Section Modulus calculation and optimization

Section Modulus calculation and optimization of Hood

Objective

To calculate section modulus of hood and optimize the design to have improved section modulus.

Section modulus

Section modulus is the ratio of moment resisted by the section to the stress in the extreme fiber. It gives us an idea about how much of load that the given structure can take.

If the section modulus increases the moment of resistance increases and hence its load bearing capacity.

• 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 the design include an area for tension and shear, the radius of gyration for compression, and themoment of inertia and polar moment of inertia for stiffness.

We use the Section of Hood design to calculate the section modulus using the formula S = I/y

S = Section Modulus

I = Moment of Inertia (in mm^4)

y = Distance between the neutral axis and the extreme end of the object ( in mm)

Before calculating inertia we distance between the neutral axis and the extreme end of the hood.

• The total distance of the hood = 485.8691 mm
• But we want the distance between the neutral axis and the end of the hood so,

y = Total distance/2 = 485.8691/2

y = 242.935 mm

Section of the Hood along y.

Calculation of section modulus,

I_max = 8.166473571 x 10^5 (mm^4)

I_min = 6.644978963 x 10^3 (mm^4)

Section modulus for max. = 8.166473571 x 10^5 / 242.935

= 3.3616 x 10^3 mm^3

Section modulus for min. = 6.644978963 x 10^3 / 242.935

= 0.027353 mm^3

The hood design section modulus is,

S Max. = 3.3616 x 10^3 mm^3

S Min. = 0.027353 mm^3

Optimized design

Inorder to increase the sectional modulus, we offset the inner panel by 1mm towords the outer panel.

I_max = 12.21754086 x 10^5 (mm^4)

I_min = 9.749457747 x 10^3 (mm^4)

Section modulus for max. = 12.21754086 x 10^5 / 242.935

= 5.02914 x 10^3 mm^3

Section modulus for min. = 9.749457747 x 10^3 / 242.935

= 0.040132 x 10^3 mm^3

The optimized hood design section modulus range is,

S Max. = 5.02914 x 10^3 mm^3

S Min. = 0.040132 x 10^3 mm^3

When we Optimized the design , section modulus is ,

S Max. is varies from 3.3616 x 10^3 mm^3 to 5.02914 x 10^3 mm^3

S Min. is varies from 0.027353 mm^3 to 0.040132 x 10^3 mm^3

Conclusion

Thus the sectional modulus for hood design is calculated and optimized design is also done to increase the section modulus of the hood.