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The concept of satellite position fixing commenced with the launch of the first Sputnik satellite by the USSR in October 1957. This was rapidly followed by the development of the Navy Navigation Satellite System (NNSS) by the US Navy. This system, commonly referred to as the Transit system, was created to provide a worldwide navigation capability for the US Polaris submarine fleet. The Transit system was made available for civilian use in 1967 but ceased operation in 1996. However, as the determination of position required very long observation periods and relative positions determined over short distances were of low accuracy, its application was limited to geodetic and low dynamic navigation uses.

In 1973, the US Department of Defense (DoD) commenced the development of NAVSTAR (Navigation System with Time and Ranging) Global Positioning System (GPS), and the first satellites were launched
in 1978.

The system is funded and controlled by the DoD but is partially available for civilian and foreign users. The accuracies that may be obtained from the system depend on the degree of access available to the user, the sophistication of his/her receiver hardware and data processing software, and degree of mobility during signal reception.

Global Positioning System logo
Global Positioning System logo
In very broad terms, the geodetic user in a static location may obtain ‘absolute’ accuracy (with respect to the mass centre of the Earth within the satellite datum) to better than ±1 metre and position relative to another known point, to a few centimetres over a range of tens of kilometres, with data post-processing. At the other end of the scale, a technically unsophisticated, low dynamic (ship or land vehicle) user, with limited access to the system, might achieve real time ‘absolute’ accuracy of 10–20 metres.

The GPS navigation system relies on satellites that continuously broadcast their own position in space and in this the satellites may be thought of as no more than control stations in space. Theoretically, a user who has a clock, perfectly synchronized to the GPS time system, is able to observe the time delay of a GPS signal from its own time of transmission at the satellite, to its time of detection at the user’s equipment. The time delay, multiplied by the mean speed of light, along the path of the transmission from the satellite to the user equipment, will give the range from the satellite at its known position, to the user. If three such ranges are observed simultaneously, there is sufficient information to compute the user’s position in three-dimensional space, rather in the manner of a three-dimensional trilateration. The false assumption in all this is that the user’s receiver clock is perfectly synchronized with the satellite clocks.

1. GPS Observing Methods

The use of GPS for positioning to varying degrees of accuracy, in situations ranging from dynamic (navigation) to static (control networks), has resulted in a wide variety of different field procedures using one or other of the basic observables. Generally pseudo-range measurements are used for navigation, whilst the higher precision necessary in engineering surveys requires carrier frequency phase measurements.

The basic point positioning method used in navigation gives the X, Y, Z position to an accuracy of better than 20 m by observation to four satellites. However, the introduction of Selective Availability (SA), see below, degraded this accuracy to 100 m or more and so led to the development of the more accurate differential technique. In this technique the vector between two receivers (baseline) is obtained, i.e. the difference in coordinates (ΔX, ΔY, ΔZ). If one of the receivers is set up over a fixed station whose coordinates are known, then comparison with the observed coordinates enables the differences to be transmitted as corrections to the second receiver (rover). In this way, all the various GPS errors are lumped together in a single correction. At its simplest the corrections transmitted could be in a simple coordinate format, i.e. δX, δY, δZ, which are easy to apply. Alternatively, the difference in coordinate position of the fixed station may be used to derive corrections to the ranges to the various satellites used. The rover then applies those corrections to its own observations before computing its position.

The fundamental assumption in Differential GPS (DGPS) is that the errors within the area of survey would be identical. This assumption is acceptable for most engineering surveying where the areas involved are small compared with the distance to the satellites.

Where the area of survey becomes extensive this argument may not hold and a slightly different approach is used called Wide Area Differential GPS.

It can now be seen that, using DGPS, the position of a roving receiver can be found relative to a fixed master or base station without significant errors from satellite and receiver clocks, ionospheric and tropospheric refraction and even ephemeris error. This idea has been expanded to the concept of having permanent base stations established throughout a wide area or even a whole country.

As GPS is essentially a military product, the US Department of Defense has retained the facility to reduce the accuracy of the system by interfering with the satellite clocks and the ephemeris of the satellite. This is known as Selective Availability (SA) of the Standard Positioning Service (SPS). This form of degradation has been switched off since May 2000 and it is unlikely, though possible, that it will be reintroduced as there are other ways that access to the system can be denied to a hostile power. The P can also be altered to a Y code, to prevent imitation of the PPS by hostile forces, and made unavailable to civilian users. This is known as Anti-Spoofing (AS). However, the carrier wave is not affected and differential methods should correct for most SA effects.

Using the carrier phase observable in the differential mode produces accuracies of 1 ppm of the baseline length. Post-processing is needed to resolve for the integer ambiguity if the highest quality results are to be achieved. Whilst this, depending on the software, can result in even greater accuracies than 1 ppm (up to 0.01 ppm), it precludes real-time positioning. However, the development of Kinematic GPS and ‘on-the-fly’ ambiguity resolution makes real-time positioning possible and greatly reduces the observing times.

The following methods are based on the use of carrier phase measurement for relative positioning using two receivers.

1.1 Static positioning

This method is used to give high precision over long baselines such as are used in geodetic control surveys. At its simplest, one receiver is set up over a station of known X, Y, Z coordinates, preferably in the WGS84 reference system, whilst a second receiver occupies the station whose coordinates are required.

Observation times may vary from 45 min to several hours. This long observational time is necessary to allow a change in the relative receiver/satellite geometry in order to calculate the initial integer ambiguity terms.

More usually baselines are observed when the precise coordinates of neither station are known. The approximate coordinates of one station can be found by averaging the pseudo-range solution at that station.

Artist's impression of GPS Block IIR satellite in Earth orbit
Artist's impression of GPS Block IIR satellite in Earth orbit
Provided that those station coordinates are known to within 10 m it will not significantly affect the computed difference in coordinates between the two stations. The coordinates of a collection of baselines, provided they are interconnected, can then be estimated by a least squares free network adjustment. Provided that at least one, and preferably more, stations are known in WGS84 or the local datum then the coordinates of all the stations can be found in WGS84 or the local datum.

Accuracies in the order of 5 mm ±1 ppm of the baseline are achievable as the majority of errors in GPS, such as clock, orbital and atmospheric errors, are eliminated or substantially reduced by the differential process. The use of permanent active GPS networks established by a government agency or private company results in a further increase in accuracy for static positioning.

Apart from establishing high precision control networks, it is used in control densification, measuring plate movement in crustal dynamics and oil rig monitoring.

1.2 Rapid static

Rapid static surveying is ideal for many engineering surveys and is halfway between static and kinematic procedures. The ‘master’receiver is set up on a reference point and continuously tracks all visible satellites throughout the duration of the survey. The ‘roving’ receiver visits each of the remaining points to be surveyed, but stays for just a few minutes, typically 2–10 min.

Using difference algorithms, the integer ambiguity terms are quickly resolved and position, relative to the reference point, obtained to sub-centimetre accuracy. Each point is treated independently and as it is not necessary to maintain lock on the satellites, the roving receiver may be switched off whilst travelling between stations. Apart from a saving in power, the necessity to maintain lock, which is very onerous in urban surveys, is removed.

This method is accurate and economic where there are many points to be surveyed. It is ideally suited for short baselines where systematic errors such as atmospheric, orbital, etc., may be regarded as equal at all points and so differenced out. It can be used on large lines (>10 km) but may require longer observing periods due to the erratic behaviour of the ionosphere. If the observations are carried out at night when the ionosphere is more stable observing times may be reduced.

1.3 Reoccupation

This technique is regarded as a third form of static surveying or as a pseudo-kinematic procedure. It is based on repeating the survey after a time gap of one or two hours in order to make use of the change in receiver/satellite geometry to resolve the integer ambiguities.

The master receiver is once again positioned over a known point, whilst the roving receiver visits the unknown points for a few minutes only. After one or two hours, the roving receiver returns to the first unknown point and repeats the survey. There is no need to track the satellites whilst moving from point to point. This technique therefore makes use of the first few epochs of data and the last few epochs that reflect the relative change in receiver/satellite geometry and so permit the ambiguities and coordinate differences to be resolved.

Using dual frequency data gives values comparable with the rapid static technique. Due to the method of
changing the receiver/satellite geometry, it can be used with cheaper single-frequency receivers (although extended measuring times are recommended) and a poorer satellite constellation.

1.4 Kinematic positioning

The major problem with static GPS is the time required for an appreciable change in the satellite/receiver geometry so that the initial integer ambiguities can be resolved. However, if the integer ambiguities could be resolved (and constrained in a least squares solution) prior to the survey, then a single epoch of data would be sufficient to obtain relative positioning to sub-centimetre accuracy. This concept is the basis of kinematic surveying. It can be seen from this that, if the integer ambiguities are resolved initially and quickly, it will be necessary to keep lock on these satellites whilst moving the antenna.

1.4.1 Resolving the integer ambiguities

The process of resolving the integer ambiguities is called initialization and may be done by setting up both receivers at each end of a baseline whose coordinates are accurately known. In subsequent data processing, the coordinates are held fixed and the integers determined using only a single epoch of data. 

These values are now held fixed throughout the duration of the survey and coordinates estimated every epoch, provided there are no cycle slips.

The initial baseline may comprise points of known coordinates fixed from previous surveys, by static GPS just prior to the survey, or by transformation of points in a local coordinate system to WGS84. An alternative approach is called the ‘antenna swap’ method. An antenna is placed at each end of a short base (5–10 m) and observations taken over a short period of time. The antennae are interchanged, lock maintained, and observations continued. This results in a big change in the relative receiver/satellite geometry and, consequently, rapid determination of the integers. The antennae are returned to their original position prior to the surveys.

It should be realized that the whole survey will be invalidated if a cycle slip occurs. Thus, reconnaissance of the area is still of vital importance, otherwise reinitialization will be necessary. A further help in this matter is to observe to many more satellites than the minimum four required.

1.4.2 Traditional kinematic surveying

Assuming the ambiguities have been resolved, a master receiver is positioned over a reference point of known coordinates and the roving receiver commences its movement along the route required. As the movement is continuous, the observations take place at pre-set time intervals, often less than 1 s. Lock must be maintained to at least four satellites, or re-established when lost. In this technique it is the trajectory of the rover that is surveyed and points are surveyed by time rather than position, hence linear detail such as roads, rivers, railways, etc., can be rapidly surveyed. Antennae can be fitted to fast moving vehicles, or even bicycles, which can be driven along a road or path to obtain a three-dimensional profile.

1.4.3 Stop and go surveying

As the name implies, this kinematic technique is practically identical to the previous one, only in this case the rover stops at the point of detail or position required (Figure 9.17). The accent is therefore on individual points rather than a trajectory route, so data is collected only at those points. Lock must be maintained, though the data observed when moving is not necessarily recorded. This method is ideal for engineering and topographic surveys.

1.4.4 Real-time kinematic (RTK)

The previous methods that have been described all require post-processing of the results. However, RTK provides the relative position to be determined instantaneously as the roving receiver occupies a position.

The essential difference is in the use of mobile data communication to transmit information from the reference point to the rover. Indeed, it is this procedure that imposes limitation due to the range over which the communication system can operate.

The system requires two receivers with only one positioned over a known point. A static period of initialization will be required before work can commence. If lock to the minimum number of satellites is lost then a further period of initialization will be required. Therefore the surveyor should try to avoid working close to major obstructions to line of sight to the satellites. The base station transmits code and carrier phase data to the rover. On-board data processing resolves the ambiguities and solves for a change in coordinate differences between roving and reference receivers. This technique can use single or dual frequency receivers. Loss of lock can be regained by remaining static for a short time over a point of known position.

The great advantage of this method for the engineering surveyor is that GPS can be used for setting-out on site. The setting-out coordinates can be entered into the roving receiver, and a graphical output indicates the direction and distance through which the pole-antenna must be moved. The positions of the point to be set-out and the antenna are shown. When the two coincide, the centre of the antenna is over the setting-out position.

1.4.5 Real-time kinematic on the fly

Throughout all the procedures described above, it can be seen that initialization or reinitialization can only be done with the receiver static. This may be impossible in high accuracy hydrographic surveys or road profiling in a moving vehicle. Ambiguity Resolution On the Fly (AROF) enables ambiguity resolution whilst the receiver is moving. The techniques require L1 and L2 observations from at least five satellites with a good geometry between the observer and the satellites. There are also restrictions on the minimum periods of data collection and the presence of cycle slips. Both these limitations restrict this method of surveying to GPS friendly environments. Depending on the level of ionospheric disturbances, the maximum range from the reference receiver to the rover for resolving ambiguities whilst the rover is in motion is about 10 km, with an achievable accuracy of 10–20 mm.

For both RTK and AROF the quality of data link between the reference and roving receiver is important. Usually this is by radio but it may also be by mobile phone. When using a radio the following issues should be considered:
  • In many countries the maximum power of the radio is legally restricted and/or a radio licence may be required. This in turn restricts the practical range between the receivers.
  • The radio will work best where there is a direct line of sight between the receivers. This may not always be possible to achieve so for best performance the reference receiver should always be sited with the radio antenna as high as possible.
  • Cable lengths should be kept as short as possible to reduce signal losses.

Another typical phone call. An owner wants to know how long it will take for the lightweight concrete in the elevated slabs of his new building to dry before he can place the floor covering. The slabs were placed 4 months ago, but tests still show a moisture-vapor-emission rate of 8 pounds per 1000 square feet in 24 hours. The floor-covering manufacturer requires the concrete to be at 3 lbs/1000 sf/24 hrs. Delaying floorcovering installation will delay building occupancy. The owner has never had this problem in other buildings he has constructed. Why won’t this concrete dry? Concrete is concrete, right?

Well, unfortunately it’s not. Many owners and contractors have told us they’ve experienced project delays while waiting for lightweight concrete to dry. Though we couldn’t find any data regarding the drying time of lightweight concrete, field experience tells us that lightweight concrete takes longer to dry than normal-weight concrete. To help fill this information gap, CONCRETE CONSTRUCTION devised a testing program to find out how long it takes lightweight concrete to dry.

The test program 

Three normal-weight concretes with water-cement ratios of 0.31, 0.37, and 0.40 were delivered to a testing lab in 1-cubic-yard loads. A lightweight concrete mix with a water cement ratio of 0.40 was also delivered to the testing lab. The proprietary mixes were supplied by the ready-mix division of CAMAS Colorado, Denver. The normal-weight concrete moisture-vapor-emission test results were reported in THE CONCRETE PRODUCER (Ref. 1). Here we compare the lightweight concrete moisture-vapor-emission test results with those for normal-weight concrete having the same water-cement ratio. The producer tightly controlled water content and water-cement ratio by closely monitoring aggregate moisture and water left in the drum. The fresh and hardened properties of the lightweight concrete were as follows:

■ 3-inch slump
■ 4.5% air content
■ 124-pound-per-cubic-foot unit weight
■ 48° F temperature
■ 6850-psi 28-day compressive strength

Workers placed and vibrated the concrete in 3-foot-square test slabs 2, 4, 6, and 8 inches thick. After striking off the surface with a 2x4 and floating it by hand, they covered the slabs with plastic sheeting for 3 days. Calciumchloride moisture-emission testing began after the sheeting was removed.

Moisture-emission tests were conducted in accordance with the test manufacturer’s instructions. Technicians ran one test on each slab at the 3-day age but thereafter ran two tests on each test slab and reported an average test value. 

The calcium-chloride test kits were left in place for 72 hours on slabs stored inside the test lab at a 70±3° F and a relative humidity of 28±5%. This is the normal indoor environment during the winter in the Rocky Mountain region, where the tests were conducted, and represents the environment found in many buildings without relative-humidity controls. 

Drying in months instead of weeks 

moisture-vapor emission rates for the test slabs after drying for up to 183 days.
The table shows moisture-vapor emission rates for the test slabs after drying for up to 183 days. Drying times are measured from the end of the 3-day curing period to the end of the 72-hour moisture-emission test. Thus the 3-day measurement was taken 6 days after concrete placement. The test data support the following conclusions.

Lightweight concrete dries slower. Regardless of the test slab thickness, the lightweight concrete took about 6 months to dry to a moisture-vapor emission rate of 3 lbs/1000 sf/24 hrs. Normal-weight concrete of the same water-cement ratio took only 6 weeks of drying in laboratory air to reach the same level (Ref. 1). From previous work (Ref. 2), we know that laboratory drying represents the fastest drying time. So field conditions that include wet-dry cycles will increase the actual time for the slab to reach the specified moisture-vapor-emission limits. 

Thickness effects

As with normal-weight concrete, the moisture-vapor-emission rates were unaffected by slab thickness. 

Don’t blame the contractor

Lightweight concrete offers many advantages. However, any owner using lightweight concrete that’s to be covered by a moisture-sensitive floor covering or any architect/engineer specifying this combination should consider the slower drying time as an important part of the construction schedule. Once lightweight concrete is specified, the contractor can’t change its drying characteristics. If owners want the benefits of lightweight concrete and a fast-track schedule, they may need to consider applying a polymer coating or sheet product to reduce moisture emissions.


1. Bruce A. Suprenant and Ward R. Malisch, “Quick-Dry Concrete: A New Market for Ready-Mix Producers,” THE CONCRETE PRODUCER, May 1998.
2. Bruce A. Suprenant and Ward R. Malisch, “Are Your Slabs Dry Enough for Floor Coverings?” CONCRETE CONSTRUCTION, August 1998.

By Bruce A. Suprenant and Ward Malisch


Reinforced concrete structural systems can be formed into virtually any geometry to meet any requirement. Regardless of the geometry, standardized floor and roof systems are available that provide cost-effective solutions in typical situations. The most common types are classified as one-way systems and two-way systems. Examined later are the structural members that make up these types of systems.

It is common for one type of floor or roof system to be specified on one entire level of building; this is primarily done for cost savings. However, there may be cases that warrant a change in framing system. The feasibility of using more than one type of floor or roof system at any given level needs to be investigated carefully.

One-Way Systems

A one-way reinforced concrete floor or roof system consists of members that have the main flexural reinforcement running in one direction. In other words, reactions from supported loads are transferred primarily in one direction. Because they are primarily subjected to the effects from bending (and the accompanying shear), members in one-way systems are commonly referred to as flexural members.
FIGURE 1 One-way slab system.
FIGURE 1 One-way slab system.

Members in a one-way system are usually horizontal but can be provided at a slope if needed. Sloped members are commonly used at the roof level to accommodate drainage requirements.

Illustrated in Fig. 1 is a one-way slab system. The load that is supported by the slabs is transferred to the beams that span perpendicular to the slabs. The beams, in turn, transfer the loads to the girders, and the girders transfer the loads to the columns.

Individual spread footings may carry the column loads to the soil below. It is evident that load transfer between the members of this system occurs in one direction.

FIGURE 2 Standard one-way joist system.
FIGURE 2 Standard one-way joist system.
Main flexural reinforcement for the one-way slabs is placed in the direction parallel to load transfer, which is the short direction. Similarly, the main flexural reinforcement for the beams and girders is placed parallel to the length of these members. Concrete for the slabs, beams, and girders is cast at the same time after the forms have been set and the reinforcement has been placed in the formwork. This concrete is also integrated with columns. In addition, reinforcing bars are extended into adjoining members. Like all cast-in-place systems, this clearly illustrates the monolithic nature of reinforced concrete structural members.

A standard one-way joist system is depicted in Fig. 2. The one-way slab transfers the load to the joists, which transfer the loads to the column-line beams (or, girders). This system utilizes standard forms where the clear spacing between the ribs is 30 in. or less. Because of its relatively heavy weight and associated costs, this system is not used as often as it was in the past.

FIGURE 3 Wide module joist system.
FIGURE 3 Wide module joist system.
Similar to the standard one-way joist system is the wide-module joist system shown in Fig. 3. The clear spacing of the ribs is typically 53 or 66 in., which, according to the Code, technically makes these members beams instead of joists. Load transfer follows the same path as that of the standard joist system.

Reinforced concrete stairs are needed as a means of egress in buildings regardless of the number of elevators that are provided. Many different types of stairs are available, and the type of stair utilized generally depends on architectural requirements. Stair systems are typically designed as one-way systems.

Two-Way Systems

As the name suggests, two-way floor and roof systems transfer the supported loads in two directions. Flexural reinforcement must be provided in both directions.

FIGURE 4 Two-way beam supported slab system.
FIGURE 4 Two-way beam supported slab system.
A two-way beam supported slab system is illustrated in Fig. 4. The slab transfers the load in two orthogonal directions to the column-line beams, which, in turn, transfer the loads to the columns. Like a standard one-way joist system, this system is not utilized as often as it once was because of cost.

A flat plate system is shown in Fig. 5. This popular system, which is frequently used in residential buildings, consists of a slab supported by columns. The formwork that is required is the simplest of all floor and roof systems. Because the underside of the slab is flat, it is commonly used as the ceiling of the space below; this results in significant cost savings.

FIGURE 5 Flat plate system.
FIGURE 5 Flat plate system.

Similar to the flat plate system is the flat slab system (Fig. 6). Drop panels are provided around the columns to increase moment and shear capacity of the slab. They also help to decrease slab deflection. Column capitals or brackets are sometimes provided at the top of columns.

The two-way system depicted in Fig. 7 is referred to as a two-way joist system or a waffle slab system. This system consists of rows of concrete joists at right angles to each other, which are formed by standard metal domes. Solid concrete heads are provided at the columns for shear strength. Such systems provide a viable solution in cases where heavy loads need to be supported on long spans.
FIGURE 6 Flat slab system.
FIGURE 6 Flat slab system.

FIGURE 7 Two way joist system.
FIGURE 7 Two way joist system.

Since the start of the formal approaches and procedures for carrying out the structural design, there have been many developments in the underlying principles and the implicit and explicit design objectives. Starting with putting limits in the allowable (working) stresses in various materials to achieve indirect safety factors, the design process slowly evolved within last few decades to more explicit consideration of different load and capacity factors. The recognition of the difference between brittle and ductile failure, and the introduction of capacity-based design approaches, led to the more comprehensive performance design using high level of analysis sophistication, and more explicit linkage between demand and performance. The most recent emphasis is on risk-based design, and a more integrated and holistic approach within the framework of consequence-based engineering. This section discusses a brief account of the progression of these design approaches and their impact on the cost, performance, and the final objective of public safety.

Structural Design Objectives and Philosophy - A Historical Overview
Structural design is the process of proportioning the structure to safely resist the applied forces and load effects in the most resource-effective and friendly manner. The term “friendly” refers to the aspect of design dealing with environmental friendliness, sustainability, ease of construction, and usability that are not explicit part of the strength consideration. Resources refer to the use of material, labor, time, and other consumables that are used to construct and maintain the structure. Ideally, the role of structural design is straight forward. It is the transformation of the effects of various environmental and man-made actions (including constraints on materials, dimensions and cost etc.) into the appropriate material specifications, structural member sizes, and arrangements (Fig. 1).
The Design Objectives and Philosophy - A Historical Overview
Figure 1 The conceptual role of structural design.
The basic objective is to produce a structure capable of resisting all applied loads without failure and excessive deformations during its anticipated life. The very first output of any engineering design process is a description of what is to be manufactured or built, what materials are to be used, what construction techniques are to be employed, and an account of all necessary specifications as well as dimensions (which are usually presented in the form of drawings). The second output is a rational justification or explanation of the design proposal developed based on either full-scale tests, experiments on small physical models, or the mathematical solution of detailed analytical models representing the behavior of real structures.

The process of structural design has passed through a long and still continuous phase of improvements, modifications, and breakthroughs in its various research areas. The structural analysis and design philosophies for new and existing buildings have a fascinating history. Perhaps, the first ever achievement in the history of structural design was the “confidence” by virtue of which early builders were able to convince themselves that the resulting structure could, indeed, be built and perform the intended function for the entirety of its intended life. Hence, the job of the very first engineers can be thought of as “to create the confidence to start building”. Over the course of the history, various scientists, mathematicians, and natural philosophers presented revolutionary ideas which resulted in improved understanding of structures and built environment. With the developments in different areas of practical sciences, the task of building design was gradually divided among more and more professionals depending upon aesthetic considerations, intended functions, materials, optimum utilization of space, lighting, ventilation, and acoustic preferences. The visual appearance, sense of space, and function (or the architecture) became a distinct concern during the 15th and 16th centuries. About a century later, designers first began to think about the load bearing aspects of structures in terms of self-weight and other sources of expected loading. Thinking separately about the role of individual materials and resulting structures grew during the late 17th and 18th centuries following Galileo’s work. The idea that the aesthetics should be given proper importance independent of the materials and load-bearing characteristics of the structure prevailed during the late 19th and the early 20th centuries.

Table 1 presents a brief timeline of some of the major developments which led to modern techniques and methodologies for analyzing and designing structures.

Table 1 Important Historical Developments Related to Structural Analysis and Design
Year (CE)
1452 - 1519
Earliest contributions from Leonardo da Vinci
Galileo Galilei examined the failure of simple structures and published his book “Two New Sciences”
Robert Hooke presented the Hooke’s law which is the basis for elastic structural analysis
Isaac Newton published his document “Principia Mathematica” containing the famous Newton’s laws of motion
Leonhard Euler and Daniel Bernoulli developed Euler_Bernoulli beam theory
Daniel Bernoulli introduced the principle of virtual work
Leonhard Euler developed the theory of buckling of columns
Claude-Louis Navier published a document analyzing the elastic behavior of structures
Carlo Alberto Castigliano presented his theorem for computing displacement as partial derivative of the strain energy
Otto Mohr formalized the idea of a statically indeterminate structures
Timoshenko corrects the Euler_Bernoulli beam equation and presented “Timoshenko’s Beam Theory”
Hardy Cross developed the moment distribution method, an important innovation in the analysis and design of continuous frames
Alexander Hrennikoff solved the discretization of plane elasticity problems using the lattice framework
R. Courant presented solution of problems by dividing a domain into finite subregions
J. Turner, R. W. Clough, H. C. Martin, and L. J. Topp introduces the term “finite element method” and published work which is widely recognized as the first comprehensive treatment of the method

It is worth noting that historically an understanding of how structures work was never a phenomenon that required detailed knowledge of mathematical procedures and laws of mechanics. A common misconception is that various new structural forms and shapes were first devised by mathematicians (and experts of geometry) and later taken up by builders and engineers. In fact, the opposite is true, with perhaps just one exception, i.e., the hyperbolic paraboloid (whose structural properties were discovered in 1930s). In the last few centuries, artists, sculptors, and builders have displayed a remarkable understanding and skill of converting materials into structures (some of which are still standing today remarking the testimony of their expertise).

The word structure (pronounced as “strək(t)SHər”) is a noun as well as a verb. As a noun, it means “the arrangement of and the relations between parts or elements of something complex,” and as a verb it refers to the process to “construct or arrange according to a plan; give a pattern or organization.” This term is used extensively in literature, and many disciplines signify these properties and processes.

When applied to the physical and built environment, the term “structure” means an assemblage of physical components and elements, each of which could further be a structure in itself, signifying the complexity of the system. The discipline of “Structural Engineering” refers to the verb part of the definition, dealing with the ways to arrange and size a system of components for construction according to a plan and serving the intended purpose. The primary purpose of any structure is to provide a stable, safe, and durable system that supports the desired function within the physical environment, of which the structure is a part of. The role of the structural engineer, therefore, is to “conceive, analyze, and design” the structure to serve its purpose.

An Overview of Structural TypesThere is hardly any aspect of our built environment or human activity that does not rely on physical structures. Buildings that provide useful places to live and work, bridges that provide us means to move across obstacles, factories that are needed to manufacture almost everything we need, dams to store water to generate power and irrigate lands, transmission towers to distribute electricity; all require structures to function, and structural engineers to design such structures. The role and importance of structural engineering and structural engineers is often underestimated and misunderstood. While a well-conceived and well-designed structure is the backbone of our built environment, a poorly conceived, designed, or constructed structure poses a serious hazard to the safety and well being of people and property. Collapse or failure of structures can claim a large number of lives and result in extensive economic loss. The role of structural engineers is, therefore, critical for overall economic development as well as for improving the community resilience to disasters.

The physical structure, or structure for brevity, can be assembled in infinite ways using very few basic element types or forms, some of which are shown in Fig. 1.1. As is evident, these are derived from or are consistent with basic geometric primitives such as line, curve, plane, surface, and solid. This compatibility can often be used to blend the form, function, and structure.
The basic member types and forms that can be used to create structural systems.
Figure 1.1 The basic member types and forms that can be used to create structural systems.
The assemblage of these components can be of many types and configurations. Some are made entirely of the skeleton-type members, some from surface-type members, and some from solid-type members, but most structures are a combination of more than one member type. Based on the member types, the structures can be broadly categorized as
  • cable structures
  • skeletal structural
  • spatial structures
  • solid structures, and
  • a combination of the aforementioned categories.
Cable Structures: Using Cables as the Main Member Type

These structures primarily transfer forces and internal actions through tension in individual cables or a set of cables. The shapes or geometry of cable profile often govern the behavior. Examples of such structures are:
  • Cable nets and fabric structures
  • Cable stayed structures
  • Cable suspended structures
Skeletal Structures: Using Beam-Type Members

These structures are composed of bar members that mainly resist the loads and forces through a combination of tension, compression, bending, shear, torsion, and warping. Such skeletal members are often called ties, struts, beams, columns, and girders. Typical application of skeletal structures can be found in the following:
Spatial Structures: Using the Membrane/Plate/Shell-Type Members

These are structures created by spatial or surface type of elements and they transfer loads through a combination of bending, compression, torsion, and in-plane and out-of-plane shear of the element surface. The cross-sections of such members are generally rectangular. Examples of such structures include:
  • General shell structures
  • Dome-type structures
  • Slab, wall structures
  • Silos, chimneys, and stacks
  • Box girder bridges
Sometimes, surface members and structures can be created by using a large number of skeletal members, covered by a skin or cladding, combining the fabric, cable, and bars to create surfaces.

Solid Structures: Using the Solid-Type Members

These structures comprise of solid bodies or members in which the forces or loads are transferred through the member bodies. Such members or structures do not have a cross-section in the conventional sense. Some of the structures are:
  • Dams, thick arches, thick tunnels
  • Pile caps, thick footings, thick slabs, pier heads, large joints, etc.
Mixed Structures: Using One or More of the Basic Element Types

Most often, the real structures are composed of one or more types of basic elements. For example, a typical building is made of columns and beams (skeletal), slabs and walls (shell), footings (solid) structures, etc.

There are several other types of structures that are either a combination of the basic forms or especially developed for a particular application or usage. These include stressed ribbon bridges, fabric structures, skeleton spiral structures, floating offshore structures, pneumatically inflated structures etc.

The slabs-on-ground does not require high protection against water penetration and moisture in arid regions that does not have soils or have any sort of drainage problems.

This precaution is not necessary if the area does not have irrigation activities going on nearby. This is the case unless the building code of that regions requires treatment.

But for all site conditions other than mentioned above, it is essential to have water proofing or damp proofing for the slabs constructed on grounds.

As per ACI 302.IR-89, there is no need for damp proofing or water proofing nor vapor retarders on sites that are well drained or those sites under the following conditions:
  1. The site has water table level very low from the ground surface
  2. A substratum of coarse aggregate that is freely draining is installed
  3. A floor covering is provided to the slab that is not affected by the moisture.

Damp Proofing of Slabs–on–Ground

The damp proofing of slabs constructed on ground can be done either below or above the surface. Mostly, the damp proofing is installed below the surface of the slab. Mostly plastic film of vapor retarders is employed below the slab surface as a damp proofing membrane.

The figure-1 below shows the installation of a vapor retarder over the surface of gravel substrate. The vapor retarders are sealed to the foundation wall as shown. This will provide continuity in the placement.

In order to avoid the penetration of sheet, brick chairs are employed other than the wire chairs.

Tamped grave substrate_
Fig.1. The plastic vapor retarders are placed above the grave substrate that is tamped.
When wood flooring has to be provided above the slabs on ground, the damp proofing is done over the surface of the floor. The damp proofing over the slab top surface is permitted only under the following conditions, when:
  1. The water table is at least 12 inches below the slab surface
  2. Installation of footing drains is carried out
The slabs-on ground with wooden flooring on the top will ask for damp proofing unless the above conditions are satisfied.

The figure-2 below shows the installation of wooden flooring over the slabs that are constructed on ground.

The wood flooring span sleepers will separate the surface from the bottom slab as shown in figure-2. The damp proofing can be applied to the slab only under the sub soil conditions mentioned above.

Wooden Flooring Above
Fig.2.Wooden Flooring Above Slabs-on-Ground

In the figure-2, an air space is created between the wooden flooring and the slabs constructed. This must be vented at the junctions so that the water penetration due to water vapor migration is avoided. This will help in maintaining an equal relative humidity both above and below the surface of the wooden flooring provided.

The top surface damp proofing of the slabs constructed on ground will be interrupted by the partitions and the columns present. Vapor retarders constructed will be interrupted by these extra elements bringing a loss of integrity of the damp proofing system.

The figure -3 below shows the same. Under such situations, the best alternative is to have damp proofing or water proofing under the slab.

The column interrupting the vapor retarder placed above a
Fig.3. The column interrupting the vapor retarder placed above a slab-on-ground

Risk in Using Vapor Retarders as a Waterproofing Solution

The substitution of vapor retarders instead of water proofing will welcome risks. The performance of the vapor retarder is dependent on the integrity of the film as well as the way it is seamed. The maintenance of a vapor retarder seam integrity in field condition is very difficult to attain in a slab on ground construction.

The use of wooden or vinyl coverings too make the vapor retarders into risk. Other risk parameters are the use of wall – sensitive adhesives. Under these situations, it is most preferred to have a heavy-duty panel or water proofing to be installed than waiting for the loss caused by the complete replacement of moisture damaged floor.

As shown in figure-2, the attachment of sleepers to the slabs-on-ground must be carried out with the help of water resistant adhesives instead of mechanical anchors.

The use of nails and other mechanical anchors will result in puncture of vapor retarders that is located on the top surface of the slab.

Considerations in Damp Proofing Slabs on Ground

When the top surface of the slab is subjected to damp proofing, the slab should have a substratum that is of a granular material. This layer of properly graded aggregate will help in preventing the rise of moisture (mainly by the principle of capillary action).

It is advised not to have a vapor retarder below the slab surface by using suspenders and other belts along with having a top surface damp proofing. The residual moisture in the concrete slabs can result in vapor pressure that can disband the vapor retarder and result in rupture.

It is not appropriate to have too many floor finishes and coatings. This is because the concrete is moisture sensitive. Moisture sensitive adhesives can be used as a mode of moisture resistance.

Liquid applied coatings in concrete slabs on ground have resulted in moisture in concrete. The following conditions can result in high level moisture contents:
  1. For those slabs that are cast on a grade with no proper functioning of the under-slab vapor retarders.
  2. Conditions when the suspended slabs are cast over the non – vented steel formworks.
  3. The conditions where the suspended slabs are constructed over the occupancies that possess higher relative humidity. These includes elements like commercial kitchen and swimming pools.
  4. The installation of suspended slabs over the crawl spaces that are unvented.
  5. The slabs with lightweight aggregates.
  6. The slabs that used a water cement ration in excess of 0.55 (w/c = 0.55).
  7. The slabs that cured in a period less than 90 day.
The manufactures of the floor finishes or damp proofing coatings highly follow the requirement of testing the concrete slab before the installation of any membranes. This testing will ensure that the moisture content in the slab is within the susceptible limits and won’t result in any failure.

The Calcium Chloride Test as specified by ASTM F1869 is used to determine the Moisture Emission Rate (MVER). This is measured in pounds per thousand square feet within 24 hours. The accepted range of MVER is three to five pounds.

The internal relative humidity in the structure is obtained by means of a hygrometer by placing probes in concrete. This is as per ASTM F710 and the established rate is 75 percent.

This result can be achieved within 1 month of drying time per inch of the concrete element tested. It recommends the installation of vapor retarders in the direction of concrete pouring.

This brief article explains the work flow procedure for site engineeers to execute steel sheet piling works. The procedure details various steps and checks that are recommended to be followed for such activities.

Method and safety

• Piling contractors must be requested to provide a written method statement as appropriate for the piling operations. Find out what induction training and information specific to a method statement is provided by immediate site supervisors to piling operatives.
Steel Sheet Piling Works - Workflow Procedure for Site Engineers

• Note that cranes must be selected and used in accordance with CP3010 and with the Construction (Lifting Operations) Regulations 1998. A firm level base of adequate bearing value must be provided, or crane mats used.

• Check that cores of pendant/bridle ropes are not fractured.

• Any crane used for raising or lowering operatives must be fitted with a dead man’s handle and the descent must be effectively controlled; the latter may be achieved by power lowering. Properly constructed man-carrying cages, which are unable to spin or tip, must be used. The cages should be regularly and carefully inspected.

• All lifting appliances and gear must carry appropriate certificates of test and examination, and must be adequate for the job, paying particular attention to the risk of damage to gear by sharp edges.

• All personnel working on piling operations must wear safety helmets (helmets appropriate for piling work are now available with retaining strap and smaller peaks). Ear and eye protection should be provided.

• Piling machine operators must be at least 18 years of age, trained, competent, medically fit and authorised by site management to operate the machine.

• When piling from a pontoon or adjacent to water, personnel must wear life jackets. Rescue equipment (e.g. a safety boat and lifebuoys with lifelines attached) must be kept ready for immediate use and enough operatives must know how to use it.

Materials handling

• When splitting bundles of sheet piles, use chocks. If large quantities of piles are handled, the use of purpose-made strops and grips is advised.

• Piles should not be stacked too high or in a cantilever position. Use spacers and chocks where necessary. Tubular piles should not be stacked more than four high and should be properly chocked.

• When lifting piles or piling hammers, use hand lines to control the load. Give due consideration to wind speed during the operation.

• Check the dimensions and alignment of clutches. If necessary perform trial clutching of piles. This is advisable for Z-shaped pile sections where the clutch is less positive than on trough sections (e.g. Larssen piles).

Gate systems

See Fig 1.
Gate system using concrete bases (showing piling, the use of hanger brackets and the provision of a safety walkway).
Figure 1. Gate system using concrete bases (showing piling, the use of hanger brackets and the provision of a safety walkway).
• Positioning (pitching) and driving sheet piling is usually done by using a temporary supporting structure (gate). This is made up of heavy steel or timber H-frames supporting horizontal-heavy H-beam guides. The H-frames can be supported on heavy steel spreaders or specially cast concrete blocks. Ensure an adequate foundation under these frames and bases to prevent subsidence and overturning during piling operations. This is particularly applicable during work in rivers, etc.

• If using concrete blocks ensure that they are suitably reinforced to withstand loads from lifting and shock loading. Vertical steel columns should have a good bottom fixing. Vertical timber should not be cast into the block but should be wedged and bolted. Where doubt exists over stability use guy lines or raking steel props.

• All horizontal gates with platforms over 2m high, or over any potentially dangerous areas, must be provided with adequate guardrails, toeboards and correct ladder access.

• Ladders must be secured and extend at least lm above staging.

• If using a cantilever system, use a tie-back where possible, as well as kentledge to provide safe anchorage.

• When piling is progressing and temporary piles are used to support the gate system, use purpose-made brackets and bolt them to the piles. Any welding necessary should be carried out by competent welders.

Pitching piles

• If shackle holes have to be burned in the pile, remove sharp burrs to prevent damage to shackle pins.

• Use quick-release shackles wherever possible:

– the sheet pile must not be lifted vertically without first checking that the pin is properly engaged through the sheet
– do not use a pull rope less than 5mm diameter
– the length of rope used must be less than the length of the pile, to prevent the extra rope snagging and pulling the release for the shackle
– secure the rope around the sheet pile to prevent snagging
– if a special lifting eye is to be welded to the pile for angled pitching, the weld should have a factor of safety of at least 2.

• Pitch long sheet piles with a pile threader, following the manufacturer’s guidance for use. Where this is not possible, use a pile pitching cage. The cage is normally hung from an adjacent pile, the operatives wearing safety harnesses hooked to the adjacent pile before the crane hook is removed from the cage.

• When feeding sheet piles through the top and bottom gates, use wood blocks or a bent bar. Never use a straight pinch bar, as fingers can easily be trapped. Use a spacer block between the guides to keep the leading free clutch in its correct alignment.

• Where access and work is carried out from ladders:

– Clutching: the ladder must be placed in the valley of a previously placed pile; the ladder must be footed and when at the top of the ladder both hands are required for clutching, a safety belt must be worn and secured to the pile using a manlock.

– Wedging: the ladder must be placed against the H-beam and footed wedges should be pre-placed on the beam. A 4 lb. lump hammer must be used as this can be swung with one hand but if two hands are required, a safety belt must be used with the lanyard wrapped around the H-beam or used with a manlock.

Note: At all times safety helmets and footware must be worn. When working at height the helmet should be secured with retaining strap.

• Changes in work method:

– The work method must not be changed without consultation of the senior site representative responsible for the piling operation.
– If windy conditions (e.g. over 30 mph gusts) make the handling of the sheet piles difficult, stop work until the senior site representative responsible for the piling operation has been consulted and a safe method of continuing the work has been devised.

A shallow foundation is often selected when the structural load will not cause excessive settlement of the underlying soil layers.

Shallow Foundations - An Overview

In general, shallow foundations are more economical to construct than deep foundations. Common types of shallow foundations are listed in Table 1 and described later:

Table 1. Types of shallow foundations

Category Common Types Comments
Shallow foundations Spread footings Spread footings (also called pad footings) are often square in plan view, are of uniform reinforced concrete thickness,
and are used to support a single column load located directly in the center of the footing.
Strip footings Strip footings (also called wall footings) are often used for load-bearing walls. They are usually long reinforced concrete
members of uniform width and shallow depth.
Combined footings Reinforced-concrete combined footings are often rectangular or trapezoidal in plan view, and carry more than one column load.
Conventional slab-on-grade A continuous reinforced-concrete foundation consisting of bearing wall footings and a slab-on-grade.
Concrete reinforcement often consists of steel rebar in the footings and wire mesh in the concrete slab.
Posttensioned slab-on-grade A continuous posttensioned concrete foundation. The posttensioning effect is created by tensioning steel tendons or cables
embedded within the concrete. Common posttensioned foundations are the ribbed foundation, California slab, and PTI foundation.
Raised wood floor Perimeter footings that support wood beams and a floor system. Interior support is provided by pad or strip footings. There is a
crawl space below the wood floor.
Mat foundation A large and thick reinforced-concrete foundation, often of uniform thickness, that is continuous and supports the entire structure.
A mat foundation is considered to be a shallow foundation if it is constructed at or near ground surface.

1. Spread Footings, Combined Footings, and Strip Footings

These types of shallow foundations are probably the most common types of building foundations. Figure 1 shows various types of shallow foundations.

Figure 1. Examples of shallow foundations. (a) Combined footing; (b) combined trapezoidal footing; (c) cantilever or strap footing; (d) octagonal footing; (e) eccentric loaded footing with resultant coincident with area so soil pressure is uniform. (Reproduced from Bowles, 1982; McGraw-Hill, Inc.)
Figure 1. Examples of shallow foundations. (a) Combined footing; (b) combined trapezoidal footing; (c) cantilever or strap footing; (d) octagonal footing; (e) eccentric loaded footing with resultant coincident with area so soil pressure is uniform. (Reproduced from Bowles, 1982; McGraw-Hill, Inc.)

2. Mat Foundation

Figure 2 shows various types of mat foundations. Based on economic considerations, mat foundations are often constructed for the following reasons (NAVFAC DM-7.2, 1982):

Figure 2. Examples of mat foundations. (a) Flat plate; (b) plate thickened under columns; (c) beam-and-slab; (d) plate with pedestals; (e) basement walls as part of mat. (Reproduced from Bowles, 1982; McGraw-Hill, Inc.)
Figure 2. Examples of mat foundations. (a) Flat plate; (b) plate thickened under columns; (c) beam-and-slab; (d) plate with pedestals; (e) basement walls as part of mat. (Reproduced from Bowles, 1982; McGraw-Hill, Inc.)
i. Large individual footings. A mat foundation is often constructed when the sum of individual footing areas exceeds about one-half of the total foundation area.

ii. Cavities or compressible lenses. A mat foundation can be used when the subsurface exploration indicates that there will be unequal settlement caused by small cavities or compressible lenses below the foundation. A mat foundation would tend to span over the small cavities or weak lenses and create a more uniform settlement condition.

iii. Shallow settlements. A mat foundation can be recommended when shallow settlements predominate and the mat foundation would minimize differential settlements.

iv. Unequal distribution of loads. For some structures, there can be a large difference in building loads acting on different areas of the foundation. Conventional spread footings could be subjected to excessive differential settlement, but a mat foundation would tend to distribute the unequal building loads and reduce the differential settlements.

v. Hydrostatic uplift. When the foundation will be subjected to hydrostatic uplift due to a high groundwater table, a mat foundation could be used to resist the uplift forces.

3. Posttensioned Slab-on-Grade

Posttensioned slab-on-grade is common in southern California and other parts of the United States. The most common uses of posttensioned slab-on-grade are to resist expansive soil forces or when the projected differential settlement exceeds the tolerable value for a conventional (lightly reinforced) slab-on-grade. For example, posttensioned slabs-on-grade are frequently recommended if the projected differential settlement is expected to exceed 0.75 in. (2 cm).

The Post-Tensioning Institute (1996) has prepared installation and field inspection procedures for posttensioned slab-on-grade. Posttensioned slab-on-grade consists of concrete with embedded steel tendons that are encased in thick plastic sheaths. The plastic sheath prevents the tendon from coming in contact with the concrete and permits the tendon to slide within the hardened concrete during the tensioning operations. Usually tendons have a dead end (anchoring plate) in the perimeter (edge) beam and a stressing end at the opposite perimeter beam to enable the tendons to be stressed from one end. However, it is often recommend that the tendons in excess of 100 ft (30 m) b stressed from both ends.

Because posttensioned slab-on-grade perform better (i.e., less shrinkage related concrete cracking) than conventional slab-on-grade, they are more popular even for situations where low levels of settlement are expected. Posttensioned slab-on-grade has become common for situations where it is desirable to limit the amount and width of concrete shrinkage cracks.

4. Shallow Foundation Alternatives

If the expected settlement for a proposed shallow foundation is too large, then other options for foundation support or soil stabilization must be evaluated. Some commonly used alternatives are as follows:

i. Grading. Grading operations can be used to remove the compressible soil layer and replace it with structural fill. Usually the grading option is only economical if the compressible soil layer is near the ground surface and the groundwater table is below the compressible soil layer or the groundwater table can be economically lowered.

ii. Surcharge. If the site contains an underlying compressible cohesive soil layer, the site can be surcharged with a fill layer placed at the ground surface. Vertical drains (such as wick drains or sand drains) can be installed in the compressible soil layer to reduce the drainage paths and speedup the consolidation process. Once the compressible cohesive soil layer has had sufficient consolidation, the fill surcharge layer is removed and the building is constructed.

iii. Densification of soil. There are many different methods that can be used to densify loose or soft soil. For example, vibro-flotation and dynamic compaction are often effective at increasing the density of loose sand deposits. Another option is compaction grouting, which consists of intruding a mass of very thick consistency grout into the soil, which both displaces and compacts the loose soil.

iv. Floating foundation. A floating foundation is a special type of deep foundation where the weight of the structure is balanced by the removal of soil and construction of an underground basement.

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