WELDING TECHNOLOGY: Controllable Variables During Welding

TOPIC: CONTROLLABLE VARIABLES:
TYPE OF WELDING: SUBMERGED ARC WELDING:
A knowledge and control of the variables in submerged arc welding are essential if welds of good quality are to be consistently obtained. The variables, in the approximate order of their importance, are:

1. Welding current
2. Welding voltage
3. Welding speed
4. Width and depth of the layer of submerged are welding flux
5. Mechanical adjustments

These variables are discussed in the following paragraphs.

a. Welding Current: Welding current is the most influential variable. It controls the rate at which welding wire is burned off, the depth of fusion, and the amount of base metal fused. If the current is too high, the depth of fusion will be too great and the weld may melt through the backing. In addition to this, the higher heat developed may excessively extend the heat affected zone of the adjacent plate. Too high a current also means a waste of power and a waste of welding wire in the form of excessive reinforcement. If the current is too low, there is insufficient penetration and not enough reinforcement.

b. Welding Voltage: Next in importance to welding current is the welding voltage. This is the potential difference between the tip of the welding wire and the surface of the molten weld metal. The welding voltage varies with the length of the gap between the welding wire and the molten weld metal. If the gap increases, the welding voltage increases; if the gap decreases, the welding voltage decreases. The welding voltage has little effect on the amount of welding wire deposited; this is determined mainly by the welding current. The voltage principally determines the shape of the fusion zone and reinforcement. High welding voltage produces a wider, flatter, less deeply penetrated weld than low welding voltage.


c. Welding Speed: With any combination of welding current and voltage, the effects of changing the welding speed conform to a general pattern:

If the welding speed is increased-

• Power or heat input per unit length of weld is decreased.
• Less welding wire is applied per unit length of weld.
• Consequently, there is less weld reinforcement.

If the welding speed is decreased-

• Power or heat input per length of weld is increased.
• More welding wire is applied per unit length of weld.
• Consequently, there is more weld reinforcement.

In addition to this pattern, welding speed may have another effect on the finished weld. Normally, only welding current affects the penetration of the weld. However, if the welding speed is decreased beyond a certain point, the penetration will also decrease. This is because a good portion of the molten weld puddle will be beneath the welding wire and the penetrating force of the arc will be cushioned by the puddle. Conversely, if the speed is increased beyond a certain point, the penetration will increase since the welding wire will precede the weld puddle.

d. Width and Depth of Welding Flux: The width and depth of the layer of granular welding flux influence the appearance and soundness of the finished weld as well as the welding action itself. If the granular layer is too deep, a rough, ropy weld is likely to result. The gases generated during welding cannot readily escape, and the surface of the molten weld metal is irregularly distorted. If the granular layer is too shallow, the welding zone will not be entirely submerged. Flashing and spattering will be present; the weld will have a bad appearance, and may be porous. An optimum depth of granular material exists for any set of welding conditions. This depth can be established by slowly increasing the granular material until the welding action is submerged and flashing no longer occurs. The gases will then puff up quietly around the welding wire, sometimes burning. It is seldom that too narrow a layer is applied. The safest procedure is to apply a layer that is three times the width of the fused portion. In large welds, a greater allowance may be necessary. A layer that is limited by too narrow confines interferes with the normal lateral flow of weld metal resulting in reinforcement that is narrow, steep-sided, and poorly “faired in” the baseplate or the edges.

e. Mechanical Adjustments: The position of the welding wire must be maintained to control the shape of the weld and the depth of penetration. The wire may be guided mechanically or manually adjusted as the weld progresses. While the welding is going on, inspection will indicate whether the backing is tight against the underside of the joint. If it is not, too much metal may flow into the space, resulting in reduced weld reinforcement, undercutting, and a ruined weld.

WELDING DEFECTS : CRACKS

Cracks:

WELDING DEFECTS : CRACKS

Process Cracks

•  Hydrogen induced cold cracking (HICC)
•  Solidification cracking (Hot Tearing)
•  Lamellar tearing
•  Re heat cracking

When considering any type of crack mechanism, three elements must be present for it’s occurrence:

• Stress: stress is always present in weldments,through local expansion and   contraction.
• Restraint: may be a local restriction, or through the plates being welded.
• Susceptible: microstructure: the structure is often made susceptible to cracking through welding, e.g high hardness

Hydrogen Cracking:

Hydrogen causes general embrittlment and in welds may lead directly to cracking.

The four essential factors for cracking to occur

• Susceptible grain structure
• Hydrogen >15ml
• Temperature less than 200°C
• Stress

Remedies for Hydrogen Cracking:

Precautions for controlling hydrogen cracking:

1. Pre heat, removes moisture from the joint preparations, and slows down the cooling rate
2. Ensure joint preparations are clean and free from contamination
3. The use of a low hydrogen welding process and correct arc length
4. Ensure all welding is carried out is carried out under controlled environmental conditions
5. Ensure good fit-up as to reduced stress
6. The use of a PWHT or Post Weld Heat Treatment

Solidification Cracks:

Essential factors for solidification cracking:

• This type of cracking is referred to as Hot Cracking
• Susceptible microstructure: Columnar grain growth
• Impurities, sulphur, phosphorous and carbon
• The amount of stress/restraint
• Most commonly occurs in sub-arc welded joints
• Joint design depth to width ratios,
• Combinations of both stress, deep narrow welds and sulphur

Precautions for controlling solidification cracking:

• Low dilution welding process
• The use of high manganese and low carbon content fillers
• Maintain a low carbon content
• Minimise the amount of stress / restraint acting on the joint during welding
• The use of high quality parent materials, low levelsof impurities
• Remove laminations
• Clean joint preparations, free from oil, paints and any other sulphur containing product.
• Joint design selection depth to width ratios  

Solidification cracking in Austenitic Stainless Steel:

• Austenitic stainless steel is particularly prone to solidification cracking
• This is due to the large grain size, which gives rise to a reduction in grain boundary area
• High coefficient of thermal expansion, with high resultant stress
• A structure that is very intolerant to contaminations, sulphur, phosphorous and other impurities.
• The precautions against cracking are the same as for plain carbon steels with extra emphasis on thorough cleaning and high dilution controls.

Lamellar Tearing:

• Lamellar tearing has a step like appearance due to the solid inclusions such as sulphides and silicates linking up under the influences of welding stresses
• It forms when the welding stresses act in the short transverse direction of the material (through thickness direction)
• Low ductile materials in the short transverse direction containing high levels of impurities are very susceptible
• The short tensile test or through thickness test is a test to determine a materials susceptibility to lamellar tearing.

Factors for lamellar tearing to occur:

• Low quality parent materials, high levels of impurities
• Joint design, direction of stress
• The amount of stress acting across the joint during welding
• Hydrogen levels in the parent material

**Note: very susceptible joints may form lamellar tearing under very low levels of stress.

 

Precautions for controlling lamellar tearing:

• The use of high quality parent materials, low levels of impurities
• The use of buttering runs
• A gap can be left between the horizontal and vertical members enabling the contractional movement to take place
• Joint design selection
• Minimise the amount of stress / restraint acting on the joint during welding
• Hydrogen precautions

In-Service Cracks:

• Fatigue cracks
• Weld decay in austenitic stainless steels
• Creep failure
• Stress corrosion cracking

Fatigue Cracks:

• Fatigue cracks occur under cyclic stress conditions
• Fracture normally occurs at a change in section, notch and weld defects i.e stress concentration area
• All materials are susceptible to fatigue cracking
• Fatigue cracking starts at a specific point referred to as a initiation point
• The fracture surface is smooth in appearance sometimes displaying beach markings
• The final mode of failure may be brittle or ductile or a combination of both

Precautions against Fatigue Cracks:

• Toe grinding, profile grinding.
• The elimination of poor profiles
• The elimination of partial penetration welds and weld defects
• Operating conditions under the materials endurance limits
• The elimination of notch effects e.g. mechanical damage cap/root undercut
• The selection of the correct material for the service conditions of the component

Weld Decay:

• Weld decay may occurs in austenitic stainless steels
• Also know as knife line attack
• Chromium carbide precipitation takes place at the critical range of 600-850oC
• At this temperature range carbon is absorbed by the chromium, which causes a local reduction in chromium content
• Loss of chromium content results in lowering the materials resistance to corrosion attack allowing rusting to occur

Precautions for Weld Decay:

• The use of a low carbon grade stainless steel e.g. 304L, 316, 316L
• The use of a stabilized grade stainless steel e.g. 321, 347, 348 recommended for severe corrosive conditions and high temperature operating conditions
• Standard grades may require PWHT, this involves heating the material to a temperature over 1100oC and quench the material, this restores the chromium content at the grain boundary, a major disadvantage of this heat treatment is the high amount of distortion

THERMODYNAMICS - THEORY

Thermodynamic Systems: 

If we want to analyze movement of energy over space, then we must define the space that would be used for the observation, we would call it as a SYSTEM, separated from the adjoining space that is known as "Surroundings", by a boundary that may be real or may be virtual depending upon the nature of the observation. The boundary is called as SYSTEM BOUNDARY. So, we shall define a system properly. A thermodynamics system refers to a three dimensional space occupied by a certain amount of matter known as ''Working Substance'', and it is the space under consideration. It must be bounded by an arbitrary surface which may be real or imaginary, may be at rest or in motion as well as it may change its size and shape. All thermodynamic systems contain three basic elements:

• System boundary: The imaginary surface that bounds the system.
• System volume: The volume within the imaginary surface.
• The surroundings: The surroundings is everything external to the system.

So we get a space of certain volume where ENERGY TRANSFER (movement of energy) is going on, what may or may not be real, and distinct, it may be virtual (in case of flow system ), again if real boundary exists, then it may be fixed (rigid boundary like constant volume system) or may be flexible (like cylinder-piston assembly). For a certain experiment the system and surroundings together is called UNIVERSE.

The interface between the system & surroundings is called as "SYSTEM BOUNDARIES", which may be real & distinct in some cases where as some of them are virtual, but it may be real, solid & distinct.

Classification of Thermodynamic Systems:

Systems can be classified as being (i) closed, (ii) open, or (iii) isolated.



(i) Closed System:

Mass cannot cross the boundaries, but energy can.

 (ii) Open System or Control Volume:

 Both mass and energy can cross the boundaries.

(iii) Isolated System:


Neither mass nor energy can cross its boundaries.






Property, Equilibrium and State:

A property is any measurable characteristic of a system. The common properties include:

• pressure (P)
• temperature (T)
• volume (V)
• velocity (v)
• mass (m)
• enthalpy (H)
• entropy (S)

Properties can be intensive or extensive. Intensive properties are those whose values are independent of the mass possessed by the system, such as pressure, temperature, and velocity. Extensive properties are those whose values are dependent of the mass possessed by the system, such as volume, enthalpy, and entropy (enthalpy and entropy will be introduced in following sections).
Extensive properties are denoted by uppercase letters, such as volume (V), enthalpy (H) and entropy (S). Per unit mass of extensive properties are called specific properties and denoted by lowercase letters. For example, specific volume v = V/m, specific enthalpy h = H/m and specific entropy s = S/m (enthalpy and entropy will be introduced in following sections).

Note that work and heat are not properties. They are dependent of the process from one state to another state.

When the properties of a system are assumed constant from point to point and there is no change over time, the system is in a thermodynamic equilibrium.

The state of a system is its condition as described by giving values to its properties at a particular instant. For example, gas is in a tank. At state 1, its mass is 2 kg, temperature is 20^oC, and volume is 1.5 m³. At state 2, its mass is 2 kg, temperature is 25^oC, and volume is 2.5 m³.

A system is said to be at steady state if none of its properties changes with time.

Process, Path and Cycle:

 
The changes that a system undergoes from one equilibrium state to another are called a process. The series of states through which a system passes during a process is called path.


In thermodynamics the concept of quasi-equilibrium processes is used. It is a sufficiently slow process that allows the system to adjust itself internally so that its properties in one part of the system do not change any faster than those at other parts.

When a system in a given initial state experiences a series of quasi-equilibrium processes and returns to the initial state, the system undergoes a cycle. For example, the piston of car engine undergoes Intake stroke, Compression stroke, Combustion stroke, Exhaust stroke and goes back to Intake again. It is a cycle.

WELDING TECHNOLOGY, AN INTRODUCTION

WELDING:

Welding is a fabrication process that joins materials, usually metals or thermoplastics, by melting the workpieces and adding a filler material to it. The workpieces and the filler material are melted to form a pool of molten material (the weld pool) that cools to become a strong joint. To weld metals, although heating is used but sometimes high pressure is also used to fuse the workpieces with filler material.

This is in contrast with soldering and brazing, which involve melting a lower-melting-point material between the workpieces to form a bond between them, without melting the workpieces.

Many different energy sources can be used for welding, including a gas flame, an electric arc, a laser, an electron beam, friction, and ultrasound. While often an industrial process, welding may be performed in many different environments, including open air, under water and in outer space.

Welding is a potentially hazardous undertaking and precautions are required to avoid burns, electric shock, vision damage, inhalation of poisonous gases and fumes, and exposure to intense ultraviolet radiation.



Metallurgy of the Welding Process:

Most solids that are used engineering materials consist of crystalline solids in which the atoms or ions are arranged in a repetitive geometric pattern which is knows as a lattice structure. The only exception is materials that are made from glass which is a combination of a supercooled liquid and polymers which are aggregates of large organic molecules.

Crystalline solids cohesion is obtained by a metallic or chemical bond which is formed between the constituent atoms. Chemical bonds can be grouped into two types consisting of ionic and covalent. To form an ionic bond, either a valence or bonding electron separates from one atom and becomes attached to another atom to form oppositely charged ions. The bonding in the static position is when the ions occupy an equilibrium position where the resulting force between them are zero. When the ions are exerted in tension force, the inter-ionic spacing increases creating an electrostatic attractive force, while a repulsing force under compressive force between the atomic nuclei is dominant.

Covalent bonding is when the constituent atoms lose an electron(s) to form a cluster of ions, resulting in a electron cloud that is shared by the molecule as a whole. In both ionic and covalent boding the location of the ions and electrons are constrained relative to each other, thereby resulting in the bond being characteristically brittle.

Metallic bonding can be classified as a type of covalent bonding for which the constituent atoms of the same type and do not combine with one another to form a chemical bond. Atoms will lose an electron(s) forming an array of positive ions. These electrons are shared by the lattice which makes the electron cluster mobile, as the electrons are free to move as well as the ions. For this, it gives metals their relatively high thermal and electrical conductivity as well as being characteristically ductile.

Three of the most commonly used crystal lattice structures in metals are the body-centred cubic, face-centred cubic and close-packed hexagonal. Ferritic steel has a body-centred cubic structure and austenitic steel, non-ferrous metals like aluminium, copper and nickel have the face-centred cubic structure.

Ductility is an important factor in ensuring the integrity of structures by enabling them to sustain local stress concentrations without fracture. In addition, structures are required to be of an acceptable strength, which is related to a materials yield strength. In general, as the yield strength of a material increases, their is a corresponding reduction in fracture toughness.

 

Steel Weld Metallurgy

Carbon: Major element in steels, influences strength, toughness and ductility

Manganese: Secondary only to carbon for strength toughness and ductility, secondary de-oxidiser and also acts as a de-sulphuriser.

Silicon: Primary de-oxidizer

Molybdenum: Effects hardenability, and has high creep strength at high temperatures. Steels containing molybdenum are less susceptible to temper brittleness than other alloy steels.

Chromium: Widely used in stainless steels for corrosion resistance, increases hardness and strength but reduces ductility.

Nickel: Used in stainless steels, high resistance to corrosion from acids, increases strength and toughness

Classification of Steel

Steels are classified into groups as follows

• 1. Low Carbon Steel 0.01 – 0.3% Carbon
• 2. Medium Carbon Steel 0.3 – 0.6% Carbon
• 3. High Carbon Steel 0.6 – 1.4% Carbon

Plain carbon steels contain only iron & carbon as main alloying elements, traces of Mn, Si, Al, S & P may also be present.

ALLOY STEEL

Alloy steel is one that contains more than Iron & Carbon as main alloying elements

Alloy steels are divided into 2 groups

• Low Alloy Steels < 7% extra alloying elements
• High Alloy Steels > 7% extra alloying elements

Steel Weld Metallurgy

The grain structure of steel will influence its weldability, mechanical properties and in-service performance. The grain structure present in a material is influenced by:

• The type and number of elements present in the material
• The temperature reached during welding and or PWHT.
• The cooling rate after welding and or PWHT

Heat Affected Zone:

The parent material undergoes microstructure changes due to the influence of the welding process. This area, which lies between the fusion boundary and the unaffected parent material, is called the heat affected zone (HAZ). The extent of changes will be dependent upon the following..

•  Material composition
•  Cooling rate, fast cooling higher hardness
•  Heat input, high heat inputs wider HAZ
•  The HAZ can not be eliminated in a fusion weld

Heat Input Calculation:

Amps = 200 Volts = 32
Travel speed = 240 mm/min
Heat input = (Amps x volts)/(Travel speed mm/sec X 1000)
Heat input = (200 X 32 X 60)/(240 X 1000)
Heat input = 1.6 kJ/mm


Heat Input:

High heat input - slow cooling

• Low toughness
• Reduction in yield strength

Low heat input - fast cooling

•  Increased hardness
•  Hydrogen entrapment
•  Lack of fusion

WELDABILITY

Weldability can be defined as the ability of a material to be welded by most of the common welding processes, and retain the properties for which it has been designed.

•  A steel which can be welded without any real dangerous consequences is said to possess Good Weldability.
•  A steel which can not be welded without any dangerous consequences occurring is said to possess Poor Weldability. Poor weldability normally generally results in the occurrence of some sort of cracking problem.

Weldability is a function of many inter-related
factors but these may be summarised as:

•  Composition of parent material
•  Joint design and size
•  Process and technique
•  Access

It is very difficult to asses weldability in absolute terms therefore it is normally assessed in relative terms.

There are many factors which affect weldabilty e.g. material type, welding parameters amps, volts travel speed, heat input.

Other factors affecting weldabilty are welding position and welding techniques.

Basically speaking weldabilty is the ease with which a material or materials can be welded to give an acceptable joint.

LOADING IN BEAMS

BEAMS & CLASSIFICATION OF BEAMS

BEAM: A beam is a structure generally a horizontal structure on rigid supports and it carries mainly vertical loads. Therefore, beams are a kind of load bearing structures.

Depending upon the types of supports beams can be classified into different catagories.

CANTI-LEVER BEAMS: 

A beam can be at stable equilibrium with a single fixed support at one end and the other end remains free, which is called as the free end while the other end is known as fixed end. This kind of beam is known as Canti lever beam. The fixed joint at the fixed end produces a horizontal, a vertical reactions and a reaction moment at the fixed end.

SIMPLE SUPPORTED BEAM: 

A beam supported as just resting freely on the walls or columns at its both ends is known as simply supported beam.

There will be two vertically upward reactions at the ends of a simply supported beam. A simply supported beam can not resist any horizontal load component.

OVER HANGING BEAM: 

A beam having its end portion or both the end portions extended in the form of a canti-lever beyond the support or supports is called as over hanging beam.

Above those beams are statically determinate. It means that those beams can be analysed applying the conditions of equilibrium. We can determine the values of the unknown reactions.

There are beams which can not be analysed applying the conditions of equilibrium of coplanar forces. These beams are also known as Statically indeterminate structures.

Those types of beams can be classified as,

Fixed beams and Continuous beams.

Fixed Beam: A beam having two fixed joints at the both ends is called fixed beam.

Continuous Beam: The beam which is at rest on more than two supports is called as continuous beam.

What are different types of supports? 

There are four types of supports,

• (i) Simple Supports, 
• (ii) Roller Supports, 
• (iii) Hinged Supports 
• (iv) Fixed Supports.

SOLUTION OF EME-102; TRUSS ANALYSIS

SOLVE THE TRUSS GIVEN BELLOW WITH THE HELP OF METHODS OF JOINT

________________________________________________________________________________

a)      REPLACE JOINTS WITH REACTIONS at A and at B

              

       

b)      Draw FBD of the TRUSS

 

Applying the conditions of Equilibrium of Coplanar Non-concurrent Force System,

 

∑ F_X = 0;        R_b – R_ah = 0  ------ (i)

(-) ← ● → (+)

∑ F_Y = 0;        R_av – 10 – 5 – 15 = 0 => R_av = 30 kN ----- (ii)

∑ M_A = 0;       10 x 4 + 5 x 4 + 15 x 2 – R_b x 3 = 0  ----- (iii)

                        R_b = 30 kN

                        Hence R_ah = R_b = 30 kN

Calculation of Angle θ

The angle θ = tan^-1(3/2) = 56.3°

All the unknown forces will be taken as Tensile, if their magnitudes is found negative, then they will be treated as compressive forces.

First we shall choose a joint having only two unknown forces, either we shall choose joint D or joint A

Let us choose joint D first.

We shall consider point D first, as it has only two unknown force. FBD of the point D is drawn.

∑ F_X = 0;      F₂ = 0

∑ F_Y = 0;      F₁ – 5 = 0

                      F₁ = 5 kN

 

Our next joint will be point E. FBD of the joint E is drawn. As F₁ = 5 kN, hence unknown forces are two. F₃ and F₄

∑ F_X = 0;     – F₃ – F₄ cos 56.3° = 0

∑ F_Y = 0;     – F₁ – 10 –  F₄ sin 56.3° = 0  [ as F₁ = 5 kN]

                           F₄ = –15/ sin 56.3° = – 18.02 kN

                    F₃ = – F₄ cos 56.3° = 10 kN

 

Our next joint is C

 F₅ and F₉ are unknown where as F₄ = – 18.02 kN

 F₂ = 0

 ∑ F_X = 0;     – F₉ + F₄ cos 56.3° = 0

            F₉ = F₄ cos 56.3° = 10 kN

 ∑ F_Y = 0;     F₅ + F₄ sin 56.3° – 15 = 0

                            F₅ = – F₄ sin 56.3° + 15 = 30 kN

 

F₃ = 10 kN;   F₅ = 30 kN

        ∑ F_X = 0;     F₃ = F₆ + F₇ cos 56.3°

        ∑ F_Y = 0;     – F₅ – F₇ sin 56.3° =0

       F₇ = – F₅/ sin 56.3° = – 36.05 kN

F₆ = F₃ – F₇ cos 56.3° = 10 + 20 = 30 kN

R_av = 30 kN;  R_ah = 30 kN

 ∑ F_X = 0;      F₆  = R_ah = 30 kN

 ∑ F_Y = 0;     F₈ = R_av = 30 kN

Sl no	Link	Force	Magnitude	Nature
01	ED	F1	5 kN	T
02	CD	F2	0
03	FE	F3	10 kN	T
04	CE	F4	18.02 kN	C
05	FC	F5	30 kN	T
06	AF	F6	30 kN	T
07	BF	F7	36.05 kN	C
08	AB	F8	30 kN	T
09	BC	F9	10 kN	T

SOLUTION OF EME-102; CENTROID 2

HOW TO FIND THE CENTROID OF A COMPOSITE AREA

(a composite area consists of several straight or curved lines.)

(i) Draw the figure in a coordinate system. Draw the dimensions too. Every dimensions will be measured with respect to origin of the coordinate system

(ii) Divide the composite area into several parts of basic geometric areas. Lebel them as part-1, part-2, part-3, .......part-n. Let the corresponding areas are A₁, A₂, A₃, .... A_n. Let the centroids are G₁(X₁,Y₁), G₂(X₂,Y₂), G₃(X₃,Y₃), ...... G_n(X_n,Y_n).

(iii) Let the centroid of the composite area be G(Xg,Yg). Hence,
Xg = (A₁X₁ + A₂X₂ +A₃X₃)/(A₁ + A₂ + A₃)

Yg = (A₁Y₁ + A₂Y₂ +A₃Y₃)/(A₁ + A₂ + A₃)

 

(a) Suppose we have certain area of magnitude (A) in a coordinate system. The centroid of the area will be at its mid-point. A centroid is denoted by G.

                       In the figure we have a complex geometrical area composed of three basic geometrical areas. Three rectangles. Let us denote the centroids as G₁, G₂, G₃ for the given areas in the figure.

We shall have to find the Centroid of the entire area composed of  A₁, A₂, A₃.

At first, the composite line is divided into three parts.

Part -1 : The middle rectangle : Let the centroid of the area A₁ be G₁(X₁,Y₁)

Area, A₁ = (100-15-15)x15 mm² = 70x15  mm²  = 1050  mm²                 
          X₁ = 7.5 mm
          Y₁ =0


Part -2 : The lower Rectangle : Let the centroid of the A₂ be G₂(X₂,Y₂)


Area, A₂ = 50 x 15  mm² = 750 mm²                
          X₂ = 25 mm
          Y₂ = - 42.5 mm


Part -3 : The upper Rectangle : Let the centroid of the area Area, A₃ be G₃(X₃,Y₃)


Area, A₃ = 50 x 15  mm² = 750 mm²                
          X₃ = 25 mm
          Y₃ = 42.5 mm






If the centroid of the composite line be G  (X_g,Y_g)

X_g = (∑A_iX_i)/(∑A_i) 

    = (A₁X₁ + A₂X₂ +A₃X₃)/(A₁ + A₂ + A₃)
    = (1050 x 7.5 + 750 x 25 + 750 x 25)/( 1050 + 750 + 750)
    = 17.79 mm
     

Y_g = (∑A_iY_i)/(∑A_i) 

    = (A₁Y₁ + A₂Y₂ +A₃Y₃)/(A₁ + A₂ + A₃)
    = {1050 x 0 + 750 x (-42.5) + 750 x 42.5}/( 1050 + 750 + 750)
    = 0

As the figure is symmetrical about X axis, hence when we take the line of symmetry as our X axis (as we have taken here), we can directly write, Y_g =0