Section Modulus calculation and optimization

Objective :-

To calculate the Section Modulus of the hood and optimize the design to improve the Section Modulus and ultimately the bending strength of the hood.

Section Modulus :-

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. It is the direct measure of the strength of the shaft section or the beam section. Higher the section modulus of a structure, the more the resistive it becomes to bending. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and moment of inertia and polar moment of inertia for stiffness. Section modulus gives us an idea about how much of load the given structure can take. If the section modulus increases the moment of resistance increases and hence its load bearing capacity. 

There are two types of section moduli, the elastic section modulus and the plastic section modulus

1. Elastic section modulus 
2. Plastic section modulus

1) 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.

Elastic Section modulus is defined as the ratio of polar moment of inertia to the radius of the shaft or the distance from the neutral axis to the outer fibres.

                    S = I`/`y

where,

          S = Section Modulus.

          I = Moment of inertia. 

          y = Distance from Neutal axis to outermost fiber.

Equations for the section moduli of common shapes are given below.

                          

                          

2) 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.

The plastic section modulus is the sum of the areas of the cross section on each side of the PNA (which may or may not be equal) multiplied by the distance from the local centroids of the two areas to the PNA:

Case :- 1

 The intersection curves of the hood design are taken so that closed region is obtained and then section inertia analysis is done.

                      

We have taken the section along the length of the hood.

                     

y = Distance from Neutal axis to outermost fiber.

y = 477.5984/2

y = 238.7992 mm

                    

 Maximum and minimum moment of inertia of section of hood is calculated by section inertia analysis tool.

                    

Moment of inertia (max) :- 8.190774405x10^5 mm^4

Moment of inertia (min) :- 4.657253104x10^3 mm^4

y = 477.5984/2 = 238.7992 mm

S = I/y

S =  4.657253104x10^3/ 238.7992

S = 19.502 mm^3

Case :- 2

Distance between the outer panel and ineer panel has been increased by 0.5mm.

                

                

Moment of inertia (max) :- 8.173719415x10^5 mm^4

Moment of inertia (min) :- 4.848083250x10^3 mm^4

y = 477.5984/2 = 238.7992 mm

S = I/y

S =  4.848083250x10^3/ 238.7992

S = 20.301 mm^3

Final Results :-

(Case 1) S = 19.502 mm^3

(Case 2) S = 20.301 mm^3

Conclusion :-

Thus we have calculated the Section Modulus of the hood as well as we have optimized the design to improve the Section modulus.

As the distance between the inner panel and outer panel of the hood increases, Moment of inertia and the Section modulus also increases, therefore the strength of the hood increases.