Section Modulus calculation and optimization

SECTION MODULUS

AIM:

To calculate the Section modulus in Hood design from various section and optimisation to improve the overall section modulus.

SECTION MODULUS:

Section Modulus is a geometric property used to calculate the bending stresses in a structural member. It 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.

Formula for section modulus,

S = I / Y

here,

S = Section Modulus

I = Moment of Inertia

y = distance between the neutral axis and the extreme end of the object

FORMATION OF INTERSECTION:

For calculation of the section modulus in design part initially the intersection curve should be formed. In hood the datum plane is created that normal to centre of the outer panel then by intersection curve command the part is intersect by the plane created normal to the surface.

Then create the sketch project the intersection curve on same plane. The curve has inner and outer panel curve. For make the single curve the bottom curve of outer panel and top curve of inner panel should be trimmed and by extended command extend the line to join inner and outer panel and trim unwanted curve.

The above diagram is Case 1 curve.

Then create the second sketch project the case 1 curve in it and trim the joint line between inner and outer panel. Inner panel curve is offset at 0.5mm downwards and joint it into the outer panel curve. It is done because to analyse the section modulus by increasing the cross section. This curve is for Case 2.

DATA:

For Case 1:

Moment of inertia for the part in case 1 is shown below

For Case 2:

Moment of inertia for the part which have offset the inner panel curve is shown below.

Distance (Y):

The value of Y is distance between neutral axis and the extreme end of the object.

The total distance is 879.8748mm but the Y value is half of that distance.

So, the Y value is 439.9374mm.

CALCULATION OF SECTION MODULUS:

For Case 1:

While calculating section modulus the value of I is always taken Minimum value.

S = I / Y

I = MOI (minimum) = 1.347718696e+04 mm⁴ = 1.347718696 x 10⁴ mm⁴

Y = 439.9374 mm

S = 1.347718696 x 10⁴ mm⁴ / 439.9374 mm

S = 30.63432 mm^3.

So, the value of Section modulus in Case 1 is S = 30.63432 mm^3.

For Case 2:

S = I / Y

I = MOI (minimum) = 1.37261556e+04 mm⁴ = 1.37261556 x 10⁴ mm⁴

Y = 439.9374 mm

S = 1.37261556 x 10⁴ mm⁴ / 439.9374 mm

S = 31.2002 mm³.

So, the value of Section modulus in Case 2 is S = 31.2002 mm³.

After calculation of both case the section modulus result is

S_1(Normal) = 30.63432 mm^3.

S_{2(After optimization) =} 31.2002 mm³.

CONCLUSION:

Thus, the section modulus of both normal and optimization cases is calculated.