Tuesday, 30 December 2014

LSD Presents: The Very Best of 2014

It has been ten months since the inception of Learn Ship Design, and though we are in our baby steps, the year has been full of adventure, undoubtedly because of the support of readers like you. It was with your trust that we have grown, and today we are read by engineers and students belonging to more than 30 countries. We want to THANK YOU for the incredible year. 

Before you read further, we have something special for you. We are launching a series for our Facebook readers. And here's what we call it: LSD FACT CARDSBe there for the official launch on New Year's Eve.

As a gesture or gratitude, we wanted to share with you, our best from the year. Here are the 'Greatest Hits' of 2014 from our Blog.

Top 10 Most Read Articles:
We also interviewed three great personalities in the maritime industry:
  1. Interview with Parks Stephenson (Forensic Analyst, Titanic)
  2. Interview with Dr. Stephen Payne (Naval Architect, Queen Mary 2)
  3. Interview with Dr. Piyush Raj (Country Head, DNV-GL, India)
For our Facebook Page readers, we have made it a point that you learn something new on ship design every day. And we have done it in an interactive way through:

- Team Learn Ship Design.

Sunday, 21 December 2014

An Interview with Piyush Raj (DNV-GL)

Dr. Piyush Raj
Dr. Piyush is the head of DNV-GL Group (India), and currently heads the DNV GL Maritime Academy in India. With an experience of more than twenty years, he has sailed as a marine engineer, following which he chose a career in management services in the maritime industry.

Having graduated as doctoral student of IIM Lucknow, Piyush has served maritime organizations with various managerial responsibilities. He is also awarded the Lloyds Register Merit Scholarship.

In an interview with Learn Ship Design, Piyush shares his experience in the maritime industry, and gives us an insight into the real structure of DNV-GL, the world's leading classification society (as of 2014).

It has recently been a year since the merger of DNV and GL. How do you think it has propelled the growth of DNV-GL to becoming the world's leading classification society?

You know, DNV and GL have been organizations with complementary skill set. We merged primarily because the guiding fundamentals for quality and innovation were same. That has helped us a lot to come together, and to provide a much wider and broader reach to our clients. To that extent we have been successful, and we feel we are in a better position to serve our clients. 

This industry demands experience. How do you value the importance of young brains in your organization?

Honestly, I don't have the complete answer. I have been working for the last twenty years, and the past two years at DNV-GL. It doesn't matter what you do as an individual. What matters, is how you set values to the organization. Even if you are experienced, if you don't bring value to the organization, it will not serve the vision. So I think, we value a lot of team work in our organization, rather than only focusing on experience.

What qualities do you look for, in graduate Naval Architects?

If you are not willing to learn from what you are going to see in the clients' place or in the office, or in the maritime environment around you, what you have learnt from the previous experience is not going to efficient. So if you ask me one single thing that is important, it is the urge to keep learning. One should stay inquisitive, and learn as you go.

What are the challenges that you face, being the world's leading classification society?

To serve our clients in the best possible way, to ensure that their challenges are being addressed, and to ensure that we remain safer, smarter and greener as a maritime industry. 

DNV-GL has recently shown the path for bio-fuels in the maritime industry. How far has it been implemented successfully

It is still being tested actually. Though the initial information has been passed on to the maritime industry, it is up to the industry and the commercial business to support it and see how well this can be implemented in the future.

What factors do you think, enabled the company to survive and grow for 150 years?

What I clearly see, is that it doesn't really matter what you do in day to day life that propels an organization. There are set values of the organization and you work for that. You must be technically confident, but as a whole, if you don't bring value to the client, it won't be appreciated. For instance, we had to provide an optimal solution that required a mathematical modelling. The iterations required were about three million, before coming down to the optimum result. But in spite of that, our client preferred to have a simplified thumb rule for the same model, which could be synced well to the workshop level. And we could satisfy that due to the enormous amount of data that we have in store for all these years. So yes, a lot of data churning, and the passion to go beyond 99 percent, have been the key. 

Monday, 17 November 2014

Fire Protection and High Speed Crafts

Safety against fire aboard ships is a major area of concern for seafarers and designers. Especially when it comes to high speed vessels, which are generally smaller in size and are prone to maximum and critical damage within no time in absence of fire protection systems. This has become an area of research and regular assessment of regulations are being done to minimize both human and material loss from such incidents. You definitely do not want to be a passenger on the receiving end on a ship when it catches fire.

Fig.1: A burning Yacht at Sydney Harbour
(Courtesy: www.presources3.news.com.au )

No wonder these regulations are put forward under the SOLAS (International Convention for the Safety of Life at Sea) treaty by deliberations at International level for which it is quite important among the international treaties relating to merchant ship safety at sea. SOLAS actually specifies minimum standards for the equipment in use and mode of operation which are part responsibility of Flag States to monitor. Classification societies have set up rules and regulations for such Vessels, IMO has its own. The Indian Register of Shipping calls them: Rules and Regulations for the Construction and Classification of High Speed Crafts and Light Crafts.

Fig.2: The SOLAS treaty 
sees to the safety of vessels
on an International Level
(Courtesy: www.imo.org)
High speed crafts are of light displacements and they generally use unconventional; shipbuilding materials like fibre reinforced plastics, aluminium alloys and the like (I hope you are familiar with the luxury yachts of today which look faster and prettier than their ancestors), but to distinguish them from conventional crafts in a more technical manner, the speed and volumetric Froude number are often the factors for applying regulations. When designing ships, you should see to it that your vessel has some quick (I mean really quickly) fire detection system, people should be able to find fire extinguishing devices and evacuation routes (and alternate routes) in case of emergencies. It is often observed in such situations that panic clouds our reason.

Let us talk about some points in general about to these High Speed Crafts. Generally such details in design like the presence of ventilation systems and their control, fire resisting divisions are submitted in a general arrangement plan in detail even to particulars of surface lamination (if used somewhere). The important thing about these measures which are somewhat similar to those for larger vessels is that the fire protection time or the time period till which you expect the ship to sustain damage till structural failure occurs.

Division of ship based on level of hazard

You should identify certain parts of the vessel according to the extent of damage in the event of a fire. Such divisions are usually called:

  • Areas of Major Fire Hazard – Mainly has to do with areas of the ship containing flammable liquids, places of certain deck area selling flammable liquids like alcohol, kitchen areas (galleys). Engine rooms of ships, especially Internal Combustion Engines, are considered along with other machinery spaces. Like I mentioned, passengers are not allowed in some of these areas except when accompanied by some fire safety crew.

Fig.3: Certain parts of a boat like the galleys (kitchens) and others spaces having flammable fluids are classified as Major Fire Hazard Areas based on their deck area.
(Courtesy: Dubois Naval Architects )
  • Areas of Moderate Fire Hazard – These include spaces for crew accommodation other than sleeping, stores on board containing alcoholic beverages. Shops not selling flammable items, etc.
  • Areas of Minor Fire Hazard – These are areas like tanks, empty spaces, areas open to the public exposed to low or no fire risk, areas for refreshment and certain cargo and machinery spaces.
Certain spaces like those with equipment for navigation, battery systems and main electronic control systems are also considered separately.

Separation of Accommodation Spaces from Remainder of Ship based on such hazards

Fig.4: It is very important to 
isolate accommodation spaces
 for passengers and crew 
from potential zones.
(Courtesywww.classicyachtforsale.com )
It is necessary to ensure that the passenger spaces have been Passengers are not allowed to go to vehicle spaces and Ro-Ro spaces during voyage, and for that reason, even cargo spaces.

Certain parts of the ship have the decks and bulkheads constructed from non-combustible or fire resisting material in such a way that the temperature on the unexposed end will not rise beyond a certain limit. 

You have to see that these 'Fire Resisting Divisions' are designed structurally in such a way that they will not fail or allow smoke or flames to pass until the end of a certain fire protection time depending on the level of hazard I spoke about earlier. Even your gaps for ventilation in entrances of public toilets need to be positioned towards the lower part of the door (guess why?).

Based on the above analogy, the materials used in the subdivisions of a ship are categorized into three main types, namely:

"A" Class Divisions: For a division to be certified as "A" Class, it has to limit the average temperature on the other side (the side opposite to which it is exposed to fire) to a maximum of 140 degree Celsius and the maximum temperature at any point on the other side to 180 degree Celsius, up to a certain time. Now based on this time up to which the material limits the above temperatures, "A" Class divisions are subdivided into four types:

  1. A-60: This type of "A" Class division can limit the temperatures up to maximum 60 minutes.
  2. A-30: This type of "A" Class division can limit the temperatures up to maximum 30 minutes.
  3. A-15: This type of "A" Class division can limit the temperatures up to maximum 15 minutes.
  4. A-0: This type of "A" Class division cannot limit the temperatures beyond 60 seconds.
"B" Class Divisions: A division is certified as "B" Class when it limits the average temperature on the other side to 140 degree Celsius and the temperature of any point on the other side to 225 degree Celsius up to a time limit depending upon the following three sub-types:

  1. B-15: Can limit the temperatures up to maximum 15 minutes.
  2. B-0: Cannot limit the temperatures beyond 60 seconds.
"C" Class Divisions: For a division to be classified as "C" Class, it has no fixed temperature limits, but certainly needs to be certified by the classification societies.

Restricting use of combustible materials as much as possible

Fig.5: Decks and bulkheads should ideally be
constructed using non-combustible materials,
sometimes another layer of material does the trick
(Courtesywww.firemaster.morganthermalceramics.com )
The separating divisions in the ship like the ceilings which are not a part of the fire resisting divisions are necessarily of the non-combustible type. They may restrict fire too which is desirable in the event of a mishap. All exposed surfaces on the vessel like the public spaces and accommodation are required to pass certain tests for toxicity and smoke from fire. Strict laws apply for both areas allowing/not allowing smoking. The exhaust pipes which are of valid concern are designed to minimize risk from fire and structures in contact with them which are potentially prone to risk are insulated with non-combustible materials.

You should see that fuel tanks are never placed in proximity to Major Fire Hazard Areas for reasons quite obvious. Use of fuel with flashpoint below 43oC is not allowed however it is relaxed to 35 oC for gas turbines. Tests are to be done to ensure that in event of a fire, the fire resistant divisions are able to withstand loads for a given period of time. Often tables depicting such times based on vessel characteristics are available.

Detection and containment of smoke or fire

Fig.6: Fire and smoke detection equipment
are a must have on every kind of vessel.
(Courtesy: Nordhaven)
Early detection is the key and often it is the best way to prevent huge loss from fire at an early stage itself. The areas of major and moderate fire hazard are required to be fitted with automatic smoke and fire detection systems, which of these are used depends entirely on the location of origin of fire. You would prefer putting a detector for heat in the galleys and smoke detection systems in corridors and toilets. In case of propulsive machinery, closed circuit television providing video footage are also set up. Speaking about power supply of these equipment on board, these are to have alternative power sources.
Sometimes when acoustic enclosures are used for certain spaces having gas turbines/generators, separate fire extinguishing systems need to be in place. All such machinery spaces of this sort require fire-resistant materials for containing fire. Common spaces, accessible or not, like those of bulkheads, linings of divisions, ceilings, corridors are required to have surfaces with low flame spread.

Viability of means of escape

Fig.6: Proper identification of escape routes
 does save lives and prevents excess panic
(Courtesywww.firemart.co.uk )
Common means of escape are generally the areas of normal access to the different parts of the boat. However, it is necessary to devise alternate routes (portholes are common) for quick escape during emergency. Your plan of ladders and stairs should be such that they would provide easy access in time of an emergency, this includes considering lack of space in places with large machinery. These routes should planned in a manner such that it would be possible to escape or enter (when rescuing passenger) through these places without possibly encountering the source of fire on the way.

Availability of extinguishing devices

Fig.7: Properly spaced Extinguising equipment
of standard sizes are of great help 
during an emergency 
(Courtesywww.wikimedia.org )
In the event the crew or passengers are required to put out fires which sometimes block essential escape routes, portable fire extinguishing devices of appropriate mass and fire-fighting outfit are to be provided, the former especially at machinery spaces, they require regular examination and are required to be easily accessible in event of a fire. When present for control stations and similar areas involving electronic equipment, these should not contain extinguishing media which is conducting in nature. Use of fire pumps, hoses and hydrants are also common just as in our fire fighting vehicles.
The outfits for the fire-fighters are required to have excellent fire resistant properties, heat protection, water-resistance and certain electrical insulation characteristics. Often lamps (sometimes fitted on protective helmets) are required with long backup facilities. Breathing apparatus is a must with at least 30 minutes of possible usage.LSD

 Article BySudripto Khasnabis

Wednesday, 29 October 2014

Plimsoll Lines- A Detailed Synopsis

Fig.1: Plimsoll Line and 
various loadlines
(Courtesy: www.rhiw.com )
Surely you know about the different kinds of ships in existence today and how the cargo or the method of loading or unloading determines the class of ship concerned.

 Among merchant ships today, the largest are the Containers, the ones with the bulk cargo (Bulk Carriers) and the tankers. Speaking in terms of deadweight, these ships range from somewhere around 50,000 DWT in Handymax Carriers to a whopping 5,50,000 DWT ULCC’s (Probably among the largest man-made objects around). 

Having said about the magnitude of things here, let us concentrate on a part of the ship, or rather a certain mark on the ship hull having a centre-dashed circle and vertical lines with branches on both sides and a horizontal line on top.


Fig.2: Samuel Plimsoll
(Courtesy: Getty Images )
In the early 19th Century, there used to be ships which were loaded to such great draughts and hence such less freeboard that they were at great risks of being drowned in rough seas. Such ships carried crew who risked their lives every time they went to the sea. Actually these ships were worth more to their owners if they drowned than they would have been had they actually completed their journey! This was because these ships were ‘over insured’ and the owners who would gain from the insurance money, took advantage of the situation during that time.

 It was not until this Gentleman named Samuel Plimsoll, a coal merchant who had written a popular book on disasters of ship overloading, started campaigning for safety at seas. Ultimately, his efforts paid off and the load lines became compulsory in British ships and spread worldwide over. Today they have been standardized and are visible on the ship hull as given in this photo. Let us try to understand these markings.

First of all, think about it, when large ships travel very long distances, they pass through oceans, the largest of seas, and sometimes, through freshwater passages in between. Now, if you remember, this means that they will be passing through different climates and different densities of water, also the salinity in sea water is also a factor to be considered. The ship’s weight, for all normal purposes would not change as much, but the different densities mean that the pressure would vary from seawater to freshwater, and so the immersed volume and draughts would change accordingly. The vessel would float to deeper depth in fresher water than in seawater. Now from certain calculations, we can find out the depths for each climatic or geographic condition directly from one primary load line. This primary load line as in almost all cases is the Summer load line. Together these are a shorthand representation of the freeboard of the same ship in different seas on Earth.


Fig.4: Screenshot from our Prezi on Plimsoll Lines.

Take a look at this screenshot from our Prezi on Plimsoll Lines, we will take each of them at a time. First, starting from the top, we have the deck line, which by convention is of 300 mm length and 25 mm breadth, for that reason all such lines are of same thickness. But the other horizontal lines are of 230 mm length. These marks are inverted on the other side of the ship hull.


The deck line is placed at exact intersection of the freeboard deck with the outer shell of hull plating. In case you want to mark the deck line, which serves as a reference to be place somewhere else, you will have to correct the freeboard calculation accordingly.


Immediately below the Deck line, we have what is called the load line mark which passes through the disc of outer diameter 300 mm, called the Plimsoll Disc. The upper edge of the line passes through the centre of the disc. The vertical line is placed a distance of 540 mm from the center of the plimsoll disc. From this, the load lines stretch on both sides to a length of 230 mm each.


This is the primary load line from which the other load lines are derived, the International Maritime Organization under the Load Lines Convention specifies certain rules for calculation of freeboards and their implementation under supervision of classification societies and flag states. This load line mark’s position depends on many factors such as length of ship, superstructures, terms linked with overall raking of the fore body and so on. These have been standardized and can be obtained from Freeboard Tables which look somewhat like this.
Fig.5: Freeboard Table for ships of 'A'-type
(Courtesy:Load Lines, 1966/1988 - International Convention on Load Lines,1966,as Amended by the Protocol of 1988)

Certain formulae are used to correct this freeboard in case values of draught slightly deviates from assumptions (T>L/15) or similar corrections accounting for block co-efficient, height of superstructures, etc.  For the purpose of such calculations, ships have been classified as type A & B. There are certain factors which decide this like the type of cargo, watertight spaces, permeability of cargo compartments, etc.

Now here's the interesting part. Refer to Fig.4 or for that matter, to any Plimsoll Lines on a ship. How are each of those loadline marks obtained? Are the vertical distances between each of the different draughts different for different ships? Or are they same? Well, read on.


The tropical load line is obtained by an addition from the summer draught (considered T hereinafter) measured from keel to the centre of Plimsoll Disc by amount 1/48th of T. That is, it is T/48 above the Summer Load Waterline (S).


This is marked above the Summer Load Waterline (S) by the following amount:

Δ is the mass displacement in salt water (in tonnes) at the summer load line.

T is the tonnes per centimeter immersion in salt water at the summer load waterline.( The TPC for any draught is the mass which must be loaded or discharged to change a ship’s mean draught in salt water by one centimeter)

When it becomes difficult to find out whether freshwater and tropical freshwater are the same things, the position of the latter line relative to former is found in same manner as that of summer load line and tropical summer load line.


The tropical freshwater mark (TF) is always marked at (T + F) above the Summer Load Waterline (S).


The winter load line is obtained this time by a deduction from the Summer Load Waterline (S), an amount of T/48. That is, it lies T/48 below the Summer Load Waterline.


When a vessel is bound to enter any part of the North Atlantic Ocean during its winter period an additional load line called the WNA load line is assigned 50 millimetres below the winter mark. By default, it is same as the winter mark (W) for other ships. A separate WNA mark is present only on vessels that donot exceed length of 100 m.

ADDITIONAL LOAD LINES (Used on Ships with TImber Freeboards)

Fig.6: The Timber Load Lines for vessels 
with deck timber cargo
(Courtesy: 1873 issue of Vanity Fair(edited))

Now, take a look at the left side of the vertical line, there another set of load lines with an additional ‘L’ prefixed to them, these are called the Timber Load Line Marks or ‘L’ for Lumber Load Line Marks. These are additional load lines assigned to certain vessels which carry timber deck cargo and are granted additional freeboard as this ship will have greater buoyancy and protection against the sea and waves. These are analogous to normal load lines and are calculated similarly from the Summer Timber load draught (This value is supplied in the table from the convention), the only exception that Winter Timber load line is 1/36th of the Summer Timber Load Draught below the Summer Timber load line. The displacement used in the formula is that of the vessel at her Summer Timber Load Draught.

Some vessels like Ro-Ro ships and Passenger Vessels have sub divisional load lines which are nothing but load lines for different loading conditions based on passengers and cargo, in any case, the these should not be above the deepest load line in salt water.

There is one more thing which you must have seen on the load line mark passing through the disk (450 mm in length) which seems to bear the initials ‘NK’, this is called the ‘Mark of assigning Authority’. They tell you which Classification Society has surveyed the load line. The initials used include AB for the American Bureau of Shipping, LR for Lloyd's Register and IR for the Indian Register of Shipping and so on.

Such Load Line Convention rules do not apply to certain kinds of vessels like the warships, new ships of 24 length or less or those existing ones of less than 150 GT, even the yachts not engaged in trade and for that reason fishing vessels. Certain Geographical regions are free from the observations of the Convention. Definitely, these lines have made our life safer at seas and international trade fairer.


It often becomes tough for us to memorize the Plimsoll Lines unless we have a good on-ship experience or good experience in working on a ship design project. For Naval Architects, it is highly important to have a clear view of the Plimsoll Lines, and the following Prezi is an attempt to make that easier for you:

Wait till the Prezi loads. Once loaded, you need to click on the arrow or use your arrow keys to watch the Prezi. It is recommended you watch it in Full Screen Mode for the best view. LSD

    Article By: Sudripto Khasnabis

Sunday, 19 October 2014

MOL Comfort- What Happened? (Part 2)


In Part 1, we focused on the position of the crack on the hull girder, following which we saw how Class NK estimated the wave induced loads on the ship during the accident scenario, considering required uncertainties in the parameters. Based on the above obtained wave loads for different sea states, the maximum and minimum wave induced vertical bending moments were estimated.Having estimated the wave induced load, it was now required to estimate the hull girder strength (of the considered three hold model). This article is about to discuss the methods involved in calculating the strength of the structure, and obtained results of the same.

3-Hold Model for Strength Analysis

The region of failure was identified by field investigations. So for the finite element analysis, a three hold model was considered. Further conditions taken during the analysis were obtained from Class NK Guidelines for Container Carrier Strength (Guidelines for Direct Strength Analysis, 2012) as shown in Table 1.

Table 1: Conditions for 3-hold model analysis.
(Courtesy: Class NK)
Fig. 1: 3-hold model used for analysis. (Photo edited)
(Courtesy: Class NK)

Estimation of Ultimate Strength

The strength of the three hold model was estimated considering uncertainties as shown in Figure 2.
Fig. 2: Factors affecting uncertainty in strength of the double bottom structure.
How was the yield stress of the structure calculated? The value of yield stress of the members were obtained from their respective mill sheets. The average of all the yield stress values of the different member materials were calculated and regarded as the mean value of hull girder ultimate strength (μ).

It is important to understand what was done next. Given the fact that the strength of a marine structure follows a probabilistic nature (that can be represented by a Probability Density), it is evident that consideration of mean value alone for determining the ultimate structure is not a valid thing to do. What if the strength of the structure at any point of time, reduces from its mean value? Therefore, it is necessary to determine the minimum ultimate strength of the structure to consider the worst case scenario.

Class NK adopted two different methods to determine the minimum hull girder ultimate strength, an the strengths obtained through each of the two methods were categorized as Case 1 and 2 (will be referred by the same hereinafter).

Case 1- The standard deviation (σ) of the yield strength of the bottom shell plates were calculated from the mill sheet values. The minimum yield stress of the hull girder was defined as the value that was less than the mean by three times the standard deviation, i.e. Minimum yield stress = μ-3σ (Refer to Figure 3)
The hull girder ultimate strength was then evaluated corresponding to the above minimum yield stress of the bottom plating. This ultimate strength was regarded as the minimum hull girder ultimate strength.

Fig. 3: Graphical representation of Case 1

Case 2- The hull girder ultimate strength was evaluated corresponding to the minimum yield stress of the bottom plating specified in the mill sheets. The obtained ultimate strength was then regarded as the minimum hull girder ultimate strength.
The obtained values of yield stress (for both the cases) were as shown in Table 2.

Table 2: Yield stress for Case 1 and Case 2.
Now, in order to find the ultimate strength, a very simple method was adopted: The loads at the time of the accident were known and categorized into the following:

  1. Hull weight corresponding to the double bottom structure (known before analysis)
  2. Hydrostatic pressure corresponding to the full draught (known before analysis)
  3. Container Loads (known before analysis, based on the loading information at the time of the accident)
  4. Allowable still water bending moment for hogging (calculated before the analysis, from loads 1, 2 and 3)
  5. Wave-induced pressure (priorly calculated from Class NK Direct Strength Analysis, 2012)
  6. Wave-induced vertial bending moment (calculated from IACS UR S11)
  7. Additional vertical bending moment (due to uncertainties)
The interesting part is how these loads were applied to the model for analysis. Initially, loads 1,2, and 3 were gradually increased every one second until they reached their known values. Then loads 4, 5, and 6 were applied in turn and increased every one second until their known values were attained. At last, load 7 was gradually increased every second until the stress in the structure exceeded the Von Mises Stress of the structure. (Graphical representation in Figure 4). The stress at which the structure failed, was regarded as the Hull Girder Ultimate Strength.

Fig. 4: Sequence of application of load on the model.
(Courtesy: Class NK)
The above method was followed for three conditions:
  1. When yield strength of the structure was corresponding to the mean value (μ)
  2. Case 1: Yield strength = μ-3σ
  3. Case 2
The hull girder ultimate strength was also obtained for three different conditions and the corresponding vertical bending moments were obtained, as shown in Table 3.

Table 3: Obtained values of Vertical Bending Moments when the hull girder fractured.
Fig. 5: Time vs. Bending moment at the section that suffered failure in the case of average yield stress. (Picture edited)
(Courtesy: Class NK)
Fig. 6: Von Mises stress at the time of peak load.
(Courtesy: Class NK)

Fig. 7: Equivalent plastic strain at the time of peak load.
(Courtesy: Class NK)

Fig. 8: Von Mises stress at the time of peak load.
(Courtesy: Class NK)

Fig. 9: Equivalent plastic strain at the time of peak load.
(Courtesy: Class NK)

What's in Part 3?

Certain factors were multiplied to the obtained values of bending moment, in order to compensate for the factors of local deformations and residual stresses due to welding. Inclusion of these factors, reduced the strength further. It is on the basis of the then obtained strength values, that the probability and extent of damage will be discussed in the next part of this series.LSD

Article By: Soumya Chakraborty