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of les structural element design. I hope that it will be a source to turn to for help as a student and a friend for reference when one has gained experience and confidence. In conclusion, I must acknowledge the invaluable assistance received from certain people in particular. I am indebted to Francis Myerscough for the thorough way he read through the draft and for his pertinent comments. Special thanks are due to Sue Dean who somehow managed to decipher the scribble and turn it into a typed manuscript. Last, but certainly not least, I am grateful to my wife and family for their patience and support during the months of writing. Trevor Draycott 1 General matters 1.1 Introduction Structural engineering can broadly be described as the study of how the various component elements of a building act together to form a supportive structure and transmit forces down to the foundations. Determining the actual size of the members or elements is only one of the interrelated matters with which the structural engineer is concerned in the design of a building or similar structure. For the purpose of description these matters may be divided into stages and defined as follows: Structural planning stage When a structural scheme is devised to suit both the purpose of the building and the site conditions which exist. Structural analysis stage When the loads are determined and their dispersal through the structure is analysed by applying the principles of structural mechanics. Structural elements design stage When the size needed for each member is calculated in relation to the material and its particular structural capacity. Structural detailing stage When detail drawings are produced to illustrate how the structure is to be constructed on site so as to comply with the engineer's design concept. Structural specification stage When the specification clauses are compiled to ensure that the standard of materials and workmanship to be employed in the works comply with the assumptions embodied in the structural engineer's design. Building and civil engineering is a team effort, requiring each discipline to have some understanding of the work in others. In this context structural element design is probably the best subject to provide architects, quantity surveyors, building control officers, clerks of works and site staff with a fundamental knowledge of the structural behaviour of the different building materials. Initially students often mistakenly believe that structural element design is just a form of applied mathematics. Some regrettably are even daunted by this belief. It cannot be denied that in order to determine the size of individual elements it is necessary to carry out calculations, but these, once understood, follow a logical sequence. To assist us in arriving at a logical design sequence we first need a set of guidelines. These may be found in the relevant British Standards or Codes of Practice which advise on how the materials we use, that is timber, concrete, masonry and steel, behave in the form of building elements such as beams, columns, slabs and walls. 2 STRUCTURAL ELEMENTS DESIGN MANUAL 1.2 British Standards Guidance on the design of building and civil engineering structures is given in various British Standards and Codes of Practice. These play an important role in the provision of structural designs which are both safe and economic and which comply with the Building Regulations and other statutory requirements. To the inexperienced the standards can be seen as sets of rules restricting freedom and choice, but in the author's opinion they should be accepted as guidelines. Just as our buildings need firm foundations, so too does our knowledge of how structures behave. Engineering judgement and flair come not from taking risks but from a sound understanding of the limits to which we can take the various materials. British Standards contribute to that understanding. In relation to their application in structural design the various standards and codes may be broadly classified into three groups: (a) Those relating to thef buildings where no access is provided to the roof, other than for routine cleaning and maintenance, a minimum uniformly distributed imposed load of 0.75 kN/m2 may be adopted or a concentrated load of 0.9 kN, whichever produces the worst load effect. A small building in this context must have a width not greater than 10 m and a plan area not larger than 200 m2, and must have no parapets or other abrupt changes in roof height likely to cause drifting of snow and hence a build-up of load. For situations outside these parameters, reference should be made to BS 6399 Part 3 for the imposed roof load to be adopted. Wind loading This may be defined as all the loads acting on a building that are induced by the effect of either wind pressure or wind suction. The pressure exerted by the wind is often one of the most important loads which exposed structures have to resist with regard to overall stability. CP 3 Chapter V Part 2 `Wind loads' gives the wind speeds to be adopted for the design of buildings relative to their geographical location within the United Kingdom. It also gives pressure coefficients for the various parts of a building, such as roofs and walls, in relation to its size and shape. This code will eventually become Part 2 of BS 6399. Combined loads Having obtained individual loading cases, that is dead, imposed and wind, the most onerous combination should be determined and the structure designed accordingly. For a member not exposed to wind, such as a floor beam, this would normally be the combination of dead and imposed loading. For a member exposed to wind, such as the rafter of a truss or portal frame, the combination of dead and imposed load would normally be used to design the member initially. It would then be checked for reversal of stress due to a combination of dead load and wind suction. Wind loading generally influences the overall stability of a building. Therefore, since the emphasis of this manual is on the design of individual structural elements, only the effects of dead and imposed loads will be examined. GENERAL MATTERS 7 Table 1.5 Imposed loads for residential buildings (BS 6399 Part 1 Table 5) Floor area usage Intensity of distributed load (kN/m2) Concentrated load (kN) Type 1: self-contained dwelling units All 1.5 Type 2: apartment houses, boarding houses, lodging houses, guest houses, hostels, residential clubs and communal areas in blocks of flats Boiler rooms, motor rooms, fan rooms and the like including the weight of machinery Communal kitchens, laundries Dining rooms, lounges, billiard rooms Toilet rooms Bedrooms, dormitories Corridors, hallways, stairs, landings, footbridges, etc. Balconies 1.4 7.5 4.5 3.0 2.0 2.0 1.5 3.0 Same as rooms to which they give access but with a minimum of 3.0 -- 7.5 4.5 2.7 -- 1.8 4.5 1.5 per metre run concentrated at the outer edge 1.0 at 1 m centres 4.5 Cat walks Type 3: hotels and motels Boiler rooms, motor rooms, fan rooms and the like, including the weight of machinery Assembly areas without fixed seating,* dance halls Bars Assembly areas with fixed seating* Corridors, hallways, stairs, landings, footbridges, etc. Kitchens, laundries Dining rooms, lounges, billiard rooms Bedrooms Toilet rooms Balconies 5.0 5.0 4.0 4.0 3.0 2.0 2.0 2.0 Same as rooms to which they give access but with a minimum of 4.0 -- 3.6 -- -- 4.5 4.5 2.7 1.8 -- 1.5 per metre run concentrated at the outer edge 1.0 at 1 m centres Cat walks * Fixed seating is seating where its removal and the use of the space for other purposes is improbable. 8 STRUCTURAL ELEMENTS DESIGN MANUAL Having discussed the types of loading encountered, let us look at some examples. These illustrate how the designer has to convert information about the construction into applied loads on individual structural elements such as beams and columns. Example 1.1 Timber beams spanning 4 m and spaced at 3 m centres as shown in Figure 1.1 support a timber floor comprising joists and boards together with a plaster ceiling. The load imposed by the dead weight of the floor joists and boards is 0.23 kN/ m2 anand resulting deflection in accordance with the guidelines appertaining to the particular beam material. Item (a) allows a load diagram to be produced and also enables a shear force (SF) diagram to be drawn from which the maximum shear force can be determined. The induced bending moments, item (b), can be derived from the SF diagram together with the location and magnitude of the maximum bending moment. This coincides with the point of zero shear, which is also known as the point of contraflexure. A bending moment (BM) diagram can then be drawn. Formulae are given in various design manuals for calculating the maximum bending moments and deflections of simply supported beams carrying standard loading patterns such as a central point load, or equally spaced point loads, or a uniformly distributed load. The loading, shear force, bending moment and deflection diagrams for the two most common load conditions are illustrated together with the relevant formulae in Figure 1.14. That for a constant uniformly distributed load (UDL) is shown in Figure 1.14a and that for a central point load in Figure 1.14b. For unsymmetrical loading patterns the reactions, shear force, bending moment and deflection values have to be calculated from first principles using the laws of basic statics. GENERAL MATTERS 15 Total UDL W L W/2 Load diagram W/2 W/2 L/2 W L/2 L Load diagram W/2 W/2 Point of contraflexure (zero shear) W/2 Point of contraflexure (zero shear) W/2 Shear force (SF) diagram W/2 Shear force (SF) diagram Maximum BM = WL/8 Maximum BM = WL/4 Bending moment (BM) diagram Bending moment (BM) diagram Maximum deflection Maximum deflection Maximum deflection at centre = I WL3 5 WL3 Maximum deflection at centre = 48 EI 348 EI Deflected shape Deflected shape (a) Beam supporting a uniformly (b) Beam supporting a central point load distributed load (UDL) Figure 1.14 Load, shear force and bending moment diagrams for standard loading conditions The resistance of a beam to bending, referred to in item (c), is derived from the theory of bending. The general expression for the theory of bending is M f E I = y = R where M I either the internal moment of resistance (MR) of the beam or the external bending moment (BM) applied to the beam second moment of area of the beam which is a geometrical property of the beam 16 STRUCTURAL ELEMENTS DESIGN MANUAL stress value for the beam (dependent on the beam material, such as timber or steel) y distance from the neutral axis (NA) of the beam to its extreme fibres E Young's modulus of elasticity for the beam (again dependent on the beam material) R radius of curvature after bending The term E/R relates to the deformation of a beam and is used in the derivation of deflection formulae. It is not used in bending calculations, and the expression therefore reduces to M I f = f y This expression may be rearranged so that M= f I y y or f = M I Now I/y is a geometric property of a beam section called the elastic modulus or section modulus, and is denoted by the symbol Z. Thus M = fZ or f= or Z= M f (1.3) M Z (1.2) (1.1) The equations can be used in design as follows: (a) Equation 1.1 may be used to calculate the internal moment of resistance (MR) for a beam of known size (Z known) and material (f known). (b) Equation 1.2 may be used to calculate the bending stress f occurring within a beam of known size (Z known) when it is subjected to an externally applied bending moment (BM known). (c) Equation 1.3 may be used for a beam of known material (f known) to calculate the beam property Z needed for the beam to resist an externally applied bending moment (BM known). The key to their use is the relationship between a beam's moment of resistance (MR) and the applied bending moment (BM). If a beam section is not to fail under load, an internal moment of resistance (MR) must be developed within the beam at least equal to the maximum external bending moment (BM) produced by the loads. That is, Internal MR = external BM GENERAL MATTERS 17 Consider the simply supported rectangular beam shown in Figuce the different end restraint conditions in relation to the various materials is given in the relevant British Standards. It should be understood that, all other things being equal, the shorter the effective length the stronger the member. There are subtle differences in the design approach for columns depending on the material. Therefore, to avoid confusion, examples on the design of columns will be dealt with in each of the respective material chapters of this manual. GENERAL MATTERS 25 Fixed Pinned L l = 0.7 L L l = 0.85 L Fixed Fixed Pinned Free L l=L L l = 2L Pinned L = Actual column height l = Effective length Fixed Figure 1.24 Effective length conditions for columns 1.7 Summary There are few aspects of structural design that do not benefit from the adoption of a methodical procedure to minimize the chance of error. In relation to the general matters dealt with in this chapter, these may be summarized into the following procedural list: (a) Evaluate the loads acting on the structure. (b) Determine the loads acting on the individual structural members. (c) Calculate the forces, shears, bending moments and so on induced in each member by the loads. (d) Design the respective members. Step (d) depends on the design guidelines for the particular material from which the members are formed. The reader should therefore refer to the relevant chapter of this manual for the design of structural elements in a specific material. 2 Timber elements 2.1 Stress grading Of all the materials used for construction, timber is unique by virtue of being entirely natural. Whilst this gives it a deserved aesthetic appeal, it also creates an initial problem for the structural engineer. In order to design any structural component efficiently, it is necessary to know in advance the strength capability of the material to be used. Timber presents a problem in this respect since we have no apparent control over its quality. All the other materials we use structurally are man made and therefore some form of quality control can be exercised during their production. To overcome this difficulty and to enable timber to compete equally with other structural materials, the stress grading method of strength classification has been devised. This is based on an assessment of features in timber that are known to influence strength. Guidance for such assessment either by visual inspection or by use of stress grading machines is given for softwoods in BS 4978 `Specification for softwood grades for structural use'. The implications of this code will be discussed in more detail here. For guidance on the stress grading of tropical hardwoods reference should be made to BS 5756 `Specification for tropical hardwoods graded for structural use'. Visual stress grading is a manual process carried out by approved graders who have been trained and have demonstrated their proficiency in the technique. The grader examines each piece of timber to check the size and frequency of specific physical characteristics: knots, slope of grain, rate of growth, wane, resin pockets and distortion. These are compared with the permitted limits given in BS 4978 to determine whether a piece is accepted into one of the two visual stress grades or rejected. The two visual grades referred to in the standard are general structural (GS) grade and special structural (SS) grade. The machine stress grading method is based on the principle that strength is related to stiffness. Therefore, since stiffness may be established by measuring deflection under load, the method offers the basis for a non-destructive testing technique. Stress grading machines employ such a technique. Timber is passed through the machine and, by means of a series of rollers, some static and some exerting pressure, bending is induced at increments along its length. The resulting deflection is measured by a computer linked to the machine and compared simultaneously with preprogrammed parameters for accepting or rejecting the timber into one of four machine grades. The four machine grades specified inrs. The design of single isolated posts and load bearing stud walls will be considered in this manual, beginning in this section with posts. It is important when selecting suitable pieces of timber for use as columns that particular attention is paid to straightness. The amount of bow permitted by most stress grading rules is not usually acceptable for the selection of column material. The amount of bow acceptable for column members should be limited to 1/300 of the length. 50 STRUCTURAL ELEMENTS DESIGN MANUAL Timber posts may be subject to direct compression alone, where the loading is applied axially, or to a combination of compression loading and bending due to the load being applied eccentrically to the member axes. A timber post may also have to be designed to resist lateral bending resulting from wind action. However, the effects of wind loading on individual structural elements will not be considered in this manual. The structural adequacy of an axially loaded post is determined by comparing the applied compression stress parallel to the grain with the permissible compression stress parallel to the grain. 2.14.1 Applied compression stress The applied stress parallel to the grain is obtained by dividing the applied load by the cross-sectional area of the timber section: c, a, par = applied load F = section area A The section area is the net area after deducting any open holes or notches. No deduction is necessary for holes containing bolts. For the section to be adequate, the applied stress must be less than the permissible stress: c, a, par < c, adm, par 2.14.2 Permissible compression stress The permissible stress c, adm, par is obtained by modifying the grade compression stress parallel to the grain, c, g, par (Table 2.2), by any of the previously mentioned K factors that may be applicable, that is K 1 wet exposure geometrical property modification factor K 2 wet exposure stress modification factor K 3 load duration modification factor Timber posts, as opposed to wall studs, are not normally part of a load sharing system as defined by BS 5268 and therefore the load sharing modification factor K 8 does not apply. 2.14.3 Slenderness of posts To avoid lateral buckling failure a further modification factor must also be applied in post calculations when the slenderness ratio is equal to 5 or more. This is obtained from BS 5268 Table 22, reproduced here as Table 2.9. It is dependent on the slenderness ratio and on the ratio of the modulus of elasticity to the compression stress (E/). TIMBER ELEMENTS 51 Table 2.9 Modification factor K 12 for compression members (BS 5268 Part 2 1988 Table 22) <5 E/c, <1.4 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.4 0.975 0.975 0.975 0.975 0.975 0.976 0.976 0.976 0.976 0.976 0.976 0.976 0.976 0.976 0.976 0.976 0.976 2.9 0.951 0.951 0.951 0.951 0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.952 5.8 0.896 0.899 0.901 0.902 0.903 0.904 0.904 0.905 0.905 0.905 0.906 0.906 0.906 0.906 0.906 0.907 0.907 5 10 20 30 40 50 Values of slenderness ratio (=L e /i) 60 70 80 90 100 120 140 160 180 200 220 240 250 Equivalent L e /b (for rectangular sections) 8.7 11.6 14.5 17.3 20.2 23.1 26.0 28.9 34.7 40.5 46.2 52.0 57.8 63.6 69.4 72.3 0.827 0.837 0.843 0.848 0.851 0.853 0.855 0.856 0.857 0.858 0.859 0.860 0.861 0.861 0.862 0.862 0.863 0.735 0.759 0.774 0.784 0.792 0.797 0.801 0.804 0.807 0.809 0.811 0.813 0.814 0.815 0.816 0.817 0.818 0.621 0.664 0.692 0.711 0.724 0.734 0.742 0.748 0.753 0.757 0.760 0.763 0.766 0.768 0.770 0.772 0.773 0.506 0.562 0.601 0.629 0.649 0.665 0.677 0.687 0.695 0.701 0.707 0.712 0.716 0.719 0.722 0.725 0.728 0.408 0.466 0.511 0.545 0.572 0.593 0.609 0.623 0.634 0.643 0.651 0.658 0.664 0.669 0.673 0.677 0.681 0.330 0.385 0.430 0.467 0.497 0.522 0.542 0.559 0.573 0.584 0.595 0.603 0.611 0.618 0.624 0.629 0.634 0.271 0.320 0.363 0.399 0.430 0.456 0.478 0.497 0.513 0.527 0.539 0.550 0.559 0.567 0.57stic strength of concrete f y characteristic strength of reinforcement K coefficient obtained from design formula for rectangular beams K' 0.156 when redistribution of moments does not exceed 10 per cent M design ultimate resistance moment; or M u design ultimate bending moment due to ultimate loads x depth to neutral axis z lever arm Deflection b width of section d effective depth of tension reinforcement fy characteristic strength of reinforcement M design ultimate bending moment at centre of the span or, for a cantilever, at the support Shear As Asb Asv bv d f cu f yv sb sv V area of tension reinforcement cross-sectional area of bent-up bars total cross-section of links at the neutral axis breadth of section used to calculate the shear stress effective depth of tension reinforcement characteristic strength of concrete characteristic strength of links (not to exceed 460 N/mm2) spacing of bent-up bars spacing of links along the member design shear force due to ultimate loads CONCRETE ELEMENTS 69 Vb v vc design shear resistance of bent-up bars design shear stress at a cross-section design concrete shear stress (from BS 8110 Table 3.9) angle of shear failure plane from the horizontal angle between a bent-up bar and the axis of a beam angle between the compression strut of a system of bent-up bars and the axis of the beam Compression Ac net cross-sectional area of concrete in a column Asc area of vertical reinforcement b width of column fcu characteristic strength of concrete fy characteristic strength of reinforcement h depth of section le effective height lex effective height in respect of major axis ley effective height in respect of minor axis lo clear height between end restraints N design ultimate axial load on a column 3.3 Design philosophy The design of timber in Chapter 2 was based on permissible stress analysis, whereas the design analysis for concrete employed in BS 8110 is based on limit state philosophy. Its object is to achieve an acceptable probability that the structure being designed will not become unfit for its intended purpose during its expected life. Therefore the various ways in which a structure could become unfit for use are examined. The condition of a structure when it becomes unfit for use or unserviceable is called a limit state. This can by definition be further subdivided into the following two categories: (a) Ultimate limit state (ULS) (b) Serviceability limit state (SLS). 3.3.1 Ultimate limit state If a ULS is reached, collapse of the member or structure will occur. Therefore the design must examine all the ULSs likely to affect a particular member. Some of the ULSs that may have to be considered are as follows: (a) (b) (c) (d) ULS ULS ULS ULS due due due due to to to to bending shear direct compression or tension overturning. 70 STRUCTURAL ELEMENTS DESIGN MANUAL 3.3.2 Serviceability limit state If an SLS is reached the appearance of the member or structure will be disrupted. Whilst this will not cause collapse it may render the member unfit for its intended service use. Some of the SLSs that may have to be considered are as follows: (a) SLS due to deflection: this should not adversely affect the appearance of the structure. (b) SLS due to cracking: this should not adversely affect the appearance or the durability of the structure. For example, excessive cracks would allow the ingress of moisture with subsequent corrosion and/or frost damage. (c) SLS due to vibration: this should not produce structural damage or cause discomfort or alarm to occupants of the building. Special precautions may be necessary to isolate the source of such vibration. Other serviceability considerations that may have to be taken into account in the design of a particular member or structure are durability, fatigue, fire resistance and lightning. Having identified the various limit states, the basic design procedure to ensure that they are not exceeded may be summarized as follows. 3.3.3 Limit state basic design procedure When designing a particular concrete element it is usual to first ensure.4 1.5 3.6.3 Ultimate design strength of materials The ultimate design strength of a material is obtained by dividing its characteristic strength by the appropriate partial safety factor referred to in Section 3.6.2: Ultimate design strength of concrete = Ultimate design strength of reinforcement = fcu = 0.67fcu 1.5 fy = 0.87f y 1.15 It is important to appreciate that the formulae and design charts given in BS 8110 have been derived with the relevant partial safety factors for strength included. Therefore it is only necessary for the designer to insert the relevant characteristic strength values f cu or fy in order to use the formulae and charts. 3.7 Practical considerations for durability Before proceeding to the actual structural design of concrete elements, a number of important practical considerations related to durability are worthy of mention since they can influence the size of members. Durable concrete should perform satisfactorily in its intended environment for the life of the structure. To achieve durable concrete it is necessary to consider several interrelated factors at different stages in both the design and construction phases. Guidance is given in BS 8110 on various factors that influence reinforced concrete durability. They include: (a) (b) (c) (d) (e) (f) (g) Shape and bulk of concrete Amount of concrete cover to reinforcement Environmental conditions to which the concrete will be exposed Cement type Aggregate type Cement content and water to cement ratio Workmanship necessary to attain full compaction and effective curing of the concrete. 76 STRUCTURAL ELEMENTS DESIGN MANUAL Factors (a) and (b) must be considered at the design stage because they influence the member size and the location of the reinforcement. These are therefore discussed in more detail below. The remaining factors listed may be catered for by including suitable clauses in the specification and by adequate site management. 3.7.1 Shape and bulk of concrete If the concrete will be exposed when the building is finished, adequate thought should be given at the design stage to its shape and bulk to prevent the ingress of moisture. The shape should be detailed to encourage natural drainage and hence avoid standing water. 3.7.2 Concrete cover to reinforcement All reinforcement must be provided with sufficient cover to avoid corrosion and guard against distortion in the event of fire. The amount of cover to protect against fire is discussed in Section 3.7.3. The amount of cover necessary to protect reinforcement against corrosion depends on both the exposure conditions that prevail and the quality of concrete used. BS 8110 Table 3.2 defines exposure conditions, and Table 3.4 gives the nominal cover to be provided with respect to the concrete quality. These tables are reproduced here as Tables 3.5 and 3.6 respectively. Table 3.5 Exposure conditions (BS 8110 Part 1 1985 Table 3.2) Environment Mild Moderate Exposure conditions Concrete surfaces protected against weather or aggressive conditions Concrete surfaces sheltered from severe rain or freezing whilst wet Concrete subject to condensation Concrete surfaces continuously under water Concrete in contact with non-aggressive soil (see class 1 of Table 6.1 of BS 8110)* Concrete surfaces exposed to severe rain, alternate wetting and drying, or occasional freezing or severe condensation Concrete surfaces exposed to sea water spray, de-icing salts (directly or indirectly), corrosive fumes or severe freezing conditions whilst wet Concrete surfaces exposed to abrasive action, e.g. sea water carrying solids or flowing water with pH 4.5 or machinery or vehicles Severe Very severe Extreme * For aggressive soil conditions see clause 6.2.3.3 of BS 8110. CONCRETE ELEMENTS 77 Table 3.6 Nominal cover to all reinforcement (including links) to meet durability requirements (BS 8110 Part 1 1985 Table 3.4) Conditions of exposure Mild Moderate Severe Very severe Extreme Maximum free water/cement ratio Minimum cement content (kg/m3) Lowest grade of concrete 25 -- -- -- -- 0.65 275 C30 Nominal cover (mm) 20 35 -- -- -- 0.60 300 C35 20* 30 40 50 -- 0.55 325 C40 20* 25 30 40 60 0.50 350 C45 20* 20 25 30 50 0.45 400 C50 * These covers may be reduced to 15 mm provided that the nominal maximum size of aggregate does not exceed 15 mm. Where concrete is subject to freezing whilst wet, air-entrainment should be used (see clause 3.3.4.2 of BS 8110). For conditions of exposure see Table 3.5 of this chapter. Note 1: This table relates to normal-weight aggregate of 20 mm nominal maximum size. Note 2: For concrete used in foundations to low rise construction (see clause 6.2.4.1 of BS 8110). Two points should be noted. First, the cover stipulated is that to all reinforcement including any links. Secondly, the values are nominal and therefore under certain circumstances may have to be increased. The amount of cover should also comply with recommendations given in BS 8110 relating to bar size, to aggregate size and to situations where the concrete is cast against uneven surfaces. It must also allow for any surface treatment, such as bush hammering, that would reduce the nominal thickness. A summary of the requirements for cover is given in Table 3.7, and typical examples are illustrated in Figure 3.2. Table 3.7 Summary of cover requirements (other than for fire resistance): cover to any bar, including links, is the greatest of the relevant values Circumstances Generally Relative to aggregate Resulting cover to single main bars Resulting cover to bundles of main bars Concrete cast against earth Concrete cast against blinding Cover Nominal value from Table 3.6 Size of coarse aggregate Bar diameter Bar diameter equivalent to area of group 75 mm 40 mm 78 STRUCTURAL ELEMENTS DESIGN MANUAL Links Links Single main bars A A B B C C B Main bars in pairs B A = Cover to a single main bar bar diameter B = Nominal cover to links value from Table 3.6 aggregate size C = Cover to group of main bars bar diameter equivalent to area of group Links Main bars Links Main bars 75 40 75 Blinding 75 Beam cast against earth Beam cast against blinding Note: For simplicity only beams have been used to illustrate the requirements for cover although similar requirements apply to other concrete members. Figure 3.2 Typical examples of cover to reinforcement 3.7.3 Fire resistance The fire resistance of a reinforced concrete member is dependent upon the cover to reinforcement, the type of aggregate that is used and the minimum dimensions of the member. Nominal cover provided for protection against corrosion may, in certain circumstances, not suffice as fire protection. Reference should be made to BS 8110 Part 1 Table 3.5 and Figure 3.2 for the amount of cover and minimum member dimensions to satisfy fire resistance requirements. Further guidance on design for fire, including information on surface treatments, is given in Section 4 of BS 8110 Part 2. 3.8 Flexural members Flexural members are those subjected to bending, for example beams and slabs. Primarily the same procedure appertains to the design of both, CONCRETE ELEMENTS 79 although there are certain subtle differences. The design of beams will therefore be studied first and then compared with the design of slabs. 3.9 Beams There are a number of dimensional requirements and limitations applicable to concrete beams which the designer needs to consider since they can affect the design: (a) (b) (c) (d) (e) Effective span of beams Deep beams Slender beams Main reinforcement areas Minimum spacing of reinforcement (f) Maximum spacing of reinforcement. Certain other aspects such as bond, anchorage, and if applicable the curtailment and lap lengths of reinforcement, require consideration at the detailing stage. The main structural design requirements for which concrete beams should be examined are as follows: (a) (b) (c) (d) Bending ULS Cracking SLS Deflection SLS Shear ULS. Let us now consider how each of these dimensional and structural requirements influences the design of beams. 3.9.1 Effective span of beams The effective span or length of a simply supported beam may be t0.40 0.50 0.57 0.63 0.72 0.80 0.91 Note 1: Allowance has been made in these figures for a m of 1.25. Note 2: The values in the table are derived from the expression 0.79[100 As /(bvd)]1/3(400/d)1/4/m where 100 As /bv d should not be taken as greater than 3, and 400/d should not be taken as less than 1. For characteristic concrete strengths greater than 25 N/mm2, the values in the table may be multiplied by (f cu/25)1/3. The value of f cu should not be taken as greater than 40. 96 STRUCTURAL ELEMENTS DESIGN MANUAL Two points need to be appreciated with respect to the use of Table 3.12. First, the tabulated values of vc only apply to grade 25 concrete. For higher characteristic strengths up to a limiting fcu of 40 N/mm2, the values may be increased by multiplying them by (fcu/25)1/3. Second, the percentage of main tensile reinforcement in the member under consideration should not be taken, for the purpose of the shear calculations, as greater than 3 per cent. Nor, again for the purpose of the shear calculations, should its effective depth be taken as greater than 400 mm. The guidance given in Table 3.11 will establish whether and in what form shear reinforcement is required, according to three values of the shear stress v: (a) v < 0.5vc Theoretically no shear reinforcement is necessary throughout the length of the beam. However, with the exception of simple lintels, nominal reinforcement in the form of minimum links should be provided in all beams of structural importance. (b) 0.5 v c < v < (vc + 0.4) Only minimum links are required. (c) (vc + 0.4) < v < 0.8 f cu or 5 N/mm2 Designed links, or a combination of designed links and bent-up bars, are necessary. The procedures for (b) and (c) are described in the following sections. In certain circumstances, near to supports, advantage may be taken of an enhanced shear strength, for which guidance is given in clause 3.4.5.8 of BS 8110 Part 1. Minimum links When minimum links are to be provided as shown in Figure 3.14, their area should be determined from the following expression: Asv where Asv total cross-section of links at the neutral axis, at a section bv breadth of section fyv characteristic strength of links (that is 250 N/mm2 or 460 N/mm2) sv spacing of links along the member BS 8110 states that the spacing of links should not exceed 0.75d. Hence, 0.4 bv sv 0.87 f yv CONCRETE ELEMENTS 97 Shear failure plane Nominal top steel Vertical links Main tensile steel Maximum shear V = reaction s v link spacing Elevation Cross-section Figure 3.14 Shear reinforcement in the form of vertical links as a trial, this limit may be substituted in the area formula as follows: A sv 0.4 bv 0.75d 0.87 fyv Should the resulting area prove impractical the link spacing may of course be reduced. Designed links When shear reinforcement greater than minimum links is necessary, it may be provided either as designed links alone or as designed links combined with bent-up bars. In both instances, it must be capable of resisting the difference between the applied design shear stress v and the design shear stress capacity of the concrete v c. Where designed links alone are to be provided, their area should be determined from the following expression: Asv b v sv (v-vc) 0.87 fyv The symbols and maximum spacing are as for minimum links. Designed links and bent-up bars Where shear reinforcement needs to be provided in the form of designed links combined with bent-up bars, the total shear resistance capacity will be the summation of the individual values for each system. In this context the contribution made by the bent-up bars should not be taken as more than 50 per cent of the total shear resistance. The shear resistance of the 98 STRUCTURAL ELEMENTS DESIGN MANUAL designed links may be determined from the information given above, whilst that of the bent-up bars is discussed in the following. Bent-up bars, as their name implies, are main tension bars that are bent up at an angle from the bottom of the beam as shown in Figure 3.15. Such bars cannot be bent up unless they are no longer HY double links at 170 mm centres. It should be appreciated that it may be practical to increase the spacing of links towards mid-span as the shear force reduces. 3.9.11 Design summary for concrete beams The design procedure for simply supported singly reinforced concrete beams may be summarized as follows: (a) Calculate the ultimate loads, shear force and bending moment acting on the beam. (b) Check the bending ULS by reference to the BS 8110 simplified stress block formulae. This will determine an adequate depth for the beam singly reinforced and the area of tension reinforcement required. (c) Ensure that the cracking SLS is satisfied by compliance with the recommendations for minimum reinforcement content and bar spacing. (d) Check the deflection SLS by reference to the recommended span to depth ratios. (e) Check the shear ULS by providing the relevant link reinforcement in accordance with the guidance given in BS 8110. 3.10 Slabs BS 8110 deals with suspended slabs as opposed to ground bearing slabs. For guidance on the design of the latter, reference should be made to other sources such as the literature published by the British Cement Association, formerly known as the Cement and Concrete Association. 104 STRUCTURAL ELEMENTS DESIGN MANUAL Suspended slabs may be designed to span in either one or two directions depending on how they are supported at the edges. In the context of BS 8110, slabs are classified into three groups: Solid slabs These, as the name implies, consist of solid concrete reinforced where necessary to resist tension (Figure 3.18). Overall slab thickness Tension reinforcement Figure 3.18 Cross-section through a solid slab Ribbed slabs For spans exceeding 4 m the self-weight of solid slabs can begin to affect their economy. In such circumstances consideration should be given to the use of ribbed slabs. These are formed in any one of the following ways: (a) As a series of in situ concrete ribs cast between hollow or solid block formers which remain part of the completed slab (Figure 3.19). (b) As a series of in situ concrete ribs cast monolithically with the concrete topping on removable forms (Figure 3.20). (c) As an apparently solid slab but containing permanent formers to create voids within the cross-section (Figure 3.21). Overall slab thickness Hollow block former Rib Tension reinforcement Figure 3.19 formers Overall slab thickness Cross-section through a ribbed slab cast with integral hollow block Voids left by removable formers Rib Tension reinforcement Figure 3.20 Cross-section through a ribbed slab cast on removable formers Overall slab thickness Voids created by permanent formers Rib Tension reinforcement Figure 3.21 Cross-section through a hollow slab cast with permanent void formers CONCRETE ELEMENTS 105 Flat slabs The title of such slabs is descriptively something of a misnomer. It is intended to describe slabs which have been designed to act in conjunction with columns as a structural frame without the necessity for beams, and hence have a flat soffit (Figure 3.22). They can however have thickened sections where the soffit is dropped to form a stiffening band running between the columns (Figure 3.23). The top of the columns may also be enlarged locally by the formation of a column head to give support to the slab over a larger area (Figure 3.24). Flat slabs may be solid or may have recesses formed in the soffit to give a series of twodirectional ribs, in which case they are often referred to as waffle or coffered slabs. Flat slab Flat slab Drop Column Column Figure 3.22 Section through a flat slab Figure 3.23 Section through a flat slab with drops Flat slab Flared column head Column Figure 3.24 Section through a flat slab with enlarged column heads The most commonly encountered suspended slabs are those used for the floors and roofs of buildings. However, sloping slabs are also used to form ramps, and concrete staircases are in fact a type of cranked slab. For the purpose of this manual only the design of solid slabs spanning in one direction will be stu = lo Table 3.15 Values of for braced columns (BS 8110 Part 1 1985 Table 3.21) End condition at top 1 1 2 3 0.75 0.80 0.90 End condition at bottom 2 0.80 0.85 0.95 3 0.90 0.95 1.00 The types of end condition that influence end fixity are defined in BS 8110 as follows: Condition 1 The end of the column is connected monolithically to beams on either side which are at least as deep as the overall dimension of the column in the plane considered (Figure 3.33). Where the column is connected to a foundation structure, this should be of a form specifically designed to carry moment. Depth of beam depth of column As above Base designed to resist moments Figure 3.33 End fixity condition 1 116 STRUCTURAL ELEMENTS DESIGN MANUAL Condition 2 The end of the column is connected monolithically to beams or slabs on either side which are shallower than the overall dimensions of the column in the plane considered (Figure 3.34). Condition 3 The end of the column is connected to members which, while not specifically designed to provide restraint to rotation of the column will nevertheless provide some nominal restraint (Figure 3.35). Depth of beam or slab < depth of column Nominal restraint between beams and column, e.g., beams designed and detailed as simply supported As above Base not designed to resist moments Figure 3.34 End fixity condition 2 Figure 3.35 End fixity condition 3 Where a more accurate assessment of the effective height is desired it may be calculated from the equations given in Section 2.5 of BS 8110 Part 2. The basic mode of failure of a braced short column is by crushing of the constituent materials due to the compressive loads. The various aspects of the design of braced short columns, including a number of dimensional considerations which can influence the design, will be considered under the following headings: (a) (b) (c) (d) (e) Column cross-section Main reinforcement areas Minimum spacing of reinforcement Maximum spacing of reinforcement Lateral reinforcement Compressive ULS Shear ULS SLS Cracking Lateral deflection. b (f) (g) (h) (i) h 3.11.1 Column cross-section The provisions of column design given in BS 8110 apply to vertical load bearing members whose greater cross-sectional dimension does not exceed four times its smaller dimension. This proviso is illustrated in Figure 3.36. It should be appreciated that square, circular or any other symmetrical shape will satisfy this requirement. For column h 4b Figure 3.36 Cross-sectional limitation for columns CONCRETE ELEMENTS 117 A vertical load bearing member whose breadth exceeds four times its thickness is classified as a wall and should be designed in accordance with the provisions for reinforced concrete walls. Initially the cross-sectional dimensions may be determined by taking into account the durability, fire resistance and slenderness requirements. It is suggested for practical reasons appertaining to the in situ casting of columns that the minimum lateral dimension should not be less than 200 mm. 3.11.2 Main reinforcement areas Sufficient reinforcement must be provided in order to control cracking of the concrete. Therefore the minimum area of compression reinforcement in a column should not be less than 0.4 per cent of the total concrete area, irrespective of the type of steel. A maximum steel content is also specified to ensure proper placing and compaction of concrete around reinforcement. Therefore the maximum area of compression reinforcement in a vertically cast column should not exceed 6 per cent of the gross cross-sectional area. If it is necessary to lap the compression bars in a column, as shown in Figure 3.37, the maximum area limit may be increased to 10 per cent at lap positions. Projecting length of Lower column length lower main bars (a) Elevation showing lower length only cast (b) Elevation showing upper and lower lengths casts Figure 3.37 Lapped compression bars in a column For practical reasons the minimum number of longitudinal bars should be four in a square or rectangular column and six in a circular column. Theor column stiffness coefficient length effective length of wall characteristic imposed load overall thickness of a wall or column effective thickness of a wall or column thickness of a pier thickness of leaf 1 of a cavity wall 132 STRUCTURAL ELEMENTS DESIGN MANUAL t2 f m thickness of leaf 2 of a cavity wall capacity reduction factor for walls and columns allowing for effects of slenderness and eccentricity partial safety factor for load partial safety factor for material 4.3 Definitions The following definitions which are relevant to this manual have been abstracted from BS 5628 Part 1: Column An isolated vertical load bearing member whose width is not more than four times its thickness, as illustrated in Figure 4.1. Effective height or length The height or length of a wall, pier or column assumed for calculating the slenderness ratio. b Effective thickness The thickness of a wall, pier or column assumed for Figure 4.1 Definition of a column calculating the slenderness ratio. Lateral support The support, in relation to a wall or pier, which will restrict movement in the direction of the thickness of the wall or, in relation to a column, which will restrict movement in the direction of its thickness or width. Lateral supports may be horizontal or vertical. Loud bearing walls Walls primarily designed to carry an imposed vertical load in addition to their own weight. Masonry An assemblage of structural units, either laid in situ or constructed in prefabricated panels, in which the structural units are bonded and solidly put together with mortar or grout. Masonry may be reinforced or unreinforced. Pier A member which forms an integral part of a wall, in the form of a thickened section placed at intervals along the wall. Slenderness ratio The ratio of the effective height or effective length to the effective thickness. Structural units Bricks or blocks, or square dressed natural stone. t b > 4t = column Single leaf wall A wall of bricks or blocks laid to overlap in one or more directions and set solidly in mortar. Double leaf ( collar jointed ) wall Two parallel single leaf walls, with a space between not exceeding 25 mm, filled solidly with mortar and so tied together as to result in common action under load. Cavity wall Two parallel single leaf walls, usually at least 50 mm apart, and effectively tied together with wall ties, the space between being left as a continuous cavity or filled with non-load-bearing material. Faced wall A wall in which the facing and backing are so bonded as to result in common action under load. Veneered wall A wall having a facing which is attached to the backing, but not so bonded as to result in common action under load. MASONRY ELEMENTS 133 4.4 Materials The fundamental properties of the individual materials that comprise a masonry wall are well understood and documented. Sadly, however, a designer's intentions may sometimes be frustrated by a lack of understanding of their combined behaviour. To use masonry successfully the designer must select bricks or blocks of appropriate quality, choose suitable mortar, specify their use correctly and devise appropriate details. It is pointed out in Part 1 of the code that wall thicknesses derived from strength considerations may be insufficient to satisfy other performance requirements. Reference should therefore be made to BS 5628 Part 3 for guidance on such matters as durability, fire resistance, thermal insulation, sound insulation, resistance to damp penetration and provision for thermal movement, together with material, component and workmanship specification matters. The main constituent materials and components used in the construction of masonry walls are as follows: (a) Bricks (b) Blocks (c) Mortar (d) Wall ties (e) Damp proof courses. Each will now be discussed in more detail. 4.4.1 Bricks Bricks are walling units not exceeding 337.5 mm in length, 225 mm in width and 112.5 mm in height. They are produced from a range of materials, such as clay, concrete and sometimes a mixture of lime and sand or crushed stone. The mixture tyEMENTS DESIGN MANUAL site supervision and inspection will be carried out to ensure that this is so. Some of the construction aspects covered by these workmanship requirements are as follows: (a) (b) (c) (d) (e) (f) Setting out Storage of materials Batching, mixing and use of mortars Laying of masonry units Constructional details Protection during construction. Special category of construction control This may be assumed when, in addition to the normal category requirements, compliance testing of the mortar strength will be carried out in accordance with Appendix A of BS 5628 Part 1. 4.8.3 Ultimate compressive strength of masonry units The ultimate compressive strength of masonry units, as mentioned earlier, is obtained by dividing the characteristic strength by the appropriate partial safety factor: Ultimate compressive strength = characteristic strength of units fk = partial safety factor m Having arrived at an ultimate compressive strength for the masonry units that are to be used, the next step is to determine the load bearing capacity of the particular member in which they are to be incorporated. In terms of masonry design such members will either be walls or columns. 4.9 Factors influencing the load bearing capacity of masonry members There are a number of interrelated factors that influence the load bearing capacity of masonry walls and columns: (a) Slenderness ratio (b) Lateral support (c) (d) (e) (f) Effective Effective Effective Capacity height hef length lef thickness tef reduction factor for slenderness. The principal factor is the slenderness ratio; all the others are related to it. Let us therefore consider the effect of each factor on walls and columns. MASONRY ELEMENTS 145 4.9.1 Slenderness ratio Vertically loaded walls and columns can fail by crushing due to direct compression or, if they are slender, by lateral buckling. A measure of the tendency to fail by buckling before crushing is the slenderness ratio (SR). In accordance with BS 5628 the slenderness ratio of a wall should be calculated as follows: SR wall = = effective height effective thickness hef tef or lef tef or effective length effective thickness The effective length is only used when this would give a lesser slenderness ratio value. For masonry columns the effective height is always used when calculating the slenderness ratio: SR column = hef effective height = effective thickness tef The slenderness ratio of a member should generally not exceed 27. However, should the thickness of a wall be less than 90 mm, in a building of two storeys, then the slenderness ratio value must not exceed 20. 4.9.2 Lateral support The effective height and the effective length are influenced by the degree of any lateral support that may be provided. With respect to the height this will be provided in the horizontal direction by the floors or roof. In the case of the length it will be provided in the vertical direction by any intersecting or return walls. BS 5628 defines the degree of resistance to lateral movement as either `simple' or `enhanced' depending on the construction details adopted. Examples of horizontal lateral support that only provide simple resistance are illustrated in Figure 4.4; those capable of providing enhanced resisTimber floor or roof joists In situ concrete floor or roof slab Metal Floor or roof strap screed Galvanized metal L strap Vertical twist ties Precast concrete floor or roof units Figure 4.4 Examples of horizontal lateral support only capable of providing simple resistance 146 STRUCTURAL ELEMENTS DESIGN MANUAL tance are illustrated in Figure 4.5. Similarly, examples of vertical lateral support that only provide simple resistance are shown in Figure 4.6; those that provide enhanced resistance are shown in Figure 4.7. Minimum bearing greater of t/2 or 90 mm Span Roof or floor Bearing Bearing Roof or floor Roof or floor Timber or concrete construction t In situ concrete slab or precast concrete units t In situ concrete slab or precast concrete units Figure 4.5 Examples of horizontal lateral support capable of providing enhanced resistance t2 t1 Intersecting wall providing lateral support 10 t1 10 t1 d t3 t1 Metal ties at 300 maximum centres capable of transmitting the design lateral forces d t1 t2 Main wall Main cavity wall t1 Figure 4.6 Examples of vertical lateral support only capable of providing simple resistance t2 t1 Intersecting walls providing lateral support 10 t1 10 t1 d t3 t1 Intersecting walls fully bonded with main walls d t1 t2 Main wall Main cavity wall t1 Figure 4.7 Examples of vertical lateral support capable of providing enhanced resistance MASONRY ELEMENTS 147 `Enhanced' lateral resistance 4.9.3 Effective height The effective height hef depends on the degree of horizontal lateral support provided and may be defined as follows for walls and columns. For walls it should be taken as h hef = 0.75 h (a) 0.75 times the clear distance between lateral supports which provide enhanced resistance, as depicted in Figure 4.8a; or (b) The clear distance between lateral supports which only provide simple resistance, as depicted in Figure 4.8b. For columns it should be taken as Case (a) `Simple' lateral resistance (a) The distance between lateral supports in respect of the direction in which lateral support is provided, shown as hef = h in Figure 4.9a and b; or (b) Twice the height of the column in respect of a direction in which lateral support is not provided, shown as hef = 2h in Figure 4.9b. It should be noted that BS 5628 suggests that lateral support to columns should preferably be provided in both horizontal directions. h hef = h et ncr Co b sla e Steel beam Case (b) h ef = h h ef = h Figure 4.8 Effective height of walls he h =h f ef =2 h h h Case (a) Figure 4.9 Effective height of columns 4.9.4 Effective length Case (b) The effective length lef is a consideration that only applies to walls, and depends on the degree of vertical lateral support provided. It may be taken as (a) 0.75 times the clear distance between lateral supports which provide enhanced resistance, as illustrated in Figure 4.10a 148 STRUCTURAL ELEMENTS DESIGN MANUAL t2 t1 L Clear distance d 10 t Intersecting walls bonded t Case (a) t1 L t1 and t2 t lef = 0.75 L d 10 t Intersecting walls bonded t Case (b) t1 L t1 t lef = 2 L Free edge t2 t1 and t2 lef = L t d 10 t Metal ties at 300 maximum centres t Case (c) t1 d 10 t Metal ties at 300 maximum centres t Case (d) L t1 t2 lef = 2.5 L Free edge Figure 4.10 Effective length of walls (b) Twice the distance between a lateral support which provides enhanced resistance and a free edge, as illustrated in Figure 4.10b (c) The clear distance between lateral supports which only provided simple resistance, as illustrated in Figure 4.10c (d) 2.5 times the distance between a lateral support which provides simple resistance and a free edge, as illustrated in Figure 4.10d. It should be appreciated that the slenderness ratio of a wall without any vertical lateral supports must be based upon its effective height. MASONRY ELEMENTS 149 4.9.5 Effective thickness The effective thickness t ef parameters for walls and columns are illustrated in Figure 2 of BS 5628. They are basically divided into two categories in relation to whether stiffening piers or intersecting walls are present or not. Category 1 b 4t b walls and columns not stiffened by piers or intersecting walls t (a) Columns as shown in Figure 4.11: tef = t or b depending in which direction the slenderness is being considered. (b) Single leaf walls as shown in Figure 4.12: tef = the actual thickness t. (c) Cavity walls as shown in Figure 4.13: tef = the greatest of 2(t1 + t2)/3 or t1 or t2. Figure 4.11 Plan on a column t 2 Leaf thickness Cavity width t1 Leaf thickness t Figure 4.12 Plan on a single leaf wall Figure 4.13 Plan on a cavity wall Category 2: walls stiffened by piers or intersecting walls (a) Single leaf wall with piers shown in Figure 4.14: tef = tK, where K is the appropriate stiffness coefficient from BS 5628 Table 5, reproduced here as Table 4.7. (b) Cavity wall withapacity Limit of force or moment which may be applied without causing failure due to yielding or rupture. Column A vertical member of a structure carrying axial load and possibly moments. Compact cross-section A cross-section which can develop the plastic moment capacity of the section but in which local buckling prevents rotation at constant moment. Dead load All loads of constant magnitude and position that act permanently, including self-weight. Design strength The yield strength of the material multiplied by the appropriate partial factor. Effective length Length between points of effective restraint of a member multiplied by a factor to take account of the end conditions and loading. Elastic design Design which assumes no redistribution of moments due to plastic rotation of a section throughout the structure. Empirical method Simplified method of design justified by experience or testing. Factored load Specified load multiplied by the relevant partial factor. H-section A section with one central web and two equal flanges which has an overall depth not greater than 1.2 times the width of the flange. I-section Section with central web and two equal flanges which has an overall depth greater than 1.2 times the width of the flange. Imposed load Load on a structure or member other than wind load, produced by the external environment and intended occupancy or use. Lateral restraint For a beam: restraint which prevents lateral movement of the compression flange. For a column: restraint which prevents lateral movement of the member in a particular plane. Plastic cross-section A cross-section which can develop a plastic hinge with sufficient rotation capacity to allow redistribution of bending moments within the structure. Plastic design Design method assuming redistribution of moment in continuous construction. 166 STRUCTURAL ELEMENTS DESIGN MANUAL Semi-compact cross-section A cross-section in which the stress in the extreme fibres should be limited to yield because local buckling would prevent development of the plastic moment capacity in the section. Serviceability limit states Those limit states which when exceeded can lead to the structure being unfit for its intended use. Slender cross-section A cross-section in which yield of the extreme fibres cannot be attained because of premature local buckling. Slenderness The effective length divided by the radius of gyration. Strength Resistance to failure by yielding or buckling. Strut A member of a structure carrying predominantly compressive axial load. Ultimate limit state That state which if exceeded can cause collapse of part or the whole of the structure. 5.4 Steel grades and sections As mentioned in Chapter 1, steel sections are produced by rolling the steel, whilst hot, into various standard profiles. The quality of the steel that is used must comply with BS 4360 `Specification for weldable structural steels', which designates four basic grades for steel: 40, 43, 50 and 55. (It should be noted that grade 40 steel is not used for structural purposes.) These basic grades are further classified in relation to their ductility, denoted by suffix letters A, B, C and so on. These in turn give grades 43A, 43B, 43C and so on. The examples in this manual will, for simplicity, be based on the use of grade 43A steel. It is eventually intended to replace the present designations with grade references related to the yield strength of the steel. Thus, for example, grade 43A steel will become grade 275A since it has a yield stress of 275 N/mm 2 . The dimensions and geometric properties of the various hot rolled sections are obtained from the relevant British Standards. Those for universal beam (UB) sections, universal column (UC) sections, rolled steel joist (RSJ) sections and rolled steel channel (RSC) sections are given in BS 4 Part 1. Structural hollow sections and angles are covered by BS 4848 Part 2 and Part 4 respectively. It is eventually intended that BS 4 Part 1 will also become part of BS 4848. Cold formed steel sections produced from light gauge plate, sheet or strip are also available. Their use is generally confined to special applications and the production of proprietary roof purlins and sheeting rails. Guidance on design using cold formed sections is given in BS 5950 Part 5. 5.5 Design philosophy The design approach employed in BS 5950 is based on limit state philosophy. The fundamental principles of the philosophy were explained in Chapter 3 in the context of concrete design. In relation to steel structures, some of the ultimate and serviceability limit states (ULSs and SLSs) that may have to be considered are as follows STEEL ELEMENTS 167 Ultimate limit states Strength The individual structural elements should be checked to ensure that they will not yield, rupture or buckle under the influence of the ultimate design loads, forces, moments and so on. This will entail checking beams for the ULSs of bending and shear, and columns for a compressive ULS and when applicable a bending ULS. Stability The building or structural framework as a whole should be checked to ensure that the applied loads do not induce excessive sway or cause overturning. Fracture due to fatigue Fatigue failure could occur in a structure that is repeatedly subjected to rapid reversal of stress. Connections are particularly prone to such failure. In the majority of building structures, changes in stress are gradual. However, where dynamic loading could occur, such as from travelling cranes, the risk of fatigue failure should be considered. Brittle failure Sudden failure due to brittle fracture can occur in steelwork exposed to low temperatures; welded structures are particularly susceptible. Since the steel members in most building frames are protected from the weather, they are not exposed to low temperatures and therefore brittle fracture need not be considered. It is more likely to occur in large welded structures, such as bridges, which are exposed to the extremes of winter temperature. In such circumstances, it is necessary to select steel of adequate notch ductility and to devise details that avoid high stress concentrations. Serviceability limit states Deflection Adequate provision must be made to ensure that excessive deflection which could adversely effect any components or finishes supported by the steel members does not occur. Corrosion and durability Corrosion induced by atmospheric or chemical conditions can adversely affect the durability of a steel structure. The designer must therefore specify a protective treatment suited to the location of the structure. Guidance on the selection of treatments is given in BS 5493 `Code of practice for protective coating of iron and steel structures against corrosion'. Certain classes of grade 50 steel are also available with weather resistant qualities, indicated by the prefix WR, for example WR 50A. Such steel when used in a normal external environment does not need any additional surface protection. An oxide skin forms on the surface of the steel, preventing further corrosion. Provided that the selfcoloured appearance is aesthetically acceptable, consideration may be given to its use in situations where exposed steel is permitted, although it should be borne in mind that it is more expensive than ordinary steel. Fire protection Due consideration should also be given to the provision of adequate protection to satisfy fire regulations. Traditionally fire protection was provided by casing the steelwork in concrete. Nowadays a number of lightweight alternatives are available in the form of dry sheet 168 STRUCTURAL ELEMENTS DESIGN MANUAL material, plaster applied to metal lathing, or plaster sprayed directly on to the surface of the steel. Intumescent paints are also marketed which froth when heated to produce a protective insulating layer on the surface of the steel. Since this manual is concerned with the design of individual structural elements, only the strength ULS and the deflection SLS will be considered further. 5.6 Safety factors In a similar fashion to concrete and masonry design, partial safety factors are once again applied separately toh is derived from the following expression: LT = nuv where n slenderness correction factor from BS 5950 u buckling parameter of the section, found from section tables or conservatively taken as 0.9 v slenderness factor from BS 5950 minor axis slenderness: = LE/ry LE effective unrestrained length of the beam ry radius of gyration of the section about its minor axis, from section tables The effective length L E should be obtained in accordance with one of the following conditions: Condition (a). For beams with lateral restraints at the ends only, the value of LE should be obtained from BS 5950 Table 9, reproduced here as Table 5.6, taking L as the span of the beam. Where the restraint conditions at each end of the beam differ, the mean value of LE should be taken. Condition (b). For beams with effective lateral restraints at intervals along their length, the value of L E should be taken as 1.0 L for normal loading conditions or 1.2 L for destabilizing conditions, taking L as the distance between restraints. Condition (c). For the portion of a beam between one end and the first intermediate restraint, account should be taken of the restraint conditions STEEL ELEMENTS 183 Table 5.5 Bending strength pb (N/mm2) for rolled sections (BS 5950 Part 1 1990 Table 11) py 340 340 328 313 298 282 266 249 232 216 200 186 172 159 147 137 127 118 110 103 96 90 84 79 75 70 66 63 60 56 54 51 49 46 44 42 39 35 33 30 28 LT 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 210 220 230 240 250 245 245 245 238 227 217 206 195 185 174 164 154 144 135 126 118 111 104 97 91 86 81 76 72 68 64 61 58 55 52 50 47 45 43 41 39 36 33 31 29 27 265 265 265 254 242 231 219 207 196 184 172 161 151 141 131 123 115 107 101 94 89 83 78 74 70 66 62 59 56 53 51 48 46 44 42 40 37 34 31 29 27 275 275 273 262 250 238 226 213 201 188 176 165 154 144 134 125 117 109 102 96 90 84 79 75 71 67 63 60 57 54 51 49 46 44 42 40 37 34 31 29 27 325 325 316 302 287 272 257 241 225 210 195 181 168 156 144 134 125 116 108 101 95 89 83 78 74 70 66 62 59 56 53 51 48 46 44 42 38 35 32 30 28 355 355 341 325 309 292 274 257 239 222 205 190 175 162 150 139 129 120 111 104 97 91 85 80 75 71 67 63 60 57 54 51 49 47 44 42 39 36 33 30 28 415 408 390 371 350 329 307 285 263 242 223 204 188 173 159 147 136 126 117 108 101 94 88 83 78 73 69 65 62 59 56 53 50 48 46 43 40 36 33 31 29 430 421 402 382 361 338 315 292 269 247 226 208 190 175 161 148 137 127 118 109 102 95 89 84 79 74 70 66 62 59 56 53 50 48 46 44 40 37 34 31 29 450 438 418 397 374 350 325 300 276 253 231 212 194 178 163 150 139 128 119 111 103 96 90 84 79 75 70 66 63 59 56 53 51 48 46 44 40 37 34 31 29 184 STRUCTURAL ELEMENTS DESIGN MANUAL Table 5.6 Effective length LE for beams (BS 5950 Part 1 1990 Table 9) Conditions of restraint at supports Compression flange laterally restrained Beam fully restrained against torsion Both flanges fully restrained against rotation on plan Both flanges partially restrained against rotation on plan Both flanges free to rotate on plan Loading conditions Normal Destabilizing 0.7 L 0.85 L 0.85 L 1.0 L 1.0 L 1.2 L Restraint against torsion 1.0 L + 2 D 1.2 L + 2 D Compression flange laterally unrestrained provided only by Both flanges free to rotate positive connection of on plan bottom flange to supports Restraint against torsion 1.2 L+ 2 D provided only by dead bearing of bottom flange on supports D is the depth of the beam. L is the span of the beam. 1.4 L + 2 D Point load applied by column Load Column at the support. Therefore the effective length LE should be taken as the mean of the value given by condition (b) and the value from Table 5.6 elating to the manner of restraint at the support. In both cases, L is taken as the distance between the restrain and the support. Main beam (a) Destabilizing detail Point load applied by column Load Column Secondary beams The destabilizing load referred to in the table exists when the member applying the load to the compression flange can move laterally with the beam in question, as illustrated in Figure 5.10a. This may be avoided by the introduction of stabilizing members such as the secondary beams shown in Figure 5.10b. The slenderness factor v is obtained from BS 5950 Table 14, reproduced here as Table 5.7, using N and /x, where is the slenderness, x is the torsional index of the section from section tables, and N is 0.5 for beams with equal flanges. To check the adequacy of a particular steel beam section, the buckling moment M b should be compared with the equivalent uniform moment M: M Mb Main beam (b) Stabilized detail Figure 5.10 Destabilizing load where M = mMA, m is the equivalent uniform moment factor from BS 5950, and MA is the maximum moment on the member or portion of the member under consideration. STEEL ELEMENTS 185 Table 5.7 Slenderness factor v for flanged beams of uniform section (BS 5950 Part 1 1990 Table 14) Compression Tension /x 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0 20.0 N 1.0 0.79 0.78 0.77 0.76 0.75 0.74 0.72 0.71 0.69 0.68 0.66 0.65 0.64 0.63 0.61 0.60 0.59 0.58 0.57 0.56 0.54 0.53 0.51 0.50 0.49 0.47 0.46 0.45 0.44 0.43 0.9 0.81 0.80 0.80 0.78 0.77 0.76 0.74 0.73 0.71 0.70 0.68 0.67 0.65 0.64 0.63 0.62 0.60 0.59 0.58 0.57 0.55 0.54 0.52 0.51 0.49 0.48 0.47 0.46 0.45 0.44 0.8 0.84 0.83 0.82 0.81 0.80 0.78 0.77 0.75 0.73 0.72 0.70 0.69 0.67 0.66 0.65 0.63 0.62 0.61 0.60 0.59 0.57 0.55 0.53 0.52 0.50 0.49 0.48 0.47 0.46 0.45 0.7 0.88 0.87 0.86 0.85 0.83 0.82 0.80 0.78 0.76 0.75 0.73 0.71 0.70 0.68 0.67 0.65 0.64 0.63 0.61 0.60 0.58 0.56 0.54 0.53 0.51 0.50 0.49 0.47 0.46 0.45 0.6 0.93 0.92 0.91 0.89 0.88 0.86 0.84 0.82 0.80 0.78 0.76 0.74 0.72 0.70 0.69 0.67 0.66 0.64 0.63 0.62 0.60 0.58 0.56 0.54 0.52 0.51 0.49 0.48 0.47 0.46 0.5 1.00 0.99 0.97 0.96 0.93 0.91 0.89 0.86 0.84 0.82 0.79 0.77 0.75 0.73 0.72 0.70 0.68 0.67 0.65 0.64 0.61 0.59 0.57 0.55 0.53 0.52 0.50 0.49 0.48 0.47 0.4 1.11 1.10 1.08 1.06 1.03 1.00 0.97 0.94 0.91 0.88 0.85 0.82 0.80 0.78 0.76 0.74 0.72 0.70 0.68 0.67 0.64 0.61 0.59 0.57 0.55 0.53 0.52 0.50 0.49 0.48 0.3 1.28 1.27 1.24 1.20 1.16 1.12 1.07 1.03 0.99 0.95 0.92 0.89 0.86 0.83 0.80 0.78 0.76 0.74 0.72 0.70 0.67 0.64 0.61 0.59 0.57 0.55 0.53 0.52 0.50 0.49 Compression Tension 0.2 1.57 1.53 1.48 1.42 1.35 1.29 1.22 1.16 1.11 1.05 1.01 0.97 0.93 0.89 0.86 0.83 0.80 0.78 0.76 0.74 0.70 0.66 0.64 0.61 0.59 0.57 0.55 0.53 0.52 0.50 0.1 2.20 2.11 1.98 1.84 1.70 1.57 1.46 1.36 1.27 1.20 1.13 1.07 1.02 0.97 0.93 0.89 0.86 0.83 0.80 0.78 0.73 0.70 0.66 0.63 0.61 0.59 0.57 0.55 0.53 0.51 0.0 12.67 6.36 4.27 3.24 2.62 2.21 1.93 1.71 1.55 1.41 1.31 1.22 1.14 1.08 1.02 0.98 0.93 0.90 0.86 0.83 0.78 0.73 0.69 0.66 0.63 0.61 0.58 0.56 0.55 0.53 Note 1: For beams with equal flanges, N = 0.5; for beams with unequal flanges refer to clause 4.3.7.5 of BS 5950. Note 2: v should be determined from the general formulae given in clause B.2.5 of BS 5950, on which this table is based: (a) for sections with lipped flanges (e.g. gantry girders composed of channel + universal beam); and (b) for intermediate values to the right of the stepped line in the table. The factors m and n are interrelated as shown in BS 5950 Table 13, reproduced here as Table 5.8. From this table it can be seen that, when a beam is not loaded between points of lateral restraint, n is 1.0 and m should be obtained from BS 5950 Table 18. The value of m depends upon the ratio of the end moments at the points of restraint. If a beam is loaded between points of lateral restraint, m is 1.0 and n is obtained by reference 186 STRUCTURAL ELEMENTS DESIGN MANUAL Table 5.8 Use of m and n factors for members of uniform section (BS 5950 Part 1 1990 Table 13) Description Members not subject to destabilizing loads* m Members loaded between adjacent lateral restraints Sections with equal flanges Sections with unequal flanges Members not loaded between adjacent lateral restraints Sections with equal flanges Sections with unequal flanges 1.0 1.0 From Table 18 of BS 5950 1.0 1.0 n Members sub and is normally regarded as part of the detailing process. Connections may be bolted, welded or a combination of both. They must be proportioned with proper regard to the design method adopted for the structure as a whole. Therefore the bolts or welds making up a connection must be capable of transmitting all direct forces and resisting any bending moments. STEEL ELEMENTS 229 The design of bolted or welded connections is beyond the scope of this manual, which is concerned with the design of individual elements. The British Constructional Steelwork Association publishes a book on the design of connections for joints in simple construction which would be useful for anyone with a particular interest in this topic. This and other sources of information relating to steel design are listed in the reference section. 5.14 References BS 4 Structural steel sections. Part 1 1980 Specification for hot-rolled sections. BS 4360 1990 British Standard Specification for weldable structural steels. BS 4848 Specification for hot-rolled structural steel sections. Part 2 1991 Hollow sections. Part 4 1972 Equal and unequal angles. BS 5493 1977 Code of practice for protective coating of iron and steel structures against corrosion. BS 5950 Structural use of steelwork in building. Part 1 1990 Code of practice for design in simple and continuous construction: hot rolled sections. Part 2 1985 Specification for materials, fabrication and erection: hot rolled sections. Steelwork Design Guide to BS 5950: Part 1. Volume 1 Section Properties; Member Capacities (1987). Volume 2 Worked Examples (1986). Steel Construction Institute. Introduction to Steelwork Design to BS 5950: Part 1 . Steel Construction Institute, 1988. Manual on Connections. Volume 1 Joints in Simple Construction Conforming with the Requirements of BS 5950: Part 1: 1985. John W. Pask. British Constructional Steelwork Association, 1988. Manual for the Design of Steelwork Building Structures. Institution of Structural Engineers, November 1989. For further information contact: The Steel Construction Institute, Silwood Park, Ascot, Berkshire, SL5 7QN. The British Constructional Steelwork Association Ltd, 35 Old Queen Street, London, SW1H 9HZ. Index Applied bending moment 14, 16, 177 Applied compression stress for timber: parallel to grain 50, 52 perpendicular to grain 39 Applied loads 8, 14 Applied shear stress for timber 38 Area modification factor for masonry 143 Areas of round bar reinforcement 81 spaced at various centres per metre width 106 Axially loaded steel columns 209 with moments 209 with nominal moments 216 Beams: castellated steel 206 compound steel 206 concrete 79 deep concrete 79 design charts for concrete 82 design formulae for concrete 82, 83, 84 design summary for concrete 103 design summary for steel 200 doubly reinforced concrete 84 effective span of concrete 79 fabricated steel 206 flanged concrete 84, 85 glued laminated timber/glulam 49 laterally restrained steel 176 laterally unrestrained steel 181 ply web 49 plywood box 49 proprietary timber 49 simply supported 14 singly reinforced concrete 82 slender concrete 80 steel 170 timber 34 universal steel 166, 170 Bearing of timber 39 Bearing stress 39 Bending deflection of timber 37 Bending moment diagram 14 Bending moments 14 Bending strength of steel 182 Bending stress 16 Bending ultimate limit state 69, 82, 108, 170, 175, 176, 181 Bent-up bars 94, 97 Blocks 134 Bottom edge notches 38 Bow 49 Braced concrete columns 113 Bricks 133 Bridge design 67 British Standards 1, 2, 3 British Standards Institution 3 Brittle failure of steel 167 Buckling 22, 23, 24 Buckling resistance 165 Buckling resistance moment 181, 182, 191 Building elements 1 Building Regulations 3 Capacity reduction factor for slenderness 150 Cased steel columns 222 Castellated steel beams 206 Cavity wall 132 Cellular blocks 135 INDEX 231 Characteristic compressive strength: for blocks 141 for bricks 140 for natural stone 142 for random rubble masonry 142 Characteristic load: dead 71, 138 imposed 71, 139 wind 71, 139 Characteristic strength 73 Codes of practice 1, 2, 3 Coffered slabs 105 Cold formed steel sections 166 Collar jointed wall 132 Columns 21, 49, 113, 132, 165, 208 baseplates 226 cased steel 222 concrete 113 concrete, short braced axially loaded 121 concrete, short braced subject to uni-axial or bi-axial bending 123 design summary for concrete 126 masonry 132 steel, axially loaded 209 steel, axially loaded with nominal moments 216 Common blocks 135 Common bricks 134 Compact steel cross-sections 165 Compound beams 206 Compression members 21, 49 Compression stress for timber: parallel to grain 50 perpendicular to grain 39 Compressive ultimate limit state 120 Concentrated loads on walls 161 Concrete: beams 79 columns 113 cover to reinforcement 76 durability 75 elements 67 fire resistance 78 slabs 103 Connections 228 Corrosion of reinforcement 85 Corrosion of steel 167 Crack widths in concrete 81, 85, 107, 108 Cracking serviceability limit state for concrete 85, 108, 126 Cube strengths of concrete 73 Damp proof courses 136 Dead load 4, 71, 138, 165, 168, 169 Deep concrete beams 79 Deflection 36, 126 of formwork 59 serviceability limit state 70, 85, 108, 167, 196 Depth modification factor 30, 35 Depth to breadth ratio 36 Design: charts 67, 82, 83, 125 formulae for rectangular concrete beams 82, 83, 84 philosophy 69, 138, 166 service stress in steel reinforcement 86 strength of steel 165, 182, 210 stresses for timber 30 Design summary for: axially loaded steel columns 211 axially loaded steel columns with moments 219 concrete beams 103 concrete columns 126 steel beams 200 timber flexural members 39 timber posts 52 vertically loaded wall or column 153 Destabilizing load 182 Distribution steel in concrete slabs 107 Double leaf wall 132 Double triangle wall ties 136 Doubly reinforced concrete beams 84 Dry exposure condition for timber 30, 31 Durability of concrete 75 232 INDEX Durability of steel 167 Duration of load on timber members 31 Eccentrically loaded timber posts 52 Economic steel design 163 Effective height of walls 132, 147 Effective height ratios for concrete columns 114 Effective length of columns 23, 24 Effective length of steel members 165, 182, 209 Effective length of walls 132, 147 Effective span of concrete beams 79 Effective thickness of walls 132, 149 Elastic: behaviour 27 design of steel 165 moment of resistance 176 theory for concrete design 70 Empirical method of design 165 End conditions for concrete columns 115, 116 End fixity 24 Engineering bricks 134 Euler critical stress for timber 52 Fabricated steel beams 206 Faced wall 132 Facing blocks 135 Facing bricks 133 Falsework 58 Fatigue ultimate limit state for steel 167 Fire protection of steel 167 Fire resistance of reinforced concrete 78 Flanged beams 84, 85 Flat slabs 105 Flexural members 34, 78 Formwork for concrete 58 Geometrical properties of timber 31 Glued laminated timber beams 49 Glulam timber beams 49 Grade stresses for timber 28 Grading rules for timber 27 Ground bearing slabs 103 Hollow blocks 135 Imposed load 6, 71, 139, 165, 168, 169 Insulating blocks 135 Interaction quantity for timber posts 52 Lateral buckling of timber beams 34, 36 Lateral buckling of walls 145 Lateral deflection of concrete columns 126 Lateral reinforcement in concrete columns 119 Lateral restraint for steel beams and columns 165 Lateral support to walls 132, 145 Lateral torsional buckling of steel beams 175, 176, 178, 181, 182 Laterally restrained steel beams 176 Laterally unrestrained steel beams 181 Lattice girders 208 Limit state philosophy 69, 138, 162, 166 Liquid retaining structures 67 Load bearing walls 132 Load factor theory for concrete design 70 Loading 3 Load-sharing systems in timber 31 Local buckling of steel beams 178 Local capacity check for steel columns 218, 219 Machine stress grading of timber 26 Main reinforcement areas for concrete: beams 80 columns 117 slabs 106 Masonry elements 131 INDEX 233 Material properties 73, 139, 169 Maximum spacing of reinforcement 81, 107, 119 Minimum spacing of reinforcement 81, 107, 118 Modification factors for timber design 30 Moisture content of timber 31 Mortar 135 Natural stone 142 Normal category of construction control for masonry 143 Normal category of manufacturing control for masonry 143 Notches in timber flexural members 38 Ordinary/common blocks 135 Overall buckling check for steel columns 218 Partial safety factors for load 71, 139, 168 Partial safety factors for materials 74, 143, 169 Permissible compression stress for timber: parallel to grain 50 perpendicular to grain 39 Permissible shear stress for timber 38 Permissible stress analysis 69, 162, 177 Permissible stress philosophy 27, 34 Physical characteristics of timber 26 Pier 132 Planed all round softwoods 31 Plastic: cross-section 165 design 165 Plate girders 208 Ply web beams 49 Plywood box beams 49 Proof strength of steel reinforcement 73 Proprietary timber beams 49 Protective treatment for steel 167 Radius of gyration 23, 24 Rankine's theory 64 Ratio of modulus of elasticity to compression stress 51 References 65, 130, 161, 229 Regularized soft woods 31 Reinforced concrete: beams 79 columns 113 slabs 103 Retarded mortar 136 Ribbed slabs 104 Rigid design of steel 163 Safety factors 70, 138, 168 Sawn softwoods 31 Second moment of area 15, 18, 24 Section: properties of steel 169 properties of timber 31 Self weight 4 Semi-compact steel cross-section 166 Semi-rigid design of steel 163 Serviceability design load for steel beams 169 Serviceability limit state: due to cracking 70 due to deflection 70, 167 due to vibration 70 Shape and bulk of concrete 76 Shape factor for concrete blocks 141 Shear deflection of timber 37 Shear failure in concrete beams 94 Shear reinforcement 94 Shear in timber 38 Shear ultimate limit state 94, 108, 126, 193 Shell bedding of blockwork 142 Short braced concrete columns 121, 122, 123 Simple design of steel 163 Single leaf wall 132 Singly reinforced concrete beams 82 234 INDEX Slabs 103 Slender concrete beams 80 Slender steel cross-section 166 Slenderness ratio 23, 51, 132, 145, 150, 151, 166, 209 Small plan areas of masonry 143 Snow loading 6 Solid blocks 135 Solid slabs 104 Span to effective depth ratios for concrete beams 85 Special category of construction control for masonry 144 Special category of manufacturing control for masonry 143 Species of timber 28 Specified loads 168 Stability ultimate limit state 167 Steel: design strength 165 elements 162 grades 166 sections 22, 166, 170 sheet piles 63 trench sheeting 63 Steel Construction Institute 22, 170 Stiffness coefficient for walls 149, 150 Strength: classes of timber 28 classification of timber 26 Stress: grading machines 26, 28 grading of timber 26 Structural: analysis stage 1 design of concrete 67 design of masonry 131 design of steelwork 162 design of timber 27 detailing stage 1 element design stage 1 engineering 1 mechanics 1, 14 planning stage 1 scheme 1 specification stage 1 units 132 Stud walls 56 Super loading 6 Superimposed loading 6 Support work for excavations 58, 63 Suspended slabs 103, 104, 105 Symbols 27, 67, 131, 163 Tensile reinforcement 82 Theory of bending 14 Timber: elements 26 species 28 temporary works 58 Timbering 63 Top edge notches 38 Ultimate bending moment on a concrete beam 82 Ultimate compressive load for concrete columns 121 Ultimate compressive strength of masonry 144 Ultimate design load 72, 139, 168 Ultimate design strength of materials 75 Ultimate design strength of steel 169 Ultimate limit state 69, 138, 166, 167 Ultimate resistance moment of a concrete beam 82 Unbraced concrete columns 113 Veneered wall 132 Vertical links 94 Vertical load resistance of masonry 152 Vertical twist wall ties 136 Visual stress grading of timber 26 Waffle slabs 105 Wall ties 136 Water tightness of concrete 85 Weather resistant steel 167 Web bearing resistance of steel beams 198 Web buckling resistance of steel beams 197 INDEX 235 Wet exposure condition for timber members 31 Wet exposure geometrical modification factor for timber 30, 31 Wet exposure stress modification factor for timber 30, 31 Wind loading 6 Wire butterfly ties 136 Yield strength of steel reinforcement 73 Young's modulu... 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