Section Modulus calculation and optimization

Aim : To obtain the section modulus of the designed car hood & further obtain further improvized Section and compare section modulus of both the hood.

Theory : Section modulus is a geometric property or a value given for cross-section used in the design of flexural members.

There are two types of section modulus

1. Elastic section modulus - Applicable up to the yield point of material. it is used in most engineering applications.
2. Plastic section Modulus - Generally used for material in which plastic behavior is observed.

Significance of section modulus

• Higher the section modulus,higher will be the resistance to bending.
• Easier to calculate strength and stresses in beams.
• if two beams are made of same material and  the section modulus of twi beams are compared, the beam with larger section modulus will be tougher and more capable to withstand larger loads

Deriving formula for section modulus.

we know from bending moment eqaution

(E/r)=(M/I)=(f/y)

where,

M= bending moment applied

I = moment of inertia

f = bending stress

y= distance from NA to extreme fiber

if we calculate the amount of bending applied on a beam

M=f*(I/y)

If we focus on the term (I/y) they both are geometrical properties of a beam or a body. the value derived from these two is called as fluctural rigidiy or section modulus. which is Z

Z=(I/y) ratio of inertia and distance of upper most fiber.

on further deriving, we know that

let us consider a rectangle who's

I=(bd^3/12)

y=(d/2)

on dividing both the values we get 

Z = (bd^2/6)-------->this is the flectural rigidity of rectangular section

it shows that Z is directly perportional to breadth and square of depth.

Now calculation for our designed hood.

from above figure

I=5.347e^3 mm4

y=488 mm

Z=(I/y)=(5.347e^3/488)

            =10.9 mm3

 

modified section data

I=5704.5071mm^4

y=488 mm

Z=(I/y)=(5704.50/488)

             =11.689mm^3

Conclusion

• Section modulus of modified section is increased.
• MOI increases with increase of section area
• MOI increases with increase of section length
• If we increase the gaap between the inner & outer panel of hood eventually section length increase thus MOI will increase.