principalstressandprincipalstrain

Principal stresses are the maximum and minimum normal stresses experienced at a point within a material, which act on planes where the shear stress is zero. 

Similarly, principal strains are the maximum and minimum normal strains that occur at that point, aligned with the principal stress directions in many common material

Principal stress and principal strain are fundamental concepts in structural engineering and design, underpinning the evaluation and analysis of materials and structures. Integral to the safety and stability of various applications, these terms reflect the internal forces and deformations that materials undergo when subjected to external loads. The significance of understanding these concepts is echoed in the applications of the principal stress formula and principal strain equation, tools that allow professionals to assess and mitigate potential risks in design.

Principal stress represents the maximum and minimum normal stresses that occur within a material when subjected to complex loading conditions. It is essential to understand this concept as it provides insights into the material’s response and its potential points of weakness. When materials are subjected to multi-directional stresses, determining the principal stress can reveal the most severe stress concentrations, which are critical to avoiding structural failures.

Principal strain represents the maximum and minimum values of strain experienced in a material subjected to loading. Understanding strain is crucial as it offers insights into material deformation – how much a material stretches or compresses under applied stresses.

 

Applications of Friction in Machines

 Applications of Friction in Machines

We investigate the action of friction in various machine applications. Because the conditions in these applications are normally either limiting static or kinetic friction, 

Wedges

 A wedge is one of the simplest and most useful machines. A wedge is used to produce small adjustments in the position of a body or to apply large forces. Wedges largely depend on friction to function. When sliding of a wedge is impending, the resultant force on each sliding surface of the wedge will be inclined from the normal to the surface by an amount equal to the friction angle. The component of the resultant along the surface is the friction force, which is always in the direction to oppose the motion of the wedge relative to the mating surfaces. 

Screw friction

A screwjack is a device used for lifting or lowering heavy loads by applying comparatively smaller efforts at the end of the lever. The thread of a screw jack may be considered as an inclined plane wound round a cylinder and the principles used in solving problems on inclined plane can be applied to solve problems involving screw friction

Torsion of circular shafts

 Torsion 

Torsion refers to the twisting of a straight bar when it is loaded by moments (or torques) that tend to produce rotation about the longitudinal axis of the bar Similar to turning a screwdriver hand which applies a torque T and twists the shank of the screwdriver. An idealized case of torsional loading is by two pairs of equal and opposite forces. Each pair of forces forms a couple that tends to twist the bar about its longitudinal axis. The torque or twisting moment is the product of one of the forces and the perpendicular distance between the lines of action of the forces.

 The moments are T1 = P 1 d1 and the second is T2 = P2 d2 

The SI unit for moment is the newton meter (Nm). 

Torsional Deformation

Let the left hand end of the bar is fixed in position with the action of the torque T.  

The right-hand end will rotate through a small angle φ known as the angle of  twist (or angle of rotation).

Because of this rotation, a straight longitudinal line pq on the surface of the bar will become a helical curve pq’.

The angle of twist changes along the axis of the bar, and at intermediate cross sections it will have a value φ(x). If every cross section of the bar has the same radius and is subjected to the same torque (pure torsion), the angle φ (x) will vary linearly between the ends.

 

importance of levelling in surveying

 This is a method of surveying in which the relative vertical heights of the points are determined by employing a level and a graduated staff. In planning a constructional project, irrespective of its extent, i.e., from a small building to a dam, it is essential to know the depth of excavation for the foundations, trenches, fillings, etc. This can be achieved by collecting complete information regarding the relative heights of the ground by levelling

What is the Importance of Levelling in Surveying

Levelling in surveying is crucial for ensuring that construction projects are built on a stable and even foundation. Accurate levelling helps prevent problems like uneven floors, poor drainage, and structural issues that can arise from an improperly prepared site. By establishing a consistent elevation 

levelling ensures that all parts of the construction site are aligned, which is essential for the integrity and longevity of the structure.

 What are the Types of Levelling:

There are several types of levelling used in surveying, each suited for different purposes:

 

1. Direct Levelling

Direct levelling involves using a levelling instrument, such as a spirit level or a theodolite, to measure height differences between points. The instrument is set up on a tripod, and readings are taken with a graduated staff placed at various locations. This method provides accurate elevation measurements and is commonly used in construction to establish a level base.

 2. Trigonometric Levelling

Trigonometric levelling uses angular measurements and distance calculations to determine height differences. By measuring angles from a known reference point and calculating the distances, surveyors can determine the elevation of various points. This method is useful for large-scale surveys where direct measurement is not feasible.

3. Barometric Levelling

Barometric levelling relies on atmospheric pressure measurements to estimate elevation differences. By comparing the air pressure at different locations, surveyors can infer height differences. This method is less precise than other types but can be useful in remote areas where other tools are unavailable.

 4. Stadia LevellingStadia levelling involves using a stadia rod and a theodolite or total station. The stadia rod has graduated markings, and the instrument measures the distance between these markings to calculate height differences. This method is useful for quickly measuring elevations over long distances and is commonly used in surveying and mapping.

 What are the Advantages of Levelling in Surveying

Levelling in surveying offers several key benefits that are essential for successful construction projects:

 

 1) Ensures Accuracy

Levelling helps in obtaining precise measurements of the land’s elevation, which is critical for laying a stable and even foundation. Accurate levelling prevents errors that could lead to structural issues or misalignments during construction.

 

2) Prevents Structural Problems:

By ensuring that the construction site is level, the risk of future structural problems, such as cracks, uneven floors, or  foundation 

failure, is greatly reduced. A level foundation supports the overall integrity and longevity of the structure.

3) Enhances Safety

Proper levelling ensures that the construction site is stable and secure, reducing the risk of accidents or structural failures. It helps in creating a safe working environment and ensures that the completed structure meets safety standards.

 

4) Improves Drainage

Levelling ensures proper grading of the land, which is crucial for effective drainage. Good drainage prevents water accumulation around the foundation, which can lead to erosion, foundation weakening, or other water-related damage.

 

5) Cost Efficiency:

Accurate levelling can save costs by minimising the need for corrections or adjustments during or after construction. It helps avoid costly rework and ensures that the project progresses smoothly without unexpected delays.

6) Supports Proper Planning

Levelling provides essential data that helps in the proper planning and design of the construction project. It allows architects and engineers to create accurate blueprints and designs that take into account the exact topography of the site.

 

INTRODUCTION TO SURVEYING

 

INTRODUCTION TO SURVEYING

 

  Surveying is the art of making measurements of objects on, above or beneath the ground to show their relative positions on paper. The relative position required is either horizontal or vertical.

APPLICATIONS OF SURVEYING

 

Some of the important applications of surveying are listed below:

 

1.   Astronomical survey helps in the study of astronomical movements of planets and for calculating local standard times.

2.   Maps prepared for countries, states and districts, etc. avoid disputes.

3.   Plans prepared record the property boundaries of private, public and government which help in avoiding unnecessary controversies.

4.   Topographical maps showing natural features like rivers, streams, hills, forests help in planning irrigation projects and flood control measures.

5.   Road maps help travelers and tourists to plan their programmers.

6.   Locality plan help in identifying location of houses and offices in the area

7.   Maps and plans help in planning and estimating various transportation projects like roads, bridges, railways and airports.

8.   For planning and executing water supply and sanitary projects one has to go for surveying first.

9.   Marine and hydrographic surveys help in planning navigation routes and harbours.

 

10. For making final payments in large projects surveying is to be carried out

11. Military surveys help in strategic planning

12. For exploring mineral wealth mine surveys are required.

13. Geological surveys are necessary for determining different strata in the earth’s crust so

                                 that proper location is found for reservoirs.

14. Archaeological surveys are required for unearthing relics of antiquity.

 

 PRIMARY DIVISIONS IN SURVEYING

 

 The survey in which earth’s curvature is considered is called geodetic surveying and the survey in which earth’s curvature is neglected is called Plane surveying.

 

CLASSIFICATION OF SURVEYING

 

Surveying may be classified based on the following three points:

 

1.   Natural of the field of survey

 

 

 

2.   Objects of survey

 

 

 

3.   Instrument used

 

 

 

4.   The methods employed

 

 

Classification Based on Nature of the Field of Survey

 

 

 

On this basis field of survey may be classified as land survey. Marine or hydraulic survey and astronomical survey.

 

 

Land survey: It involves measurement of various objects on land. This type of survey may be further classified as given below:

 

 

i.    Topographic surveys: They consist of measurement of various points to plot natural features such as rivers, streams, lakes, hill and forests as well as man  – made features like roads, railways, towns, villages and canals.

 

 

ii.  Cadastral survey: These surveys are for marking boundaries of municipalities, states, etc. the surveys made to mark properties of individual also come under this category.

 

 

iii. City survey: The surveys made in connection with the construction of streets, water supply and sewage lines fall under this category.

 

 

Marine of Hydrographic Surveys: The survey conducted to find depth of water at various points in bodies of water like sea, river and lakes fall under this category of surveying. Finding depth of water at specified points is known as soundings.

 

 

Astronomical Surveys: Observations made to heavenly bodies like sun and stars to locate absolute position of points on the earth and for the purpose of calculating local times is known as astronomical survey.

 

 

Classification Based on Object of Surveying

 

 

 

On the basis of objective of surveying, the classification can be as engineering survey. Military survey, mines survey, geological survey and archaeological survey.

 

 

1.   Engineering survey: The objective of this type of surveying is to collect data for designing roads, railways, irrigation, water supply and sewage disposal projects. These surveys may be further subdivided into:

 

 

a.   Reconnaissance survey for determining feasibility ad estimation of the scheme.

 

 

 

b.   Preliminary survey for collecting more information to estimate the cost o the project selected, and

 

 

c.   Location survey to set the work on the ground.

 

 

 

2.   Military Survey: This survey is meant for working out points of strategic importance.

 

 

 

3.   Mine survey: This is used for exploring mineral wealth.

 

 

 

4.   Geological survey: this survey is for finding different strata in the earth’s crust.

 

 

 

5.   Archaeological survey: this survey is for unearthing relics of antiquity.

 

 

 

Based on the instruments used, surveying may be classified into the following:

 

 

 

1.   Chain Survey

 

 

 

2.   Compass Survey

 

 

 

3.   Plane Table Survey

 

 

 

4.   Theodolite Survey

 

 

 

5.   Tacheometric Survey

 

 

 

6.   Modern Survey using electronic equipment like distance metres and total stations.

 

 

 

 

7.   Photographic and Aerial Survey.

 

 

 

Classification Based on the Methods Employed

 

 

 

Based  on  the  methods  employed,  surveying  may  be  classified  as  triangulation  and traversing.

 

 

1.   Triangulation:  In  this  method  control  points  are  established  through  a  network  of triangles

 

 

2. Traversing: In this scheme of control points consist of a series of connected points established through linear and angular measurements. If last line meets the starting point it is called as closed traverse. If it does not meet, it is known as open traverse.

 

 

MEASUREMENTS

 

 

 

Linear measurements are horizontal or vertical only. Here angular measurements are also  involved.  Commonly  used  linear  units  in  surveying  are  kilometre,  metre  and millimetres. For measurement of angles sexagesimal system is used. In this 1 circumference

= 360 degrees

 

SCALES

 

 

 

It is not possible and also not desirable to make maps to full scale. All distances are reduced by fixed proportion and drawings are made. The scale of a map or the drawing is the fixed proportion which every distance on the map bears to he corresponding distance on the ground. Thus, if 1 mm on the paper represents 1m on the ground, then the scale is 1 mm = 1 m ( or 1 cm = 10m or 1: 1000.

 

 

To make scale independent of units it is preferable to use representative factor, which is defined as the ratio of distance of one unit on paper to one unit on ground. Thus,

1mm = 1m is equivalent to RF=1/1000.

 

 

 

 

Plain Scale: On a plain scale it is possible to read two dimensions directly such as unit and tenths.

 

 

Diagonal Scale: In plain scales only units and tenths could be shown whereas in diagonal scales it is possible to show units, tenths and hundredths. Units and tenths are shown as in plain scale. To show hundredths, principle of similar triangles is used

 

 

PRINCIPLES OF SURVEYING

 

 

 

To get accurate results one should follow the two basic principles explained below:

 

 

 

1.  Work from whole to part

 

 

 

In surveying large areas, a system of control points is identified and they are located with high precision. Then secondary control points are located using less precise methods. With respect the secondary control point’s details of the localized areas are measured and plotted. This is called working from whole t part. This principle in surveying helps in localizing the errors. If the surveying is carried out by adding localized areas, errors accumulate.

 

 

2.  Fixing positions of new control points

 

 

 

For fixing new control points with respect to already fixed points, at least two independent processes should be followed. IF A and B are two already located control points and with respect  to  them  new  control  point  C  is  to  be  located,  apart  from  the  minimum  two measurements required, one more reading should be taken. Fixing of check lines and tie lines will also serve this purpose.