now the Section Modulus of the Hood is,
   Smax = Imax/y = 9.192498e+07/442.5666 = 2.0771e+5 mm^3.
   Smin = Imin/y = 2.8436826e+05/442.5666 = 642.5434 mm^3.
   
   

Table for the Section Inertia Analysis

Case No.	Minimum Moment of Inertia	Maximum Moment of Inertia	Length	Section Modulus minimum	Section Modulus Maximum	Sectional Area
1	1.479498e+04 mm^4	4.915211e+06 mm^4	442.5666 mm	33.4299 mm^3	1.1106e+4 mm^3	73.542295 mm^2
2	2.8436826e+05 mm^4	9.192498e+07 mm^4	442.5666 mm	642.5434 mm^3	2.0771e+5 mm^3	1.3777412e+03 mm^2

CONCLUSION:-

The strength of the material is directly proportional to the moment of inertia, hence increase in sectional area there is have increase in overall mass of an object ,hence have increase in strength.