## Description

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Section modulus is a term that not many people are familiar with, but this term is something that bending and rolling companies deal with on a daily basis. Section modulus is a geometric property for a given cross-section used in the design of steel beams or flexural members. The relationship between many geometric properties such as tension, compression and shape of the member lead to the calculation of its section modulus.

*What Is The Section Modulus*

It is termed as the ratio of second moment of area and distance from N.A (Neutral axis) to the extreme fiber. Also it is the measure of strength of given member. The stress in the outermost section of beam is computed with the help of section modulus. It is indicated by S.

Section modulus is indicated as follows:

Here, I is “moment of inertia” and y is distance from “neutral axis” to top or bottom of fiber.

Unit of a “section modulus” is in.3(mm3).

Section modulus depends only on the cross section shape of the beam. Cross section shapes like rectangular, square, circular, I section and T, composite section etc.

For symmetric sections, the value of “section modulus” is for both above and below of centroid of the fiber.

An asymmetric section has two values for top and bottom of the fiber due to different distance from centroid to the top and bottom of the material, the maximum “section modulus” is S m ax and the minimum section modulus is S min.

*Importance:*

• It is significant for beam and flexural member design.

• More the section modulus, more the member is resistant to bending of the beam.

• It is easier to calculate stresses in beam and an exact measure of strength of steel.

• If two beams are made of same material and comparing the “section modulus” of two beams, the beam with bigger section modulus will be tougher and more capable to withstand larger loads.

### “elastic section modulus” and “plastic section modulus”

There are two types of section modulus; the “elastic section modulus” and the “plastic section modulus”. A bender roller company puts their focus on the elastic section modulus. The elastic model is used by bender roller companies to determine the section modulus needed to bend a steel member. For comparison, changing the roll orientation of a structural steel member can also greatly change the section modulus information required. Bending steel channels the hardway can increase the modulus by at least 500%, and in some cases, the section modulus increases by over 1000% due to rolling against the strong-axis of the channel web instead of rolling with the flanges in or out.

**Section Modulus Calculations for HSS**

### **Section Modulus** of the bending machine

Bender roller companies usually have a range of machines with different maximum section modulus capabilities. A 3X3 rolling machine has a maximum section modulus of 1.3 to 1.9 cubic inches, where as a 13X13 rolling machine has a maximum section modulus of 80-290 cubic inches. Obviously the larger pieces of metal will require a higher maximum section modulus, so ensuring the piece to be formed is on the proper machine will improve bending quality and lessen the labor involved. A good comparison would be to imagine two weightlifters trying to lift the same weight. If you have a smaller person who normally lifts in the 100-150lb range and another who lifts in the 150-200lb range, they both can lift a 150lb weight, but it will be easier for the one who normally lifts more to do it for an extended time, and his form will be better.

Some of the largest machines can even have section modulus capacities that near or even exceed 1000 cubic inches. These larger machines are usually specialized beam bending machines. They have been specially developed for heavy beam bending. These machines are equipped with features that enable an adjustable bending distance and simultaneous movement of the pushing and pulling rolls.

It is extremely important the estimators and operators are familiar with the section modulus of every member that comes through the doors of a bending and rolling company. Not knowing the section modulus of a member or not knowing the capabilities of a machine could lead to ruining the material or even seriously damaging their machine.

## Know The Difference: Section Modulus, Moment Of Inertia, Modulus Of Elasticity

**MODULUS**** OF ****ELASTICITY****: **The ratio of stress to strain or the stiffness of the material of a structural member (resistance to deformation).

Essentially, the **modulus** of **elasticity** is a more general term regarding the overall stiffness of a member.

E= Modulus of Elasticity. If E increases, then so does the stiffness.

**MOMENT OF INERTIA: **The bending stiffness of a structural member’s cross-sectional shape.

Moment of inertia is specific to bending of the cross section of the member .

**SECTION ****MODULUS****: **The ratio of the maximum moment on a beam and the maximum fiber stress (or moment of inertia over distance to nuetral axis of the member).

The section **modulus** is used to to find the minimum required beam that will support the bending load by looking in tables provided, such as in the Manual of Steel Construction.

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