Type of Loads on Structures

The objective of a structural engineer is to design a structure that will be able to withstand all the loads to which it is subjected while serving its intended purpose throughout its intended life span. In designing a structure, an engineer must consider all the loads that can realistically be expected to act on the structure during its planned life span. The loads that act on civil engineering structures can be grouped according to their nature and source into three classes: (1) dead loads due to the weight of the structural system itself and any other material permanently attached to it; (2) live loads, which are movable or moving loads due to the use of the structure; and (3) environmental loads, which are caused by environmental effects, such as wind, snow, and earthquakes.

In addition to estimating the magnitudes of the design loads, an engineer must also consider the possibility that some of these loads might act simultaneously on the structure. The structure is finally designed so that it will be able to withstand the most unfavorable combination of loads that is likely to occur in its lifetime.

1) Dead Loads

Dead loads are gravity loads of constant magnitudes and fixed positions that act permanently on the structure. Such loads consist of the weights of the structural system itself and of all other material and equipment permanently attached to the structural system. For example, the dead loads for a building structure include the weights of frames, framing and bracing systems, floors, roofs, ceilings, walls, stairways, heating and air conditioning systems, plumbing, electrical systems etc. The calculation of dead loads of each structure are calculated by the volume of each section and multiplied with the unit weight.

The weight of the structure is not known in advance of design and is usually assumed based on past experience. After the structure has been analyzed and the member sizes determined, the actual weight is computed by using the member sizes and the unit weights of materials. The actual weight is then compared to the assumed weight and the design is revised if necessary. The unit weights of some common construction materials are given in Table 1. The weights of permanent service equipment, such as heating and air-conditioning systems, are usually obtained from the manufacturer.

Table 1: Unit Weights of Construction Materials

Sl. No.	Material	Unit Weight (kN/m^3)
1	Aluminum	25.9
2	Brick	18.8
3	Plain Cement Concrete	24
4	Reinforced Cement Concrete	25
5	Structural Steel	77.0
6	Wood	6.3

2) Live Loads/ Imposed loads 

Live loads are loads of varying magnitudes and positions caused by the use of the structure. Live loads are either movable or moving loads without any acceleration or impact. These loads are assumed to be produced by the intended use or occupancy of the building including weights of movable partitions or furniture etc. Live loads keep on changing from time to time. Sometimes, the term live loads are used to refer to all loads on the structure that are not dead loads, including environmental loads, such as snow loads or wind loads. However, since the probabilities of occurrence for environmental loads are different from those due to the use of structures, the current codes use the term live loads to refer only to those variable loads caused by the use of the structure. 

The magnitudes of design live loads are usually specified in building codes. In India, the minimum values of live loads to be assumed are given in IS 875 (part 2)–1987. It depends upon the intended use of the building. The position of a live load may change, so each member of the structure must be designed for the position of the load that causes the maximum stress in that member. Different members of a structure may reach their maximum stress levels at different positions of the given load. For example, as a truck moves across a truss bridge, the stresses in the truss members vary as the position of the truck changes.

Table 2: Minimum Floor Live Loads for Buildings

Sl. No.	Occupancy or Use	Live Load (kPa)
1	Hospital patient rooms, residential dwellings, apartments, hotel guest rooms, school classrooms	1.92
2	Library reading rooms, hospital operating roomsand laboratories	2.87
3	Dance halls and ballrooms, restaurants, gymnasiums	4.79
4	Light manufacturing, light storage warehouses,wholesale stores	6.00
5	Heavy manufacturing, heavy storage warehouses	11.97

Buildings Subjected to Environmental Loads

Because of the inherent uncertainty involved in predicting environmental loads that may act on a structure during its lifetime, the consequences of the failure of the structure are usually considered in estimating design environmental loads, such as due to wind, snow and earthquakes. In general, the more serious the potential consequences of the structural failure, the larger the magnitude of the load for which the structure should be designed.

a) Wind Loads 

Wind loads are produced by the flow of wind around the structure. Wind load is primarily horizontal load caused by the movement of air relative to earth. The magnitudes of wind loads that may act on a structure depend on the geographical location of the structure, obstructions in its surrounding terrain, such as nearby buildings, and the geometry and the vibration characteristics of the structure itself. Although the procedures described in the various codes for the estimation of wind loads usually vary in detail, most of them are based on the same basic relationship between the wind speed ‘V’ and the dynamic pressure ‘q’ induced on a flat surface normal to the wind flow, which can be obtained by applying Bernoulli’s principle and is expressed as

q = 1/ 2 rV^2

where ‘r’ is the mass density of the air 

Wind load is required to be considered in structural design especially when the height of the building exceeds two times the dimensions transverse to the exposed wind surface. For low rise building up to four to five stories, the wind load is not critical because the moment of resistance provided by the continuity of floor system to column connection and walls provided between columns are sufficient to accommodate the effect of these forces. The horizontal forces exerted by the components of winds are to be kept in mind while designing the building. The calculation of wind loads depends on the two factors, namely velocity of wind and size of the building. In India, calculation of wind load on structures is given below by the IS-875 (Part 3) -1987. Using colour code, basic wind pressure ‘Vb’ is shown in a map of India. Designer can pick up the value of Vb depending upon the locality of the building. To get the design wind velocity Vz the following expression shall be used: 

Vz = k1.k2.k3.Vb 

Where 

k1 = Risk coefficient 

k2 = Coefficient based on terrain, height and structure size

k3 = Topography factor 

The design wind pressure is given by

pz = 0.6 V^2 * z 

where pz is in N/m^2 at height Z and Vz is in m/sec. 

Up to a height of 30 m, the wind pressure is considered to act uniformly. Above 30 m height, the wind pressure increases.

Table 3: Risk Categories of Buildings for Environmental Loads

Risk category	Occupancy or Use	Importance Factor
		Snow Loads (Is)	Earthquake Loads (Ie)
I	Buildings representing low risk to human life in the case of failure, such as agricultural and minor storage facilities.	0.8	1.0
II	All buildings other than those listed in Risk Categories I, III, and IV. This risk category applies to most of the residential, commercial and industrial buildings (except those which have been specifically assigned to another category).	1.0	1.0
III	Buildings whose failure would pose a substantial risk to human life, and/or could cause a substantial economic impact or mass disruption of everyday public life. This category contains buildings such as: theaters, lecture and assembly halls where a large number of people congregate in one area; elementary schools; small hospitals; prisons; power generating stations; water and sewage treatment plants; telecommunication centers; and buildings containing hazardous and explosive materials.	1.1	1.25
IV	Essential facilities, including hospitals, fire and police stations, national defense facilities and emergency shelters, communication centers, power stations and utilities required in an emergency, and buildings containing extremely hazardous materials.	1.2	1.5

b) Snow Loads

In many parts of the world, snow loads must be considered in designing structures. The design snow load for a structure is based on the ground snow load for its geographical location, which can be obtained from building codes or meteorological data for that region. Once the ground snow load has been established, the design snow load for the roof of the structure is determined by considering such factors as the structure’s exposure to wind and its thermal, geometric, and functional characteristics. In most cases, there is less snow on roofs than on the ground. In India, the code IS 875 (Part-4):1987 deals with snow loads on roofs of the building. 

c) Earthquake Loads

An earthquake is a sudden undulation of a portion of the earth’s surface. Although the ground surface moves in both horizontal and vertical directions during an earthquake, the magnitude of the vertical component of ground motion is usually small and does not have a significant effect on most structures. It is the horizontal component of ground motion that causes structural damage and that must be considered in designs of structures located in earthquake-prone areas. 

Fig.1 Deformation during an earthquake

During an earthquake, as the foundation of the structure moves with the ground, the above-ground portion of the structure, because of the inertia of its mass, resists the motion, thereby causing the structure to vibrate in the horizontal direction. These vibrations produce horizontal shear forces in the structure. For an accurate prediction of the stresses that may develop in a structure, in the case of an earthquake, a dynamic analysis, considering the mass and stiffness characteristics of the structure, must be performed. The response of the structure to the ground vibration is a function of the nature of foundation soil, size and mode of construction and the duration and intensity of ground motion. In India, IS 1893– 2014 gives the details of calculations for structures standing on soils which will not considerably settle or slide appreciably due to earthquake.

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Hydrology

Hydrology means the science of water. It is the science that deals with the occurrence, circulation and distribution of water on the earth and earth’s atmosphere. As a branch of earth science, it is concerned with the water in streams and lakes, rainfall and snowfall, snow and ice on the land and water occurring below the earth’s surface in the pores of the soil and rocks. In a general sense, hydrology is a very broad subject of an inter-disciplinary nature depending upon allied sciences, such as meteorology, geology, statistics, chemistry, physics and fluid mechanics. Hydrology also deals with estimation of water resources, study of precipitation, runoff, evapotranspiration and their interaction. It also involves the study of problems such as floods and droughts and strategies to combat them. Hydrology is basically an applied science.

Engineering hydrology deals with all these aspects which are pertinent to planning, design and operation of hydraulic engineering projects for the control and use of the available water. Hydrology finds its application in the design and operation of water resources projects to estimate the magnitudes of flood flows at different times of a year to decide reservoir capacity, spillway discharge, dimensions of hydraulic structures etc.

Hydrologic Cycle

Water occurs on the earth in all its three states, viz. liquid, solid and gaseous and in various degrees of motion. Evaporation of water from water bodies such as oceans and lakes, formation and movement of clouds, rain and snowfall, streamflow and groundwater movement are some examples of the dynamic aspects of water. The various aspects of water related to the earth can be explained in terms of a cycle known as the hydrologic cycle. Hydrologic cycle is the water transfer cycle, which occurs continuously in nature. The three important phases of the hydrologic cycle are

1. Evaporation and Evapotranspiration
2. Precipitation
3. Runoff

Schematic Diagram of Hydrologic Cycle

The total water of earth, excluding deep ground water, is in constant circulation from the earth (including oceans) to atmosphere and back to the earth and oceans. This cycle of water amongst earth, oceans and atmospheric systems is known as hydrologic cycle. The hydrologic cycle can be visualized to begin with the evaporation (due to solar heat) of water from the oceans, streams and lakes of the earth into the earth’s atmosphere. The water vapour, under suitable conditions, get condensed to form clouds moving with wind all over the earth’s surface and which, in turn, may result in precipitation (in the form of rain water, snow, hail, sleet etc.) over the oceans as well as the land surface of the earth. Part of the precipitation, even while falling, may evaporate back into the atmosphere. Another part of the precipitation may be intercepted by vegetation on the ground or other surfaces. The intercepted precipitation may either evaporate into the atmosphere or fall back on the earth’s surface.

The greater part of the precipitation falling on the earth’s surface is retained in the upper soil from where it may return to the atmosphere through evaporation and transpiration by plants find its way, over and through the soil surface as runoff, to stream channels and the runoff thus becoming stream flow. Yet another part of the precipitation may penetrate into the ground to become part of the ground water. The water of stream channels, under the influence of gravity, moves towards lower levels to ultimately meet the oceans. Water from ocean may also find its way into the adjoining aquifers. Part of the stream water also gets evaporated back into the atmosphere from the surface of the stream. The ground water also moves towards the lower levels to ultimately reach the oceans. The ground water, at times, is a source of stream flow. Further, it is a continuous recirculation cycle in the sense that there is neither a beginning nor an end or a pause.

Block Diagram of Hydrologic Cycle

The hydrologic cycle is a very complex phenomenon that has been taking place since the earth formed. It should also be noted that the hydrologic cycle is a continuous recirculation cycle with neither a beginning nor an end. Hydrologic system is defined as a structure or volume in space surrounded by a boundary that receives water and other inputs, operates on them internally and produces them as outputs. The global hydrologic cycle can be termed a hydrologic system containing three subsystems such as the atmospheric water system, the surface water system and the subsurface water system. Another example of the hydrologic system is storm-rainfall-runoff process on a watershed. Watershed (or drainage basin or catchment) is a topographic area that drains rain water falling on it into a surface stream and discharges surface stream flow through one particular location identified as watershed outlet or watershed mouth. Each path of the hydrologic cycle involves one or more of the following aspects.

1. Transportation of water
2. Temporary storage
3. Change of state

Hydrologic Systems

The hydrologic system was defined as a structure or a volume in space, surrounded by a boundary, that accepts water and other inputs, operates on them internally, and produces them as outputs. The structure (for surface or subsurface flow) or volume in space (for atmospheric moisture flow) is the totality of the flow paths through which the water may pass from the point it enters the system to the point it leaves. The boundary is a continuous surface defined in three dimensions enclosing the volume or structure. A working medium enters the system as input, interacts with the structure and other media, and leaves as output. Physical, chemical and biological processes operate on the working media within the system; the most common working media involved in hydrologic analysis are water, air and heat energy.

Global Hydrologic Cycle

The global hydrologic cycle can be represented as a system containing three subsystems: the atmospheric water system, die surface water system and the subsurface water system. Another example is the storm rainfall- runoff process on a watershed, which can be represented as a hydrologic system. The input is rainfall distributed in time and space over the watershed and the output is stream flow at the watershed outlet. The boundary is defined by the watershed divide and extends vertically upward and downward to horizontal planes.

Global Hydrologic Cycle

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Water Demand

The community, society and industry need water for different uses. Water consumption in a community is characterized by several types of demand, including domestic, public, commercial and industrial uses. Domestic demand includes water for drinking, cooking, washing, laundering and other household functions. Public demand includes water for fire protection, street cleaning and use in schools and other public buildings. Commercial and industrial demands include water for stores, offices, hotels, laundries, restaurants and most manufacturing plants. There is usually a wide variation in total water demand among different communities. This variation depends on population, geographic location, climate, extent of local commercial and industrial activity and the cost of water.

An accurate estimation of water demand helps to determine the quantities of water when the water will be used various demand patterns. Water demand is the accurate estimation of total water. The unit of water demand is lpcd (liter per person (capita) per day). While planning the water supply scheme for an area, it is essential to determine the total water required for different purposes. It is necessary to determine the consumption and fluctuation of water demand on a daily, weekly, monthly and yearly basis, before designing any type of water supply scheme. Different types of water demand include the following. 

1) Domestic Water Demand 

Domestic Water demand includes the water required for drinking, cooking, bathing, lawn sprinkling, gardening, sanitation purpose, etc. It depends upon habits, social status, and climatic conditions of people. Domestic water demand accounts for 55 to 60% of the total water consumption. As per IS 1172-1983, the domestic consumption in India accounts for 135 lpcd (liters/capita/day) without full flushing system. The value is 200 lpcd with full flushing system. Generally about half (50%) of the total daily amount of water is spent on household consumption. The household consumption of water depends on the following factors.

• Personal habits of people 
• Social status of individual 
• Local climatic condition 
• Customs of the local people

2) Industrial Water Demand 

The per capita consumption of industries is generally taken as 50 lpcd. It represents the need of industries, either existing or likely to start in the future. This quantity will thus vary with the number and types of industries present in the city. 

3) Institutional and Commercial Water Demand 

On an average, per capita demand of 20 lpcd is required to meet institutional and commercial water demand. For highly commercialized cities, this value can be 50 lpcd. It includes the use of institutions such as hospitals, hotels, restaurants, schools and colleges, railway stations, offices, etc. This quantity will certainly vary with the nature of the city and with the number and types of commercial establishments and institutions present in it.

4) Public and Civil Use 

The per capita consumption for public and civic use can be taken as 10 lpcd. This water is used for road washing, public parks, sanitation etc. This includes watering in a public park, gardening, washing, sprinkling on roads, use in a public fountain etc. 

5) Fire Demand 

The fire demand is generally taken as 1 lpcd. It is the amount of water required for firefighting purpose in case of a fire break out in an area. Per capita fire demand is ignored while calculating the total per capita water requirement of a particular city because most areas have fire hydrants placed in the water main at 100 to 150 meters apart.This water is required to be available at a pressure of about 100 to 150 kN/m^2or 10 to 15m head of water. If the population is less than 50000, fire demand is not calculated. For larger city fire demand was calculated. 

6) Waste and Thefts 

This consumption accounts for 55 lpcd. Even if the waterworks are managed with high proficiency, a loss of 15% of total water consumption is expected. This includes water loss in leakage due to bad plumbing or damaged meters, stolen water and other losses and wastes.

As Per IS 1172 : 1993 Indian Standard Code of Basic Requirements for Water Supply, Drainage and Sanitation

Water Supply for Residences (As Per IS 1172 : 1993)

A minimum of 10 to 100 liter per head per day may be considered adequate for domestic needs of urban communities, apart from non domestic needs as flushing requirements. As a general rule the following rates per capita per day may be considered minimum for domestic and non domestic needs. 

Rate of Demand for Various Communities (As Per IS 1172 : 1993)

Sl. No.	Type of Community	Rate of Demand (lpcd)
1	For communities with population up to 20000 and without flushing system	40 lpcd (min)
	a) water supply through stand post
	b) water supply through house service connection	70 to 100 Ipcd
2	For communities with population 20000 to 100,000 together with full flushing system	100 to 150 Ipcd
3	For communities with population above 100000 together with full flushing system	150 to 200 lpcd

It is also noted that the value of water supply given as 150 to 200 liter per head per day may be reduced to 135 liter per head per day for houses for Lower Income Groups (LIG) and Economically Weaker Section (EWS) of society, depending upon prevailing conditions. Out of the 150 to 200 liter per head per day, 45 liter per head per day may be taken for flushing requirements and the remaining quantity for other domestic purposes.

Minimum requirements for water supply for buildings other than residences shall be in accordance with the following table.

Water Requirements for Buildings Other than Residences (As Per IS 1172 : 1993)

Sl. No.	Type of Residence	Rate of Demand (per liter, day)
1	Factories where bathrooms are required to be provided	45 per head
2	Factories where no bath rooms are required to be provided	30 per head
3	Hospital ( including laundry) a) Number of beds not exceeding 100	340 per head
	b) Number of beds exceeding 100	450 per head
4	Nurses' homes and medical quarters	135 per head
5	Hostels	135 per head
6	Hotel	180 per head
7	Offices	45 per head
8	Restaurants	70 per seat
9	Cinemas, concert halls and theatres	15 per seat
10	Schools	45 per head
	a) Day schools
	b) Boarding schools	135 per head

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Water Supply and Wastewater Engineering

Water supply and wastewater drainage were among the public facilities designed by civil engineers to control environmental pollution and protect public health. The availability of water had always been a critical component of civilizations. Ancient Rome, had water supplied by nine different aqueducts up to 80 km (50 miles) long, with cross sections from 2 to 15 m (7 to 50 ft). The purpose of the aqueducts was to carry spring water, which was better to drink than Tiber River water.

As cities grew, the demand for water increased dramatically. During the eighteenth and nineteenth centuries the poorer residents of European cities lived under abominable conditions, with water supplies that were grossly polluted, expensive or nonexistent. In London the water supply was controlled by nine different private companies and water was sold to the public. People who could not afford to pay for water often begged or stole it. During epidemics of disease the privation was so great that many drank water from furrows and depressions in plowed fields. Droughts caused water supplies to be curtailed and great crowds formed to wait their “turn” at the public pumps.

In the New World, the first public water supply system consisted of wooden pipes, bored and charred, with metal rings shrunk on the ends to prevent splitting. The first such pipes were installed in 1652 and the first citywide system was constructed in Winston-Salem, NC, in 1776. The first American water works was built in the Moravian settlement of Bethlehem. A wooden water wheel, driven by the flow of Monocacy Creek, powered wooden pumps that lifted spring water to a hilltop wooden reservoir from which it was distributed by gravity.

One of the first major water supply undertakings was the Croton Aqueduct, started in 1835 and completed six years later. This engineering marvel brought clear water to Manhattan Island, which had an inadequate supply of groundwater. Although municipal water systems might have provided adequate quantities of water, the water quality was often suspected.

The earliest known acknowledgment of the effect of impure water is found in Susruta Samhitta, a collection of fables and observations on health, dating back to 2000 BCE, which recommended that water be boiled before drinking. Water filtration became commonplace toward the middle of the nineteenth century. The first successful water supply filter was in Parsley, Scotland, in 1804, and many less successful attempts at filtration followed. A notable failure was the New Orleans system for filtering water from the Mississippi River. The water proved to be so muddy that the filters clogged too fast for the system to be workable. This problem was not alleviated until aluminum sulfate (alum) began to be used as a pretreatment to filtration. The use of alum to clarify water was proposed in 1757, but was not convincingly demonstrated until 1885. Disinfection of water with chlorine began in Belgium in 1902 and in America, in Jersey City, in 1908.

Between 1900 and 1920 deaths from infectious disease dropped dramatically, owing in part to the effect of cleaner water supplies. Human waste disposal in early cities presented both a nuisance and a serious health problem. Often the method of disposal consisted of nothing more than flinging the contents of chamberpots out the window. Around 1550, King Henri II repeatedly tried to get the Parliament of Paris to build sewers, but neither the king nor the parliament proposed to pay for them. The famous Paris sewer system was built in the nineteenth century. Storm water was considered the main “drainage” problem, and it was in fact illegal in many cities to discharge wastes into the ditches and storm sewers. Eventually, as water supplies developed, the storm sewers were used for both sanitary waste and storm water. Such “combined sewers” existed in some of major cities until the 1980s.

The first system for urban drainage in America was constructed in Boston around 1700. There was surprising resistance to the construction of sewers for waste disposal. Most American cities had cesspools or vaults, even at the end of the nineteenth century. The most economical means of waste disposal was to pump these out at regular intervals and cart the waste to a disposal site outside the town. Engineers argued that although sanitary sewer construction was capital intensive, sewers provided the best means of wastewater disposal in the long run. Their argument prevailed and there was a remarkable period of sewer construction between 1890 and 1900. The sewerage systems in America were built in 1880. One of the system namely Memphis system was a complete failure. It used small pipes that were to be flushed periodically. No manholes were constructed and cleanout became a major problem. The system was later removed and larger pipes with manholes were installed.

Initially, all sewers emptied into the nearest watercourse, without any treatment. As a result, many lakes and rivers became grossly polluted. Wastewater treatment first consisted only of screening for removal of the large floatables to protect sewage pumps. Screens had to be cleaned manually and wastes were buried or incinerated. The first mechanical screens were installed in Sacramento, in 1915 and the fist mechanical commuter for grinding up screenings was installed in Durham. The first complete treatment systems were operational by the turn of the century, with land spraying of the effluent being a popular method of wastewater disposal.

Civil engineers were responsible for developing engineering solutions to these water and wastewater problems of these facilities. There was, however, little appreciation of the broader aspects of environmental pollution control and management until the mid-1900s. As recently as 1950 raw sewage was dumped into surface waters in the United States and even streams in public parks and in U.S. cities were fouled with untreated wastewater. The first comprehensive federal water pollution control legislation was enacted by the U.S. Congress in 1957.

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Stress

Stress is the internal resistance offered by the body to the external load applied to it per unit cross sectional area. Stresses are normal or tangential to the plane to which they act and are tensile, compressive or shearing in nature.

When a member is subjected to loads it develops resisting forces. To find the resisting forces developed a section plane may be passed through the member and equilibrium of any one part may be considered. Each part is in equilibrium under the action of applied forces and internal resisting forces. The resisting forces may be conveniently split into normal and parallel to the section plane. The resisting force parallel to the plane is called Shearing resistance. The intensity of resisting force normal to the sectional plane is called Normal resistance.

Forces Acting on Rectangular Rod

Consider a rectangular rod subjected to axial pull P. Let us imagine that the same rectangular bar is assumed to be cut into two halves at section XX. The each portion of this rectangular bar is in equilibrium under the action of load P and the internal forces acting at the section XX has been shown in figure. The symbol ‘σ’ is used to represent stress.

Where A is the area of the X –X section

Here we are using an assumption that the total force or total load carried by the rectangular bar is uniformly distributed over its cross section. But the stress distributions may be far from uniform, with local regions of high stress known as stress concentrations. If the force carried by a component is not uniformly distributed over its cross sectional area, A, we must consider a small area, ‘δA’ which carries a small load ‘δP’, of the total force ‘P', Then definition of stress is

Unit of Stress

The basic units of stress in S.I units i.e. (International system) are N/m^2 (or Pa). When Newton is taken as unit of force and millimeter as unit of area, unit of stress will be N/mm^2. The other derived units used in practice are kN/mm^2, N/m^2 or kN/m^2. A stress of one N/m2 is known as Pascal and is represented by Pa.

Hence, 1 MPa = 1 MN/m^2 = 1 × 10^6 N/(1000 mm^2) = 1 N/mm^2.

Thus one Mega Pascal is equal to 1 N/mm^2.

Types of Stress

The two basic stresses exists are Normal stress and Shear stress. Other stresses either are similar to these basic stresses or as a combination of this.

Example : Bending stress is a combination tensile, compressive and shear stresses.

                  Torsional stress, as encountered in twisting of a shaft is a shearing stress.

1) Normal stress

If the stresses are normal to the areas concerned, then these are termed as normal stress. The normal stress is generally denoted by a Greek letter (σ). Stress is said to be normal stress when the direction of the deforming force is perpendicular to the cross-sectional area of the body. Normal stress can be further classified into three types based on the dimension of force. This is also known as uniaxial state of stress, because the stresses acts only in one direction however, such a state rarely exists, therefore we have biaxial and triaxial state of stresses where either the two mutually perpendicular normal stresses acts or three mutually perpendicular normal stresses acts as shown in the figures below.

Uniaxial State of Stress

Biaxial State of Stress

Triaxial State of Stress

The normal stresses can be either tensile or compressive whether the stresses acts out of the area or into the area.

a) Tensile Stress

Consider a bar subjected to force P as shown in figure. To maintain the equilibrium the end forces applied must be the same, say P. If the deforming force or applied force results in the increase in the object’s length then the resulting stress is termed as tensile stress.For example when a rod or wire is stretched by pulling it with equal and opposite forces (outwards) at both ends. 

Tensile Force

b) Compressive Stress 

If the deforming force or applied force results in the decrease in the object’s length then the resulting stress is termed as compressive stress. For example: When a rod or wire is compressed/squeezed by pushing it with equal and opposite forces (inwards) at both ends.

Compressive Force

Sign convections for Normal stress

Tensile stress is taken as +ve

Compressive stress is taken as –ve

2) Shear Stress

The cross sectional area of a block of material is subject to a distribution of forces which are parallel, rather than normal, to the area concerned. Such forces are associated with a shearing of the material and are referred to as shear forces. The resulting stress is known as shear stress.

Shear Force

Bearing Stress

When one object presses against another, it is referred to a bearing stress (They are in fact the compressive stress).

Bending Stress 

Bending stress is the stress that results from the application of a bending moment to a material, causing it to deform. This results in the development of a combination of tensile and compressive stresses through the cross-section of the material and creates a stress gradient that causes the material to bend. 

Bending Stress in Beam

Torsional stress 

Torsional shear stress or Torsional stress may be defined as that shear stress which acts on a transverse cross-section that is caused by the action of a twist.

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History of Solid Mechanics

Solid mechanics developed in the outpouring of mathematical and physical studies by the great achievement of Sir. Isaac Newton’s (1642-1727) laws of motion. Leonardo da Vinci (1452-1519) sketched in his notebooks about the possible test of the tensile strength of a wire. The Italian experimental scientist Galileo Galilei (1564-1642) had investigated the breaking loads of rods in tension and concluded that the load was independent of length and proportional to the cross section area, this being a first step towards a concept of stress. He also investigated how the breaking of heavy stone columns, laid horizontally in storage as beams, depended on the number and condition of their supports.

The English scientist Robert Hooke discovered in 1660, but published only in 1678, the observation that for many materials that displacement under a load was proportional to force, thus establishing the motion of (linear) elasticity but not yet in a way that was expressible in terms of stress and strain. E. Mariotte in France published similar discoveries in 1680 and reached an understanding of how beams like those studied by Galileo resisted transverse loading by developing extensional and compressive deformations. It was for Swiss mathematician and mechanician James Bernoulli (1654-1705) to observe that the proper way of describing deformation was to give force per unit area, or stress, as a function of the elongation per unit length, or strain, of a material fiber under tension.

Swiss mathematician and mechanician Leonhard Euler (1707-1783) proposed a linear relation between stress and strain in 1727. The notion that there is internal tension acting across surfaces in a deformed solid was expressed by German mathematician and physicist Gottfried Wilhelm Leibniz in 1684 and James Bernoulli in 1691. Also, Bernoulli and Euler introduced the idea that at a given section along the length of a beam there were internal tensions amounting to a net force and a net torque. Euler introduced the idea of compressive normal stress as the pressure in a fluid in 1752.

The French engineer and physicist Charles-Augustine Coulomb (1736-1806) was apparently the first to relate the theory of a beam as a bent elastic line to stress and strain in an actual beam. The French mathematician Parent introduced the concept of shear stress in 1713, but Coulomb was the one who extensively developed the idea in connection with beams and with the stressing and failure of soil in 1773, and studies of frictional slip in 1779. It was the great French mathematician Augustin Louis Cauchy (1789-1857), originally educated as an engineer, who in 1822 formalized the stress concept in the context of a general three-dimensional theory, showed its properties as consisting of a 3 by 3 symmetric array of numbers that transform and gave the specific development of the theory of linear elastic response for isotropic solids.

The 1700’s and early 1800’s were a productive period in which the mechanics of simple elastic structural elements were developed well before the beginnings in the 1820’s of the general three-dimensional theory. The development of beam theory by Euler, who generally modeled beams as elastic lines which resist bending, and by several members of the Bernoulli family and by Coulomb, remains among the most immediately useful aspects of solid mechanics, in part for its simplicity and in part because of the pervasiveness of beams and columns in structural technology. James Bernoulli proposed in his final paper of 1705 that the curvature of a beam was proportional to bending moment.

The middle and late 1800’s were a period in which many basic elastic solutions were derived and applied to technology and to the explanation of natural phenomena. French mathematician Barre de Saint-Venant derived in the 1850’s solutions for the torsion of non-circular cylinders, which explained the necessity of warping displacement of the cross section in the direction parallel to the axis of twisting. The German physicist Heinrich Rudolph Hertz developed solutions for the deformation of elastic solids as they are brought into contact, and applied these to model details of impact collisions.

Poisson, Cauchy and George G. Stokes showed that the equations of the theory predicted the existence of two types of elastic deformation waves which could propagate through isotropic elastic solids. These are called body waves. Lord Rayleigh (John Strutt) showed in 1887 that there is a wave type that could propagate along surfaces, such that the motion associated with the wave decayed exponentially with distance into the material from the surface. This type of surface wave, now called a Rayleigh wave, propagates typically at slightly more than 90% of the shear wave speed, and involves an elliptical path of particle motion that lies in planes parallel to that defined by the normal to the surface and the propagation direction.

In 1898 G. Kirsch derived the solution for the stress distribution around a circular hole in a much larger plate under remotely uniform tensile stress. The same solution can be adapted to the tunnel-like cylindrical cavity of circular section in a bulk solid. His solution showed a significant concentration of stress at the boundary, by a factor of three when the remote stress was uniaxial tension. Then in 1907 the Russian mathematician G. Kolosov, and independently in 1914 the British engineer Charles Inglis, derived the analogous solution for stresses around an elliptical hole. Their solution showed that the concentration of stress could become far greater as the radius of curvature at an end of the hole becomes small compared to the overall length of the hole.

The Italian elastician and mathematician V. Volterra introduced in 1905 the theory of the elastostatic stress and displacement fields created by dislocating solids. This involves making a cut in a solid, displacing its surfaces relative to one another by some fixed amount, and joining the sides of the cut back together, filling in with material as necessary. The mathematical techniques advanced by Volterra are now in common use by Earth scientists in explaining ground displacement and deformation induced by tectonic faulting. Also, the first elastodynamic solutions for the rapid motion of a crystal dislocations by South African materials scientist F. R. N. Nabarro, in the early 1950’s, were quickly adapted by seismologists to explain the radiation from propagating slip distributions on faults.

Austrian-American civil engineer Karl Terzaghi in the 1920’s developed the concept of effective stress, whereby the stresses which enter a criterion of yielding or failure are not the total stresses applied to the saturated soil or rock mass, but rather the effective stresses, which are the difference between the total stresses and those of a purely hydrostatic stress state with pressure equal to that in the pore fluid. German applied mechanician Ludwig Prandtl developed the rudiments of the theory of plane plastic flow in 1920 and 1921.

The finite element method and other computational techniques (finite differences, spectral expansions, boundary and integral equations) have made a major change in the practice of and education for, engineering in the various areas that draw on solid mechanics. Previously, many educators saw little point in teaching engineers much of the subject beyond the techniques of elementary beam theory developed in the 1700’s by Bernoulli, Euler and Coulomb. More advanced analyses involved sufficiently difficult mathematics as to be beyond the reach of the typical practitioner and were regarded as the domain of advanced specialists who would, themselves, find all but the simpler cases intractable. The availability of software incorporating the finite element method and other procedures of computational mechanics and design analysis has placed the advanced concepts of solid mechanics into the hands of a far broader community of engineers. At the same time, it has created a necessity for them and other users to have a much deeper education in the subject, so that the computational tools are used properly and at full effectiveness.

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