Section Modulus calculation and optimization

Aim : To calculate section modulus of hood and optimize the design to have improved 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 second moment of area and polar second moment of area for stiffness. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below. There are two types of section moduli, the elastic section modulus and the plastic section modulus. The section moduli of different profiles can also be found as numerical values for common profiles in tables listing properties of such.

Section modulus is a direct measure of a strength of any cross sectional area of an object about an reference axis.

The formula of section modulus is given by,

S=I / Y

Where,

I = Moment of inertia (mm^4)

Y = Distance between neutral axes and outermost fiber (mm)

Steps to calculate section modulus:-

• Step 1:- Find location of centroid of given cross section.
• Step 2:- Find moment of inertia about neutral axis (INAINA)
• Step 3:- Find YmaxYmax from neutral axis.
• Step 4:- Find elastic section modulus using the formula provided above.

Hood Design in UG NX

Case 1: Original cross section of the hood.

Using the Intersection Curve command, the cross section of the hood is obtained.

Now, to obtain the value of 'y', the distance from the neutral axis (construction line) and the extreme edge of the hood is measured.

The calculation for finding the area is made using the Section Inertia Analysis within NX CAD. The result of the software is given below.

From the data above:

$Imax=94089695m{m}^4\&Imin=288960m{m}^4$

$U\sin gthef\text{or}\mu laS=\frac{I}{y},Smax=\frac{94089695}{440}=213840.2m{m}^{3}Smin=\frac{288960}{440}=656.73m{m}^{}$

Case 2: Modified hood cross section.

The original cross section curve is modified by offsetting the lower half of the cross section loop 1mm downwards. This simulates the increase of the depth of emboss within the drawing operation by 1mm.

Running the command on the modified cross section, the results obtained are as follows:

Calculating the maximum and minimum section modulus:

$Smax=\frac{93246986}{440}=211925m{m}^{3}Smin=\frac{294250}{440}=668.75m{m}^3$

Result :

1) The increase in Minimum Section Modulus is 1.83%.

2) Section Modulus increases with increase in cross section area.