The code BS 8110, part 1 in clause 2.1.1 states that the aim of design is the achievement of an acceptable probability that the structure will perform satisfactorily during its life. It must carry the loads safely, not deform excessively and have adequate durability and resistance to the effects of misuse and fire. The clause recognizes that no structure can be made one hundred percent safe and that it is only possible to reduce the probability of failure to an acceptably low level.
Clause 2.1.2 states that the method recommended in the code is limit state design where account is taken of theory, experiment and experience. It adds that calculations alone are not sufficient to produce a safe, serviceable and durable structure.
Correct selection of materials,quality control and supervision of construction are equally important.
3.1.2 Criteria for a Safe Design:
Limit StatesThe criterion for a safe design is that the structure should not become unfit for use, i.e. that it should not reach a limit state during its design life. This is achieved, in particular, by designing the structure to ensure that it does not reach1. The ultimate limit state (ULS): the whole structure or its elements should not collapse, overturn or buckle when subjected to the design loads2. Serviceability limit states (SLS): the structure should not become unfit for use due to excessive deflection, cracking or vibration
The structure must also be durable, i.e. it must not deteriorate or be damaged excessively by the environment to which it is exposed or action of substances coming into contact with it.
The code places particular emphasis on durability (see the discussion in Chapter 2). For reinforced concrete structures the normal practice is to design for the ultimate limit state, check for serviceability and take all necessary precautions to ensure durability.
3.1.3 Ultimate Limit State(a) Strength
The structure must be designed to carry the most severe combination of loads to which it is subjected. Each and every section of the elements must be capable of resisting the axial loads, shears and moments derived from the analysis.
The design is made for ultimate loads and design strengths of materials with partial safety factors applied to loads and material strengths.
This permits uncertainties in the estimation of loads and in the performance of materials to be assessed separately. The section strength is determined using plastic analysis based on the short-term design stress-strain curves for concrete and reinforcing steel.(b) StabilityClause 2.2.2.1 of the code states that the layout should be such as to give a stable and robust structure. It stresses that the engineer responsible for overall stability should ensure compatibility of design and details of parts and components.
Overall stability of a structure is provided by shear walls, lift shafts, staircases and rigid frame action or a combination of these means. The structure should be such as to transmit all loads, dead, imposed and wind, safely to the foundations.(c) RobustnessClause 2.2.2.2 of the code states that the planning and design should be such that damage to a small area or failure of a single element should not cause collapse of a major part of a structure. This means that the design should be resistant to progressive collapse. The clause specifies that this type of failure can be avoided by taking the following precautions.
1. The structure should be capable of resisting notional horizontal loads applied at roof level and at each floor level. The loads are 1.5% of the characteristic dead weight of the structure between mid-height of the storey below and either mid-height of the storey above orthe roof surface. The wind load is not to be taken as less than the notional horizontal load.
2. All structures are to be provided with effective horizontal ties. These are
(a) peripheral ties
(b) internal ties
(c) horizontal ties to column and walls
The arrangement and design of ties is discussed in section 14.3.
3. For buildings of five or more storeys, key elements are to be identified, failure of which would cause more than a limited amount of damage. These key elements must be designed for a specially heavy ultimate load of 34 kN/m applied in any direction on the area supported by the member. Provisions regarding the application of this load are set out in BS 8110: Part 2,section 2.6.
4. For buildings of five or more storeys it must be possible to remove any vertical load bearing element other than a key element without causing more than a limited amount of damage. This requirement is generally achieved by the inclusion of vertical ties in addition to the other provisions noted above.
3.1.4 Serviceability Limit States
The serviceability limit states are discussed in BS 8110: Part 1, section 2.2.3. The code states that account is to be taken of temperature, creep, shrinkage, sway and settlement and possibly other effects.
The main serviceability limit states and code provisions are as follows.
(a) DeflectionThe deformation of the structure should not adversely affect its efficiency or appearance. Deflections may be calculated, but may tend to be complicated and in normal cases span-toeffective depth ratios can be used to check compliance with requirements.(b) CrackingCracking should be kept within reasonable limits by correct detailing.
Crack widths may be calculated, but may tend to be complicated and in normal cases cracking can be controlled by adhering to detailing rules with regard to bar spacing in zones where the concrete is in tension. In analysing a section for the serviceability limit states the behaviour is assessed assuming a linear elastic relationship for steel and concrete stresses. Allowance is made for the stiffening effect of concrete in the tension zone and for creep and shrinkage.
3.2 CHARACTERISTIC AND DESIGN LOADS
The characteristic or service loads are the actual loads that the structure is designed to carry. These are normally thought of as the maximum loads which will not be exceeded during the life of the structure. In statistical terms the characteristic loads have a 95% probability of not being exceeded.The characteristic loads used in design and defined in BS 8110: Part 1, clause 2.4.1, are as follows:
1. The characteristic dead load Gk is the self-weight of the structure and the weight of
finishes, ceilings, services and partitions;
2. The characteristic imposed load Qk is caused by people, furniture, and equipment etc.
on floors and snow on roofs. Dead and imposed loads for various types of buildings are given
in BS 6399: Part 1, 1996. Loadings for buildings. Code of practice for dead and imposed
loads.
3. The characteristic wind load Wk depends on the location, shape and dimensions of the
buildings. Wind loads are estimated using BS 6399: Part 2, 1997. Loadings for buildings.
Code of practice for wind loads.
The code BS 8110 states that nominal earth loads En are to be obtained in accordance with
normal practice. Reference should be made to BS 8004:1986: Code of Practice for Foundations and textbooks on Geotechnics. A useful work isBowles, Joseph E., 1995, Foundation analysis and design, (McGraw-Hill), 5th Edition.The structure must also be able to resist the notional horizontal loads defined in clause 3.1.4.2 of the code. The definition for these loads was given in section 3.1.3(c) above. design load=characteristic load×partial safety factor for load =Fk γfThe partial safety factor γf takes account of
1. possible increases in load
2. inaccurate assessment of the effects of loads
3. unforeseen stress distributions in members
4. the importance of the limit state being consideredThe code states that the values given for γf ensure that serviceability requirements cangenerally be met by simple rules. The values of γf to give design loads and the load combinations for the ultimate limit state are given in BS 8110: Part 1, Table 2.1.
These factors are given in Table 3.1. The code states that the adverse partial safety factor is applied to a load producing more critical design conditions. The beneficial factor is applied to a load producing a less, critical design condition.
| Table 3.1 Load combinationsLoad type Dead load Imposed load Load combination Adverse Beneficial Adverse Beneficial Earth and Water pressure Wind | ||||||
| 1 . Dead and imposed (and earth and water pressure) | 1.4 | 1.0 | 1.6 | 0 | 1.4 | – |
| 2. Dead and wind (and earth and water pressure) | 1.4 | 1.0 | – | – | 1.4 | 1.4 |
| 3. Dead, wind and imposed (and earth and water pressure) | 1.2 | 1.2 | 1.2 | 1.2 | 1.2 | 1.2 |
For example in the case of a beam with an overhang as shown in Fig.3.1, maximum upward
reaction at the left hand support and maximum bending moment in the main span occur when there is minimum load on the overhang and maximum load in the main span. On the other hand, possibility of uplift and maximum bending moment in the main span causing tension at top occurs when there is minimum load on the main span and maximum load on the overhang.
In considering the effects of exceptional loads caused by misuse or accident γf can be taken as 1.05. The loads to be applied in this case are the dead load, one-third of the wind load and one-third of the imposed load except for storage and industrial buildings when the full imposed load is to be used.Fig.3.1 Beam with an overhang.
3.3 MATERIALS: PROPERTIES AND DESIGN STRENGTHS
The characteristic strengths or grades of materials are as follows:Concrete: fcu is the 28 day cube strength in Newtons per square millimetre. The minimum grades for reinforced concrete are given in Table 3.3 in the code. These are grades C30, C35, C40, C45 and C50 in Newtons per square millimetre.Reinforcement: fy is the yield or proof stress in Newtons per square millimetre. The specified characteristic strengths of reinforcement given in Table 3.1 in the code are Hot rolled mild steel fy=250 N/mm2High yield steel, hot rolled or cold worked fy=460 N/mm2Clause 3.1.7.4 of the code states that a lower value may be used to reduce deflection or control cracking. The reason for this is that a lower stress in steel at SLS reduces the number and widths of cracks.
The resistance of sections to applied stresses is based on the design strength which is defined as
The factor γm takes account of
1. uncertainties in the strength of materials in the structure
2. uncertainties in the accuracy of the method used to predict the behaviour of members
3. variations in member sizes and building dimensionsValues of γm from Table 2.2 in the code used for design for the ultimate limit state are given in Table 3.2.
For exceptional loads γm is to be taken as 1.3 for concrete and 1.0 for steel.Fig.3.2 Short-term design stress-strain curve for (a) normal-weight concrete and (b) reinforcement
| Table 3.2 Values of γm for the ultimate limit state Reinforcement 1.05 | |
| Concrete in flexure or axial load | 1.5 |
| Shear strength without shear reinforcement | 1.25 |
| Bond strength | 1.4 |
| Others, e.g. bearing strength | ≥1.5 |
The short-term design stress-strain curves for normal-weight concrete and reinforcement from Figs 2.1 and 2.2 in the code are shown in Figs 3.2(a) and 3.2(b) The curve for concrete in compression is an idealization of the actual compression behaviour which begins with a parabolic portion where the slope of the tangent at the origin equals the short-term value of Young’s modulus. At strain εo which depends on the concrete grade, the stress remains constant with increasing load until a strain of 0.0035 is reached when the concrete is considered to have failed and is incapable of resisting any stress.
Expressions for Ec and εo are given in the figure. The maximum design stress in the concrete is given as 0.67fcu/γm. The coefficient 0.67 takes account of the relation between the cube strength and the bending strength in a flexural member. It is not a partial factor of safety.
The stress-strain curve for reinforcement shown in Fig.3.2(b) is bilinear with one yield point. The behaviour and strength of reinforcement are taken to be the same in tension and compression.
3.4 STRUCTURAL ANALYSIS
3.4.1 General ProvisionsThe general provisions relating to analysis of the structure set out in BS 8110: Part 1, section 2.5, are discussed briefly. The methods of frame analysis outlined in section 3.2 are set out.
Examples using these methods are given later in the book.
The object of analysis of the structure is to determine the axial forces, shears and moments throughout the structure. The code states that it is generally satisfactory to obtain maximum design values from moment and shear envelopes constructed from linear elastic analysis and to allow for moment redistribution if desired and for buckling effects in frames with slender columns. The code also states that plastic methods such as yield line analysis may also be used.
The member stiffness to be used in linear elastic analysis can be based on
1. the gross concrete section ignoring reinforcement: This is the method most frequently used in practice because it does not require data about the reinforcement present.
2. the gross concrete section including reinforcement on the basis of the modular ratio
3. the transformed section (the compression area of concrete and the transformed area of reinforcement in tension and compression based on the modular ratio are used)
The code states that a modular ratio of 15 may be assumed. It adds that a consistent approach should be used for all elements of the structure.
3.4.2 Methods of Frame AnalysisThe complete structure may be analysed elastically using a matrix computer program adopting the basis set out above. It is normal practice to model beam elements using only the rectangular section of T-beam elements in the frame analysis (Fig. 1.3). The T-beam section is taken into account in the element design.
Approximate methods of analysis are set out in the code as an alternative to a rigorous
analysis of the whole frame. These methods are discussed below.3.4.3 Monolithic braced frameShear walls, lifts and staircases provide stability and resistance to horizontal loads. A braced frame is shown in Fig.3.3. The approximate methods of analysis and the critical load arrangements are as follows.Fig.3.3 Braced multi-storey building: (a) plan; (b) rigid transverse frame; (c) side elevation.
(a) Division into subframesThe structural frame is divided into sub-frames consisting of the beams at one level and the columns above and below that level with ends taken as fixed. The moments and shears are derived from an elastic analysis (Figs 3.4(a) and 3.4(b)).(b) Critical load arrangementThe critical arrangements of vertical load are
1. all spans loaded with the maximum design ultimate load of 1.4Gk+1.6Qk2. alternate spans loaded with the maximum design ultimate load of 1.4Gk+1.6Qk and all other spans loaded with the minimum design ultimate load of 1.0Gk where Gk is the total dead load on the span and Qk is the imposed load on the span.
The load arrangements are shown in Fig.3.4(b).(c) Simplification for individual beams and columnsThe simplified sub-frame consists of the beam to be designed, the columns at the ends of the beam and the beams on either side if any. The column and beam ends remote from the beam considered are taken as fixed and the stiffness of the beams on either side should be taken asone-half of their actual value (Fig.3.4(c)).
The moments for design of an individual column may be found from the same sub-frame analysis provided that its central beam is the longer of the two beams framing into the column.(d) Continuous beam simplificationThe beam at the floor considered may be taken as a continuous beam over supports providing no restraint to rotation.
This gives a more conservative design than the procedures set out above. Pattern loading as set out in (b) is applied to determine the critical beam moments and shear for design (Fig.3.4(d)).(e) Asymmetrically loaded columnThe asymmetrically loaded column method is to be used where the beam has been analysed on the basis of the continuous beam simplification set out in (d) above.
The column moments can be calculated on the assumption that the column and beam ends remote from the junction under consideration are fixed and that the beams have one-half their actual stiffnesses. The
imposed load is to be arranged to cause maximum moment in the column (Fig.3.4(e)). Examples of the application of these methods are given Chapter 14.
3.4.4 Rigid Frames Providing Lateral Stability
Where rigid frames provides lateral stability, they must be analysed for horizontal and vertical loads. Clause 3.1.4.2 of the code states that all buildings must be capable of resisting a notional horizontal load equal to 1.5% of the characteristic dead weight of the structure applied at roof level and at each floor.
The complete structure may be analysed for vertical and horizontal loads using computer analysis program. As an alternative the code gives the following Fig 3.4 Analysis for vertical load: (a) frame elevation; (b) subframes; (c) simplified subframe; (d) continuous beam simplification; (c) column moments analysis for (d)method for sway frames of three or more approximately equal bays (the design is to be basedon the more severe of the conditions):
1. elastic analysis for vertical loads only with maximum design load 1.4Gk+1.6Qk (refer to
sections 3.4.3(a) and 3.4.3(b) above)
2. or the sum of the moments obtained from (a) elastic analysis of subframes as defined in section 3.4.3(a) with all beams loaded with 1.2Gk+1.2Qk (horizontal loads are ignored)
(b) elastic analysis of the complete frame assuming points of contraflexure at the centres of all beams and columns for wind load 1.2Wk only
The column bases may be considered as pinned if this assumption gives more realistic analyses. A sway frame subjected to horizontal load is shown in Fig.3.5. Method of analysis for horizontal load, the portal method, is discussed in Chapter 13. Examples in the use of these methods are also given.Fig.3.5 Horizontal loads.3.4.5 Redistribution of MomentsPlastic method of analysis for steel structures based on the stress-strain curve shown inFig.3.6(a), which gives the moment-rotation curve in Fig.3.6(b), can be used for the analysis of reinforced concrete structures provided due attention is paid to the fact reinforced concretesections have limited ductility.
In order to prevent serious cracking occurring at serviceability limit state, the code adopts a method that gives the designer control over the amount of redistribution and hence of rotation that is permitted to take place. In clause 3.2.2 the code allows a reduction of up to 30% of the peak elastic moment to be made whilst keeping internal and external forces in equilibrium. The conditions under which this can carried out are set out later in Chapter 13.
Fig.3.6 (a) Stress-strain curve; (b) moment-rotation curve; (c) elastic and plastic moment di
