This document provides information about I-beams, including: - I-beams are commonly used in construction and have a high moment of inertia due to their shape, making them resistant to bending. - The web of the I-beam provides resistance to shear forces. - Various equations are presented to calculate properties like cross-sectional area, moments of inertia, stresses, and shear stresses for I-beams. - Different types of steel joints that can be used with I-beams are also described.

1. Moment of Inertia of I-beam (I-section)
*Beam is a structural element used in construction works to support loads and moments. Beams are
generally manufactured from steel and aluminum. Different shapes and dimensions are supplied by beam
suppliers.
*I beam is a type of beam often used in trusses in buildings. I beam is generally manufactured from
structural steels with hot and cold rolling or welding processes. Top and bottom plates of an I-beam are
named as flanges and the vertical plate which connects the flanges is named as web. Different
dimensions of I beam exist in the market and can be supplied by the beam suppliers. Due to its shape, I
beam has high moment of inertia and stiffness which makes it resistant to bending moments. The web
provides resistance against shear forces. These beams are not resistant to torsional loading (twisting)
and they shall not use in the cases where torsion is dominant.
List of Equations of I-beam

2. Definitions:
 Second Moment of Area: The capacity of a cross-section to resist bending.
 Radius of Gyration (Area): The distance from an axis at which the area of a body may be
assumed to be concentrated and the second moment area of this configuration equal to the
second moment area of the actual body about the same axis.
 Section Modulus: The moment of inertia of the area of the cross section of a structural member
divided by the distance from the center of gravity to the farthest point of the section; a measure of
the flexural strength of the beam.
Input Parameters
Parameter Symbol Unit
Flange-flange inner face weight H mm/cm/m/inch/ft
Width B mm/cm/m/inch/ft
Flange thickness h mm/cm/m/inch/ft
Web thickness b mm/cm/m/inch/ft
Length L mm/cm/m/inch/ft
Density p
g/cm3
kg/m3
lb/in3
Axial Stress (aka compressive stress, tensile stress) is a measure of the axial force acting on a beam
quantitatively measuring the internal forces acting within in the beam. Compressive stress means the
member is in compression (being smashed) vs. tensile stress which means the beam is in tension (being
pulled apart).
A couple of important things to note about axial stress are:
 Excluding the self-weight of the beam, the axial stress in a column with no external loads is
constant (see Figure 2)
 Except for concrete, tensile forces will normally have greater capacities than compressive forces
(think of trying to pull a Popsicle stick apart vs stepping on it and breaking it through
compression).
 Axial stress will commonly be used when analyzing columns
Output Parameters
Parameter Symbol Unit
Cross-section Area A mm2 / cm2 / inch2/ ft2
Mass M kg / lb
X Second Moment of Area Ixx mm4 / cm4 / inch4 / ft4
Y Second Moment of Area Iy y mm4 / cm4 / inch4 / ft4
X Section Modulus Sxx mm3 / cm3 / inch3 / ft3
Y Section Modulus Sy y mm3 / cm3 / inch3 / ft3
X Radius of Gyration rx mm / cm / m / inch / ft
Y Radius of Gyration ry mm / cm / m / inch / ft
CoG distance in X direction xcog mm / cm / m / inch / ft
CoG distance in Y direction ycog mm / cm / m / inch / ft

3. Calculate the Axial Stress in a member
*After the axial force of the member is found, Axial Stress (both compressive and tensile stress) are found
by taking:
fa = Pc/t
A
where:
fa = the axial stress acting on the member (ksi)
Pc/t = The compressive or tensile force acting on the column (lbs, kips, kgs)
A = the cross-sectional area of the column (in2, mm2)
Bearing stress is a contact pressure between separate bodies. It differs from compressive stress
because compressive stress is the internal stress caused by a compressive force.
FORMULA:
𝜎 𝑏 = 𝑃 𝑏
𝐴b
Where: 𝑃 𝑏 − 𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑣𝑒 𝑙𝑜𝑎𝑑
𝐴 𝑏 − 𝑐ℎ 𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐 𝑎𝑟𝑒𝑎 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝑡𝑜 𝑃b
𝜎 𝑏 − 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑠𝑠
Bearing Area Stress Equation for Plate and Bolt or Pin
Bt = F / (t d)
where:
Bt = Bearing area stress area (N/mm2, lbs/in2)
F = Applied Force (N, lbs)
t = Thickness (mm, in)
d = Diameter (mm, in)
A shear stress, often denoted τ, is defined as the component of stress coplanar with a material cross
section. Shear stress arises from the force vector component parallel to the cross section.
The formula to calculate average shear stress is force per unit area:
F
A
where:
 = the shear stress;
F = the force applied;
A = the cross-sectional area of material with area parallel to the applied force vector.
Shear Stress Equation Single Shear

4.  Shear stress average = Applied force / area or;
 Shear stress average = F/(r2) or;
 Shear stress average = 4F/(d2)
Where
 Shear stress average = (N/mm2, lbs/in2)
 F = Applied Force (N, lbs)
 pi or 3.14157
 r = Radius (mm, in)
 d = Diameter (mm, in)
Shear stress is a kind of stress that acts parallel or tangential to the surface. The shear stress is denoted
by  (tau). Shearing stresses are commonly found in rivets, pins and bolts. If the plates, which are
connected by a rivet as shown in the following figure, are subjected to tension forces, shear stresses will
develop in the rivet. The shear force P in the shear plane is equal to tension force F. The average shear
stress in the plane is av e= F/A. This joint is said to be in single shear.
If the plates, which are connected by a rivet as shown in the following figure, are subjected to tension
forces, shear stresses will develop in the rivet. This joint is said to be in double shear. To determine the
average shear stress in each shear plane, free-body diagrams of rivet and of the portion of rivet located
between the two planes are drawn. Observing that the shear P in each of the planes is P = F/2, the
average shearing stress is av e = F/2A.
Parameter Symbol Formula
Shear Stress (Single Shear) av e av e = F/A
Shear Stress (Double Shear) av e av e = F/2A
Shear Stress (Triple Shear) av e av e = F/3A
Types of Steel Joints

5.  Beam-to-column joints with
 Welded moment connection on the flanges
 Bolted, end-plate moment connection on the flanges
 Simple shear connection on the flanges or on the web
 Gusset plate connection with double plate flange splice of I sections or plate splice of
hollow sections on the flanges or on the web
 Beam-to-beam (web) joints with
 Bolted, end-plate moment connection
 Simple shear connection
 Web finplate
 Beam splice joints with
 Bolted, end-plate moment connection
 Simple shear connection
 Beam splice plate connection
 Column base joints with
 Bolted, base-plate moment connection
 Rigid connection with ground beam
 Hollow section (truss) joints with
 K and N connection
 T and Y connection
 Multiplanar truss
 Tension chord splice connection
 Splice plate component
 One side, simple splice plate
 One side, double splice plate
 Two side, double splice plate
 Two side, simple splice plate
Cold working is the process of strengthening metals through plastic deformation. This is made possible
through the dislocation movements that are produced within a material's crystal structure.

6. This is a technique commonly used in non-brittle metals that have remarkably elevated melting points. A
number of polymers can also be strengthened using this method. However, cold-worked areas in metal
are more prone to corrosion due to heightened dislocation concentration.
Cold working is also known as work hardening.
Cold working involves the alteration of the size and shape of metals by means of plastic deformation. This
process includes:
 Rolling
 Pressing
 Drawing
 Spinning
 Heading
 Extruding
It is performed under the point of re-crystallization, typically at room temperature. The tensile strength and
hardness are enhanced depending on the extent of cold working. As the strength increases, the values of
impact and ductility weaken.
Although work hardening may be beneficial as it improves surface finish, strength properties, dimension
control and reduced directional properties, it must be noted that it also has various disadvantages. Hence,
industries, such as those that utilize metal parts, like boilers, should be aware that the process of cold
working may result in:
 Reduced ductility
 Higher force needed for deformation
 Strain hardening
 Unwanted residual stress
A simple example to represent these cons is a nail that corrodes in parts where it has been bent or
hammered, such as the body or head. Thus, industries that work on metals and utilize the cold-working
process should apply the appropriate corrosion protection.
Working with ignition sources near flammable materials is referred to as "hot work." Welding, soldering
and cutting are examplesof hot work. Fires are often the result of the "quick five minute" job in areas
not intended for welding or cutting. Getting a hot work permit before performing hot work is just one of
steps involved in a hot work management program that helps to reduce the risk of starting a fire by hot
work in areas where there are flammable or combustible materials.
Bolted joints are one of the most common elements in construction and machine design. They consist of
fasteners that capture and join other parts, and are secured with the mating of screw threads.

7. There are two main types of bolted joint designs: tension joints and shear joints:
In the tension joint, the bolt and clamped components of the joint are designed to transfer an applied
tension load through the joint by way of the clamped components by the design of a proper balance of
joint and bolt stiffness. The joint should be designed such that the clamp load is never overcome by the
external tension forces acting to separate the joint. If the external tension forces overcome the clamp load
(bolt preload) the clamped joint components will separate, allowing relative motion of the components.
The second type of bolted joint transfers the applied load in shear of the bolt shank and relies on the
shear strength of the bolt. Tension loads on such a joint are only incidental. A preload is still applied but
consideration of joint flexibility is not as critical as in the case where loads are transmitted through the
joint in tension. Other such shear joints do not employ a preload on the bolt as they are designed to allow
rotation of the joint about the bolt, but use other methods of maintaining bolt/joint integrity. Joints that
allow rotation include clevis linkages, and rely on a locking mechanism (like lock washers, thread
adhesives, and lock nuts).
Advantages: Bolted
 Lower manufacturing costs
 Easier and less expensive to transport
 Shipping savings outweigh additional installation costs
 Limited bolt thread prevents over tightening; nuts stay tight with serrated flange
 Easier to handle and unload
 Easier to reconfigure and repair.
The welded connections are solid, non-detachable connections based on the principle of local melting
of connected parts using heat or pressure. The joining of components proper may be achieved technically
using two methods:
 Fusion welding (arc, flame, plasma, laser, thermite, electro slag, ... welding)
The weld is a result of local melting of the material of connected parts, and usually also filler
metal, without pressure.
 Pressure welding (resistance, induction, ultrasonic, friction, explosion, ... welding)
After melting in, the components join in the contact spot using mechanical pressure or impacts.
An optimum result of the welding process should be a weld with mechanical properties similar as far as
possible to the properties of the basic material. According to their function, we can divide welds into:
 Force welds - load-bearing welds used to transfer external load
 Tack welds - welds providing only compactness of the whole (with no or negligible external load)
 Caulk welds - welds providing staunchness of connected parts (vessels, pipelines, etc.)
Advantages: Welded
 Reduced installation costs. Less sorting of materials.
 Less staging area required
 Uprights with offset or slope-back front legs, or with seismic or full-depth base plates, are
generally stronger
 Welded-on seismic base plates allow for beam placement at ground level
 Less hardware and reduced chance of short shipments due to fewer components