This document provides an introduction to machine foundation design, which involves structural dynamics, structural engineering, and geotechnical engineering. It discusses the differences between static and dynamic analysis, and covers fundamental concepts in vibration theory like natural frequency, damping, and resonance that are important for machine foundation design. Harmonic motion is described as the simplest form of vibration induced by machines. Different types of vibrating machines are discussed, including reciprocating machines, rotary machines, and impact machines. Machine foundations must be designed to withstand the vibratory loads from machine operation while preventing excessive vibration that could damage the machine or foundation.
The document discusses machine foundations used in the oil and gas industry. It begins by introducing the different types of machines, such as centrifugal and reciprocating machines, and how they are classified based on speed. It then discusses the various types of foundations used to support these machines, including block foundations and frame foundations. The document outlines the inputs needed for foundation design, which include project specifications, soil parameters, and machine details from the vendor. It describes the process of analyzing machine foundations, including dynamic and static analyses. Key aspects like natural frequencies, displacements, and strength are evaluated.
Design Procedure of Tabletop Foundations for Vibrating MachinesKee H. Lee, P.Eng.
The document provides an overview of the design procedure and requirements for analyzing the dynamic response of a tabletop foundation that supports large rotating equipment. It outlines the steps, which include: 1) preliminary sizing and geometry of the foundation, 2) determining design loads from the equipment, 3) dynamic analysis to calculate natural frequencies and mode shapes, 4) response spectrum or time history analysis to evaluate vibration performance, and 5) structural sizing to satisfy strength requirements. Key considerations discussed include avoiding resonant vibrations, applying dynamic loads as harmonic functions, and limiting vibration velocities and foundation settlements.
Design of steel structure as per is 800(2007)ahsanrabbani
It does not offer resistance against rotation and also termed as a hinged or pinned connections.
It transfers only axial or shear forces and it is not designed for moment
It is generally connected by single bolt/rivet and therefore full rotation is allowed
Dynamic analysis of machine foundation: when a static force cannot give the f...Gary Yung
This paper presents various design approaches for machine foundations from a rule of thumb static design to a comprehensive dynamic analysis and discusses their design limitations.
This document provides tables of computed moment and reaction coefficients for rectangular plates under different loading and boundary conditions. The tables allow engineers to quickly analyze plate components in structures by providing normalized moment and reaction values for a variety of plate geometry ratios and representative load cases, including uniform, varying, point, and line loads. Five boundary conditions, nine ratios of plate dimensions, and eleven representative load cases are considered. Supplementary appendices demonstrate an example application and explain the finite difference method used to generate the table values.
The Pushover Analysis from basics - Rahul LeslieRahul Leslie
Pushover analysis has been in the academic-research arena for quite long. The papers published in this field usually deals mostly with proposed improvements to the approach, expecting the reader to know the basics of the topic... while the common structural design practitioner, not knowing the basics, is left out from participating in those discussions. Here I’m making an effort to bridge that gap by explaining the Pushover analysis, from basics, in its simplicity.
A write up on this topic can be found at http://rahulleslie.blogspot.in/p/blog-page.html, though does not cover the full spectrum presented in this slide show.
Earthquake Load Calculation (base shear method)
The 3-story standard office building is located in Los Angeles situated on stiff soil. The
structure of the building is steel special moment frame. All moment-resisting frames are
located at the perimeter of the building. Determine the earthquake force on each story in
North-South direction.
This document discusses multi-degree-of-freedom (MDOF) systems and their analysis. It introduces concepts such as flexibility and stiffness matrices, natural frequencies and mode shapes, orthogonality of modes, and equations of motion. Methods for analyzing free and forced vibration of MDOF systems in the time domain are presented, including modal superposition and direct integration. An example 3DOF system is analyzed to illustrate the concepts.
The document discusses machine foundations used in the oil and gas industry. It begins by introducing the different types of machines, such as centrifugal and reciprocating machines, and how they are classified based on speed. It then discusses the various types of foundations used to support these machines, including block foundations and frame foundations. The document outlines the inputs needed for foundation design, which include project specifications, soil parameters, and machine details from the vendor. It describes the process of analyzing machine foundations, including dynamic and static analyses. Key aspects like natural frequencies, displacements, and strength are evaluated.
Design Procedure of Tabletop Foundations for Vibrating MachinesKee H. Lee, P.Eng.
The document provides an overview of the design procedure and requirements for analyzing the dynamic response of a tabletop foundation that supports large rotating equipment. It outlines the steps, which include: 1) preliminary sizing and geometry of the foundation, 2) determining design loads from the equipment, 3) dynamic analysis to calculate natural frequencies and mode shapes, 4) response spectrum or time history analysis to evaluate vibration performance, and 5) structural sizing to satisfy strength requirements. Key considerations discussed include avoiding resonant vibrations, applying dynamic loads as harmonic functions, and limiting vibration velocities and foundation settlements.
Design of steel structure as per is 800(2007)ahsanrabbani
It does not offer resistance against rotation and also termed as a hinged or pinned connections.
It transfers only axial or shear forces and it is not designed for moment
It is generally connected by single bolt/rivet and therefore full rotation is allowed
Dynamic analysis of machine foundation: when a static force cannot give the f...Gary Yung
This paper presents various design approaches for machine foundations from a rule of thumb static design to a comprehensive dynamic analysis and discusses their design limitations.
This document provides tables of computed moment and reaction coefficients for rectangular plates under different loading and boundary conditions. The tables allow engineers to quickly analyze plate components in structures by providing normalized moment and reaction values for a variety of plate geometry ratios and representative load cases, including uniform, varying, point, and line loads. Five boundary conditions, nine ratios of plate dimensions, and eleven representative load cases are considered. Supplementary appendices demonstrate an example application and explain the finite difference method used to generate the table values.
The Pushover Analysis from basics - Rahul LeslieRahul Leslie
Pushover analysis has been in the academic-research arena for quite long. The papers published in this field usually deals mostly with proposed improvements to the approach, expecting the reader to know the basics of the topic... while the common structural design practitioner, not knowing the basics, is left out from participating in those discussions. Here I’m making an effort to bridge that gap by explaining the Pushover analysis, from basics, in its simplicity.
A write up on this topic can be found at http://rahulleslie.blogspot.in/p/blog-page.html, though does not cover the full spectrum presented in this slide show.
Earthquake Load Calculation (base shear method)
The 3-story standard office building is located in Los Angeles situated on stiff soil. The
structure of the building is steel special moment frame. All moment-resisting frames are
located at the perimeter of the building. Determine the earthquake force on each story in
North-South direction.
This document discusses multi-degree-of-freedom (MDOF) systems and their analysis. It introduces concepts such as flexibility and stiffness matrices, natural frequencies and mode shapes, orthogonality of modes, and equations of motion. Methods for analyzing free and forced vibration of MDOF systems in the time domain are presented, including modal superposition and direct integration. An example 3DOF system is analyzed to illustrate the concepts.
This document discusses response spectra and design spectra. It begins by explaining how response spectra are developed by analyzing the response of single-degree-of-freedom systems to ground motion records and plotting the maximum response versus natural period. Design spectra are then developed as smooth versions of response spectra to account for uncertainties in natural period. The key differences between response and design spectra are also summarized.
This document provides design aids for reinforced concrete structures based on Indian Standard IS: 456-1978 Code of Practice for Plain and Reinforced Concrete.
The design aids cover material strength and stress-strain relationships, flexural members, compression members, shear and torsion, development length and anchorage, working stress design, deflection calculation, and general tables. Charts and tables are provided for preliminary and final design of beams, slabs, and columns. Assumptions made in developing the design aids are explained. An example illustrates the use of the design aids. Important points regarding the use and limitations of the charts and tables are noted.
The design aids were prepared based on examination of international handbooks and consultation with Indian
This document presents a literature review and overview of machine foundation design for a civil engineering course project. It discusses the increasing vibrations caused by advancing machinery technology. Various types of machine foundations are described, including block, box, spring mounted block, combined block, tabletop, tabletop with isolator, inertia block in structure, and pile supported foundations. Foundation design criteria aim to limit motion amplitudes. Soil exploration is important to understand foundation response to dynamic loads. Depth of site exploration should be sufficient. In conclusion, thermal power plants require extensive foundation studies due to heavy equipment, and foundation issues cause about 19% of equipment problems annually.
This document analyzes methods to reduce vibrations transmitted from machines to foundations. It examines a frame foundation model supported by springs, hard rock basalt layers, and soft rubber layers beneath the foundation. Dynamic analysis was conducted to determine the foundation's natural frequency and plot transmissibility curves. Results show that a soft rubber layer is most effective at isolating vibrations, with support reaction decreasing significantly as stiffness increases, indicating better vibration control compared to spring or hard rock basalt supports. The document concludes with recommendations for machine foundation design to minimize vibration transfer.
Design of column base plates anchor boltKhaled Eid
This document discusses the design of column base plates and steel anchorage to concrete. It covers base plate materials and design for different load cases including axial, moment, and shear loads. It also discusses anchor rod types, materials, and design for tension and shear loading based on calculations of the steel and concrete breakout strengths according to building codes.
Shear Force And Bending Moment Diagram For FramesAmr Hamed
This document discusses analyzing shear and moment diagrams for frames. It provides procedures for determining reactions, axial forces, shear forces, and moments at member ends. Examples are given of drawing shear and moment diagrams for simple frames with different joint conditions, including pin and roller supports. Diagrams for a three-pin frame example are shown.
The document discusses buckling and its theories. It defines buckling as the failure of a slender structural member subjected to compressive loads. It provides examples of structures that can experience buckling. It explains Euler's theory of buckling which derived an equation for the critical buckling load of a long column based on its bending stress. The assumptions of Euler's theory are listed. Four cases of long column buckling based on end conditions are examined: both ends pinned, both ends fixed, one end fixed and one end pinned, one end fixed and one end free. Effective lengths are defined for each case and the corresponding critical buckling loads given. Limitations of Euler's theory are noted. Rankine's empirical formula for calculating ultimate
This document provides an overview of the design of steel beams. It discusses various beam types and sections, loads on beams, design considerations for restrained and unrestrained beams. For restrained beams, it covers lateral restraint requirements, section classification, shear capacity, moment capacity under low and high shear, web bearing, buckling, and deflection checks. For unrestrained beams, it discusses lateral torsional buckling, moment and buckling resistance checks. Design procedures and equations for determining effective properties and capacities are also presented.
This document summarizes the design of a single reinforced concrete corbel according to ACI 318-05. The corbel is 300mm wide and 500mm deep with 35MPa concrete and 415MPa steel reinforcement. It was designed to resist a vertical load of 370kN applied 100mm from the face of the column. The design includes checking the vertical load capacity, calculating the required shear friction and main tension reinforcement, and designing the horizontal reinforcement. The provided reinforcement of 3 No.6 bars for tension and 3 No.3 link bars at 100mm spacing was found to meet all design requirements.
This document provides an overview of wind load calculation procedures according to the International Building Code (IBC) 2012 and American Society of Civil Engineers (ASCE) 7-10 standards. It defines important terms related to wind loads and explains changes made in ASCE 7-10 from the previous ASCE 7-05 standard. The major wind load calculation procedures covered are the directional procedure for buildings of all heights, the envelop procedure for low-rise buildings, and the wind tunnel procedure. Steps of the directional procedure are outlined, including determining the risk category, basic wind speed, wind parameters, velocity pressure coefficients, and velocity pressure.
04-LRFD Concept (Steel Structural Design & Prof. Shehab Mourad)Hossam Shafiq II
The document discusses load and resistance factor design (LRFD) methods for structural design. It provides information on:
1) Types of loads that must be considered in design like dead, live, and environmental loads. Load factors are used to increase calculated loads to account for uncertainties.
2) Resistance factors are used to reduce nominal member strength to account for variability in material strength and dimensions.
3) The LRFD method aims for a 99.7% reliability target where factored resistance must exceed factored loads based on load combinations outlined in codes.
SFD & BMD Shear Force & Bending Moment DiagramSanjay Kumawat
The document discusses shear force and bending moment in beams. It defines key terms like beam, transverse load, shear force, bending moment, and types of loads, supports and beams. It explains how to calculate and draw shear force and bending moment diagrams for different types of loads on beams including point loads, uniformly distributed loads, uniformly varying loads, and loads producing couples or overhangs. Sign conventions and the effect of reactions, loads and geometry on the shear force and bending moment diagrams are also covered.
1. The document describes a problem involving the elongation of a tapered bar made of plastic that has a hole drilled through part of its length and is under compressive loads at its ends.
2. It provides the dimensions, material properties, and loads and asks for the maximum diameter of the hole if the shortening of the bar is limited to 8 mm.
3. The solution sets up an equation for the shortening of the bar in terms of the hole diameter and substitutes the given values to solve for the maximum hole diameter of 23.9 mm.
This document gives the class notes of Unit 3 Compound stresses. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document provides information about shear stress and shear force in structural elements like beams. It defines shear stress and explains how to calculate it. It discusses the distribution of shear stress across different cross section shapes, including rectangular, circular, T-sections, and wide flange sections. It also describes how shear stress affects steel and concrete materials and what reinforcement is used to address problems caused by shear stresses.
Structural Analysis, Hibbeler, 8th ed Textbook Bahzad5
This document provides tables and equations for analyzing beam deflections and slopes for various types of beams. It includes equations to determine the deflection (u), slope (v), maximum deflection (umax), and maximum slope (vmax) at different locations along beams subjected to a combination of loads, including concentrated forces (P), uniformly distributed loads (w), and moments (M). It also provides equations for determining deflections and slopes of beams with variable cross sections.
This document discusses the calculation of wind loads for structural design. It provides background on wind loads and defines key terms. It outlines wind speed areas in Tanzania and the design procedure, which involves determining the site wind speed, characteristic wind pressure, external and internal pressures on the structure, and the net pressure. Examples are provided to demonstrate calculating wind loads. Load factors of safety and load combinations are also defined.
This document provides an overview of different seismic analysis methods for reinforced concrete buildings according to Indian code IS 1893-2002, including linear static, nonlinear static, linear dynamic, and nonlinear dynamic analysis. It describes the basic procedures for each analysis type and provides examples of how to calculate design seismic base shear, distribute seismic forces vertically and horizontally, and determine drift and overturning effects. Case studies are presented comparing the results of static and dynamic analysis for regular and irregular multi-storey buildings modeled in SAP2000.
Shear Force And Bending Moment Diagram For Beam And Framegueste4b1b7
This document discusses shear force and bending moment diagrams for beams. It provides the following key points:
1) Shear force and bending moment diagrams show the variation of shear force V and bending moment M over the length of a beam, which is necessary for design analysis.
2) The maximum bending moment is the primary consideration in design, and its value and position must be determined.
3) The procedure for drawing shear force and bending moment diagrams involves first calculating support reactions, then plotting the shear diagram with slope equal to loading, and finally the moment diagram with slope equal to shear.
This document summarizes a paper on the design of machine foundations and the effects of earthquakes. It discusses the need for improved interaction between foundation designers and machine manufacturers to ensure better machine performance. It describes design methodologies and modeling approaches for machine foundations subjected to dynamic loads. Specifically, it recommends using finite element analysis with caution, discusses vibration isolation techniques, and touches on modeling and analyzing the effects of earthquakes on machine foundations.
This document discusses ground reinforcement in seismic areas to improve the bearing capacity of shallow foundations. It presents the yield design theory framework for evaluating seismic bearing capacity, which defines a bounding surface delimiting allowable load combinations. This framework has been extended to a new design concept using soil reinforcement with inclusions to significantly improve foundation seismic bearing capacity. Numerical studies and experiments have validated this concept and the theoretical tools.
This document discusses response spectra and design spectra. It begins by explaining how response spectra are developed by analyzing the response of single-degree-of-freedom systems to ground motion records and plotting the maximum response versus natural period. Design spectra are then developed as smooth versions of response spectra to account for uncertainties in natural period. The key differences between response and design spectra are also summarized.
This document provides design aids for reinforced concrete structures based on Indian Standard IS: 456-1978 Code of Practice for Plain and Reinforced Concrete.
The design aids cover material strength and stress-strain relationships, flexural members, compression members, shear and torsion, development length and anchorage, working stress design, deflection calculation, and general tables. Charts and tables are provided for preliminary and final design of beams, slabs, and columns. Assumptions made in developing the design aids are explained. An example illustrates the use of the design aids. Important points regarding the use and limitations of the charts and tables are noted.
The design aids were prepared based on examination of international handbooks and consultation with Indian
This document presents a literature review and overview of machine foundation design for a civil engineering course project. It discusses the increasing vibrations caused by advancing machinery technology. Various types of machine foundations are described, including block, box, spring mounted block, combined block, tabletop, tabletop with isolator, inertia block in structure, and pile supported foundations. Foundation design criteria aim to limit motion amplitudes. Soil exploration is important to understand foundation response to dynamic loads. Depth of site exploration should be sufficient. In conclusion, thermal power plants require extensive foundation studies due to heavy equipment, and foundation issues cause about 19% of equipment problems annually.
This document analyzes methods to reduce vibrations transmitted from machines to foundations. It examines a frame foundation model supported by springs, hard rock basalt layers, and soft rubber layers beneath the foundation. Dynamic analysis was conducted to determine the foundation's natural frequency and plot transmissibility curves. Results show that a soft rubber layer is most effective at isolating vibrations, with support reaction decreasing significantly as stiffness increases, indicating better vibration control compared to spring or hard rock basalt supports. The document concludes with recommendations for machine foundation design to minimize vibration transfer.
Design of column base plates anchor boltKhaled Eid
This document discusses the design of column base plates and steel anchorage to concrete. It covers base plate materials and design for different load cases including axial, moment, and shear loads. It also discusses anchor rod types, materials, and design for tension and shear loading based on calculations of the steel and concrete breakout strengths according to building codes.
Shear Force And Bending Moment Diagram For FramesAmr Hamed
This document discusses analyzing shear and moment diagrams for frames. It provides procedures for determining reactions, axial forces, shear forces, and moments at member ends. Examples are given of drawing shear and moment diagrams for simple frames with different joint conditions, including pin and roller supports. Diagrams for a three-pin frame example are shown.
The document discusses buckling and its theories. It defines buckling as the failure of a slender structural member subjected to compressive loads. It provides examples of structures that can experience buckling. It explains Euler's theory of buckling which derived an equation for the critical buckling load of a long column based on its bending stress. The assumptions of Euler's theory are listed. Four cases of long column buckling based on end conditions are examined: both ends pinned, both ends fixed, one end fixed and one end pinned, one end fixed and one end free. Effective lengths are defined for each case and the corresponding critical buckling loads given. Limitations of Euler's theory are noted. Rankine's empirical formula for calculating ultimate
This document provides an overview of the design of steel beams. It discusses various beam types and sections, loads on beams, design considerations for restrained and unrestrained beams. For restrained beams, it covers lateral restraint requirements, section classification, shear capacity, moment capacity under low and high shear, web bearing, buckling, and deflection checks. For unrestrained beams, it discusses lateral torsional buckling, moment and buckling resistance checks. Design procedures and equations for determining effective properties and capacities are also presented.
This document summarizes the design of a single reinforced concrete corbel according to ACI 318-05. The corbel is 300mm wide and 500mm deep with 35MPa concrete and 415MPa steel reinforcement. It was designed to resist a vertical load of 370kN applied 100mm from the face of the column. The design includes checking the vertical load capacity, calculating the required shear friction and main tension reinforcement, and designing the horizontal reinforcement. The provided reinforcement of 3 No.6 bars for tension and 3 No.3 link bars at 100mm spacing was found to meet all design requirements.
This document provides an overview of wind load calculation procedures according to the International Building Code (IBC) 2012 and American Society of Civil Engineers (ASCE) 7-10 standards. It defines important terms related to wind loads and explains changes made in ASCE 7-10 from the previous ASCE 7-05 standard. The major wind load calculation procedures covered are the directional procedure for buildings of all heights, the envelop procedure for low-rise buildings, and the wind tunnel procedure. Steps of the directional procedure are outlined, including determining the risk category, basic wind speed, wind parameters, velocity pressure coefficients, and velocity pressure.
04-LRFD Concept (Steel Structural Design & Prof. Shehab Mourad)Hossam Shafiq II
The document discusses load and resistance factor design (LRFD) methods for structural design. It provides information on:
1) Types of loads that must be considered in design like dead, live, and environmental loads. Load factors are used to increase calculated loads to account for uncertainties.
2) Resistance factors are used to reduce nominal member strength to account for variability in material strength and dimensions.
3) The LRFD method aims for a 99.7% reliability target where factored resistance must exceed factored loads based on load combinations outlined in codes.
SFD & BMD Shear Force & Bending Moment DiagramSanjay Kumawat
The document discusses shear force and bending moment in beams. It defines key terms like beam, transverse load, shear force, bending moment, and types of loads, supports and beams. It explains how to calculate and draw shear force and bending moment diagrams for different types of loads on beams including point loads, uniformly distributed loads, uniformly varying loads, and loads producing couples or overhangs. Sign conventions and the effect of reactions, loads and geometry on the shear force and bending moment diagrams are also covered.
1. The document describes a problem involving the elongation of a tapered bar made of plastic that has a hole drilled through part of its length and is under compressive loads at its ends.
2. It provides the dimensions, material properties, and loads and asks for the maximum diameter of the hole if the shortening of the bar is limited to 8 mm.
3. The solution sets up an equation for the shortening of the bar in terms of the hole diameter and substitutes the given values to solve for the maximum hole diameter of 23.9 mm.
This document gives the class notes of Unit 3 Compound stresses. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document provides information about shear stress and shear force in structural elements like beams. It defines shear stress and explains how to calculate it. It discusses the distribution of shear stress across different cross section shapes, including rectangular, circular, T-sections, and wide flange sections. It also describes how shear stress affects steel and concrete materials and what reinforcement is used to address problems caused by shear stresses.
Structural Analysis, Hibbeler, 8th ed Textbook Bahzad5
This document provides tables and equations for analyzing beam deflections and slopes for various types of beams. It includes equations to determine the deflection (u), slope (v), maximum deflection (umax), and maximum slope (vmax) at different locations along beams subjected to a combination of loads, including concentrated forces (P), uniformly distributed loads (w), and moments (M). It also provides equations for determining deflections and slopes of beams with variable cross sections.
This document discusses the calculation of wind loads for structural design. It provides background on wind loads and defines key terms. It outlines wind speed areas in Tanzania and the design procedure, which involves determining the site wind speed, characteristic wind pressure, external and internal pressures on the structure, and the net pressure. Examples are provided to demonstrate calculating wind loads. Load factors of safety and load combinations are also defined.
This document provides an overview of different seismic analysis methods for reinforced concrete buildings according to Indian code IS 1893-2002, including linear static, nonlinear static, linear dynamic, and nonlinear dynamic analysis. It describes the basic procedures for each analysis type and provides examples of how to calculate design seismic base shear, distribute seismic forces vertically and horizontally, and determine drift and overturning effects. Case studies are presented comparing the results of static and dynamic analysis for regular and irregular multi-storey buildings modeled in SAP2000.
Shear Force And Bending Moment Diagram For Beam And Framegueste4b1b7
This document discusses shear force and bending moment diagrams for beams. It provides the following key points:
1) Shear force and bending moment diagrams show the variation of shear force V and bending moment M over the length of a beam, which is necessary for design analysis.
2) The maximum bending moment is the primary consideration in design, and its value and position must be determined.
3) The procedure for drawing shear force and bending moment diagrams involves first calculating support reactions, then plotting the shear diagram with slope equal to loading, and finally the moment diagram with slope equal to shear.
This document summarizes a paper on the design of machine foundations and the effects of earthquakes. It discusses the need for improved interaction between foundation designers and machine manufacturers to ensure better machine performance. It describes design methodologies and modeling approaches for machine foundations subjected to dynamic loads. Specifically, it recommends using finite element analysis with caution, discusses vibration isolation techniques, and touches on modeling and analyzing the effects of earthquakes on machine foundations.
This document discusses ground reinforcement in seismic areas to improve the bearing capacity of shallow foundations. It presents the yield design theory framework for evaluating seismic bearing capacity, which defines a bounding surface delimiting allowable load combinations. This framework has been extended to a new design concept using soil reinforcement with inclusions to significantly improve foundation seismic bearing capacity. Numerical studies and experiments have validated this concept and the theoretical tools.
The document provides an overview of the design procedure and requirements for analyzing the dynamic response of a tabletop foundation that supports large turbine equipment. It outlines the steps, which include preliminary sizing, determining design loads, performing a modal analysis to identify natural frequencies, and conducting a dynamic analysis using time-history or response spectrum methods. Design criteria are specified, such as limiting vibration velocities, operating within 0.8-1.2 times the foundation's natural frequency, and not exceeding 75% of allowable bearing capacity under static and dynamic load combinations. The document describes the loads considered, including static, seismic, and dynamic loads from unbalanced rotating masses, and how they are modeled in the structural analysis.
Analysis and Design of RECTANGULAR SEWERAGE TANK_2023.docxadnan885140
This document provides an overview of the analysis and design of a rectangular sewerage tank. It begins with an introduction to the project, which involves developing an understanding of structural analysis and design of rectangular tanks. The document then reviews relevant previous literature on the topic. It presents the theoretical basis for a matrix analysis method and design approach, including developing stiffness matrices to model the structural behavior. It also describes a computer program developed for the analysis. The document outlines that the project will be presented over five chapters covering the introduction, literature review, theory, computer program, and conclusions/recommendations.
Performance of Flat Slab Structure Using Pushover AnalysisIOSR Journals
Performance Based Seismic Engineering is the modern approach to earthquake resistant design. It
is a limit-state based design approach extended to cover complex range of issues faced by structural engineers.
Flat slabs are becoming popular and gaining importance as they are economical as compared to beam-column
connections in conventional slab. Many existing flat slabs may not have been designed for seismic forces so it is
important to study their response under seismic conditions and to evaluate seismic retrofit schemes. In this
paper we have discussed the results obtained by performing push over analysis on flat slabs by using most
common software SAP2000. A (G+7) frame having 5 bays is considered for analysis. It is observed that the
performance point of flat slab is more as compared to conventional building.
IRJET- Projection Effect on Seismic Response of Square Symmetric Structure (U...IRJET Journal
This document discusses a study that analyzes the seismic response of a square symmetric structure with different types of projections.
A 5-story square structure with a waffle slab system is initially modeled in ETABS. Three types of projections are then applied - Plus, H, and H-Plus shapes - keeping the total projection area the same. Response spectrum analysis and equivalent static force analysis are performed to obtain seismic parameters like storey deflection, storey shear, base shear, and time period for each model.
The results, including modal displacements and deformations, are then compared between the three models to understand how the different geometric orientations of the projections influence the dynamic response of the structure. In particular, the
International Refereed Journal of Engineering and Science (IRJES)irjes
International Refereed Journal of Engineering and Science (IRJES) is a leading international journal for publication of new ideas, the state of the art research results and fundamental advances in all aspects of Engineering and Science. IRJES is a open access, peer reviewed international journal with a primary objective to provide the academic community and industry for the submission of half of original research and applications
International Refereed Journal of Engineering and Science (IRJES)irjes
International Refereed Journal of Engineering and Science (IRJES) is a leading international journal for publication of new ideas, the state of the art research results and fundamental advances in all aspects of Engineering and Science. IRJES is a open access, peer reviewed international journal with a primary objective to provide the academic community and industry for the submission of half of original research and applications
Analysis and Design of RECTANGULAR SEWERAGE TANK_2023.docxAdnan Lazem
This document provides an introduction, literature review, and theoretical basis for analyzing and designing rectangular sewerage tanks. The introduction discusses underground rectangular concrete walls that are subjected to lateral hydrostatic pressure. The objective is to provide a solution for soil-structure interaction using finite element methods. Chapter 2 reviews previous literature on linear analysis of in-plane structures using stiffness matrix methods. Chapter 3 describes the theory behind the stiffness matrix method, including developing the element [B] matrix, [k] matrix, [kBT] and [BKBT] matrices. The document is divided into 5 chapters that cover the introduction, literature review, theory, description of a computer program developed for the analysis, and discussion of results and recommendations.
Analysis and Design of CIRCULAR SEWERAGE TANK_2023.docxadnan885140
This document provides an overview of the analysis and design of a circular sewerage tank. It discusses the development of a stiffness matrix method to analyze the structural behavior of cylindrical walls subjected to radial pressure. The objective is to determine the internal forces and edge reactions. The analysis involves developing element stiffness and transformation matrices and assembling them into a global stiffness matrix. The matrix equations are then solved to obtain displacements and internal forces for design. The document outlines the theory, literature review, analysis method, computer program, and conclusions for the project on the circular sewerage tank.
Vibrations are oscillations in mechanical systems that can occur freely without external forces. While some vibrations cause problems, others can be beneficial. The role of vibration analysis is to model and predict potential problems to inform design modifications before manufacturing. Modeling vibrations accurately is challenging and requires considering different levels of complexity depending on assumptions about system rigidity and mass distributions. Linear systems obey the principle of superposition, which will guide the course's focus on analyzing free and forced vibrations of linear systems using generalized coordinates to describe particle kinematics.
This thesis examines the design of dynamically loaded foundations for pumps and compressors. It provides background on different machine and foundation types that must account for dynamic loads. Key design criteria are avoiding resonance, limiting vibration amplitudes, and restricting settlement. An Excel file is created to calculate foundation parameters for rotary and reciprocating machines based on machine properties, soil properties, and theoretical models representing different vibration modes as spring-mass-damper systems. The resulting file allows checking foundation compliance with criteria for dynamically loaded foundations.
Structural morphology optimization by evolutionary proceduresFranco Bontempi
The paper deals with the identification of optimal structural morphologies through evolutionary procedures.
Two main approaches are considered. The first one simulates the Biological Growth (BG) of natural structures like the bones and the trees. The second one, called Evolutionary Structural Optimization (ESO), removes material at low stress level. Optimal configurations are addressed by proper optimality indexes and by a monitoring of the structural response. Design graphs suitable to this purpose are introduced and employed in the optimization of a pylon carrying a suspended roof and of a bridge under multiple loads.
This document discusses two evolutionary procedures - Biological Growth (BG) and Evolutionary Structural Optimization (ESO) - for identifying optimal structural morphologies. BG simulates natural growth processes by adding material in high stress areas and removing it in low stress areas. ESO removes inefficient material starting from an overdesigned structure based on rejection criteria related to stress levels. These procedures are applied to optimize the morphology of a pylon and a bridge, monitored through design graphs showing evolution of optimality indexes and structural response. BG optimizes a pylon by forcing swelling to maintain the initial length. ESO optimizes a bridge by subdividing the domain into tension and compression parts and removing material based on principal stress criteria for each load case.
Structural morphology optimization by evolutionary proceduresStroNGER2012
The paper deals with the identification of optimal structural morphologies through evolutionary procedures.
Two main approaches are considered. The first one simulates the Biological Growth (BG) of natural structures like the bones and the trees. The second one, called Evolutionary Structural Optimization (ESO), removes material at low stress level. Optimal configurations are addressed by proper optimality indexes and by a monitoring of the structural response. Design graphs suitable to this purpose are introduced and employed in the optimization of a pylon carrying a suspended roof and of a bridge under multiple loads.
IRJET- Seismic Evolution of Soft Storeyed Structures When Exposed to Earth Qu...IRJET Journal
This document summarizes a study on strengthening soft-story buildings to improve their seismic performance. Soft-story buildings, which have open or weaker first floors, perform poorly in earthquakes. The study models an 8-story reinforced concrete building under different structural configurations, including bare frame, infill masonry walls, shear walls, and bracing systems. Nonlinear static pushover analysis is used to evaluate the capacity and seismic response of each model. The results show that including infill walls, shear walls or bracing systems increases the building's lateral stiffness and decreases its fundamental natural period compared to the bare frame model. Strengthening the ground floor improves the seismic resistance of soft-story buildings.
SEISMIC RESPONSE STUDY OF MULTI-STORIED REINFORCED CONCRETE BUILDING WITH FLU...IRJET Journal
This document summarizes a study that analyzed the seismic response of multi-story reinforced concrete buildings with the addition of fluid viscous dampers. The study used ETABS software to model buildings with and without dampers and subjected them to modal, time history and pushover analyses. It was found that buildings with fluid viscous dampers experienced reduced time periods of up to 90% and reduced base shear of up to 70% compared to buildings without dampers. Maximum story displacements were also reduced with the addition of fluid viscous dampers.
Buildings are designed to withstand earthquake forces through controlled damage and energy dissipation rather than remaining entirely elastic. Structures are designed for a fraction of the maximum elastic force and are allowed to yield in strong shaking. This reduces costs while ensuring life safety. The design philosophy aims for no damage in minor quakes, repairable damage in moderate quakes, and structural damage but no collapse in severe quakes. Inelastic behavior is achieved through ductility in structural elements, which must be carefully detailed through testing.
Pushover analysis was performed on a 12-story building model designed for seismic zones 3 and 5 in India. The analysis assessed damage at different performance levels from immediate occupancy to collapse. For the zone 3 design, yielding initially occurred in beams and then columns. The structure remained within collapse prevention limits, indicating ductile behavior. Similarly, the zone 5 design remained ductile with initial yielding in beams and columns. The structures designed using linear analysis for both seismic zones were found to perform well under pushover analysis and experience damage within acceptable limits.
Similar to Machine Foundation Design - An Introduction (20)
1. Machine Foundation Design | Lawrence Galvez
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MACHINE FOUNDATION DESIGN
Lawrence O. Galvez, LM.PICE, M.ASEP
ABSTRACT: This lecture paper serves as an introduction in the complex analysis and design
of machine foundation which involves familiarity in areas of structural dynamics, structural
engineering and geotechnical engineering. This paperis aimed for graduate or practicing civil
or structural design engineers who are new to the subject but is familiar with the areas of civil
engineering knowledge cited above; although this paper can also be a handy reference for
those already doing machine foundation design. It discusses a brief review of structural and
soil dynamics which both play important roles in response of a machine-foundation system
due to vibratory loadings induced by the operation of the machine. Current state-of-the-art
approach in creating mathematical models using finite element method is discussed together
with a recommended step-by-step procedure in doing the analysis and design to satisfy
strength and serviceability requirements. An example design of a block foundation is shown
to help the reader familiarize in the design process and use rational assumptions in getting a
good preliminary geometry of foundation before starting with a detailed analytical model.
Main references for this paper were taken from the course syllabus of Advance Foundation
Engineering & Design in Graduate School of Engineering of University of the City of Manila
but other salient references were gathered from internationally recognized codes, standards
and practices.
KEYWORDS: machine foundation; resonance; rocking vibration; soil dynamics, block
foundation
1. INTRODUCTION
Foundations supporting vibratory loadings are often present in the industries of oil & gas,
petrochemicals, heavy manufacturing and power generations. These vibratory loadings are caused by
the unbalanced machine forces as well as the static weight of the machine. If these vibrations are
excessive they may damage the machine or cause it not to function properly. It should be noted that the
initial cost of construction of a machine foundation is generally a small fraction of the total cost of the
machine, accessories and installation, but the failure of the foundation as a result of poor design or
construction can translate to heavy dollar losses (Prakash and Puri, 1988). For example, a turbo-
generator unit in a power plant may cost around $20 to $ 50 million and an estimated loss of $250,000
per day if it malfunctioned; it is therefore crucial for a foundation engineer to give special attention to
the foundation design of vibrating machines.
Historically, analysis and design of machine foundations were done by approximate rule-of-thumb
procedure which consist of sizing the foundation based on the weight and type of vibrating machines
being supported or by strengthening the soil beneath the foundation by using piles. These procedures
generally works; however, this often results to considerable overdesign (Bowles, 1997).
With the advent of improved manufacturing technology, machines now are of higher ratings which give
rise to considerably higher dynamic forces and thereby higher stresses which demands improved
performance and safety (Bhatia, 2008).
The analysis and design of foundation and structures subjected to vibratory loads is considered a very
complex problem because of the interaction of structural engineering, geotechnical engineering and the
theory of vibrations (Arya, 1979); added to these, from author’s experience, is that a designer should
be keen in the details of machine’s (equipment’s) loadings, configurations or generalarrangements and
design operations which are already a basic part of mechanical engineering. However,due to practical
availability of commercial finite element analysis software nowadays, a designer can create a good
mathematical model of machine-foundation system with reasonable time to have a reliable prediction
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of the dynamic response of the system and create necessary changes in the model to mitigate unwanted
amplitudes of vibrations i.e. to control the vibrations in the system.
2. STRUCTURAL DYNAMICS
2.1 Static vs Dynamic Analysis of Foundations
Design of concrete foundations supporting static or pseudo-static loadings usually involves
computation of internal forces (e.g. axial, shear, moments, etc.) by satisfying the equations of
equilibrium (FH=0; FV= 0; FM= 0) and then check for strength and serviceability requirements.
Static loadings are dead loads or permanent loads while the pseudo-static are occupancy live loads,
wind and earthquake loads. (Note that earthquake loads mentioned denotes the use of approximate
equivalent static lateral force procedure per building codes). For static analysis the material and
geometric properties needed are density, Young’s modulus of elasticity, stiffness, thermal coefficient
and Poisson’s ratio.
For foundations supporting large vibratory a.k.a. “dynamic” loadings, a dynamic analysis is required
to determine the dynamic response of the structure. The response of the structure is measured in the
form of vibration amplitudes (e.g. displacements, velocity or accelerations); these are done by
satisfying the equation of motions based on Newton’s second law of motion (i.e. F = m a). In dynamic
or vibration analysis, in addition to material and geometric properties needed in static analysis;
damping coefficient and natural frequency of the machine-foundation system are required.
2.2 Theory of Vibrations
In the analysis and design of machine-foundation system, a designer should be first familiar with
fundamentals of theory of vibration. As mentioned previously, traditional approach in controlling
vibrations in design of foundations was to increasing the mass (or weight). It was only in the 1950s
where foundation engineers begin to use vibration analyses which was based on a theory of a surface
load on elastic half-space (i.e.the portion of supporting soil supporting the foundation which is assumed
to behave elastically), see Figure 1.
Figure 1. Foundation base in equilibrium position just prior to being displaced slightly
downward by a quick push
(Source: J.E. Bowles, 1997)
According to Bowles (1997), Figure 1 is similar to a beam-on-elastic-foundation case except the beam
uses several static soil springs in the analysis but here the foundation uses only one spring and it is a
dynamic soil spring i.e. dependent on time. Note that since the usual value of unbalance loads is
3. Machine Foundation Design | Lawrence Galvez
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relatively small compared to the weight of the machine-foundation system the assumption that the soil
behaves elastically is acceptable. The soil spring in (a) has been compressed in an amount of zs =
W/Kz wherein zs and Kz are both static values; in (b) the footing experiences a quick push in the z
direction and a quick release which makes the block moves up and down (i.e. it vibrates), hence,the zs
and Kz at this time are dynamic values.
Displaced or compressed value:
In Figure 1a, we can write the differential equation to describe the motion in a form of F=ma from
Newton’s second law of motion to be:
Solving by the methods given in differential equation textbooks afterdividing through by the massterm
m and defining 2
n = Kz / m,also known as the angular frequency, we can obtain the period of vibration
T as:
And the natural frequency fn as any one of the following:
From Eq. (b) it would appear that the vibration will continue forever; we know from experience that
this is not so. There must be some damping present,so we will add a damping device termed a dashpot
(analog = automobile shock absorbers) to the idealized model. To maintain symmetry we will add half
the dashpot to each edge of the base as shown in Figure 1b. Dashpots are commonly described as
developing a restoring force that is proportional to the velocity (ź) of the moving mass being damped
(i.e. being restrained). Knowing this conceptof the dashpot (also damping or viscous force) cz,a vertical
force summation gives the following differential equation:
Equation (c) is the equation of motion for a Single Degree of Freedom System (SDOF) with damping.
The solution of this equation yields the dynamic characteristic of the system e.g. natural frequency of
the system.
From the solution of the differential equation (c), the critical damping (in units of force/velocity) is
defined as:
Critically damped system happens when,
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When a forcing function, F, is introduced to the system, the equation becomes
According to Arya (1979), vibrations developed by operating machinery produces several effects that
needs to be considered in the design aside from the usual static loads. The usual procedure in doing a
vibration analysis is to establish a mathematical model of the realstructure.The structuralconfiguration
of machine foundation is generally determined by geotechnical consultant and machine manufacturer,
these initial configurations may change to suit design criteria or avoid interference of other fixed objects
such aspipelines and other ancillary items. The common configurations or types of machine foundations
are shown in Figures 2a and 2b.
Figure 2a. Types of machine foundations (a) Block foundations (b) Box or caisson
foundations (c) Complex foundations
(Source: S. Prakash, 1991)
F (t) (d)
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Figure 2b. Types of foundations for vibrating machines
(Source: S. Arya, 1979)
The following basic definitions are important in the vibration (dynamic) analysis:
Vibration - an oscillation of the partsof a fluid or an elastic solid whose equilibrium has been disturbed
Period (T) - if motion repeat itself in equal intervals of time, it is called a periodic motion and the time
elapsed in repeating the motion is called its period of vibrations. It is the time needed for one
complete cycle of vibration to pass a given point. As the frequency of a wave increases the period of
the wave decreases, i.e. frequency is the reciprocal of period
Figure 3. Graph of Period of vibration along time, t
Cycle - motion completed during a period is referred to as a cycle
Frequency (f) - the number of cycles of motion in a unit of time is called the frequency of vibrations
Natural frequency (fn) - if an elastic system vibrates under the action of forces inherent in the system
and in the absence of any externally applied force, the frequency with which it vibrates is its natural
frequency
Forced vibrations - vibrations that occur under the excitation of external force are termed forced
vibrations
Degrees of freedom (n) - number of independent coordinates necessary to describe the motion of a
system specifies the degreesof freedom of the system. When a system have severaldegrees of freedom,
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the system is called multidegree of freedom system (MDOF). Figure 4a shows degrees of freedom a
rigid block foundation. Figure 5 shows systems with different degrees of freedom.
Figure 4a. Degrees of freedom of a rigid block foundation
(Source: S. Prakash, 1991)
The rigid block foundation has six degrees of freedom (also called modes of vibrations)
1. Translation along Z axis
2. Translation along X axis
3. Translation along Y axis
4. Rotation along Z axis
5. Rotation along X axis
6. Rotation along Y axis
(Note: Each degrees of freedom of the system will produce different natural frequencies)
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Figure 4b. Types of motion of a rigid foundation due to unbalanced forces of
reciprocating machines: (a) pure vertical translation; (b) pure rocking; (c) simultaneous
horizontal sliding and rocking (d) pure torsional oscillations
(Source: S. Prakash, 1981)
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Figure 5. Systems with different degrees of freedom (a) One degree of freedom (n=1);
(b) Two degrees of freedom (n =2); (c) Three degrees of freedom (n=3); (d) Infinite
degrees of freedom (n=∞)
(Source: S. Prakash, 1991)
Resonance - if the frequency of excitation force coincides with any one of the natural frequencies of
the system, resonance will occur. This is a phenomenon that is being avoided in machine foundation
design because it will the amplitudes (e.g. displacement, velocity or acceleration) of vibrations to be
excessive and cause damage to the system.
Normal mode ofvibrations - when the amplitude of some point of the system vibrating in one of the
principal modes is made equal to unity, the motion is called the normal of vibrations
n = 1
Simple pendulum
(a)
(b)
n = 2
Equilibrium
Position
(c)
(d)
n = 3
m1
m2
m3
n = ∞
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Damping - damping is associated with energy dissipation and opposes the free vibrations of a system.
If the force of damping is proportional to its velocity, it is called viscous damping. If it is not dependent
on its material property and it is contributed by geometry of the system it is called geometrical damping.
2.3 Harmonic Motion
The simplest form of motion is harmonic motion,which is represented by sine or cosine functions. The
excitation in structures or foundations caused by the unbalanced force in the machines are generally in
the form of harmonics under steady-state condition.
Rewriting equation (d) with a harmonic force;
where; Fo = unbalanced mass of the machine; t = time
Fo sin (t) (e)
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In dynamic system, the excitation force present arises out of unbalances in the rotating masses. Shown
below are the forces generated for reciprocating and centrifugal machines.
Figure 6. (a) Crank mechanism of a reciprocating machine; (b) Forces from a
centrifugal machine (rotating mass excitation)
(Source: S. Arya, 1979)
For reciprocating machines:
For centrifugal machines:
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Figure 7a. Rotating vector representation of a harmonic function x = A sin t
(Source: S. Arya, 1979)
Figure 7b. Harmonic motion representation of displacement (x), velocity (ẋ) and
acceleration (ẍ)
(Source: S. Arya, 1979)
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3. VIBRATING (DYNAMIC) MACHINES
There are many kinds of machines that generates periodic forces; the three most important categories
are:
a. Reciprocating machines: machines that produced unbalanced force (such as compressor and
reciprocating engines). The operating speeds of such machines are usually less than 600 rpm.
For the analysis of their foundations, the unbalanced forces can be considered to vary
sinusoidally.
Figure 8a. Single cylinder crank mechanism (a simple reciprocating machine)
(Source: Prakash and Puri, 1988)
Figure 8b. Reciprocating machine diagram
(Source: ACI 351.3R, 2004)
b. Rotary machines: high-speed machines like turbogenerators or rotary compressors may have
speed of more than 3,000 rpm and up to 10,000 rpm. High speed rotary machines are well
balances and the eccentricity e is generally very small. However, due to their high speed of
rotation, the magnitude of exciting loads may be significant and may cause the effective
eccentricity to increase due to wear and tear.
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Figure 8. Unbalanced forces due to rotary machines, (a) single rotor; (b) two rotors with
equal unbalanced forces in phase; (c) two rotors with equal unbalanced forces but with
a phase difference of 180o; (d) two rotors with equal unbalanced forces at any phase
(Source: Prakash and Puri, 1988)
Dynamics loads during operations are caused by unbalanced loads (created when the mass centroid of
rotating part does not coincide with the center of rotation) with a frequency corresponding to machine
speed. These loads are usually given by the machine manufacturer. If not, they may be calculated via
the balance quality grade G of the rotor.
G = e
where; e is in (mm) and is in (rad/s)
From ISO 1940/1 specification the usual value of G is 2.5 mm/s
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Figure 9. Rotating machine diagram
(Source: ACI 351.3R, 2004)
Figure 10. Simple cycle gas turbine
(Source: General Electric)
c. Impact machines: machines that produce impact loads like forging hammers. Their speeds are
from 60 to 150 blows per minute. Their dynamic loads attain a peak in a very short interval and
then practically die out.
3.1 Typical assembly of machine
Machine would necessarily include:
- A drive machine
- A driven machine
- A coupling device
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3.2 Machine - Foundation Loading Data
Loadings due to self-weight of machine and unbalanced (dynamic) loading is provided by machine
manufacturer. This is sometimes called vendor data. Other loadings due to machine operation are listed
including loading due to temperature operation, accidental loads due to malfunctioning, loss of blades,
emergency torques, etc. A sample of foundation loading data is shown below.
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3.3 Machine - Mechanical Outline
A designer should review the mechanical outline (drawings) of the machine to properly model later the
machine in the structural analysis. Shown below is a sample of machine drawings from vendor.
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3.4 Machine - Anchor bolt layout and details
The layout of anchor bolts should be carefully reviewed by the foundation designer to make sure all the
location of loadings will match on what is considered in the analysis. Shown below is a sample of
anchor bolt layout and details of a machine.
3.5 Machine - Dynamic Loads from Vendor Data
The rated (operating) and critical speeds of the machine and unbalance loadings are taken from vendor
data.
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3.6 Machine - Suggested Load Combinations from Vendor => there are specific load combinations
usually recommended by vendor to protect the machine during operation and accidental situation. The
designer should include this in his analysis and design.
3.7 Machine - Dynamic Design Criteria
Sample of dynamic design criteria for rotating machine is shown below
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Allowable amplitude of vertical vibration (note: 1 cps = 1 Hertz)
4. SOIL DYNAMICS
Definitions
Soil Mechanics - coined by Dr. KarlTerzhagi who is recognized as the “father of soil mechanics”.
Soil mechanics deals with engineering properties of soil under stress.
Soil dynamics - is that branch of soil mechanics which deals with engineering properties of and
behavior of soil under dynamic stress.
Types of dynamic loads that may act on foundations and structures:
- earthquakes
- bomb blasts
- operation of reciprocating and rotating machines and hammers
- construction operation (such as pile driving)
- quarrying
- fast-moving traffic
- wind
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- wave action of water
Earthquake constitutes to the single most important sources of dynamic loads on structures and
foundations. Every earthquake is associated with a certain amount of energy released at its source
and can be assigned a magnitude (M) which is just a number (Richter, 1958).
Definition of earthquake terms
Shown below is a sample of soil behavior during the Canterbury earthquake in NZ.
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Figure 11. Sample Damage of Niagata earthquake 1964
(Source: S. Prakash, 1991)
Automobile sunk in during Niagata
earthquake 1964
Sewage treatment tank floated to surface during
Niagata earthquake 1964 (after Idriss, 1967)
Tilting of building during Niagata earthquake
1964 (After Seed and Idriss, 1967
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Due to ground motion during an earthquake, footings may settle, building may tilt, soils may liquefy
and loses ability to support structures, and light structures may float.
Below are the sample ground acceleration readings of past earthquakes captured in accelerogram.
Compared to the graph of dynamic loading for reciprocating and rotary machines, the machine’s
dynamic loadings are sinusoidal in nature.Although in reality it is not perfectly sinusoidal e.g.the peaks
in any two cycles may be different.
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Figure 12. Trace of vertical acceleration of ground due to pile driving
(Source: S. Prakash, 1991)
Natural undamped frequency of point bearing piles on rigid rock
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4.1 Soil behavior during dynamic loading
During earthquake, the ground may be susceptible two categories:
4.2 Dynamic Soil parameters needed for dynamic analysis of machine foundation
Dynamic loading of soils are divided into small and large strain amplitude responses. In a machine
foundation, the amplitudes of dynamic motion and, consequently, the strains in the soil are usually low,
whereas a structure that is subjected to an earthquake may undergo large deformations and thus induce
large strains in soil.
The “elastic halfspace model” is usually used in determining the response of the soil that is subjected
to harmonic loading. In this model, it presumesthat a circular footing restsupon the surface of an elastic
halfspace (the soil) extending to an infinite depth, which is homogeneous and isotropic and whose
stress-strainproperties canbe defined by two elastic constants,usually shearmodulus (G) and Poisson’s
ratio (v).
Dynamic soil parameters to be taken from field and/or laboratory test or from published correlations of
static properties of soil:
- Dynamic shear modulus, G
- Poisson’s ratio, v
- Soil Damping ratios, D
4.3 Geotechnical investigation to determine dynamic soil properties
Note: all of these soil investigation should be reported in detailed in geotechnical report.
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Sample schematic of cross-hole test on field
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Figure 13. Crosshole Test
(Source: S. Arya, 1979)
Sample schematic of down-hole test on field
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Sample schematic of spectral analysis of shear wave
Figure 13. Surface Oscillator Test
(Source: S. Arya, 1979)
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Sample of Downhole Test Results
Borehole plan
Bore
Hole
No.
Soil
Dept
h (m)
Type
of
Soil
N-
Valu
e
Seismic
Wave
Velocity
VP
VS
Poi-
sson
Ratio
Dynamic Soil
Properties (MPa)
G Ed
Kd
Silty Sand
and
Gravel
Silty Sand
and
Gravel
Sandston
e
Sandston
e
Sandston
e
Sandston
e
Sandston
e
Marl
Marl
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4.4 Computation of Equivalent Soil Springs
Table 1. Equivalent Spring Constants (Source: S. Arya, 1979)
Figure 14. Coefficients z, x and
(Source: S. Arya, 1979)
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Table 2. Equivalent damping ratios (Source: S. Arya, 1979)
5. STRUCTURAL ANALYSIS AND DESIGN (for block foundation)
Two Stages:
Static Analysis includes check for strength of foundation, stability of foundation and
check for soil bearing capacity (actual soil bearing should be less than 50~75% of
allowable bearing capacity)
Dynamic Analysis includes determination of natural frequencies of the machine-
foundation system and checking of response vibration amplitudes
5.1 Foundation Trial Sizing Check
- Footing thickness shall be greater than the maximum of ( 0.60 m ; the rigid criterion 0.60
+ L / 30) , provide additional 0.60m on both sides for maintenance purpose
- Footing width shall be greaterthan 1.0~1.5 x vertical distance (foundation base to machine
C.G.) + 0.60 m on both sides for maintenance purpose
- Mass ratio check (for rotary machines: foundation mass = 2 to 3 times of machine mass;
for reciprocating machines: 3 to 5 times of machine mass)
- Foundation eccentricity check shall not be greater the 5% on both plan dimensions (i.e.
the centroid of mass of machine-foundation system wrt base contact area)
Note: Table-top type foundation will have different requirement in trial sizing.
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5.2 Structural Modeling
5.2.1 Finite element modeling (Note: Modeling is a critical part in the structural analysis)
5.2.2 Modeling of supports
(Note: Static soil spring is different from dynamic soil spring; dynamic modulus of elasticity, Ec’
of concrete = 1.60* static modulus of elasticity, Ec)
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5.3 Time-History Analysis
5.3.1 Dynamic input in analysis software
Sample of input in analysis software (operating speed)
Sample of input in analysis software (emergency speed)
5.3.2 Unbalanced loads model
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5.3.3 Determine machine-foundation system natural frequencies, fn
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5.3.4 Investigate the shapes of observed critical modes
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5.3.7 Show plots of governing amplitudes
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6. SUMMARY OF DESIGN CHECKING
Static Design check for serviceability and strength requirements, update accordingly; follow
best practices in reinforced concrete detailing; check seismic requirements if project is located in
high seismic zone area.
Dynamic Design verify if vibration amplitudes are below allowable values, review and/or adjust
accordingly; check mode shapes of the system, check if natural frequencies are outside the resonance
range, check other requirement checking required by vendor e.g. deflection of bearing points,
misalignment of rotor.
Below is a schematic flow of dynamic design process.
Figure 15. Schematic diagram of a machine-foundation system subjected to dynamic
loads
(Source: K. Bhatia, 2008)
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REFERENCES
J.E. Bowles (1997) “Foundation Analysis and Design 5th
Ed. - Chapter 20 Design of foundation for
vibration controls”
S. Prakash (1991) “Soil Dynamics - Chapter 9 Machine Foundation”
S. Prakash (1991) “Soil Dynamics - Chapter 1 Introduction and 2 Theory of Vibration”
Prakash and Puri (1988) “Foundation for Machines - Analysis and Design”
Prakash and Puri (2006) “Journal on Foundation for Vibrating Machines”
S. Arya et al. (1979) “Design of structures and foundations for vibrating machines”
K.G. Bhatia (2008) “Journal on Foundations for industrial machines and earthquake effects”
American Concrete Institute ACI 351.3R (2004) “Foundations for Dynamic Equipment”
Technical Paperon“Seismic Design of Buried Structures in PHandNZ” presentedby Lawrence Galvez
in 17th
ASEP International Convention” (2015)
Lecture notes on Advance Foundation Engineering and Design Subject in University of the City of
Manila - Prof. Rolando D. Rabot, ASEAN Engr, M.Engg, Ph.D-Te
OTHER SUGGESTED REFERENCES FOR READING
German Standards
DIN 4024 Part 1 Machine Foundations; flexible structures that support machines rotating machines
DIN 4024 Part 2 Machine Foundations; rigid structures that support machines periodic excitation
British Standards
CP 2012 Code of Practice for Foundations for machinery
American Standards
American Society of Civil Engineers (ASCE) Task Committee on “Design of large steam turbine-
generator foundations”
ABOUT THE AUTHOR
Lawrence “LG” Galvez is a licensed civil engineer professional involved in structural engineering and
design of industrial and infrastructure projects for local and international clients. His experience in civil
and structural design are from oil & gas, petrochemicals, mining, telecommunications, water &
wastewater, power generation, bridge & railway and land development industries.
LG is a PICE Life Member and a Regular Member of ASEP. He can be reach thru email:
wrence23_ph@yahoo.com.