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Equipment Foundation Design

• satyendra
• October 25, 2023
• 11 Comments
• Dead load, Dynamic load, Equipment foundation, Live load, Seismic load, Soil, Static load, Thermal load, Vibration isolation, Wind load,

Equipment Foundation Design

Heavy equipments with reciprocating, impacting, or rotating masses needs a support system which can resist dynamic forces and the resulting vibrations. When excessive, such vibrations can be detrimental to the equipments, its support system, and any operating personnel subjected to them. The super-structure of vibrating and rotating equipments is known as equipment foundation. It essentially consists of a mass of reinforced concrete. Design of equipment foundation involves consideration of static and dynamic loads.

The type, configuration, and installation of a foundation or support structure for dynamic equipment can depend on (i) site conditions such as soil characteristics, topography, seismicity, climate, and other effects, (ii) equipment base configuration such as frame size, cylinder supports, pulsation bottles, drive mechanisms, and exhaust ducts etc. (iii) process needs such as elevation requirements with respect to connected process equipment and hold-down requirements for piping, (iv) anticipated loads such as the equipment static weight, and loads developed during erection, start-up, operation, shut-down, and maintenance, (v) erection needs such as limitations or constraints imposed by construction equipment, procedures, techniques, or the sequence of erection, (vi) operational needs such as accessibility, settlement limitations, temperature effects, and drainage, (vii) maintenance needs such as temporary access, lay-down space, in-plant crane capabilities, and equipment removal considerations, (viii) regulatory factors or building code provisions such as tied pile caps in seismic zones, (ix) economic factors such as capital cost, useful or anticipated life, and replacement or repair cost, (x) environmental needs such as secondary containment or special concrete coating requirements, and (xi) recognition that certain equipments, particularly big reciprocating compressors, rely on the foundation to add strength and stiffness which is not inherent in the structure of the equipment.

While designing foundations for the equipments, there is normally a question about taking into account dynamic loads, which directly affect the calculation and the design. It also raises the question of choosing the right constructive solution to the foundation in which it works under the influence of a dynamic load so that it does not have undesirable phenomena associated with the vibrations.

When designing a foundation for equipments, the designation of its dimensions, the choice of concrete and reinforcement need careful attention. The design engineers are always to solve the problem in complex situations. They not only have to carry out the calculations, but also, on the basis of a dynamic calculation, give an accurate forecast of the expected level of fluctuations of the foundation. They are required to ensure that the oscillations are permissible and do not exceed certain limits. The amplitude of vibration of the equipment at its operating frequency is the most important parameter to be determined in designing the equipment foundation, in addition to the natural frequency of the equipment foundation soil system.

In the past, simple methods of calculation were used very frequently involving the multiplication of static loads by an estimated dynamic factor, the result being treated as an increased static load without any knowledge of the actual safety factor. Because of this uncertainty, the value of the adopted dynamic factor was normally very high, although practice had shown that during operation harmful deformations did result in spite of using such excessive factors. This necessitated a deeper study of dynamic loading.

The development of equipments of higher capacities has given rise to considerably higher stresses thereby posing problems with respect to performance and safety. This has called for development partly in the field of vibration technique and partly in that of soil mechanics. Hence new theoretical procedures have been developed for calculating the dynamic response of foundations. It is well established that the cost of foundations is but a small fraction of that of the equipments and inadequately constructed foundations can result in failures and shutdowns exceeding several times the cost of the capital investment needed for properly designed and built foundations.

Based on the scientific investigations carried out in the last few decades, it has been established that it is not enough to base the design only on vertical loads multiplied by a dynamic factor, even if this factor introduces a dynamic load several times higher than original one. It is to be noted that operation of the equipments generates not only vertical forces, but also forces acting perpendicular to the axis, hence it is not enough to take into account the vertical load and to multiply it by a selected dynamic factor.

It has also been found that the suitability of equipment foundations depends not only on the forces to which they are going to be subjected to, but also on their behaviour when exposed to dynamic loads which depends on the speed on the equipment and natural frequency of the foundation. Hence, a vibration analysis become necessary. In other words, it can be said that each and every equipment foundation does need detailed vibration analysis providing insight in to the dynamic behaviour of foundation and its components for satisfactory performance of the equipment.

The dynamics of equipment-foundation system is an involved task in itself and consideration of earthquake effects further add to its complexity. The complete knowledge of load transfer mechanism from the equipment to the foundation and also the complete knowledge of excitation forces and associated frequencies are necessary for correct evaluation of equipment performance. The performance, safety, and stability of equipments depend largely on their design, manufacturing, and inter-action with environment. In principle, equipment foundations are to be designed such that the dynamic forces of equipments are transmitted to the soil through the foundation in such a way that all kinds of harmful effects are eliminated. Hence, all equipment foundations, irrespective of size and type of equipment, are to be regarded as engineering issue and their design are to be based on sound engineering practices.

The dynamic loads from the equipments causing vibrations are to be duly accounted for to provide a solution, which is a technically sound and economically sound. For a technically correct and economical solution, a close co-operation between manufacturer and the foundation design engineer is necessary.

Vibrational issues have been drawing attention of engineers, since decades, world over to find ways and means to have desired satisfactory performance of the equipments and to minimize failures. In the past, needed importance has not been given to the equipment foundation design. Simple methods of calculation have been used for strength design of the foundation by multiplying static loads with an estimated dynamic factor. This has resulted in consideration of increased static loads without any knowledge of actual safety factor. Even with these so-called excessive loads, harmful effects have been observed during operation. Based on a number of studies carried out in the last few decades, it has been established that it is not enough to base the design on vertical loads only, multiplied by an arbitrary dynamic factor.

Improvement in manufacturing technology has provided equipments of higher ratings with better tolerances and controlled behaviour. The increased dependence of the production plants on equipments provides no room for failure and demands equipment and systems with higher performance reliability. All the issues cannot be solved theoretically since a good quantity of assumptions are to be made for the analysis and these assumptions need validation through experiments. Laboratory and field measurements are hence introduced to determine carefully the effects of different parameters on the dynamic response of equipment foundation. Hence, a detailed vibration analysis becomes necessary. It is also realized that a careful dynamic investigation of soil properties is necessary as the elastic properties of the soil exercise considerable influence on the design of the foundation.

It is obvious that the cost of equipment foundation is a small fraction of that of the equipment and inadequately constructed foundations can result in failures and shutdowns whose cost itself can exceed several times the cost of the properly designed and built foundations. Though, advanced computational tools are available for precise evaluation of dynamic characteristics of the equipment foundation system, their use in design office, which has been limited in the past, has now been found to be quite common.

The equipment foundation system can be modelled either as a two-dimensional (2-D) structure or three-dimensional (3-D) structure. For mathematical modelling and analysis, valid assumptions are made keeping in view that the (i) the mathematical model is to be compatible to the prototype structure within a reasonable degree of accuracy, (ii) the mathematical model is to be such that it can be analyzed with the available mathematical tools, and (iii) the influence of each assumption is to be quantitatively known with regard to the response of the foundation.

Vibration isolation techniques have also been used to reduce vibrations in the equipments. Isolation leads to reduction in the transmissibility of the exciting forces from the equipment to the foundation and vice-versa. Uses of vibration isolation devices is one of the methods by which one can achieve satisfactory performance which in turn can result in minimizing failures and reduce downtime on account of high vibrations. However, for equipment on elevated foundations, it is desirable to have support structure stiffness sufficiently higher than overall stiffness of isolation system in order to get the desired isolation efficiency.

The support structure, a 3-D elevated structural system, possesses several natural frequencies. The vibration isolation system, comprising of equipment, inertia block, and the isolation devices, also has six modes of vibration having specific stiffness values corresponding to each mode of vibration. Hence the comparison between stiffness of structure and isolator becomes complex task. It is of interest to note that lateral stiffness of elevated structures is very much lower than its vertical stiffness. If this lower, (lateral) stiffness is comparable to the stiffness of isolators, it certainly affects the overall stiffness and hence the response of the equipment foundation system. Hence, lateral stiffness of support structure is also to be computed and considered while selecting the isolators. Finally, it is desirable to carry out detailed dynamic analysis of the complete system including sub-structure.

Design philosophy – Equipment foundation system, in broader sense, comprises of equipment, supported by foundation resting over soil subjected to dynamic loads namely (i) generated by equipment itself, (ii) applied externally, or (iii) caused by external sources and transmitted through soil. A typical system is as shown in Fig 1.

Fig 1 Equipment foundation system qualification subjected to dynamic loads

Irrespective of the source of dynamic load, the basic philosophy underlying design of equipment foundation is that (i) the dynamic forces of the equipments are transmitted to the soil through the foundation in such a way that all kinds of harmful effects are eliminated and the amplitudes of vibration of the equipment as well as that of the foundation are well within the specified limits, (ii) foundation is structurally safe to withstand all static and dynamic forces generated by the equipment. For accomplishing these objectives, every foundation needs to be analyzed for dynamic response, and thereafter for strength design.

Equipment foundation system – In any equipment foundation system, the equipment is considered supported by a foundation and the foundation in turn rests on the soil. By design, the foundations for equipments can be block, wall, and box type. Block foundations are made in the form of blocks and slabs. The box foundations consist of rigid walls connecting the upper and lower plates. Wall foundations are formed by columns embedded in the lower slab, with the upper parts of the columns being joined by beams or slabs. From the point of view of the work of equipments, block and box foundations are the foundations of a rigid type, and the wall foundations are of an elastic type. A typical equipment foundation system is as shown in Fig 2a.

Fig 2 Examples of equipment foundation

It is necessary to address as to how the equipment, foundation, and soil are inter-connected. The alternatives are (i) equipment can either be connected to the foundation directly through the foundation bolts, or it can be connected through isolation devices, (ii) the foundation can either be a solid block resting directly on the soil or it can be resting on the piles, and (iii) the foundation can also be a frame structure (frame foundation) resting directly on the soil or it can be resting on the group of piles. These interfaces, hence, are necessary to be appropriately addressed, for evaluating the dynamic response of the equipment correctly. Hence, the three main constituents of equipment foundation system which play important role in overall controlling equipment performance are (i) equipment, (ii) foundation, and (iii) soil and these need to be adequately addressed.

Equipments – Equipment type and its characteristics play an important role while selecting the type of foundation. When designing foundations for equipment, the primary issue is the need to take into account the calculations of dynamic loads. All equipments, without exception, transmit vibrations of varying intensity to the foundations, however, when some equipments operate, considerable inertia forces arise, while the operation of other equipments is characterized by a very small level of dynamic effects. In this regards, dynamic calculations of the foundations are to be made for the equipments.

Based on type of motion, the equipments are broadly classified as (i) rotary equipments, e.g., high-speed equipments like turbo-generators or rotary compressors, (ii) reciprocating equipments, e.g., the equipments which produce periodic unbalanced forces, such as steam engines, (iii) equipments having impact effects, i.e., those equipments which produce impact loads, e.g., forging hammers, and (iv) other equipments which generates dynamic loads such as ore crushers, and metal shredders etc. While part of the dynamic load from these types of equipment tends to be based on rotating imbalances, there is also a random character to the dynamic signal which varies with the particular operation.

Based on the speed of operation, the equipments are grouped as (i) very low speed equipments, speed range up to 100 revolutions per minute (rpm), (ii) low speed equipments, speed range from 100 rpm to 1,500 rpm. (iii) medium speed equipments, speed range from 1,500 rpm to 3,000 rpm, and (iv) high speed equipments, speed range of 3,000 rpm and above.

For foundation design, broadly, the informations which are needed are (i) geometric configuration of the equipment, (ii) loads from the equipment such as mass of the stationary as well as rotating parts of the equipment and load-transfer mechanism from the equipment to the foundation, (iii) critical equipment performance parameters such as critical speeds of rotors, balance grade, and acceptable levels of amplitudes of vibration, (iv) dynamic forces generated by the equipment i.e., forces generated under various operating conditions and their transfer mechanism to the foundation for dynamic response analysis, and (v) additional forces such as forces generated under emergency or faulted conditions, test condition, erection condition, and maintenance condition of the equipment, and forces because of the bearing failure (if applicable) for strength analysis of the foundation.

Equipment parameters – The equipment parameters needed in the analysis of the foundation are (i) static weight of equipment and accessories, (ii) characteristics of dynamic loads imposed by the equipment operation and their point of application, and (iii) rotation speed of the equipment. Normally, the weight of the equipment, centre of gravity (CG), surface areas, and operating speeds are readily available from the manufacturer of the equipment.

Foundations – Foundations of equipments can experience movements through a number of causes such as (i) elastic and inelastic compression of the sub-soil because of the weight of the equipment, (ii) ground water lowering, producing an increase in effective stress beneath the foundation, (iii) vibration because of the pile driving, or equipment vibrations etc. which is of particular importance in granular soils, (iv) seasonal swelling and shrinking of expansive clays, (v) adjacent excavation and construction which can cause movement of the foundations, and (vi) regional subsidence or movement.

The eccentricity of the foundation is important. If foundation eccentricity is higher than the permissible value, the vertical mode of vibration is no longer remain uncoupled from the lateral and rotational modes. It is undoubtedly easy to write equations of motion for such uncoupled modes, but getting closed-form solutions for those equations is not that simple, and computations can turn out to be complex. Further, getting transient response history can be a tedious task, though it is possible to evaluate transient response at any of the defined frequencies. It is hence desired to use finite element (FE) analysis, wherever feasible, in order to include all these aspects. Further, this gives improved reliability on account of lesser number of approximations / assumptions. This also permits visualization of animated mode shapes, and viewing of response amplitude build-up and stress concentration locations. Different types of equipment foundations, applications and design aspects are described below.

Block foundation is used for equipments of large mass and a small natural frequency. The ability to use block foundation mainly depends on the quality of near surface soils and designed as rigid structures. The dynamic response of a rigid block foundation depends only on the dynamic load, foundation’s mass, dimensions, and soil characteristics. Majority of the normally used foundations in the industry are block foundations (Fig 2b) and frame foundations (Fig 2c).

In case of a block foundation, equipment is mounted over a solid block, normally made of concrete. This block in turn rests directly on the soil. In this case, both the equipment and the foundation block are considered as non-elastic inertia bodies and the soil is treated as mass-less elastic media i.e., having only stiffness and no inertia.

In a frame foundation, equipment is supported on the deck slab. This deck slab in turn is supported on base raft through columns, and base raft rests directly over soil or on group of piles. Size of deck slab, number of columns, height of columns above base raft etc. are primarily dependent on equipment layout. In this case, equipment is treated as non-elastic inertia body whereas deck slab, and columns are considered as elastic inertia bodies and soil is considered as elastic media. In certain specific cases, base raft is also considered as elastic inertia body. .

Box equipment foundation is used in the cases of less mass with higher natural frequency equipments. Because of hollow concrete block as shown in the Fig 3a. The mass of this foundation is less than block type foundation as it is hollow. The natural frequency of the box type foundation is increased.

Spring mounted block foundation (Fig 3b) is used for high vibrating equipments and to isolate from thermal forces. Spring mounted block foundation comprises of vertical columns consisting a horizontal frame at their tops. The equipment is laid and supported within the frame. The foundation is very useful to isolate from thermal forces vibrations.

Combined block foundations (Fig 3c) are similar to simple block foundation. They are used to support closely spaced equipments. Combined blocks are more difficult to design because of the combination of forces from two or more equipments and because of a possible lack of stiffness of a larger foundation base raft.

Table-top foundation (Fig 3d) allows for ducts, piping, and ancillary items to be located below the equipment. Elevated support is common for large turbine-driven equipment such as electric generators. Table-top structures are considered to be flexible, hence their response to dynamic loads can be quite complex.

Table-top with isolator foundation (Fig 3e) is used for high vibrating equipments like pumps, blowers, and fans etc. Table-top structures are considered to be flexible, hence their response to dynamic loads can be quite complex. Springs and dampers located at the top of supporting columns are sometimes used to minimize the response to dynamic loading. The effectiveness of isolators depends on the equipment speed and frequency.

Inertia block in equipment foundation (Fig 3f) is used for small moving blocks, and equipments etc. In this situation, small dynamic equipments are normally designed with a supporting inertia block to alter natural frequencies away from equipment operating speeds and resist amplitudes by increasing the resisting inertia force.

Pile supported foundation (Fig 3g) is used in soft ground conditions and where excessive settlement can take place, e.g., drilled piers, auger cast piles, and driven piles. Any of the above-mentioned foundation types can be supported directly on soil or on piles. Piles use end bearing, frictional side adhesion, or a combination of both to transfer axial loads into the underlying soil.

Fig 3 Types of equipment foundations

Tuning of the foundation – Foundation, for which its vertical natural frequency is above the operating speed of the equipment, is termed as over-tuned foundation or high-tuned foundation and the foundation, for which its vertical natural frequency is below the operating speed of the equipment, is termed as under-tuned foundation or low-tuned foundation.

Foundation materials – Plain concrete, brick, reinforced cement concrete (RCC), pre-stressed concrete, and steel are the materials used for the construction of the equipment foundation. Foundations using steel structures have also been used for frame foundations. The sizes of structural members in steel foundations are less than those for RCC foundations and hence the space requirement is much less. As regards vibration, steel structures undoubtedly involve higher risk. Natural frequencies are low and the foundation is deeply under-tuned. The resistance to fire of a steel structure is lower than that of RCC structure. Majority of the high tuned foundations are built of reinforced concrete. Vibration amplitudes are reduced because of the relatively higher damping present in the concrete.

Foundation analysis and design – Every foundation is analyzed for its dynamic response and checked for strength and stability. Using the equipment, soil and foundation parameters, amplitudes of vibration are computed at the equipment as well as the foundation level. In addition, foundation is designed for its strength and stability to withstand applicable static and dynamic forces. For this, the dynamic forces of the equipment are translated into equivalent static forces on the foundation. Strength check of the foundation is also done for forces because of the environmental effects like wind and earthquake etc.

If the strength analysis indicates that there is a need for change in the foundation size, a recheck on the dynamic analysis with the revised foundation size is a necessity. Typical foundation parameters needed for design of equipment foundation system are (i) foundation geometry, (ii) material properties i.e., mass density, dynamic modulus of elasticity, Poisson’s ratio, and coefficient of thermal expansion etc., (iii) strength parameters i.e., yield strength (YS), ultimate tensile strength (UTS), allowable strength in compression, tension, bending, and shear etc.

Soil – Soil dynamics deals with engineering properties and behaviour of soil under dynamic stress. It is an established fact that the soil properties considerably influence the dynamic response of equipment foundation system. Identical equipments with identical foundations have been reported to behave differently in different soil conditions. For block foundation, the soil influence is predominant. The dynamic response largely depends upon mass of the equipment, mass of the block, the geometry of the block, and the soil dynamic properties. However, for frame foundations, it is normally reported that consideration of soil-structure interaction (i) induces additional modes pertaining to soil deformation with relatively low frequencies, and (ii) has a tendency to marginally improve structural frequencies.

The suitability of a given soil to support a dynamic equipment foundation is important. Issues can include excessive settlement caused by dynamic or static loads, liquefaction, dimensional stability of a cohesive soil, frost heave, or any other relevant soils concern.

In general, issues involving the dynamic properties of soils are divided into small and large strain amplitude responses. For equipment foundations, the amplitudes of dynamic motion, and hence the strains in the soil, are normally low (strains less than 0.001 %). A foundation which is subjected to an earthquake or blast loading is likely to undergo large deformations and, hence, induce large strains in the soil.

The key soil properties, Poisson’s ratio and dynamic shear modulus, can be considerably affected by water table variations. Prudence suggests that in determining these properties, such variations be considered and assessed, normally in conjunction with the geo-technical engineers. This approach frequently results in expanding the range of properties to be considered in the design phase.

Soil system is a complex entity in itself and there are several uncertainties associated with its modelling. Correct evaluation of dynamic soil properties, however, is the most difficult task. These properties can vary from site to site, from location to location, and from equipment to equipment as well as with variation of depth of foundation. Under the influence of dynamic forces, the foundation interacts with the soil activating dynamic soil-structure interaction, which considerably influences the dynamic response of equipment foundation system.

Depending upon type of analysis, soil is represented as an elastic half space with the help of equivalent soil springs represented by elastic sub-grade reaction coefficients. Typical soil parameters and dynamic properties of soil used in the equipment foundation design are Young’s modulus of elasticity, shear modulus, Poisson’s ratio. mass density, soil damping, coefficients of uniform compression of the soil, coefficients of non-uniform compression of the soil, coefficients of uniform shear of the soil, coefficients of non-uniform shear of the soil.

The important aspects of soil properties, which influence soil-structure interaction, are energy transfer mechanism, soil mass participation in the vibration of foundations, effect of embedment of foundation, applicability of Hook’s law to soil, reduction in permissible soil stress, and dynamic soil parameters.

Dynamic soil properties – Soil dynamics deals with engineering properties and behaviour of soil under dynamic stress. For the dynamic analysis of equipment foundations, soil properties, such as Poisson’s ratio, dynamic shear modulus, soil density, and damping of soil, are normally needed. Satisfactory design of an equipment foundation needs information on soil profile, depth of different layers, physical properties of soil, and ground water level. This information can be obtained by normal sub-surface exploration techniques. In addition, it is necessary to determine dynamic shear modulus, material damping, poisons ratio and mass density of soil for dynamic analysis of the equipment foundation.

Dynamic shear modulus of a soil is normally determined from laboratory or field tests. Material damping can be determined from vibration tests on soil columns in the laboratory. The values of dynamic shear modulus and damping can be estimated from empirical estimations for preliminary design purposes. The soil characteristics needed in analysis of foundation are (i) shear modulus, (ii) Poisson’s ratio, (iii) damping of soil, (iv) soil density, and (v) allowable soil pressure.

Vibration isolation – Isolation means reduction in the transmissibility of the exciting forces from the equipment to the foundation and vice-versa. Vibration isolation devices have been used to achieve satisfactory performance. Isolation in broader sense includes (i) control of transmission of dynamic forces from equipment to the foundation and thereby to the adjoining structures and equipment, (ii) isolation of equipment from the vibration effects of the adjoining system, (iii) isolation from external forces like earthquake shock, and blast etc.

In cases, where a bunch of vibratory equipments are to be mounted on a common elevated platform, vibration isolation can turn out to be a better proposition. Vibration isolation design for equipment foundation systems includes, isolation requirement, isolation design, selection of isolation devices, and influence of sub-structure (wherever applicable) on the response etc.

Field performance and feed-back – It goes without saying that proof of the pudding is in eating only. A feed-back from the site for the equipment’s performance hence is necessary. The data needs to be recorded at frequent intervals at site, compiled over a period of time and feedback provided to design office for drawing necessary inferences from the same and use these for design updates.

It is the normal practice in the industry to pay higher attention only to those equipments which do not perform well. More frequently than not, for every malfunction one keeps on trying modifications in the equipment, like better balancing, and replacing bearings etc. till satisfactory results are achieved. It is worth noting that every time the malfunction occurs the cause is not the equipment alone but it can also be the foundation. In certain cases, desired results are achieved by correcting the source, which can be other than the equipment.

Criteria for design – The main issues in the design of concrete foundations which support the equipments are (i) defining the anticipated loads, (ii) establishing the performance criteria, and (iii) providing for these through proper proportioning and detailing of the structural members. It needs careful attention to the interfaces between equipment, mounting system, and concrete foundation. The loads on equipment foundations can be both static and dynamic.

Static loads are principally a function of the weights of the equipment and all its auxiliary equipment. Under static loads, the foundation is required to be safe against shear failure and the settlement of the basement is to be within the normal limits.

Dynamic loads, which occur during the operation of the equipment, result from forces generated by unbalance, inertia of moving parts, or both, and by the flow of fluid and gases for some equipments. The magnitude of these dynamic loads mainly depends upon the equipment’s operating speed and the type, size, weight, and arrangement or position of moving parts within the equipment casing. The basic goal in the design of an equipment foundation is to limit its motion to amplitudes which neither endanger the satisfactory operation of the equipment nor disturb people working in the immediate vicinity. Allowable amplitudes depend on the speed, location and criticality, or function of the equipment. The basic requirements which are to be met in the foundations for dynamic loads of the equipments are described below.

There is to be no resonance, i.e., the natural frequency of the equipment foundation-soil system is not to coincide with the operating frequency of the equipment. In fact, a zone of resonance is normally defined and the natural frequency of the system is required to lie outside this zone. The foundation is high tuned when its fundamental frequency is higher than the operating speed or low tuned when its fundamental frequency is lower than the operating speed. This concept of a high or low tuned foundation is shown in Fig 4.

Fig 4 Concept of high and low tuned foundations

The amplitudes of motion at operating frequencies are not to exceed the limiting amplitudes, which are normally specified by equipment manufacturers. If the computed amplitude is within tolerable limits, but the computed natural frequency is close to the operating frequency, then it is important that this situation be avoided. The natural frequency of the foundation-soil system is not to be the whole number multiple of the operating frequency of the equipment to avoid resonance with the higher harmonics. The settlement is to be within permissible limits.

The combined centre of gravity of the equipment and the foundation is to be, to the extent possible, in the same vertical line as the centre of gravity of the base line. All rotating and reciprocating parts of the equipment are to be so balanced so that the unbalanced forces and moments are minimized. The foundation is to be so planned as to permit subsequent alteration of natural frequency by changing the base area or mass of the foundation, if found necessary subsequently. From the practical point of view, the following additional requirements are also to be fulfilled.

The ground water table is to be below the base plane by at least one-fourth of the width of the foundation. Since ground-water is a good conductor of waves, this limits the propagation of vibration. Equipment foundations are to be separated from adjacent building components by means of expansion joints. Any pipes carrying hot fluids, if embedded in the foundation, are to be properly isolated. The foundation is to be protected from lubricating oil by means of suitable chemical treatment, which is acid-resistant. Equipment foundations are to be taken to a level lower than the level of foundations of adjoining structures.

Design approach for equipment foundation – The task for designing of foundations for equipments with dynamic loads in addition to the normal data on the equipment is to contain (i) the technical characteristics of the equipments (name, type, number of rotations per minute, power, and total weight, etc.), (ii) information about the magnitudes, places of application, and directions of action of static loads, as well as about amplitudes and frequencies, places of application, and direction of dynamic loads, (iii) data on the maximum permissible deformations of the foundations and their basement, (iv) requirements for placement of equipment on the foundations, (v) drawings of the dimensions of the foundation within the location of the equipment, fasteners, as well as auxiliary equipment, communications, and hole sizes, (vi) drawings of all communications adjacent to the foundation, (vii) data on the geological conditions of the construction site and soil properties, (viii) information about the location of the designed foundation relative to the nearest structures, and (ix) requirements for the protection of the foundation from ground-water, as well as other external factors characteristic of the design environment.

General theory – The analysis of the equipment foundation is normally performed by idealizing it as a simple system as explained here. Fig 5 shows a schematic sketch of a rigid concrete block resting on the ground surface and supporting an equipment. Let it be assumed that the operation of the equipment produces a vertical unbalanced force which passes through the combined centre of gravity of the equipment-foundation system. Under this condition, the foundation vibrates only in the vertical direction about its mean position of static equilibrium. The vibration of the foundation results in transmission of waves through the soil. These waves carry energy with them. This loss of energy is termed ‘geometrical damping’.

The soil below the footing experiences cyclic deformations and absorbs some energy which is termed ‘material damping’. The material damping is normally small compared to the geometrical damping and can be neglected in the majority of the cases. However, material damping can also become important in some cases of equipment foundation vibrations. The problem of a rigid block foundation resting on the ground surface (Fig 5a) can hence be represented in a reasonable manner by a spring-mass-dashpot system shown in Fig 5b. The spring in this figure is the equivalent soil spring which represents the elastic resistance of the soil below the base of the foundation. The dashpot represents the energy loss or the damping effect. The mass in Fig 5b is the mass of the foundation block and the equipment. If damping is neglected, a spring-mass system shown in Fig 5c can be used to represent the problem defined in Fig 5a. Single degree of freedom models shown in Fig 5b and 5c can, in fact, be used to represent the problem of equipment foundation vibration in any mode of vibration if appropriate values of equivalent soil spring and damping constants are used.

Fig 5 Vertical vibrations and possible modes for cyclic displacement of equipment foundation

All foundations in practice are placed at a certain depth below the ground surface. As a result of this embedment, the soil resistance to vibration develops not only below the base of the foundation but also along the embedded portion of the sides of the foundation. Similarly, the energy loss because of radiation damping occurs not only below the foundation base but also along the sides of the foundation. The type of models shown in Fig 5b and Fig 5c can be used to calculate the response of embedded foundations if the equivalent soil spring and damping values are suitably modified by taking into account the behaviour of the soil below the base and on the sides of the foundation.

A typical concrete block is regarded as rigid as compared to the soil over which it rests. Hence, it can be assumed that it undergoes only rigid-body displacements and rotations. Under the action of unbalanced forces, the rigid block can hence undergo displacements and oscillations as given below and shown in Fig 5d.

The cyclic displacements of a foundation can have six possible modes namely (i) displacement in the vertical direction, (ii) displacement in the longitudinal direction, (iii) displacement in the lateral direction, (iv) rotation about the vertical axis (yawing or torsional), (v) rotation about the longitudinal axis (rocking), and (v) rotation about the lateral axis (pitching).

Fig 5a, Fig 5b, and Fig 5c show a foundation resting on a soil which can be approximated to be an equivalent spring and dashpot. This foundation is being subjected to a sinusoidally varying force ‘P’ which is equal to Pz.Sinwt, where ‘w’ is the circular frequency of vibration (rpm), and ‘z’ is the amplitude (i.e., maximum displacement) of vibration.

Design parameters

Foundation and equipment load – Foundations supporting different types of equipments are to withstand all the forces which can be imposed on them during their service life. Equipment foundations are unique since they can be subjected to considerable dynamic loads during operation in addition to normal design loads of gravity, wind, and earthquake. The magnitude and the characteristics of the operating loads depend on the type, size, speed, and layout of the equipments.

Normally, the weight of the equipment, centre of gravity, surface areas, and operating speeds are readily available from the manufacturer of the equipment. Establishing appropriate values for dynamic loads is best accomplished through careful communication and clear understanding between the equipment manufacturer and foundation design engineer as to the purpose, and planned use for the requested information, and the definition of the information provided. It is in the best interests of all parties (equipment manufacturer, foundation design engineer, owner, and operator) to ensure effective definition and communication of data and its appropriate use.

Equipments always experience some level of unbalance, vibration, and force transmitted through the bearings. Under some off-design conditions, such as wear, the forces can increase considerably. The equipment manufacturer and foundation design engineer are to work together so that their combined knowledge achieves an integrated system structure which robustly serves the needs of its owner and operator and withstands all expected loads.

The normally used methods for determining equipment-induced forces and other design loads for foundations supporting equipments are described below. They include definitions and other information on dynamic loads to be requested from the equipment manufacturer and alternative assumptions to apply when such data are unavailable or are under-predicted.

There are two types of loads on the equipment foundations. These are static loads, and dynamic loads. Static loads are (i) dead loads, (ii) live loads, (iii) wind loads, (iv) seismic loads, (v) static operating loads, (vi) special loads for elevated-type foundations, (vii) erection and maintenance loads, and (viii) thermal loads. Dynamic loads are (i) rotating equipment load, (ii) reciprocating equipment load, (iii) impulsive equipment load, (iv) loading conditions, and (v) load combinations.

Dead loads – A major function of the foundation is to support gravity (dead) loads because of the weight of the equipment, auxiliary equipment, pipe, valves, and dead-weight of the foundation structure. The weights of the equipment components are normally supplied by the equipment manufacturer. The distribution of the weight of the equipment on the foundation depends on the location of support points (chocks, sole-plates) and on the flexibility of the equipment frame. Typically, there are multiple support points, and, hence, the distribution is statically indeterminate. In several cases, the equipment manufacturer provides a loading diagram showing the vertical loads at each support points. When this information is not available, it is normal to assume the equipment frame is rigid and that its weight is appropriately distributed between support points.

Live loads—Live loads are produced by personnel, tools, and maintenance equipment and materials. The live loads used in design are to be the maximum loads expected during the service life of the equipment. For the majority of the designs, live loads are uniformly distributed over the floor areas of platforms of elevated support structures or to the access areas around at grade foundations. Typical live loads vary from 2.9 kPa for personnel to as much as 7.2 kPa for maintenance equipment and materials.

Wind loads – Loads because of the wind on the surface areas of the equipment, auxiliary equipment, and the support foundation are based on the design wind speed for the particular site and are normally calculated in accordance with the governing local code or standard. Wind loads rarely govern the design of equipment foundations except, perhaps, when the equipment is located in an enclosure which is also supported by the foundation.

Majority of the structural systems involving equipments and equipment foundations are relatively stiff (natural frequency in the lateral direction higher than 1 Hz). Hence, the systems can be treated as rigid with respect to the wind gust effect factor, and simplified procedures can be used. If the equipment is supported on flexible isolators and is exposed to the wind, the rigid assumption cannot be reasonable, and more elaborate treatment of the gust effects is necessary. Appropriate consideration of the exposure conditions and importance factors is also needed to be consistent with the facilities requirements.

Seismic loads – Equipment foundations located in seismically active regions are analyzed for seismic loads. Before the year 2000, these loads were determined as per the methods prescribed in the regional building codes and standards. The publication of the IBC (International building code) provides building officials with the opportunity to replace the former regional codes with a code which has international applicability. The IBC and its reference documents contain provisions for design of non-structural components, including dynamic equipments, for seismic loads. For equipment supported above grade or on more flexible elevated pedestals, seismic amplification factors are also specified.

Static operating loads – Static operating loads include the weight of gas or liquid in the equipment during normal operation and forces, such as the drive torque developed by some equipments at the connection between the drive mechanism and driven equipment. Static operating loads can also include forces caused by thermal growth of the equipment and connecting piping. Time varying (dynamic) loads generated by equipments during operation are covered under dynamic loads.

Some equipments, e.g., compressors and generators, need some form of drive mechanism, either integral with the equipment or separate from it. When the drive mechanism is non-integral, such as a separate electric motor, reciprocating engine, and gas or steam turbine, it produces a net external drive torque on the driven equipment. The torque is equal in magnitude and opposite in direction on the driver and driven equipment. The normal torque (sometimes called drive torque) is normally applied to the foundation as a static force couple in the vertical direction acting about the centre-line of the shaft of the equipment.

The magnitude of the normal torque is frequently computed from the equation ‘NT = (9550 x Ps)/fo’ newton-metre (N-m), where ‘NT’ is the normal torque in N-m, ‘Ps’ is the power being transmitted by the shaft at the connection in kilowatts, and ‘fo’ is the operating speed in rpm (revolutions per minute).

The torque load is normally resolved into a vertical force couple by dividing it by the centre-to-centre distance between longitudinal sole-plates or anchor points (Fig 6a). When the equipment is supported by transverse sole-plates only, the torque is applied along the width of the soleplate assuming a straight-line variation of force (Fig 6b). Normal torque can also be caused by jet forces on turbine blades. In this case it is applied to the foundation in the opposite direction from the rotation of the rotor.

Fig 6 Equivalent forces for torque loads

The torque on a generator stator is applied in the same direction as the rotation of the rotor and can be high because of start-up or an electrical short circuit. Start-up torque, a property of electric motors, is to be obtained from the motor manufacturer. The torque created by an electrical short circuit is considered a malfunction, emergency, or accidental load and is normally reported separately by the equipment manufacturer. Frequently in the design for this phenomenon, the magnitude of the emergency drive torque is determined by applying a magnification factor to the normal torque. Consultation with the motor manufacturer is necessary to establish the appropriate magnification factor.

Special loads for elevated-type foundations – For ensuring adequate strength and deflection control, special static loading conditions are recommended in some proprietary standards for large equipment on elevated-type foundations. These special loads are (i) vertical force equal to 50 % of the total weight of each equipment, (ii) horizontal force (in the transverse direction) equal to 25 % of the total weight of each equipment, and (iii) horizontal force (in the longitudinal direction) equal to 25 % of the total weight of each equipment. These forces are additive to normal gravity loads and are considered to act at the centre-line of the equipment shaft. These three loads are not considered to act concurrently with one another.

Erection and maintenance loads – Erection and maintenance loads are temporary loads from equipment, such as cranes and fork-lifts, needed for installing or dismantling equipment components during erection or maintenance. Erection loads are normally furnished in the manufacturer’s foundation load drawing and are to be used in conjunction with other specified dead, live, and environmental loads. Maintenance loads occur any time the equipment is being drained, cleaned, repaired, and realigned or when the components are being removed or replaced. Loads can result from maintenance equipment, davits, and hoists. Environmental loads, such as full wind and earth-quake, are not normally assumed to act with maintenance loads, which normally occur for only a relatively short duration.

Thermal loads – Changing temperatures of equipments and their foundations cause expansions and contractions, and distortions, causing the different parts to try to slide on the support surfaces. The magnitude of the resulting frictional forces depends on the magnitude of the temperature change, the location of the supports, and on the condition of the support surfaces. The thermal forces do not impose a net force on the foundation to be resisted by soil or piles since the forces on any surface are balanced by equal and opposite forces on other support surfaces. Thermal forces, however, can govern the design of the grout system, pedestals, and hold downs.

Calculation of the exact thermal loading is very difficult since it depends on a number of factors, including distance between anchor points, magnitude of temperature change, the material and condition of the sliding surface, and the magnitude of the vertical load on each sole-plate. Lacking a rigorous analysis, the magnitude of the frictional load can be calculated as ‘Force = (friction coefficient) x (load acting through sole-plate)’.

The friction coefficient normally varies from 0.2 to 0.5. Loads acting through the sole-plate include equipment dead load, normal torque load, anchor bolt load, and piping loads. Heat transfer to the foundation can be by convection across an air gap (e.g., gap between sump and block) and by conduction through points of physical contact. The resultant temperature gradients induce deformations, strains, and stresses.

When evaluating thermal stress, the calculations are strongly influenced by the stiffness and restraint against deformation for the structural member in question. Hence, it is important to consider the self-relieving nature of thermal stress because of the deformation to prevent being overly conservative in the analysis. As the thermal forces are applied to the foundation member by the equipment, the foundation member changes length and hence provides reduced resistance to the equipment forces. This phenomenon can have the effect of reducing the thermal forces from the equipment.

Accurate determinations of concrete surface temperatures and thermal gradients are also important. Under steady-state normal operating conditions, temperature distributions across structural sections are normally linear. The air gap between the equipment casing and foundation provides an important means for dissipating heat, and its effect is to be included when establishing surface temperatures. Normally, the expected thermal deflection at different bearings is estimated by the manufacturer, based on past field measurements on existing units. The equipment erector then compensates for the thermal deflection during installation.

Rotating equipment loads – Typical heavy rotating equipments include centrifugal air and gas compressors, horizontal and vertical fluid pumps, generators, rotating steam and gas turbine drivers, centrifuges, electric motor drivers, fans, and blowers. These types of equipments are characterized by the rotating motion of one or more impellers or rotors. The rotating equipment loads are described below.

Dynamic loads because of unbalanced masses – Unbalanced forces in rotating machines are created when the mass centroid of the rotating part does not coincide with the axis of rotation. In theory, it is possible to precisely balance the rotating elements of rotating equipments. In practice, this is never achieved and slight mass eccentricities always remain. During operation, the eccentric rotating mass produces centrifugal forces which are proportional to the square of equipment speed. Centrifugal forces normally increase during the service life of the equipment because of the conditions such as equipment wear, rotor play, and dirt accumulation.

A rotating equipment transmits dynamic force to the foundation predominantly through its bearings (with small, normally unimportant exceptions such as seals and the air gap in a motor). The forces acting at the bearings are a function of the level and axial distribution of unbalance, the geometry of the rotor and its bearings, the speed of rotation, and the detailed dynamic characteristics of the rotor-bearing system. At or near a critical speed, the force from rotating unbalance can be substantially amplified, sometimes by a factor of five or more.

Ideally, the determination of the transmitted force under different conditions of unbalance and at different speeds results from a dynamic analysis of the rotor-bearing system, using an appropriate combination of computer programmes for calculating bearing dynamic characteristics and the response to unbalance of a flexible rotor in its bearings. Such an analysis is normally be performed by the equipment manufacturer. Results of such analyses, especially values for transmitted bearing forces, represent the best source of information for use by the foundation design engineer. Equipment manufacturer provides the following informations.

Design levels of unbalance and basis – This information documents the unbalance level the subsequent transmitted forces are based on. Dynamic forces transmitted to the bearing pedestals under the several conditions namely (i) under design unbalance levels over operating speed range, (ii) at highest vibration when negotiating critical speeds, (iii) at a vibration level where the equipment is just short of tripping on high vibration, and (iv) under the maximum level of upset condition the equipment is designed to survive (e.g., loss of one or more blades).

Items (i) and (ii) document the predicted dynamic forces resulting from levels of unbalance assumed in design for normal operation. Using these forces, it is possible to predict the normal dynamic vibration of the equipment on its foundation. Item (iii) identifies a maximum level of transmitted force with which the equipment can operate continuously without tripping, the foundation is to have the strength to tolerate such a dynamic force on a continuous basis. Item (iv) identifies the higher level of dynamic force, which can occur under occasional upset conditions over a short period of time. If the equipment is designed to tolerate this level of dynamic force for a short period of time, then the foundation is also be able to tolerate it for a similar period of time.

If an independent dynamic analysis of the rotor-bearing system is performed by the end user or by a third party, such an analysis can provide some or all of the above dynamic forces transmitted to the foundation. By assuming that the dynamic force transmitted to the bearings equals the rotating unbalanced force generated by the rotor, information on unbalance can provide an estimate of the transmitted force.

Equipment unbalance provided by the manufacturer – When the mass unbalance (eccentricity) is known or stated by the manufacturer, the resulting dynamic force amplitude is given by the equation 1 which is ‘Fo = (mr x em x wo-square x 2Sf)/1,000’ in newtons, where ‘Fo’ is the dynamic force amplitude (zero-to-peak) in newtons, ‘mr’ is the rotating mass in kilograms, ‘em’ is the mass eccentricity in mm, ‘wo’ is the circular operating frequency of the equipment in rad/s. and ‘Sf’ the service factor, used to account for increased unbalance during the service life of the machine, normally higher than or equal to 2.

Equipment unbalance meeting industry criteria – Several rotating equipments are balanced to an initial balance quality either in accordance with the manufacturer’s procedures or as specified by the purchaser. ISO 1940 defines balance quality in terms of a constant em x wo. For example, the normal balance quality ‘Q’ for parts of process-plant equipment is 6.3 mm/s. For meeting these criteria, a rotor intended for faster speeds is to be better balanced than one operating at a slower speed. Using this approach, equation 1 can be rewritten as ‘Fo = (mr x Q x wo x Sf/1,000’ in newtons.

Dynamic load determined from an empirical formula – Rotating equipment manufacturers frequently do not report the unbalance which remains after balancing. Hence, empirical formulas are frequently used to ensure that foundations are designed for some minimum unbalance, which normally includes some allowance for increasing unbalance over time. One general purpose empirical method assumes that balancing improves with equipment speed and that there is a linear relationship between the unbalanced forces and the equipment speed. The zero-to-peak centrifugal force amplitude from one such normally used expression is given by the equation 2 which is ‘Fo = (Wr x fo)/6,000 where ‘Wr’ is rotating weight in newton and ‘fo’ is the operating speed in rpm.

Equation 2 appears to be very different. The exponents on the speed of rotation vary from 1 to 1.5 – 2, constants vary widely, and different variables appear. Some equations use mass, others use weight. In reality, the equation is more similar than they appear. Given the right understanding of Q as a replacement for ‘ew’, and equation 1 takes on the same character. This equation then indicates that the design force at operating speed varies linearly with both the mass of the rotating body and the operating rotational speed.

The centrifugal forces because of the mass unbalance are considered to act at the centre of gravity of the rotating part and vary harmonically at the speed of the equipment in the two orthogonal directions perpendicular to the shaft. The forces in the two orthogonal directions are equal in magnitude and 90-degree out of phase and are transmitted to the foundation through the bearings. Schenck has provided useful information about balance quality for various classes of equipments.

Equipment unbalance determined from trip vibration level and effective bearing stiffness – Since a rotor is frequently set to trip on high vibration, it can be expected to operate continuously at any vibration level up to the trip limit. Given the effective bearing stiffness, it is possible to calculate the maximum dynamic force amplitude as Fo = Vmax x Keff where ‘Vmax’ is the maximum allowable vibration in mm, and ‘Keff’ is the effective bearing stiffness in N/mm. For using this approach, the manufacturer is to provide effective bearing stiffness or the engineer is to calculate it from the bearing geometry and operating conditions (such as viscosity and speed).

Loads from multiple rotating equipments – If a foundation supports multiple rotating equipments, the engineer is required to compute unbalanced force based on the mass, unbalance, and operating speed of each rotating component. The response to each rotating mass is then combined to determine the total response. Some engineers, depending on the specific situation of equipment size and criticality, find it advantageous to combine the unbalanced forces from each rotating component into a single resultant unbalanced force.

The method of combining two dynamic forces is up to individual judgment and frequently involves some approximations. In some cases, loads or responses can be added absolutely. In other cases, the loads are treated as out-of-phase so that twisting effects are increased. Frequently, the operating speed of the equipment is required to be considered. Even if operating speeds are nominally the same, the design engineer is to recognize that during normal operation, the speed of the equipments vares and beating effects can develop. Beating effects develop as two equipments operate at close to the same speed. At one point in time, responses to the two equipments are additive and motions are maximized. A short time later, the responses cancel each other and the motions are minimized. The net effect is a continual cyclic rising and falling of motion.

Reciprocating equipment loads – Internal-combustion engines, piston-type compressors and pumps, some metal forming presses, steam engines, and other equipments are characterized by the rotating motion of a master crank-shaft and the linear reciprocating motion of connected pistons or sliders. The motion of these components causes cyclically varying forces, frequently called reciprocating forces.

Primary and secondary reciprocating load – The simplest type of reciprocating equipment uses a single crank mechanism as shown in Fig 7a. The idealization of this mechanism consists of a piston which moves within a guiding cylinder, a crank of length ‘r’ which rotates about a crank shaft, and a connecting rod of length ‘L’. The connecting rod is attached to the piston at point ‘P’ and to the crank at point ‘C’. The wrist pin ‘P’ oscillates while the crank pin ‘C’ follows a circular path. This idealized single cylinder shows the concept of an equipment producing both primary and secondary reciprocating forces.

Fig 7 Crank mechanism and double-acting compressor cylinder and piston

Compressor gas loads – A reciprocating compressor raises the pressure of a certain flow of gas by imparting reciprocating motion on a piston within a cylinder. The piston normally compresses gas during both directions of reciprocating motion. As gas flows to and from each end, the pressure of the gas increases as it is compressed by each stroke of the piston. The increase in pressure within the cylinder creates reaction forces on the head and crank ends of the piston which alternate as gas flows to and from each end of the cylinder.

The gas force contributed to the piston rod equals the instantaneous difference between the pressure force acting on the head and crank end of the piston as shown in Fig 7b. The formulations which can be used to estimate the maximum force acting on the piston rod of an individual double-acting cylinder are given by equations (i) ‘Frod = [(Phead)(Ahead) – (Pcrank)(Acrank)] x F1’, (ii) ‘Ahead = (‘pi’/4)(Bc)square’, and (iii) ‘Acrank = (‘pi’/4)[(Bc)square – (Drod)square)’, where ‘Frod’ is the force acting on piston rod in newton, ‘Ahead’ and ‘Acrank’ are the head and crank areas in square millimetres, ‘Bc’ is  the cylinder bore diameter in mm, ‘Drod’ is the rod diameter in mm, ‘Phead’ and ‘Pcrank’ are instantaneous head and crank pressures in MPa, and ‘F1’ is the  = correction factor.

The head and crank end pressures vary continuously and the differential force takes both positive and negative net values during each cycle of piston motion. The normal approach is to establish the head and crank pressures using the maximum and minimum suction and discharge pressures. For design purposes, it is normal to multiply equation (i) by a factor F1 to help account for the natural tendency of gas forces to exceed the values based directly on suction and discharge pressures because of the flow resistances and pulsations. Equipments with good pulsation control and low external flow resistance can achieve F1 as small as 1.1, and for equipments with low compression ratio, high pulsations, or highly resistive flow through piping and nozzles, F1 can approach 1.5 or even higher. A reasonable working value for F1 is 1.15 to 1.2.

Preferably, the maximum rod force resulting from gas pressures is based on knowledge of the continuous variation of pressure in the cylinder (measured or predicted). In a repair situation, measured cylinder pressure variation using a cylinder analyzer provides the most accurate value of gas forces. Even without cylinder pressure analysis, extreme operating values of suction and discharge pressure for each stage is to be recorded before the repair and used in the Equation (i).

On new compressors, the engineer is required to ask the equipment manufacturer to provide values for maximum compressive and tensile gas loads on each cylinder rod and, if these are based on suction and discharge pressures, to recommend a value of F1.

Gas forces act on the crank-shaft with an equal and opposite reaction on the cylinder. Hence, crank-shaft and cylinder forces globally balance each other. Between the crank-shaft and the cylinder, however, the compressor frame expands or contracts in tension or compression under the action of the gas forces. The forces because of frame deflections are transmitted to the foundation through connections with the compressor frame. When acting without slippage, the frame and foundation become an integral structure and together expand or contract under the gas loads.

The magnitude of gas force transferred into the foundation depends on the relative flexibility of the compressor frame. A very stiff frame transmits only a small fraction of the gas force while a very flexible frame transmits majority of or all of the force. Similar comments apply to the transfer of individual cylinder inertia forces.

Based on limited comparisons using finite element analysis, the guideline which is suggested for gas and inertia force loads transmitted to the foundation by a typical compressor are given by equations (iv) ‘Fblock = Frod/Fred’,  (v) ‘(Fbolt)CHG = [(Frod)/(Nbolt)CHG]/Fred’ and (vi) ‘(Fbolt)frame = [(Funbalance/(Nbolt)]/Fred’, where ‘Fblock’ is the force acting outward on the block from which concrete stresses are to be calculated in newton, ‘(Fbolt)CHG’ is the force to be restrained by friction at the cross head guide (CHG) tie-down bolts in newton, ‘(Fbolt)frame is the force to be restrained by friction at the frame tie-down bolts, in newton, ‘Fred’ is a force reduction factor with suggested value of 2, to account for the fraction of individual cylinder load carried by the compressor frame (frame rigidity factor), ‘(Nbolt)CHG’ is the number of bolts holding down one cross-head guide, ‘(Nbolt)frame’ is the number of bolts holding down the frame, per cylinder, ‘Frod’ is the force acting on piston rod, from equation (i) in newton, and ‘Funbalance’ is the maximum value calculated using parameters for a horizontal compressor cylinder in newton.

The factor ‘Fred’ is used to simplify a complex problem, hence avoiding the application of unrealistically high loads on the anchor bolts and the foundation block. The mechanics involved in transmitting loads are complex and cannot easily be reduced to a simple relationship between a few parameters beyond the given load equations. A detailed finite-element analysis of metal compressor frame, chock mounts, concrete block, and grout account for the relative flexibility of the frame and its foundation in determining individual anchor bolt loads and implicitly provide a value for ‘Fred’. If the frame is very stiff relative to the foundation, the value for ‘Fred’ is higher, implying more of the transmitted loads are carried by the frame and less by the anchor bolts and foundation block. Based on experience, a value of 2 for this factor is conservatively low, however, higher values have been seen with frames designed to be especially stiff.

Simplifying this approach, one study suggests using a finite element analysis to calculate forces transmitted to the anchor bolts. If a finite element analysis is not possible, the engineer is required to get from the equipment manufacturer or calculate the maximum horizontal gas force and maximum horizontal inertia force for any throw or cylinder. The mounts, anchor bolts, and blocks are then designed for ‘Fthrow = (higher of FGmax or FImax)/2’, where ‘Fthrow’ is the horizontal force to be resisted by each throw’s anchor bolts in newton, ‘FGmax’ is the maximum horizontal gas force on a throw or cylinder in newton, and ‘FImax’ is the maximum horizontal inertia force on a throw or cylinder in newton.

Reciprocating inertia loads for multi-cylinder equipments – As a practical matter, majority of the reciprocating equipments have more than one cylinder, and manufacturers arrange the equipment components in a manner which minimizes the net unbalanced forces. As an example, rotating parts like the crank-shaft can be balanced by adding or removing correcting weights. Translating parts like pistons and those which show both rotation and translation, like connecting rods, can be arranged in such a way as to minimize the unbalanced forces and moments generated. Rarely, if ever, is it possible to perfectly balance reciprocating equipments.

The forces generated by reciprocating mechanisms are functions of the mass, stroke, piston arrangement, connecting rod size, crank throw orientation (phase angle), and the mass and arrangement of counter-weights on the crank-shaft. For this reason, calculating the reciprocating forces for multi-cylinder equipments can be quite complex and are hence normally provided by the equipment manufacturer. If the equipment is an integral engine compressor, it can include, in one frame, cylinders oriented horizontally, vertically, or in between, all with reciprocating inertias.

Some equipment manufacturers place displacement transducers and accelerometers on strategic points on the equipment. They can then measure displacements and accelerations at those points for several operational frequencies to determine the magnitude of the unbalanced forces and couples for multi-cylinder equipments.

Estimating reciprocating inertia forces from multi-cylinder equipments – In cases where the manufacturer’s data are unavailable or components are being replaced, the engineer is required to use hand calculations to estimate the reciprocating forces from a multi-cylinder equipment.

Impulsive equipment loads—The impulsive load generated by a forging hammer is caused by the impact of the hammer ram onto the hammer anvil. This impact process transfers the kinetic energy of the ram into kinetic energy of the entire hammer assembly. The post-impact velocity of the hammer is represented by the equation ‘vh = (Mr/Mh) x (1+ah) x vr’, where ‘vh’ is the post-impact hammer velocity in m/s, ‘Mr’ is the ram mass including dies and ancillary parts in kg, ‘Mh’ is the hammer mass including any auxiliary foundation in kg, ‘ah’ is the ram rebound velocity relative to impact velocity, and ‘vr’ is the ram impact velocity in m/s.

Normal experience indicates that ‘ah’ is around 60 % for several forging hammer installations. From that point, the hammer foundation performance can be assessed as a rigid body oscillating as a single degree-of-freedom system with an initial velocity of ‘vh’.

For metal-forming presses, the dynamic forces develop from two sources namely (i) the mechanical movement of the press components, and (ii) material-forming process. Each of these forces is unique to the press design and application and needs to be evaluated with proper information from the press manufacturer and the owner.

The press mechanics frequently include rotating and reciprocating components. The dynamic forces from these individual pieces follow the rules established earlier for rotating and reciprocating components. Only the press manufacturer familiar with all the internal components can knowledgeably calculate the specific forces.

Loading conditions – During their lives, equipment support structures and foundations undergo different loading conditions including erection, testing, shut down, maintenance, and normal and abnormal operation. For each loading condition, there can be one or more combinations of loads which apply to the structure or foundation. The loading conditions which normally considered in design are (i) erection condition represents the design loads which act on the structure / foundation during its construction, (ii) testing condition represents the design loads which act on the structure / foundation while the equipment being supported is undergoing testing, such as hydrotest, (iii) empty (shutdown) represents the design loads which act on the structure when the supported equipment is at its least weight because of removal of process fluids, applicable internals, or both as a result of maintenance or other out-of-service disruption, (iv) normal operating condition represents the design loading during periods of normal equipment operation, and (v) abnormal operating condition represents the design loading during periods when unusual or extreme operating loads act on the structure / foundation.

Load combinations – Tab 1 shows the general classification of loads for use in determining the applicable load factors in strength design. In considering soil stresses, the normal approach is working stress design without load factors and with overall factors of safety identified as appropriate by geo-technical engineers.

The load combinations frequently used for the different load conditions are (i) erection load consisting of (a) dead load + erection forces, (b) dead load + erection forces + reduced wind + snow, ice, or rain, and (c) dead load + erection forces + seismic + snow, ice, or rain, (ii) testing load consisting of (a) dead load + test loads, (b) dead load + test loads + live + snow, ice, or rain,  and (c) dead load + test loads + reduced wind + snow, ice, or rain, (iii) empty (shutdown) load consisting of (a) dead load + maintenance forces + live load + snow, ice, or rain, (iv) normal operation load consisting of (a) dead load, (b) dead load + thermal load + equipment forces + live loads + wind + snow, ice, or rain, and (c) dead load + thermal load + equipment forces + seismic + snow, ice, or rain, and (v) abnormal operation load consisting of dead load + upset (abnormal) machine loads + live + reduced wind. It is normal to only use some fraction of full wind, such as 80 % in combination with erection loads and 33 % for test loads, because of the short duration of these conditions.

The preliminary design – For preliminary design of the concrete block foundations, the length and width are to be 300 millimetres (mm) to 600 mm longer and wider, respectively, than the equipment (if block mounted) or the skid (if skid mounted).

Block foundations are required to have a minimum of 50 % of the block thickness embedded in the soil, unless otherwise specified by the equipment user.

Minimum depths are (i) 1.2 m to 1.5 m for drivers less than 1,840 kW. (ii) 1.8 m for drivers in the range of 1,840 kW to 3,680 kW, and 1.8 m to 2.5 m drivers higher than 3,680 kW.

The width of the foundation is to be at least 1.5 times the vertical distance from the base to the equipment centre line (Fig 8a), unless analysis has demonstrated that a lesser value is going to perform adequately.

The ratio of the height of the equipment crankshaft above the base to the width of the foundation block (or the pile group in the plan, if applicable) is not to be more than 0.65.

The top of the finished foundation is to be minimum 100 mm above the finished elevation of the floor slab or grade to prevent damage to the equipment from runoff or wash-down water.

For minimizing torsional effects, a vertical line drawn through the centroid of the equipment or resultant of several equipments shall pass within a distance of 5 % of the plan dimensions of the base from the centroid of the contact area (or pile group) as shown in Fig 8b.

Fig 8 Some ratios in concrete block foundation

Pile foundations – Pile foundations are the part of a structure used to carry and transfer the load of the structure to the bearing ground located at some depth below ground surface. The main components of the foundation are the pile cap and the piles. Piles are long and slender members which transfer the load to deeper soil or rock of high bearing capacity avoiding shallow soil of low bearing capacity. The main types of materials used for piles are wood, steel, concrete, or combination of different materials in the same pile. Piles made from these materials are driven, drilled, or jacked into the ground and connected to the pile caps. Depending upon type of soil, pile material and load transmitting characteristic piles are classified accordingly.

Based on the load transmission and functional behaviour, piles can be classified as (i) end bearing piles (point bearing piles), (ii) friction piles (cohesion piles), and (iii) combination of friction and cohesion piles. End bearing piles transfer their load on to a firm stratum located at a considerable

depth below the base of the structure and they derive most of their carrying capacity from the penetration resistance of the soil at the toe of the pile. In case of friction pile, the carrying capacity is derived mainly from the adhesion or friction of the soil in contact with the shaft of the pile. These piles transfer their load to the ground through skin friction. The process of driving such piles does not compact the soil appreciably. These types of pile foundations are normaally known as floating pile foundations. Combination of friction and cohesion pile is an extension of the end bearing pile when the bearing stratum is not hard, such as a firm clay. The pile is driven far enough into the lower material to develop adequate frictional resistance. A farther variation of the end bearing pile is piles with enlarged bearing areas. This is achieved by forcing a bulb of concrete into the soft stratum immediately above the firm layer to give an enlarged base.

Function of piles – As with other types of foundations, the purpose of a pile foundations is (i) to transmit a foundation load to a solid ground, and (ii) to resist vertical, lateral, and uplift load. A structure can be founded on piles if the soil immediately beneath its base does not have adequate bearing capacity. If the results of site investigation show that the shallow soil is unstable and weak or if the magnitude of the estimated settlement is not acceptable, a pile foundation is to be considered. Further, a cost estimate can indicate that a pile foundation can be cheaper than any other compared ground improvement costs.

In the case of heavy constructions, it is likely that the bearing capacity of the shallow soil is not satisfactory, and the construction is then be built on pile foundations. Piles can also be used in normal ground conditions to resist horizontal loads. Piles are a convenient method of foundation for works over water, such as jetties or bridge piers.

Procedure for construction of foundation – It starts with a decision on its depth, width, and marking layout for excavation and centre-line of foundation. Foundation is the part of the structure below the plinth level in direct contact of soil and transmits the load of super-structure to the ground. Normally, it is below the ground level. If some part of the foundation is above ground level, it is also covered with earth filling. This portion of the structure is not in contact with air, and light etc., or to say that it is the hidden part of the structure.

Footing is a structure constructed in brickwork, masonry, or concrete under the base of a wall or column for distributing the load over a large area.

Foundation design precautions – The precautions needed for foundation design are (i) foundation is to be designed to transmit combined dead load, imposed load, and wind load to the ground, (ii) net loading intensity of pressure coming on the soil is not to exceed the safe bearing capacity, (iii) foundation is to be designed in such a way that settlement to the ground is limited and uniform to avoid damage to the structure, and (iv) design of the foundation, super-structure, and characteristics of the ground are to be studied to get the overall economy.