Section Modulus calculation and optimization

SECTION MODULUS

Objective:

calculating the section modulus of the previously designed hood, analysing the report and optimising the design for a better section modulus.

what is section modulus?
section modulus is the geometric property of a given cross-section in the design of beams and columns.

for a general design, elastic section modulus is used which is applicable up to the yield point for most metals.

S=I/y, where I is the second moment of area or Area moment of inertia,y is the distance from the neutral axis to extreme fibre.

moment of inertia I,is the resistance offered against the bending or twisting due to the Load.

section modulus equations for some of the cross sections are shown below

Section modulus equations^[3]

Cross-sectional shape	Figure	Equation	Comment
Rectangle			Solid arrow represents neutral axis
doubly symmetric I-section (major axis)		,	NA indicates neutral axis
doubly symmetric I-section (minor axis)		[4]	NA indicates neutral axis
Circle		[3]	Solid arrow represents neutral axis
Circular hollow section			Solid arrow represents neutral axis
Rectangular hollow section			NA indicates neutral axis
Diamond			NA indicates neutral axis
C-channel			NA indicates neutral axis

Section modulus is also referred to as polar modulus or torsional sectional modulus.

section modulus is often determined to know the yield Moment,

M_y = S ⋅ σ_y,whrere σ_y is the yield strength of the material.

Calculating section modulus of the hood previously designed in the Catia software

taking a cross-section from the midway of the hood assembly and extracting the intersection of the surfaces in the joining them to form the closed curve.

The closed curve is then filled using the surface and going to the "Measure inertia" command in Catia,I Moment of Inertia max and min values are obtained.

After getting the Imax,Imin values and total length.

S=I/y,

Smin=Imin/y =2.058*10^6/440.06=4.676*10^3 mm^3

Smax=Imax/y =8.32*10^6/440.06=18.906*10^5mm^3

Hood design optimisation

in order to increase the section modulus and the strength of the material,the gap between the inner panel and the outer panel is increased by 0.5 mm and the resulting sketch is again analysed for the moment of inertia.

The optimised moment of inertia is obtained as shown above,

Smax=8.608*10^8 mm^4/440.06=19.56*10^5 mm^3
Smin=2.149*10^6 mm^4/440.06=4.883*10^3 mm^3

hence by changing the gap between the panels the moment of inertia is increased and the section modulus is also increased there by increasing the strength of the hood panel.