Design of structural elements

2.1. Introduction

 All structures are composed of a number of inter
connected elements such as slabs, beams, columns,
 walls and foundations. Collectively, they enable the
 internal and external loads acting on the structure
 to be safely transmitted down to the ground. The
 actual way that this is achieved is difficult to model
 and many simplifying, but conservative, assump
tions have to be made. For example, the degree
 of fixity at column and beam ends is usually uncer
tain but, nevertheless, must be estimated as it
 significantly affects the internal forces in the element.
 Furthermore, it is usually assumed that the reaction
 from one element is a load on the next and that
 the sequence of load transfer between elements
 occurs in the order: ceiling/floor loads to beams to
 columns to foundations to ground (Fig. 2.1).
 Chapter 2
 Basic structural
 concepts and
 material properties
 Fig. 2.1 Sequence of load transfer between elements of a
 structure.
 compressive loading. These steps are summarized
 in Fig. 2.2 and the following sections describe the
 procedures associated with each step.
 2.2 Design loads acting on
 structures
 At the outset, the designer must make an assess
ment of the future likely level of loading, including
 self-weight, to which the structure may be subject
 during its design life. Using computer methods or
 hand calculations the design loads acting on indi
vidual elements can then be evaluated. The design
 loads are used to calculate the bending moments,
 shear forces and deflections at critical points along
 the elements. Finally, suitable dimensions for the
 element can be determined. This aspect requires
 an understanding of the elementary theory of
 bending and the behaviour of elements subject to
 The loads acting on a structure are divided into
 three basic types: dead, imposed and wind. For
 each type of loading there will be characteristic and
 design values, as discussed in Chapter 1, which must
 be estimated. In addition, the designer will have to
 determine the particular combination of loading
 which is likely to produce the most adverse effect
 on the structure in terms of bending moments,
 shear forces and deflections.
 2.2.1 DEAD LOADS, Gk
 , gk
 Dead loads are all the permanent loads acting on
 the structure including self-weight, finishes, fixtures
 and partitions. The characteristic dead loads can be
 9
Basic structural concepts and material properties
 Fig. 2.2 Design process.
 Example 2.1 Self-weight of a reinforced concrete beam
 Calculate the self-weight of a reinforced concrete beam of breadth 300 mm, depth 600 mm and length 6000 mm.
 From Table 2.1, unit mass of reinforced concrete is 2400 kg m−3. Assuming that the gravitational constant is
 10 m s−2 (strictly 9.807 m s−2), the unit weight of reinforced concrete, ρ, is
 ρ = 2400 × 10 = 24 000 N m−3 = 24 kN m−3
 Hence, the self-weight of beam, SW, is
 SW = volume × unit weight
 = (0.3 × 0.6 × 6)24 = 25.92 kN
 estimated using the schedule of weights of building
 materials given in BS 648 (Table 2.1) or from manu
facturers’ literature. The symbols Gk
 and gk
 are
 normally used to denote the total and uniformly
 distributed characteristic dead loads respectively.
 Estimation of the self-weight of an element tends
 to be a cyclic process since its value can only be
 assessed once the element has been designed which
 requires prior knowledge of the self-weight of the
 element. Generally, the self-weight of the element
 is likely to be small in comparison with other dead
 and live loads and any error in estimation will tend
 to have a minimal effect on the overall design
 (Example 2.1).
 2.2.2 IMPOSED LOADS Qk
 , qk
 Imposed load, sometimes also referred to as live
 load, represents the load due to the proposed oc
cupancy and includes the weights of the occupants,
 furniture and roof loads including snow. Since
 imposed loads tend to be much more variable
 than dead loads they are more difficult to predict.
 10
 BS 6399: Part 1: 1984: Code of Practice for Dead and
 Imposed Loads gives typical characteristic imposed
 f
 loor loads for different classes of structure, e.g.
 residential dwellings, educational institutions,
 hospitals, and parts of the same structure, e.g.
 balconies, corridors and toilet rooms (Table 2.2).
 2.2.3 WIND LOADS
 Wind pressure can either add to the other gravita
tional forces acting on the structure or, equally
 well, exert suction or negative pressures on the
 structure. Under particular situations, the latter may
 well lead to critical conditions and must be con
sidered in design. The characteristic wind loads
 acting on a structure can be assessed in accordance
 with the recommendations given in CP 3: Chapter
 V: Part 2: 1972 Wind Loads or Part 2 of BS 6399:
 Code of Practice for Wind Loads.
 Wind loading is important in the design of ma
sonry panel walls (Chapter 5). However beyond that,
 wind loading is not considered further since the em
phasis in this book is on the design of elements rather
11
 Table 2.1 Schedule of unit masses of building materials (based on BS 648)
 Asphalt
 Roofing 2 layers, 19 mm thick 42 kg m−2
 Damp-proofing, 19 mm thick 41 kg m−2
 Roads and footpaths, 19 mm thick 44 kg m−2
 Bitumen roofing felts
 Mineral surfaced bitumen 3.5 kg m−2
 Blockwork
 Solid per 25 mm thick, stone 55 kg m−2
 aggregate
 Aerated per 25 mm thick 15 kg m−2
 Board
 Blockboard per 25 mm thick 12.5 kg m−2
 Brickwork
 Clay, solid per 25 mm thick 55 kg m−2
 medium density
 Concrete, solid per 25 mm thick 59 kg m−2
 Cast stone 2250 kg m−3
 Concrete
 Natural aggregates 2400 kg m−3
 Lightweight aggregates (structural) 1760 + 240/
 −160 kg m−3
 Flagstones
 Concrete, 50 mm thick 120 kg m−2
 Glass fibre
 Slab, per 25 mm thick 2.0–5.0 kg m−2
 Gypsum panels and partitions
 Building panels 75 mm thick 44 kg m−2
 Lead
 Sheet, 2.5 mm thick 30 kg m−2
 Linoleum
 3 mm thick 6 kg m−2
 loads, γf
 (Chapter 1). The value for γf
 depends on
 several factors including the limit state under
 consideration, i.e. ultimate or serviceability, the
 accuracy of predicting the load and the particu
lar combination of loading which will produce the
 worst possible effect on the structure in terms of
 bending moments, shear forces and deflections.
 than structures, which generally involves investigat
ing the effects of dead and imposed loads only.
 2.2.4 LOAD COMBINATIONS AND
 DESIGN LOADS
 The design loads are obtained by multiplying the
 characteristic loads by the partial safety factor for
 Plaster
 Two coats gypsum, 13 mm thick 22 kg m−2
 Plastics sheeting (corrugated) 4.5 kg m−2
 Plywood
 per mm thick 0.7 kg m−2
 Reinforced concrete 2400 kg m−3
 Rendering
 Cement: sand (1:3), 13 mm thick 30 kg m−2
 Screeding
 Cement: sand (1:3), 13 mm thick 30 kg m−2
 Slate tiles
 (depending upon thickness 24–78 kg m−3
 and source)
 Steel
 Solid (mild) 7850 kg m−3
 Corrugated roofing sheets, 10 kg m−2
 per mm thick
 Tarmacadam
 25 mm thick 60 kg m−2
 Terrazzo
 25 mm thick 54 kg m−2
 Tiling, roof
 Clay 70 kg m−2
 Timber
 Softwood 590 kg m−3
 Hardwood 1250 kg m−3
 Water 1000 kg m−3
 Woodwool
 Slabs, 25 mm thick 15 kg m−2
 Design loads acting on structures
Basic structural concepts and material properties
 12
 Table 2.2 Imposed loads for residential occupancy class
 Floor area usage Intensity of distributed load Concentrated load
 kN m−2 kN
 Type 1. Self-contained dwelling units
 All 1.5 1.4
 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 7.5 4.5
 including the weight of machinery
 Communal kitchens, laundries 3.0 4.5
 Dining rooms, lounges, billiard rooms 2.0 2.7
 Toilet rooms 2.0
Bedrooms, dormitories 1.5 1.8
 Corridors, hallways, stairs, landings, footbridges, etc. 3.0 4.5
 Balconies Same as rooms to which 1.5 per metre run
 they give access but with concentrated at
 a minimum of 3.0 the outer edge
 Cat walks–1.0 at 1 m centres
 Type 3. Hotels and motels
 Boiler rooms, motor rooms, fan rooms and the like, 7.5 4.5
 including the weight of machinery
 Assembly areas without fixed seating, dance halls 5.0 3.6
 Bars 5.0
Assembly areas with fixed seatinga 4.0
Corridors, hallways, stairs, landings, footbridges, etc. 4.0 4.5
 Kitchens, laundries 3.0 4.5
 Dining rooms, lounges, billiard rooms 2.0 2.7
 Bedrooms 2.0 1.8
 Toilet rooms 2.0
Balconies Same as rooms to which 1.5 per metre run
 they give access but with concentrated at the
 a minimum of 4.0 outer edge
 Cat walks–1.0 at 1 m centres
 Note. a Fixed seating is seating where its removal and the use of the space for other purposes are improbable.
 In most of the simple structures which will be
 considered in this book, the worst possible com
bination will arise due to the maximum dead and
 maximum imposed loads acting on the structure
 together. In such cases, the partial safety factorsfor
 dead and imposed loads are 1.4 and 1.6 respect
ively (Fig. 2.3) and hence the design load is givenby
 Fig. 2.3
 Design load = 1.4Gk
 + 1.6Qk
 However, it should be appreciated that theoret
ically the design dead loads can vary between the
 characteristic and ultimate values, i.e. 1.0Gk
 and
 1.4Gk
 . Similarly, the design imposed loads can
 vary between zero and the ultimate value, i.e. 0.0Qk
 and 1.6Qk
 . Thus for a simply supported beam with
 an overhang (Fig. 2.4(a)) the load cases shown in
 Figs 2.4(b)–(d) will need to be considered in order
 to determine the design bending moments and shear
 forces in the beam