Section Modulus calculation and optimization

Title:- to calculate section modulus for hood model and improve strength

1. Introduction

In this project we will calculate section modulus using hood model in the NX cad. There are two cases in this project. In Case 1, we will calculate the section modulus using the hood model from the previous project. In case 2 we increased the space between inner panel and outer panel by 0.5mm and we calculate section modulus. By comparing these two cases, let us check which one has more strength.

2. Objective

• Case 1:- To calculate section modulus of hood geometry with the help of NX software.
• Case 2:- Area of hood is changed and find section modulus
• Compare both cases and decide which one is better strength

3. Center of gravity ,moment of inertia and section of modulus

Centroid :- it is defined as a point about which the entire length, area or volume is assumed to be concentrated. It is related to distribution of length, area and volume.

Center of gravity:- C.G is defined as a point about which the entire weight of the body is assumed to be concentrated.

consider small elements of equal size and shape whose weight are dW1, dw2, dw3....... dWn.

dw1=dw

dw2=dw

dw3=dw

dWn=dw

total weight of the body = sum of all individual weight

W= dW1 + dW2 + dW3 + ..... + dWn

now, sum of moments of all individual weight about y- axis

= dw1 . X1 + dW2 . X2 + dW3 . X3 + ..... + dWn . Xn

= ∑ dWi . Xi

= ∫ X . dw .......... (1)

moment of resultant weight about y axis

= W . (bar x) ..........(2)

equating 1 and 2

W . (bar x) = ∫ X . dw

-- (bar x) = ∫ X . dw / ∫ dw

---(bar y) = ∫ y . dw / ∫ dw

center of mass

-- (bar x) = ∫ X . dm / ∫ dm

---(bar y) = ∫ y . dm / ∫ dm

center of area

-- (bar x) = ∫ X . dA / ∫ dA

---(bar y) = ∫ y . dA / ∫ dA

center of volume

-- (bar x) = ∫ X . dV / ∫ dV

---(bar y) = ∫ y . dV / ∫ dV

INERTIA, MOMENT OF INERTIA

INERTIA :- The property of an object by virtue of which it cannot change its state of rest or of uniform motion along a straight line on its own, is called inertia .

body offer resistance against any change on body, i.e A body is stationary, and we set it in motion by applying a force, Then the body will want to resist the motion and come stationary.

inertia of rest

inertia of motion

inetia of direction

MOMENT OF INERTIA :- Any body offering resistace against of moment, bending or twisting, if we apply any external load on the body, how much resistance its offering to tend to deform.

consider a plane figure , whose moment of inertia is required to be found out about X axis and Y axis as showe in figure.

dA= area of strip

x=distance of the center of gravity of the x strip on y axis

y=distance of the center of gravity of the y strip on x axis

we know that the moment of inertia of the strip about y axis

= dA . x .x

Moment of inertia of the whole area may be found out by integrating above equation .

Ix = ∑ dA . x .x

Iy = ∑ dA . y .y

SECTION MODULUS (Z):-

It is the ratio of moment of inertia divided by distance of extreme fiber from neutral axis

section modulus is a direct mesure of strength of any sectional area of an object about an reference axis (neutral axis)

Z= I / Y

Zx = Ix / (d/2)

Zy = Iy / (d/2)

moment of inertia and section modulus for various section

BENDING Equation

`M/ I = F / Y = E/ R`

M= moment of resistance

I= moment of inertia

F=bending stress

Y= distance from the neutral axis

E= modulus of elasticity

R= radius of curvature of beam

M/I = F/Y

M/F =I/y

M/F= Z (Z= I/Y)

let assume M=1

1/F = Z

F= 1/ z

So whenever the value of section modulus is increased, the stress on it will decrease. And its strength will increase directly.

4. Case -1

In this case we will find the section modulus by making a section of the hood model.

We can find section area, moment of inertia and center of gravity of hood with the help of NX Cad software.

section modulus (Z1)

Z1 = I1 /Y1

I1= moment of inertia of hood (case 1) = 1.425579130e+04 [mm4]

Y1= distance from the neutral axis to body = 440.25 mm

Z1= 32.3811 mm3

5. Case -2

In this case we will move the inner panel downwards by 0.5 mm, so that the section of the hood will increase.And after section increased, we calculate moment of inertia and section modulus.

section modulus (Z2)

Z2 = I2 /Y2

I2= moment of inertia of hood (case 1) = 1.429485790e+04 [mm4]

Y2= distance from the neutral axis to body = 440.25 mm

Z2= 32.4679 mm3

6. Comparison of case 1 and case 2

We compare the parameters of case 1 and case 2 and the parameters are in the table below.

	MOMENT OF INERTIA MAX.	MOMENT OF INERTIA MIN.	SECTION MODULUS
MODEL - 1	4.936943061E+06[MM4]	1.425579130e+04 [mm4]	32.3811 mm3
MODEL - 2	4.874227427E+06[MM4]	1.429485790e+04 [mm4]	32.4679 mm3

According to the theory, as the section of modulus increases, the strength of the body increases.In these two cases the modulus of section of the second case is higher so the strength of the case 2 model is higher.

7. Conclusion

Over all, in this project, section modulus of hood model is calculated.We have seen how the area changes, the moment of inertia and section modulus change. The greater the section modulus, the greater the strength. In case 1 its section modulus is less due to less area.Whereas in case 2 the section modulus is higher as the area is larger.