They should recognize the inherent shrinkage-compensating admixtures, polymers, silica fumes, conflicts in these requirements, the physical processes that fly ash, and fibers. These systems may use a combination of preblended or A dynamic machine may tend to get hotter and grow more field-mixed concrete and polymer concrete or grout to than its foundation in the horizontal plane.
The growth can reduce downtime to 12 to 72 h, depending on foundation reach several tenths of an inch 0. Most machines—such as The machine-mounting system broadly categorized as compressors, steam turbines, motors, and generators—do either an anchorage-type or an isolator-type attaches the not internally relieve their own thermal growth, so the dynamic machine to its foundation.
It represents a vital mounting system should allow for thermal growth. The mounting system should provide a stable platform through convection, radiation, and conduction. While from which to align the machine. Any deflections of the convection and radiation dominate in the regions where an mounting system that occur should remain sufficiently air gap separates the machine base from the foundation, the uniform at different points to preserve acceptable alignment mounting system provides the primary path for conduction.
The specifications and use of adjustable Ten critical performance criteria can be identified as chock mounts has become increasingly widespread to generally applicable to isolator and anchorage-type compensate for loss of alignment resulting from creep and mounting systems: other permanent deformations; and 1.
A machine-mounting system should tolerate expected The mounting system should impose tolerable loads, differential thermal growth across the interface. This can stresses, and deformations on the foundation itself. Appro- occur by combining strength to resist expansion forces and priate foundation design to make the loads, stresses, and stresses, flexibility to accommodate the deflections, and deformations tolerable remains an essential part of this tolerance for relative sliding across the interface as the performance criterion.
Some of the loads and stresses to machine grows relative to the foundation ; consider include: 2. Flexible mounts that deflect rather than restrain the concrete resulting from the typically higher expansion forces become an option only in cases where the machine of polymer grout than concrete best accommodated and any rigidly attached structure have the structural rigidity with expansion joints ; and needed to avoid damaging internal stresses and deflections.
A nominally rigid mount should transmit dynamic system. Air gaps and low conductivity epoxy chocks forces with only microlevel elastic deformation and negligible help minimize such deformation. A machine-mounting system should perform its function high lateral loads while stresses and deflections in bolt, for a long life—typically 25 years or more.
Specifications foundation, chocks, and grout remain acceptably low. Creep means time-dependent deflection example, once per year.
Engineers, installers, and operators of under load. The bolts that tie the machine to the mounting system, different coefficients of thermal expansion, when two and which form an integral part of the mounting system, adjacent components of similar coefficients have different should have sufficient stretch and create enough normal temperatures or a combination of both. Machine force across all interfaces to meet the force transmission and mounts with epoxy materials can experience both types deflection performance stated above; of differential thermal expansion; 7.
The mounts, soleplates, and Friction defines the maximum force parallel to an grout layers compressed by the anchor bolt should tolerate interface that the interface can resist before sliding for a the compressive stresses imposed on them; given normal force between the two interfacing materials; 8.
Oil aggravates cracks in concrete, particularly under alternating stresses where it induces a hydraulic action. The GMRC reports referred to address all these secondary issues as they pertain to reciprocating compressors. Check the structural integrity of the concrete foundation and machine-mounting system.
These methods can be identified attenuated and absorbed by the block and soil system. For recipro- on machine characteristics, including unbalanced forces, cating machinery and sensitive machinery, rule-of-thumb speed, weight, center of gravity location, and mounting; procedures by themselves may not be sufficient.
Usually, and at least five times the weight of a reciprocating machine. The machine footprint, weight, and reduced so that the foundation block weight, including pile unbalanced forces govern the size of the foundation. Thus, the engineer should consider These ratios are machine weights inclusive of moving and information from the following three categories before the stationary parts as compared with the weight of the concrete foundation can be preliminarily sized: foundation block.
Additionally, many designers require the 1. The shape of the foundation differential displacement. Geotechnical information maintenance space if required. Environmental conditions plan dimensions of the foundation.
On soft Usually, the preliminary foundation size is established materials, a thinner section may be sufficient, whereas on using the rule-of-thumb method, and then the performance stiffer soils, a thicker section might be required to support the criteria, for both machine and foundation, are verified using rigid body assumption.
If the rigid body assumption is not the equivalent static loading method or dynamic analysis. If applicable, more elaborate computation techniques, such as the equivalent static loading method or dynamic analysis finite element methods, are used. Gazetas provides shows that the foundation is inadequate, the engineer revises some direction in this regard.
One rule-of thumb criterion for the foundation size and repeats the analysis. Another criterion is vibrations. The concept of this method is to provide sufficient given in Section 4. Separation in the vertical direction may also be appro- forces.
Refer to Section 3. Normally, dynamically loaded foundations are not for both reciprocating and rotating machines. When there is placed above building footings or in such locations that the more than one rotor, however, amplitudes are often dynamic effects can transfer into the building footings. To obtain the maximum translational static loading method is a simplified and approximate way of and maximum torsional amplitudes, other phase relationships applying pseudodynamic forces to the machine-supporting may also be investigated.
A complete dynamic analysis of a system is normally This method is used mainly for the design of foundations for performed in two stages: machines weighing 10, lbf 45 kN or less. Determination of the natural frequencies and mode For design of reciprocating machine foundations by the shapes of a machine-foundation system; and static method, the machine manufacturer should provide the 2. Calculation of the machine-foundation system response following data: caused by the dynamic forces.
Resonance is prevented when the Calculated natural frequencies, deformations, and forces ratio of the machine operating frequency to the funda- within the structure supporting the machine should satisfy mental frequency of the machine-foundation system established design requirements and performance criteria falls outside the undesirable range Section 3. In outlined in Section 3.
Any or all of the six frequencies vibration parameters and, therefore, is often used in the final may be compared with the excitation frequency when design stage and for critical machine foundations.
Dynamic checking for resonance conditions. Longitudinal force is applied along the shaft axis. The engineer can conservatively take both the lateral and the longitudinal force as tudes at critical points.
Vertical, lateral, and longitudinal forces are not considered to act concurrently for many types of rotating machines. Calculation of the machine-foundation system response caused by the dynamic forces provides the vibration param- eters—such as displacement, velocity, and acceleration of the masses—and also the internal forces in the members of the machine support system.
Then, these vibration parame- ters are compared with the defined criteria or recommended allowable values for a specific condition Sections 4. This section presents a general introduction to this subject and a summary of approaches and formulae often used to evaluate the stiffness and damping of both soil- supported and pile foundations.
These stiffness and damping relationships, collectively known as impedance, are used for determining both free-vibration performance and motions of the foundation system due to the dynamic loading associated with the machine operation. The simplest mathematical model used in dynamic analysis of machine-foundation systems is a single degree-of- freedom representation of a rigid mass vertically supported on a single spring and damper combination Fig. This model is applicable if the center of gravity of the machine-foundation system is directly over the center of Fig.
The the supporting media is necessary for this model. Because the lines ; Novak and Sheta ; Lakshmanan and Minai The structural representation of these foundations is typically For this model, the engineer needs to calculate the horizontal modeled using finite element techniques.
These impedance values, dimensional plane stress elements, plate bending elements, especially the rocking terms, are usually different in three-dimensional elements, or some combination of these.
The supporting media for these flexible foundations is Application of the lateral dynamic forces can cause a addressed in one of three basic manners. The most simplistic machine-foundation system to twist about a vertical axis.
As in the soil. These spring parameters are computed from the spring vertical model, if the in-plan eccentricities between the center constants determined assuming a rigid foundation assumption of gravity and center of resistance are small, this analysis is or by some similar rational procedure. The other two addressed with a single degree-of-freedom representation. If the support is provided by piles or with a spring and dashpot Fig. Lumped mass includes isolators, the equivalent springs and dampers act at the center the machine mass, foundation mass, and, in some models, of stiffness of those elements.
When the foundation is soil mass. Nevertheless, the total restoring force generated by the column at the top of the lumped mass is the sum of the elastic force in the column and the inertia force of the mass.
Hall, and Woods The dynamic stiffness, being the constant of proportionality between the applied force and displacement, becomes example vertical, is said to have only one degree of freedom Fig. The spring, presumed to be massless, represents the elasticity of the system and is characterized by the stiffness constant k.
Thus, with vibration of an element having distributed mass, The stiffness constant is defined as the force that produces a the dynamic stiffness generally varies with frequency. At low unit displacement of the mass. For a general displacement v frequency, this variation is sometimes close to parabolic, as of the mass, the force in the spring the restoring force is kv.
Because the spring is massless, the dynamic stiffness parameters that are frequency dependent. The magnitude and constant k is equal to the static constant kst, and k and the character of this frequency effect depend on the size of the body, restoring force kv are independent of the rate or frequency at vibration mode, soil layering, and other factors.
The dashpots of Fig. The magnitude of the damper force is length Fig. Equation shows that for a given constant c and displacement amplitude v, the ampli- tude of viscous damping force is proportional to frequency Fig. Several ways are used to account for variations of the dynamic stiffness with frequency in the soil. The equivalent circular foundation is not the same for Veletsos and Nair ; Veletsos and Verbic ; and all directions of motion.
For the three translational direc- Veletsos and Wei have developed appropriate tions, the equivalent circular foundation is determined based equations that represent the impedance to motion offered on an area equivalent to the rectangular foundation; thus, by uniform soil conditions. They developed these these three share a common equivalent radius R. For the formulations using an assumption of uniform elastic or three rotational directions, three unique radii are determined viscoelastic half-space and the related motion of a rigid that have moments of inertia equivalent to their rectangular or flexible foundation on this half-space.
Motions can be counterparts. These relationships are reflected in the translational or rotational. While the calculations can be following equations manually tedious, computer implementation provides acceptable efficiency.
Some of the simpler relevant equations are presented in later sections of this report. Nevertheless, the variation of dynamic For rocking, different equivalent radii are determined for stiffness with frequency can be represented by a each horizontal direction.
For long geometry or variable soil conditions, the trend is to foundations, the assumption of an infinite strip foundation obtain the stiffness and damping of foundations using may be more appropriate Gazetas The domain mathematics or with complex domain mathematics. The half-space can be homogeneous or non- subjective basis and is typified by the damped stiffness models homogeneous layered and isotropic or anisotropic. The complex domain impedance method. The major advantages of this elastic half-space is easier to describe mathematically and is applied in the technique are that it accounts for energy dissipation impedance models of Veletsos and others Veletsos and Nair through elastic waves geometric damping, also known ; Veletsos and Verbic ; Veletsos and Wei Computer programs, such as DYNA, are very useful in this regard.
This assumption in some cases is reasonable. In elastic half-spaces with rigid foundations, except for hori- other cases, it is accepted for lack of any better model and zontal motions, which make a slightly different rigidity because the scope of the foundation design does not warrant assumption.
For a rigid circular foundation the applicable more sophisticated techniques. These are commonly referred formulas are given in Eq. For a rectangular to as half-space models. Alternatively, Eq.
In the norm, ranges from approximately 2. For ranges from approximately 0. Specific are expressly validated for the range of dimensionless relationships can be found in a variety of sources Richart, frequencies from 0 to 1. Implicitly, the other directions are similarly Richart and Whitman , usually in a graphical form.
The limited, as the stiffness parameters are actually static stiff- original source materials contain the mathematical relation- ness values. Often, presentations of the data extend the range ships. There is little difference between using either the circular to ao values as high as 1.
The mass of these models is determined solely as the trans- lational mass and rotational mass moment of inertia for the 4 appropriate directions. For three cases vertical, rocking, and torsional motion , these terms are the same as presented in the Richart- 3 Whitman lumped parameter model. Although material damping is often neglected, as where presented in Section 4. This overestimation can be reduced Constant approximations of Ci1 and Ci2 are given in by the inclusion of material damping Section 4.
Table 4. Poly- For surface foundations, slippage reduces stiffness and nomial expansions of these approximations are also available to increases damping; for embedded foundations, slippage cover a wider range of dimensionless frequencies.
The inclusion of the weakened zone 4. This typically requires more damping relationships. Rather than theoretically assessing complete computer-based numerical analysis. Given all the approximations involved, the agreement required if the soil deposit is a shallow layer. In such cases, between the solutions—the half-space theory and the finite the stiffness increases and geometric damping decreases and element modeling—is very good. For a homoge- Karabalis and Beskos ; Kobayashi and Nishimura neous layer of thickness H with soil shear wave velocity Vs, ; Wolf and Darbre The damping and the reactions acting on the footing sides as equal to those parameters generated by the material alone to be used for of an independent layer overlying the half-space Fig.
In the impedance models, the imaginary the variation of the soil properties with depth. This half-space solutions for the embedment effect. This correction is not an absolute breakpoint based on the approach works quite well, and its accuracy increases with computed layer frequency and the excitation frequency. Short of using computer-based numerical solution tech- Equation a to d describe the side resistance of niques that reasonably represent the loss of geometric the embedded cylinder, analogous to the surface disc, using damping, the foundation engineer should apply judgement to complex, frequency-dependent impedance decrease the geometric damping for shallow layer sites.
The lack of confining pressure at the surface often leads to separation of the soil from the foundation Torsional impedance: d and to the creation of a gap as indicated on Fig. The dimensionless The aforementioned procedures for the inclusion of material parameters Si1 and Si2 relate to the real stiffness and the damping into an elastic solution are accurate but not always damping out-of-phase component of the impedance , convenient.
When the elastic solution is obtained using a respectively. These parameters depend on the dimensionless numerical method, the impedance functions are obtained in frequency ao Eq.
In such cases, an approximate approach often used generated by the footing embedment, not the impedance in to account for material damping multiplies the complex other directions. In complete form, these Si parameters also impedance, evaluated without regard to material damping, depend on material damping of the side layer soils. The values terms are as previously defined. If a and the damping as the imaginary term of the impedance, the large frequency range is important, parameter S should be adjusted stiffness and damping terms considering material considered as frequency dependent and calculated from the damping become expression of impedance functions given in Novak, Nagami, and Aboul-Ella and Novak and Sheta In some cases, where ki and ci are calculated assuming perfect elasticity, consideration of the difference in location of the embedment and ci includes only geometric damping.
Studies indicate impedance and the basic soil impedance may be included in that this approximate approach gives sufficient accuracy at the analysis. For vertical translation and torsion, the total low dimensionless frequencies, but the accuracy deteriorates stiffness and damping results in simple addition of the two with increasing frequency.
Equation and show values. For horizontal translation and rocking, coupling that material damping reduces stiffness in addition to between the two motions should be considered.
The most direct way is to introduce the Veletsos and Verbic ; Veletsos and Nair This approach is more commonly used Another way is to carry out the purely elastic solution and with the Richart-Whitman formulations and does not alter then introduce material damping into the results by applying the stiffness. In such circumstances, broad judgements are the correspondence principle of viscoelasticity. With steady- often applied at the same time so that if the geometric state oscillations considered in the derivation of footing damping is large, the material damping may be neglected.
This simple additive approach is generally recognized as the This replacement should be done consistently wherever least accurate of the possible methods. G occurs in the elastic solution. This includes the shear 4. Pile damping was estimated. In groups of closely spaced piles, the The engineer can determine the constants experimentally character of dynamic stiffness and damping is further or theoretically.
The theoretical approach is commonly used complicated by interaction between individual piles known because experiments, though very useful, are difficult to as pile-soil-pile interaction or group effect. In the theoretical approach, dynamic stiffness is Therefore, recent approaches for determining stiffness and generated by calculating the forces needed to produce a unit damping of piles consider soil-pile interaction in terms of amplitude vibration of the pile head in the prescribed direction continuum mechanics and account for propagation of elastic Fig.
The problem solutions are based on a few For a single pile, the impedance at the pile head can be approaches, such as the continuum approach, the lumped determined from the following mass model, the finite element model, and the boundary integral method Fig. Similarly, V S v2 the effects of embedment are often neglected. If circumstances indicate that the embedment effect may be significant, the Ep Ip procedures outlined in Section 4.
Once these parameters stiffness and damping are established for the single pile, Ep Ip the group effects are determined. Coupling between horizontal translation and rotation: Dynamic response of a pile-supported foundation depends on the dynamic stiffness and damping of the piles. If the pile heads are pinned into the foundation because the piles are stiff in that direction.
In the horizontal direction, head piles. The vertical constants labeled v are the same for piles tend to be very flexible. Consequently, parameters fi1 the fixed and pinned heads. If, however, the to the pile mass density; piles are closely spaced, they interact with each other. Then stiffness and damping of the pile These factors affecting the functions f are not of equal group can be determined by the summation of stiffness and importance in all situations.
Often, some of them can be damping constants of the individual piles. In many cases, neglected, making it possible to present numerical values of initial calculations are performed neglecting the interaction. An overall group efficiency factor is then determined and The pile stiffness diminishes with frequency quickly if the applied to the summations. This happens when the In the vertical and horizontal directions, the summation is soil shear modulus is very low or when the pile is very stiff.
For torsion and sliding coupled with In addition, dynamic stiffness can be considered practically rocking, the position of the center of gravity CG and the independent of frequency for slender piles in average soil.
Thus, the The imaginary part of the impedance pile damping group stiffness and damping with respect to rotation derive grows almost linearly with frequency and, therefore, can be from the horizontal, vertical, and moment resistance of indi- represented by constants of equivalent viscous damping ci , vidual piles and the pile layout. For the damping remain as the principal source of energy dissipation.
With these considerations and notations or both. Apart from these situations, frequency independent shown on Fig. The studies of the dynamic pile-soil-pile interaction The summations extend over all the piles. The vertical eccentricity yc must be with frequency, and these variations are more dramatic addressed as presented in Section 4. This critical length may be estimated from the where kr is the stiffness of individual pile considered in formula Randolph isolation.
Dynamic group effects are complex, and there is no simple where way of alleviating these complexities. The equivalent pier may only be applicable for very The interaction factors for horizontal translation u and closely spaced piles and may overestimate damping.
The summation in the denominator then represents a summation of factors between the reference pile and all other piles in the group. The reference pile should not Fig. The displacement means either a translation or rotation.
These dynamic interaction factors are used in association with stiffness and damping of single piles where in the same way that static interaction factors are used. An increase in The difference between the two previous formulas for kgv damping and strong variation with frequency is often is usually not great. For horizontal stiffness, the approximate obtained. For rotation of a thin rigid cap, the rocking stiffness comes 4.
For thick caps, these corrections can be intro- duced into the equations of the rotation of the cap in the in which the transformation matrix [T] depends on direction vertical plane—the case where pile interaction is neglected. The horizontal and vertical stiff- For torsion of the cap, ignoring the contribution from nesses for the individual battered pile can then be combined individual pile twisting, the group stiffness can be written with the other pile stiffnesses as presented in Section 4.
Group interaction The pile stiffness matrix in global coordinates becomes usually increases the damping ratio, not necessarily the damping constant c. Thus, most engineers diligently adhere to guidelines to minimize such in-plan eccentricities. For carried forward. This transformation The same process may be applied to the damping terms, or, to the CG may be developed on stiffness and damping terms for more accuracy, the transformation can take place using or based on impedance. For simplicity of analysis, many founda- this judgement is tions are treated as a rigid body, and their center of gravity is used as the point of reference for all displacements and rotations.
In this analysis, a horizontal translation greater plan dimension of the foundation block in ft m. This gives rise to a coupling between translation and vibration analysis. Note that tions Fig. The applicability of Eq. Finite element dynamic analysis shows that in Fig. By applying unit translations to a free body of the some of these large combined block foundations may not foundation, examining the forces developed in the support behave as rigid foundations. Analysis of the frequency and system by the translation, and determining the forces needed dynamic response of such foundations using the finite to cause this unit translation, the coupled impedances can be element methods given in Section 4.
A SDOF analysis can be a very effective tool in designing Nevertheless, in most rigid machine-foundation systems, a rigid foundation. When used in conjunction with a para- the horizontal motion is coupled with the rocking motion due metric study the use of a SDOF in the direction of interest to the system center of gravity CG being at one height and can often bound the solution. Furthermore, the use of an the center of resistance CR being at a different level.
A two approximate SDOF analysis can show the feasibility of satis- DOF model represents the coupled response of the system fying particular vibration criteria and can provide a rough for this condition. In general, a six DOF degree of freedom check on more-detailed analysis.
If the foundation earlier, a SDOF system may not be sufficient to represent a is well laid out so that the CG and the CR are positioned over rigid machine-foundation system. For example, a dynamic each other vertically aligned , then the six DOF model force from a rotating machine acting on shaft supports causes mathematically uncouples to become two problems of two translation and rocking motions of the system, and a two DOF DOF rocking about one horizontal axis coupled with trans- system is a more accurate representation of the system.
For a lation along the other horizontal axis for both horizontal two DOF system, the following frequency equation can be directions and two SDOF problems vertical motion and used in solving for the two natural frequencies torsional motion about the vertical axis. When rotational rocking or torsional motions of the foun- If the particular SDOF system under investigation dation exist, it is important to compute displacements at the involved rotational motions, the stiffness term in Eq.
Thus, the motions. These combined motions may be less than or stiffness and mass terms are specifically associated with a greater than the motions of the CG, which are determined specific direction of motion of the machine-foundation through the modal combination.
The calculated natural frequency is then compared 4. The forced response analysis can be and a three or more DOF system should be used. The model should include the machine, structure, and stiffnesses of supporting medium soil or piles.
This calculation forced response analysis is then carried out on a mode-by- is also called normal mode or free vibration analysis. The mode basis, in some cases for a limited number of modes. For these multi-DOF models representing structural the machine-foundation system. The analysis set to zero. The equation of motion reduces to: should account for variation in parameters such as structural stiffness, mass, and soil properties.
Section 4. The machine can be and mode shapes eigenvectors are obtained. An examination quite stiff compared with the structural members. If so, the is then made to determine how the frequencies associated machine can be represented by a mass point or points with the excitation forces generated by machine operation concentrated at their centers of gravity and connected to their match up with the natural frequencies of the system.
If these supports using rigid links. Solid elements with matching operating frequencies are close to the computed system densities can also be used to simulate the mass and mass natural frequencies, a resonance condition exists. Section moment of inertia of the machine. If the equipment is not so 3. The forced response analysis can take the form of a 4. The 4. For the analysis of rotating or reciprocating the design of foundations supporting dynamic equipment.
Such equipment linear structure to a set of given harmonic loads. In the direct solution method, the equations of motion nents that primarily act in flexure, others that are primarily can be solved in the time domain.
This method does not require axial, and others may act primarily in shear. Applicable a natural frequency analysis Eq. This sections of ACI are often used to establish minimum numerical method is more general and flexible than the requirements for axial, flexural, and shear reinforcement. In mode superposition method. In the mode superposition some cases, engineering firms have supplemented these method, a natural frequency analysis is performed first.
For corners and notches. Such criteria are typically structure although not in any simple form. Established relationships specific for example, only for turbine-generator pedestals or suggest that the ratio of dynamic to static modulus can vary only for foundation slabs over 6 ft 1. In practice, engineers treat this strain-rate effect addressed in this document.
In some firms, engineers perform calculations Largely because of the broad range represented in this using the higher dynamic modulus while other firms and class of construction, accepted standards have not evolved.
The distinction is more impor- reinforcement applicable across the board for these designs. A The difference can also be important in compressor founda- minimum concrete strength of psi 21 MPa can be tions where the stiffness of the machine frame must be eval- applied. For most foundations and foundations supporting uated against the stiffness of the concrete structure.
For API equipment, a strength of psi 28 MPa is simple, block-type foundations, the concrete modulus of commonly specified and may be required.
In most cases, the elasticity has no real effect on the design. Most reinforcing steel is most commonly used for dynamic hammer manufacturers are familiar with German DIN machine foundations. Good design practice requires particular Standard That document is summarized in the attention to the detailing of the reinforcement, including following paragraphs for general information.
Excessive reinforcement can create should consider the effect of vibrations on nearby structures and constructibility and quality problems and should be avoided. One reference equation suggested by DIN is Some firms specify a minimum reinforcing of 3. The foundation weight should be increased or Other equipment can require more significant consideration decreased to make up for a lighter or heavier anvil.
In such cases, ACI provides guidance, The design of the foundation block considers a statically particularly where the flexural characteristics of the founda- equivalent load determined from the impact energy and tion are most important.
Minimum reinforcement of the foundation address fatigue include: block is set at 1. Bending and shear concrete motion. Suitable factors specified by ACI ; and development of the reinforcement is very important. Post-tensioning puts the block in compression, offsetting the dynamic and shrinkage stresses. This ideal- ization maximizes the compression at the top where it is needed the most.
An average pressure of psi kPa translates to psi kPa at the top, providing the necessary residual compression. Vertical post-tensioning rods are anchored as deep as possible into the foundation mat and are sleeved or taped along their length to allow them to stretch. The embedded end is anchored by a nut with a diameter twice the rod diam- eter and a thickness 1. Horizontal rods are nonbonded sleeved and anchored at each end of the block through thick bearing plates designed to distribute the load on the concrete.
High-strength steel rods are recom- mended for post-tensioning compressor blocks Smalley and Pantermuehl The concrete should have a day strength of at least psi 24 MPa , superior tensile strength, and, when Fig. Compliance courtesy of Robert L. This is especially true for machine anchorage are the anchor bolts and the support combustion turbines, steam turbines, and compressors. The system directly under the machine frame at the anchor bolt engineer should address the effects of these thermal condi- location.
Support systems range from a full bed of grout to tions in the design phase. Inadequate consideration of the various designs of soleplates and chocks, fixed or adjustable, thermal effects can lead to early cracking of the foundation, shown in Fig. Additionally, isolation support systems which is then further increased by the dynamic effects. Various styles of anchor bolts are shown in Fig. Calculation of thermal induced bending requires proper 4. ACI provides some guidance that can machinery require that sufficient clamping force be available be extrapolated to hot equipment.
The methodologies that may be transferable to certain machine clamping force should allow smooth transmission of unbal- foundations. Heat transfer calculations can also be anced machine forces into the foundation so that the machine performed either one-, two-, or three-dimensionally.
In the presence of unbalanced forces, a machine and the concrete; that has a low clamping force psi [2. Shrinkage cracks or ment manufacturer. Higher values are appropriate for more surface drying cracks are expected in any concrete block aggressive machines. Clamping force, also known as foundation, especially when the water content is excessive. Do not combine values from the two systems. Conditions can change over time due to machine wear ASTM strength, min.
Properties as given in the designation Grade Diameter, mm min. Because M64 and A M B7 smaller the number and diameter of anchor bolts are determined by M64 to M the machine manufacturer, the engineer can maximize capacity by specifying the higher-strength steels.
The practi- required frictional holding capacity Fr Section 3. Because holes in the frame and cross-head 4. A pound-mass, when subjected to a force of is the unit of force that, when acting on a mass of one slug, one pound, accelerates To compute a minimum required In addition to the depth, the engineer should pay attention yield stress for this application to the bolt style. Load In general, problems involving the dynamic properties of Design loads classification soils are divided into acii and large strain amplitude Weight of structure, equipment, internals, insulation, and platforms responses.
The displacement means either a translation or rotation. See also single degree-of-freedom system and multi- analysis neglects the initial conditions and involves only the degree-of-freedom system. This overestimation can be reduced Constant approximations of Ci1 and Ci2 are given in by the inclusion of material damping Section 4. The mechanical drive because the inertia forces at low speeds are small. For construction, the design drawings or specifi- segments and allow them cure and shrink as long as the cations should provide bolt diameters, types, overall lengths, threaded lengths, projections, materials, the method of bolt construction schedule permits before the intervening tightening, and required torques.
Some small presses may have inclinable beds combinations frequently used for the various load conditions so that the slide is not moving vertically. In specifying grout systems, the engi- High-range water-reducing admixtures may be an appro- neer should consider the different characteristics of each priate choice because they are consistent with their general type of I think you intended for it to be zero and I think the default value is zero The isolation system provides the stiffness and apply.
In Note that the expressions contain two terms each with a other cases, An overall group efficiency factor is then determined and The pile stiffness diminishes with frequency quickly if the applied to the summations. For the three translational direc- Veletsos and Wei have developed appropriate tions, the equivalent circular foundation is determined based equations that represent the impedance to motion offered on an area equivalent to the rectangular foundation; thus, by uniform soil conditions.
These methods involve measuring the soil characteristics, in-place, as close as possible to the actual foundation location s.
The air gap Calculation of the exact thermal loading is very difficult between the machine casing and foundation provides a because it depends on a number of factors, including significant means for dissipating heat, and its effect should distance between anchor points, magnitude of temperature be included when establishing Aci Specification for aci Click here to download full list of books.
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Use of Fly Ash in Concrete. Product details Aci As an engineering aid to those persons engaged in the design of foundations for machinery, this document presents many current practices in the engineering, construction, repair, and upgrade of dynamic equipment foundations. Aco to Know Us.
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