Structural design for serviceability - Thesis Example

Introduction Serviceability limit in structures refers to the conditions under which the normal operations of the structures are disrupted by excessive deflection, vibration, or deterioration. Design specifications, in general have been based upon the limit state design method in which two classes of limit states are accepted: ultimate limit states and serviceability limit states. Ultimate limit state keeps the safety of the structure under control and must be met. On the contrary, serviceability issues involve people and the object’s response to the behaviour of structure under load, and it should be met.

As standards advance toward probability-based limit state design methods, serviceability issues are expected to become an integral part of design consideration.Whether a structure has passed a limit state is really a matter of perception. As far as the ultimate limit state is concerned, the perception is technical, and there are sets of rules and regulations which are established by building codes. However, in the case of serviceability limit the perception is often non-technical, as they involve the judgments and anticipations of occupants.

As a consequence, serviceability limits in general have not been codified since desirable limits frequently alter from application to application. Hence, they remain a matter of contractual agreement between the owner and designer, and thus are not specified in the building codes.The purpose of the current project will be to explore and gather the history of serviceability criteria used for various types of structures. Design deflection and vibration criteria will be relaxed by increasing the floor span and reducing the member size, and the likely effects will be perceived.

The paper will later look into possible techniques used for improving structural stiffness without incurring additional cost and materials. The objectives of this study are: to gain better understanding of structural serviceability performance needs of each country, to exchange data on structural serviceability and to develop performance-based design procedures for structural serviceability.The object of serviceability design is acceptable performance during expected service conditions for the design life.

The objective maybe is to prevent damage to ceiling plaster or wall glazing elements to maintain a pleasing appearance or to prevent uncomfortable movement. Deflection is typically limited to some proportion of the span.Building construction may be such that there is a wall located near the mullion, and excessive deflection can cause the mullion to contact the wall and cause damage. Also, if deflection of a wall is quite noticeable, public perception may raise undue concern that the wall is not strong enough.

Deflection limits are typically expressed as a distance between anchor points divided by a constant number. Since steel deflects at 1/3 the rate of aluminum, the steel can resist much of the load at a lower cost or smaller depth.Vibration limits on the other hand makes people uneasy and creates fear of structural collapse, although such fear is usually unwarranted because of the small displacements and stresses that are actually produced. Nevertheless, perceptible vibration is usually considered to be undesirable because it affects people’s sense of well-being and their ability to carry out tasks.

Excessive floor vibration has become a greater problem as new rhythmic activities, such as aerobics, and long-span floor structures have become more common. This update describes the nature of floor vibration and provides options for avoiding it through design, or in the case of existing buildings, reducing or eliminating it through alterations.Floor vibration is up-and-down motion caused by forces applied directly to the floor by people or machinery, or by vibration transmitted through building columns, from other floors or from the ground.

The problems associated with floor vibration are not new. In 1828, Tredgold wrote “girders should always be made as deep as they can to avoid the inconvenience of not being able to move on the floor without shaking everything in the room”(Tredgold, T, 1824, Elementary Principles of Carpentry,2nd Ed., Publisher unknown)The main factor underlying most vibration problems is resonance, which occurs when a load is exerted on a floor at a particular frequency. When the natural frequency of the floor coincides with, or is close to, the forcing frequency, resonance occurs and the consequences are most severe.

On storey height, the taller the columns supporting the floor on which the rhythmic activity takes place the lower the natural frequency of the floor. Selecting the location for a rhythmic activity is therefore the most important consideration in the design of floors. Most floor vibration problems are caused by resonance and, for light-frame construction, sudden deflections due to footsteps. Vibration can also be controlled by stiffening the floor structure, although sometimes the problems can be addressed by adding damping or by isolating equipment.

Proper placement of an activity or machinery in a building is the most important consideration.Chapter 2Review of Related LiteratureTypical Floors in Modern Buildings Modern floors, which are frequently reported to have annoying vibration, are thin, lightweight concrete slabs supported by open-web steel joists. This economical floor system is commonly used in office buildings, schools, retail spaces, restaurants, etc. It should be noted that on occasions a sturdy floor with thick, normal weight concrete slabs, the kind that does not fit the modern floor description, exhibits unacceptable vibration.

The occurrence of vibration in such floors is most probably due to the lack of enough non-structural, architectural features on the floor, hanging from underside of the floor, and even on the floor below. Also, having less office related live load such as filing cabinets in a paperless office can contribute to the floor vibration problem. Steady State and Transient Floor Vibration Floor vibration can be classified as either transient or steady-state, depending upon the type of excitation and its duration.

Floors subject to operating machines have a steady-state response because machines usually run continuously for a long period of time. Conversely, floor vibration due to occupants activities cannot easily be categorized as being either transient or steady-state. For the residential and office type environments, the excitation is the intermittent movement of a small number of occupants; therefore, the floor vibration is mostly transient. But many steady-state, walking-induced floor vibration cases have also been reported in office buildings.

In a commercial environment, the floor vibration is mostly steady-state because the excitation is for the most part rhythmic walking with an approximately constant frequency. And in gymnasiums, the forcing function is that of dancing or exercise activities resulting also in mostly steady state floor vibration. As stated earlier, such low-frequency activities can excite a floor at its forcing frequency and its higher order harmonics one of which might fall close or exactly match one of the floor resonant frequencies causing the floor to resonate.

Modeling of Floor Dynamics Mathematical model of a vibrating floor is invaluable for investigating the dynamic behavior of a floor and exploring the most suitable vibration mitigation solution for it. Floor models are normally constructed by identifying the modal parameters (natural frequencies, mode shapes, and damping ratios) of the floor via. experimental and/or finite element modal analysis. Considering that most of the vibration energy is in the first few modes, it is common to include only these modes in the floor model.

In addition to contributing to the construction of the floor model, mode shapes describing how the vibrating floor deforms at each natural frequency identify the nodal lines and the antinodes (points of maximum deflection). This information is invaluable for gaining insight to the vibration problem and optimally placing the mitigation treatment on the floor. Figure 1 shows the natural frequencies and mode shapes of the first 3 modes of a test floor at Virginia Polytechnic Institute and State University (VPI).

This 15 by 25 ft, one-bay floor is composed of a steel frame of two side girders (W14X22) and seven parallel joists (16K4) supporting a concrete slab on a metal deck. The lightweight concrete slab is 3.5 in. thick and is supported by 1.0 C metal deck. The floor is supported at the corners by four steel pipe columns, each with a diameter of 8 in. It has five modes of vibration in the frequency range of 0 to 30 Hz, all having less than 1% damping. Mode 1 at 7.16 Hz Mode 2 at 10.44 Hz Mode 3 at 15.

9 Hz Figure 1 The first 3 mode Shapes Floor Vibration Control To have a floor which is lightweight, provides open-space and yet is not prone to vibration (meeting the current serviceability guidelines), damping should be incorporated into its make up. If adequate damping is not provided by the construction material, architectural elements, other live load, etc, then a damping solution should be added to the floor. Arguably the most cost effective and least disruptive techniques to damp annoying floor vibration is adding tuned mass dampers TMD(s) to the floor.

The two time traces in Figure 2-b show the transient vibration responses, to a heel drop excitation (see Figure 2-a), of the first mode of the VPI floor without and with a tuned mass damper. Evident from Figure 2-b, without the TMD the floor vibration lingers for many seconds but with the damper in place only the initial impact is felt and the vibration subsides quickly. Figure 2 Heel drop excitation (a) and floor vibration response (b) The heel-drop impact is commonly used to evaluate the vibratory characteristics of a floor.

This perturbation is the dynamic load of a 190 lb. (85.5 kg) person who stands on the toes of both feet, then strikes thefloor with both heels from a distance of 2 inch (5 cm.); see Figure 2-a.DEICON Tuned Mass Damper DEICON offers tuned mass dampers developed specifically for abating floor vibration. The tuned mass damper(s) is(are) normally installed below the floor in the ceiling cavity. In case such installation causes disruption to the occupant (in an existing floor), tuned damper can be installed on the floor enclosed in a decorative cabinet; such installation expedites the fine-tuning time of the damper to just an hour or two.

The device, not having any motor or other active elements, is maintenance free and quiet (makes no noise). Hydraulic DesignDependant factorsThe amount of rainfall a surface water drainage system will need to deal with depends on the following:The length or duration of storm.The return period or frequency between storms.Geographical location of site.The length or duration of stormRainfall intensity varies inversely with duration. For example, the shorter the storm generally the more intense the rain will be.

Conversely, the longer the storm the less intense the rainfall will be.Storm return periodsThe intensity of a storm does not only depend upon its duration but also on how often it will occur. A storm that occurs every week will be considerably less intense than one that happens once in ten years or once in a hundred years. By selecting a longer return period the designer can reduce the risk of flooding occurring.Geographical locationThe location of the development can have a significant effect on rainfall intensity.

Generally the western side of the UK experiences higher and longer periods of rainfall but not always the intensity.Infiltration & attenuationWhen infiltration is being considered a number of important issues need to be addressed:Field tests must be conducted to determine the suitability of the ground and establish an infiltration rate as recommended in BRE Digest 365The soakaway must be designed to half empty in 24 hours or lessThey must be located a minimum of 5m away from a buildingGround water table must be at least 1m below the bottom of the soakawayA non-woven needle punched geotextile filter fabric should be used to encapsulate cells to allow free flow of water.

The storage capacity of attenuation and infiltration systems can be determined from the following equation:Inflow (m3/min) x duration (min) - outflow (m3/min) x duration (min) = Storage CapacityDesign factors checklistThe calculation method to be used - BRE (infiltration only) or CIRIA (infiltration or attenuation).The geographical location of the site (for selection of local rainfall statistics).The storm profiles to be used (return period in years).The catchment areas discharging into the storm water system (roofs and other hard surface areas).

Soil infiltration rate (derived from porosity test conducted on the site) and the ground water table level.Allowable outflow rate in l/s (for attenuation systems).Safety Factor to be applied which is normally agreed with the local authority, environment agency or water company (dependent on consequence of flooding). Eurocode-Basis of structural design is divided into 6 sections and four annexes (A-D), as shown in Figure 3. In this diagram, the size of each segment of the pie is proportional to the number of paragraphs in the relevant section.

Figure 3 Contents of the Eurocode EN 1990 describes the basis for the design and verification of buildings and civil engineering works, including geotechnical aspects, and gives guidance for assessing their structural reliability. It covers the design of repairs and alterations to existingconstruction and assessing the impact of changes in use. Because of their special nature,some construction works (such as nuclear installations and dams) may need to be designed to provisions other than those given in EN 1990.

Figure 4 Scope of EN 1990, Basic of Structural DesignRequirements The basic requirements of a structure are to sustain all likely actions and influences, to remain fit for purpose, and to have adequate structural resistance, durability, and serviceability. These requirements must be met for the structure’s entire design working life, including construction. The structure must not suffer disproportionate damage owing to adverse events, such as explosions, impact, or human error.

The events to be taken into account are those agreed with client and relevant authorities. In addition, the design must avoid or limit potential damage by reducing, avoiding or eliminating hazards. This can be achieved by tying structural members together, avoiding collapse without warning, and designing for the accidental removal of a structural member. The Design working life is the assumed period for which the structure or part of it is to be used for its intended purpose with anticipated maintenance but without major repair being necessary.

( EN 1990§1.5.2.8)Figure 5 compares the design working life of various structures according to EN 1990 (dark lines) with the modifications made to these time periods by the UK National Annex to EN 1990 (lighter lines). The most significant change is the extension of category 5to 120 years-although this only really affects fatigue calculations. Figure 5 Design working life of various structures Figure 6 Design according to the EurocodeAssumptions EN 1990 makes important assumptions about the way structures are designed and executed (see Figure 6).

It is assumed that people with appropriate qualifications, skill, and experience will choose the structural system, design the structure, and construct the works. It is also assumed that construction will be adequately supervised and quality controlled; and the structure will adequately be maintained and used in accordance with the design assumptions. Because they vary from country to country, EN 1990 gives no guidance as to what appropriate qualifications are needed to perform these tasks.

Likewise, adequate supervision and control is not further defined in the Eurocode. Principles and Application Rules A distinctive feature of the structural Eurocodes is the separation of paragraphs into principles and applications rules (see figure 6). Design which employs the Principles and Application Rules is deemed to meet the requirements provided the assumptions given in EN 1990 to EN 1999 are satisfied. [EN 1990§1.3(1)] Principles – identified by letter P after their paragraph numbers – are general statements and definitions that must be followed, requirements that must be met, and analytical models that must be used.

The English verb that appears in Principle is “shall” [ EN 1990§1.4(2)& (3)] Application Rules – identified by the absence of a letter after their paragraph numbers are generally recognized rules that comply with the principles and satisfy their requirements. English verbs that appear in Application Rules include “may”, should, can, etc. [EN 1990 § 1.4(4)]Principles of limit state design The Structural Eurocodes are based on limit state principles, in which a distinction is made between ultimate and serviceability limit states.

Ultimate limit states are concerned with the safety of people and the structure. Examples of ultimate limit states include loss of equilibrium, excessive deformation, rupture, loss of stability, transformation of the structure into a mechanism, and fatigue. Serviceability limit states are concerned with the functioning of the structure under normal use, the comfort of the people, and the appearance of the construction works. Serviceability limit states maybe reversible or irreversible. Limit state design involves verifying that relevant limit states are not exceeded in specified design situation.

Verifications are performed using structural and load models, the details of which are established from three basic variables: actions, material properties, and geometrical data. Actions are classified according to their duration and combined indifferent proportions for each design situation.Design situations Design situations are conditions in which the structure finds itself at different moments in its working life. In normal use, the structure is in a persistent situation; under temporary conditions, such as when it is being built or repaired, the structure is in a transient situation; under exceptional conditions, such as during a fire or explosion, it is in an accidental situation or a seismic situation.

[EN 1990 § 3.2(2)P] Society is willing to accept that fires and explosions may lead to building damage-necessitating repair-whereas snow and wind should not. None of these events must lead to collapse. The Structural Eurocodes define partial factors for accidental or seismic situations that are typically 1.0.These factors are considerably lower than those specified for persistent and transient situations, typically 1.2-1.5. The development of different design situations help to determine what level of reliability the design requires and what actions need to be considered as part of that design situation.

Figure 7 Overview of Limit State DesignUltimate Limit States Ultimate limit states are concerned with the safety of people and the structure.[EN1990§3.3(1)P] EN1990 identifies three Ultimate Limit States (ULSs) that must be verified where relevant; loss of equilibrium (EQU); failure by excessive deformation, transformation into a mechanism, rupture or loss of stability (STR); and failure caused by fatigue or other time-related effects (FAT). ( Limit states GEO, UPL, and HYD, which are relevant to geotechnical design) These three letter acronyms are used throughout the Eurocodes as shorthand for the limit states, which for structures, are defined more fully as follows.

Limit State EQU Limit state EQU, dealing with static equilibrium, is defined as: Loss of static equilibrium of the structure… considered as a rigid body, where minor variations in the [actions or their distribution] … are significant, and the strengths of … materials … are generally not governing. [EN1990§6.4.1(1)P(a)] Limit state EQU does not occur when the destabilizing design effects of actions Ed,dst are less than or equal to the destabilizing design effects Ed,stb: Ed,dst≤Ed,stb as illustrated in Figure 8 [EN 1990 exp (6.7)]Figure 8 Verification of Limit State EQU For example, consider a motorway gantry (see Figure 9) subjected to a design horizontal wind load Pd = 250kN acting at height h= 7.

5m above the base of the gantry. The design destabilizing moment about the toe of the structure MEd,dst is given by :MEd,dst= Pd x h = 250kN x 7.5m=1875kNm If the design self-weight of the gantry is Wd = 1600kN and its base width B = 2.5m, then the design stabilizing moment about the toe MEd,stb is : MEd,stb = Wd x B = 1600kN x 2.5 = 2000kNm 2 2Figure 9 Motorway Gantry Subject to Wind Load Limit state EQU is therefore avoided (in the direction of the wind), since :MEd,dst = 1875kNm≤MEd,stb = 2000kNm In this book, we define the ‘utilization factor’ for the EQU limit state as the ratio of the destabilizing and stabilizing effects:^EQU = Ed,dst Ed,stb For a structure to satisfy design requirements, it must have a utilization factor less than or equal to 100%.

If ^ exceeds 100%, although it may not necessarily lose equilibrium, the structure is less reliable than required by the Eurocodes. For the motorway gantry of figure 9: ^EQU = MEd,dst = 1875kNm = 94% MEd,stb 2000kNmLimit State STR Limit state STR , dealing with rupture or excessive deformation, is defined as: Internal failure or excessive deformation of the structure … where the strength of construction materials … governs. [EN 1990 § 6.4.1(1)P(b)]To prevent limit state STR from occurring, design effects of actions Ed must be less than or equal to the corresponding design resistance Rdr that is Ed ≤ Rd as illustrated in Figure 10.

[EN 1990 exp. (6.8)]Figure 10 Verification of Limit State STR Returning to the example of Figure 9, the bending moments induced in the motorway gantry under its self-weight are shown on Figure 11. If the maximum design bending moment in the structure is MEd = 500kNm and the minimum design bending resistance of the cross-section is MRd = 600kNm, then limit state STR is avoided, since : MEd = 500kNm ≤ MRd = 600kNm In this book we define the ‘utilization factor’ for the STR limit state as the ratio of the effect of action to its corresponding resistance:^STR = Ed Rd For a structure to satisfy design requirements, it must have a utilization factor less than or equal to 100%.

If the ^ exceeds 100%, although it may not necessarily fail, the structure is less reliable than required by the Eurocodes.For the motorway gantry of Figure 11:^STR = MEd = 500kNm = 83% MRd 600kNmFigure 11 Bending moments acting in the motorway gantry of Figure 9Limit State FAT In materials science, fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. Fatigue is mainly relevant to road and rail bridges and tall slender structures subject to wind.

The subject receives particular attention in Eurocodes1 (actions3), 3 (steel structures4), and 9 (aluminum structures5) but is not mentioned in Eurocode 7. Serviceability Limit States Serviceability limit states (SLSs) are concerned with the functioning of the structure, the comfort of people, and the appearance of the construction works. [EN 1990 & 3.4(1)P] To prevent serviceability limit states from occurring, design effects of actions Ed – which in this instance are entities such as settlement, distortion, strains, etc.

– must be less than or equal to the corresponding limiting value of that effect Cdr that is : Ed ≤ Cd as illustrated in Figure 12. [ EN 1990 exp (6.13)]Figure 12 Verification of Serviceability limit state (SLS) Returning to the example of Figure 9, if the maximum settlement under that gantry can tolerate is sCd = 15 mm and the calculated settlement under the design actions is sEd = 12 mm, then the serviceability limit state is avoided, since:sEd = 12 mm ≤ sCd = 15 mm In this book, we define the ‘utilization factor’ for the serviceability limit state as the ratio of the effect of actions to its corresponding limiting value: ^STR = Ed Rd For a structure to be serviceable, it must have a utilization factor less than or equal to 100%.

For the motorway gantry of Figure 9:^SLS = sEd = 12 mm = 80% sCd 15 mm Actions, combinations, and effects The use of the word action to describe loads (and other entities that act like loads) reminds us of Newton’s Third Law of Motion: “to every action there is always opposed an equal reaction” In Eurocode terms, the reaction is known as an effect. That is : Action = Cause reaction = effect The following sub-sections explain the way in which the Structural Eurocodes define actions, combination of actions, and the effects that arise from them.

Evaluating Deflections Total deflection in any beam is the sum of bending deflection, shear deflection, and in a fabricated beam, deflection due to movement in the fabricated joint. The diagram below shows the equations for calculating short-term bending deflection for two common cases.Deflection formulae for a simply supported beam with two common loading casesBending Deflection The bending deflection is inversely proportional to the modulus of elasticity of the timber. The E-value given in the code is an average value for the species and grade under consideration.

The modulus of elasticity of radiata pine may vary from 3 to 12 GPa depending on wood quality. Pieces containing pith or corewood are usually at the low end, whereas timber from thew outer wood of older trees (flat growth rings) may be nearer by the high end of this range. There is also variation between trees and between sites, with dense timber from the north of New Zealand tending to have higher stiffness than less dense timber. Deflection is inversely proportional to the moment of inertia, I, a geometrical property of the cross-section.

For rectangular beams, the moment of inertia is calculated fromI = b d / 12where b is the width of the beam d is the depth of the beamShear Deflection In addition to bending deflection, beams are deformed by shear stresses leading to additional deflection known as shear deflection. Shear deflections are not normally calculated for solid rectangular beams as they are usually less than 10% of elastic bending deflections and in any case, the E-values given for graded timber generally include some allowance for shear deflection.

Shear deflections must be checked for heavily loaded plywood web beams or I-beams.Deflection due to joint slip In nailed plywood web beams, slip at the flange–web joints result in significant additional beam deflections. The amount of slip depends on the nail stiffness, the spacing of the nails and the properties of the web material. For most beams, deflections due to joint slip is no more than 15 times the bending deflection, but for short squat beams, it may be two times. If the flanges are mechanically spliced, some deflection may also result from movement in the splice.

There is no joint slip in glued plywood web beams. Bolted joints cannot provide fully rigid connections because of the need to drill slightly oversize holes to allow bolts to be inserted.Cantilever beam constructionLong Term Deflection Initial elastic deflections are directly proportional to the level of load and are recoverable if the load is removed. Creep is additional deflection that occurs with time under the action of permanent loads. Creep is primarily dependent on changes in moisture content and on the level of stress in the timber.

Long term deflections of green timber allowed to dry in service are extremely variable for individual members. These deflections are partly due to creep and partly due to shrinkage and may vary from zero deflection to five times the initial elastic deflection. Mechano-sorptive creep causes increased deflection with time due to fluctuations in moisture content. The use of kiln dried timber is the best method of controlling long term deflections, especially for important members carrying heavy loads and is recommended for most structural applications.

Sources: Allen, Dr. D.E. & Pernica, Dr. G. 1998 Control of Floor Vibration, National Research Council of Canada, December 1998 ISSN 1206-1220Hisashi, Okada,etal 1999 Estimation on Structural Serviceability Performance, Annual Report of BRI, vol. 1998 p. 205-206, http://en.wikipedia.org/wiki/Curtain_wall#Deflectionhttp://decodingeurocode7.com/downloads/02.%20Basis%20of%20structural%20design%20(sample).pdfhttp://www.deicon.com/floor_vibration_control.htmlhttp://www.marleyplumbinganddrainage.

com/diyer/content/2/180/hydraulic-design.htmlhttp://www.nzwood.co.nz/images/uploads/file/Designed%20PDFs%20updated/NZW13611%20SD-Serviceability-2.pdf