Section Modulus calculation and optimization

SECTION MODULUS

OBJECTIVE:

Use the Section from your Hood design and calculate the section modulus using the formula

S = I/y

S = Section Modulus

I = Moment of Inertia

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

Come up with a new section that has improved the section modulus of the previous section and mention what change you made that has increased the strength.

WHAT IS SECTION MODULUS?

Section modulus is defined as the ratio of moment of inertia of a section about the neutral axsis to the distance of the outermost layer fromt the neutral axsis.It is defned by the symbol Z.

Hence mathametically section modulus is given by,

I

S = --------- ......... (1)

Y

where,

I = M.O.I. about neutral axsis

and Ymax = Distance of the outtermost layer from the neutral axsis.

WHAT IS M.O.I ? AND HOW TO CLACULATE M.O.I.?

Moment of inertia is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation. Or in more simple terms, it can be described as a quantity that decides the amount of torque needed for a specific angular acceleration in a rotational axis. Moment of Inertia is also known as the angular mass or rotational inertia. The SI unit of moment of inertia is kg m².

Moment of inertia is usually specified with respect to a chosen axis of rotation. It mainly depends on the distribution of mass around an axis of rotation. MOI varies depending on the axis that is chosen.

In General form,

Moment of Inertia is expressed as I = m × r²

where,

m = Sum of the product of the mass.

r = Distance from the axis of the rotation.

What are the Factors on which Moment of Inertia Depends?

The moment of inertia depends on the following factors,

• The density of the material
• Shape and size of the body
• Axis of rotation (distribution of mass relative to the axis)

By changing the size and shape of the body , we can change the moment of inertia (M.O.I.) of the body.

So that we can increase or decrease the M.O.I of the body.

If moment of inertia increases then strength of the body also increases.

Now let's move on to the objective,

SECTION MODULUS FOR DESIGNED HOOD:

MOI (max) : 5.024694774e+006[MM^4]

MOI (min) : 1.522213087e+004[MM^4]

we should take the minimum moment of inertia to calculate the section modulus.

Because we should calculate what is the minimum load value is required to deform the panel.In other words ,what is the minimum load that the panel can withstand.

then the value of 'Y' is calculated between the neutral axsis and the extreme point on the panel.

which is equal to,

Y = 440.0371 mm

So substituting the value of Y and I min to the section modulus formula (1)

we get ,

1.522213087e+004 [mm^4]

S = -----------------------------------------------

440.0371 mm

S = 34.5928mm^3

SECTION MODULUS FOR NEW SECTION-1:

Section modulus for the designed hood is mentioned above..Now to increase the MOI we have to change the shape of the panel.

So that I offset the curve of inner panel to 0.5 mm upwards,But the value i got is less than the previous value

MOI (max) : 5.020497306e+006[MM^4]

MOI (mini) : 1.402988466e+004[MM^4]

Redo the same step with this MOI minimum value

and value for "Y" is same because I didn't change the length of the panel.

so then ,

1.402988466e+004[mm^4]

S = ----------------------------------------------

440.0371 mm

S = 31.8834 mm^3

SECTION MODULUS FOR NEW SECTION-2:

The edited section has the lower MOI value than the original design.so I edited again to increase the value for MOI.

This time I offset the curve of inner panel to 0.2 mm downwards , then i got slightly increase in MOI of panal than the original design.

MOI (max) : 5.021070636e+006[mm^4]

MOI ( mini) : 1.530571157e+004[mm^4]

again one more time I substitute the MOI minimum value to the section modulus formula with the same value of 'Y'

1.530571157e+004[mm^4]

S = ------------------------------------------

440.0371 mm

S = 34.7828mm^3

SECTION MODULUS VALUES BEFORE AND AFTER CHANGE IN SHAPE:

BEFORE,

S = 34.5928mm^3

AFTER,

S = 34.7828mm^3

So there is 0.2mm increase in the section modulus value after change in shape that is offset of inner panel curve to 0.2 mm downwards.

CONCLUSION:

As per the objective , section modulus of the designed hood is calculated and comed up with the new section which has higher section modulus value than previous one.