Sw Hfg
Where necessary the punching shear resistance outside the shear reinforced 4.3.4.5.2 3 area should be checked by considering further critical perimeters. This would be approximately at the next critical perimeter taken to be at a BS 8110 distance 0.75d beyond the previous one. No further shear reinforcement Figure 3.17 required. The tensile reinforcement T16 150 mm crs. should extend for a full anchorage length beyond the perimeter at 420 mm from the column face. Column A 1 300 mm x 300 mm...
Beams
This Section covers the design of beams for shear and torsion, and supplements the examples given in Section 2. The requirements for adequate safety against lateral buckling are also examined. EC2 1 differs from BS 8110 2 because the truss assumption used in shear design is explicit. Leading on from this, two alternative methods are given in the Code. 2 Variable Strut Inclination VSI . The standard method assumes a concrete strut angle of 45 cotG 1 and that the direct shear in the concrete, V...
Design Whs
Provide a 15 mm chamfer to the outside edge of the nib and assume the line of action of the load occurs at the upper edge of the chamfer. Permissible design ultimate bearing stress 0.6 for dry bearing Therefore minimum width of bearing 0.6 x 20 x 1000 Minimum width of bearing for non-isolated member 40 mm Allowance for nib spalling 20 mm Allowance for inaccuracies 25 mm Nominal bearing width 40 20 25 85 mm Allow an additional 25 mm for chamfer on supported member. Width of nib projection 85 25...
Limit state of cracking
No check is required at transfer since beam is totally in compression. Design crack width for post-tensioned member under frequent load combinations The method adopted to determine the minimum reinforcement required is to 4.4.1.2. 5 carry out a rigorous calculation of the crack width where the flexural tensile stress 4.4.1.2 7 under rare loads exceeds 3 N mm2. If the calculated crack width under 4.4.2.4 frequent loads does not exceed 0.2 mm then further bonded reinforcement is not required....
Introduction And Symbols 1
The main objective of this publication is to illustrate through worked examples how EC2 1 may be used in practice. It has been prepared for engineers who are generally familiar with design practice in the UK, particularly to BS 8110 2 gt . The worked examples relate primarily to in-situ concrete building structures. The designs are in accordance with EC2 Part 1 as modified by the UK National Application Document'1'. Where necessary, the information given in EC2 has been supplemented by guidance...
S Lkv
Thus for classes S2 and S3 the slump may vary between 50 mm and 150 mm. It is not logical that mixes with this variation of slump, and hence w c ratio, should have a standard value of shrinkage strain. If the values in EC2 Table 3.4 are assumed to relate to the median slump for classes S2 and S3 of 100 mm, then the values for slumps of 40 mm to 100 mm should be multiplied by a factor between 0.7 and 1.0 and values for slumps of 100 mm to 160 mm should be multiplied by a factor between 1.0 and...
Effective dimensions of beam
Effective span t lo c 2 lt 0.1 y c2 2 lt 0.1 g Note that EC2 effective spans typically come to the mid-point of the supports. Figure 2.4 Active height hj lesser of h and I h 10920 gt I 5750 mm Therefore This thickness is used to be consistent with the CIRIA Guide 2 example. It will be necessary under EC2 to demonstrate that the required reinforcement can be accommodated within this width. The effective dimensions of the beam are shown in Figure 11.3
Slenderness limits
The Code requires that a beam has an adequate factor of safety against buckling. Providing that the following requirements are met, the safety against lateral 4.3.5.7 2 buckling may be assumed to be adequate b width of the compression flange, which can be taken as gt eff 2.5.2.2.1 3 for T and L beams unrestrained length of the compression flange taking lateral 2.5.2.2.1 4 bracing into account For example, consider the beam shown in Figure 3.16. For example, consider the beam shown in Figure...
Detailing of principal bending moment reinforcement
CIRIA Guide 2 states 'Reinforcement is not to be curtailed in the span and may CIRIA be distributed over a depth of 0.2h . A minimum steel percentage in relation Guide 2 to the local area of concrete in which it is embedded is given in Cl.2.4.1 A maximum bar spacing for a maximum crack width of 0.3 mm is given in Table 2 of the CIRIA Guide. Reinforcement may be distributed over depth 0.2 x 5750 1150 mm i.e. minimum number of bars in face 7
Summary of reinforcement
4T12 longitudinal bars R8 links 80 mm crs. Plus reinforcement for flexure of the nib 3T25 longitudinal bars in tension face 7T16 bars in each side face T12 links 160 mm crs. Plus reinforcement for flexure The reinforcement details are shown in Figure 3.15
Info Cxp
0 7 7 - 0.385 lt 0.35 area enclosed within the centre line of the thin-wall section 310 - 90 x 200 - 90 24.2 x 103 mm2 By reference to Figure 3.1 it may be seen that the value of cot may be taken NAD anywhere between the limits of 0.67 to 1.5. Table 3 To minimize link reinforcement take cot 1.5. Note that this value must be consistent with the value taken for normal shear. The spacing of torsion links should not exceed
Info Iau
Figure 4.6 Detail at interior support Figure 4.6 Detail at interior support 4.1.2.2.14 Transverse reinforcement at laps EC2 permits ribbed slabs to be treated as solid slabs for the purposes of analysis, provided that the flange and transverse ribs have sufficient torsional stiffness. 4.1.3.1 Design example of a ribbed slab Design a ribbed slab spanning between beams as shown in Figure 4.7. In addition to self-weight, the slab carries a characteristic dead load of 1.0 kN m2 and an imposed load...
Info Gex
For a corner panel use structural system 2. It may be normally assumed that slabs are lightly stressed p lt 0.5 . NAD 6.4 e and f allows the basic span effective depth ratio to be interpolated, according to the reinforcement provided, for values in the range 0.15 lt p lt 0.5 . Basic span effective depth ratio p 0.5 32 Basic span effective depth ratio p 0.27 39.9 Using reinforcement with f gt 400 N mm2, this value should be multiplied 4.4.3.2 4 to reflect the actual service steel stress by the...
Info Tqb
In calculating 1 the influence of the reinforcement will be ignored since, if 4.3.2.3 1 straight bars are used, they will not extend d Zbnet beyond the critical section. V 0.35 x 1.075 x 1.2 x 2750 x 525 1000 652 kN Eqn 4.18 V gt 1 hence no requirement for shear reinforcement The critical perimeter is shown in Figure 2.12. Design load on base 1801 kN Length of critical perimeter u 4 x 300 ir 2 x 1.5 x 525 1000 6.15 m
Info Pec
For curved bars with concrete side cover of at least 30 a 0.7 For bars in the bottom half of a pour, good bond may be assumed. Hence for 5.2.2.1 2 0 lt 32 mm Actual distance from critical section to end of bar 2500 400 1 0.34 x 1.2 x 1.195 x 2500 x 405 x 10 3 493 kN Check that V gt VR to avoid crushing of compression struts. 0.7 - 0.55 lt 0.5 N mm2 200 0.55 x 20 x 2500 x 0.9 x 405 x 10 2 2 5012 gt 405 kN OK Length of base from face of column a 1050 mm
Info Ovk
Use method without direct calculation. 4.4.2.3 Estimate service stress in reinforcement under quasi-permanent loads, using the following approximation 4.4.2.3 3 The relevant loads are shown in Table 7.2. Table 7.2 Column loads for cracking check Table 7.2 Column loads for cracking check
Info Ymy
The shear resistance with no axial load Assume gt 50 of reinforcement curtailed at support
Combined footing
Design a combined footing supporting one exterior and one interior column. An exterior column, 600 mm x 450 mm, with service loads of 760 kN dead and 580 kN imposed and an interior column, 600 mm x 600 mm, with service loads of 1110 kN dead and 890 kN imposed are to be supported on a rectangular footing that cannot protrude beyond the outer face of the exterior column. The columns are spaced at 5.5 m centres and positioned as shown in Figure 7.2. The allowable bearing pressure is 175 kN m2, and...
Info Uvt
Second order eccentricity e2 0.1 1 0 e2 88002 x 13.07 x 107 K2 101.2 Kz mm etot ee ea e2 13-2 22 101.2K2 mm
Pilecap design example using truss analogy
A four-pile group supports a 500 mm square column which carries a factored load of 2800 kN. The piles are 450 mm in diameter and spaced at 1350 mm centres. Assume a pilecap depth of 800 mm. Allow the pilecap to extend 150 mm beyond the edge of the piles, to give a base 2.1 m square as shown in Figure 7.7. Use 2.1 m x 2.1 m x 0.8 m deep pilecap For components in non-aggressive soil and or water, exposure class is 2 a . Minimum concrete strength grade is C30 37. For cement content and w c ratio...
Info Fmn
b W gt 4 y bd 47.6 1524 mm Eqn 5. Continuing all T32 bars to end A 9650 mm2 A VJfA 1896 x 103 400 4740 mm2 Hence required anchorage, 0f- bnet at a direct support Figure 5.12 f- b X 4740 9650 500 mm gt 0.3 b OK Anchorage up to face of column 600 - 75 525 mm OK The anchorage may be increased to I if preferred, by providing a bend at the end of the bar. The requirement for transverse reinforcement along the anchorage length does 5.2.3.3 not apply at a direct support. Secondary reinforcement ratio...
Compression reinforcement
Compression reinforcement is required in any section where n gt im. The amount can be calculated from ' mechanical ratio of compression steel d' depth from compression face to centroid of compression reinforcement A' area of compression reinforcement The area of tension reinforcement can now be obtained from Equations above for w' and o gt are valid for d'lx lt 1 - fy 805.
Complete Design Example
Design calculations for the main elements of a simple in-situ concrete office block are set out. The structure chosen is the same as that used in Higgins and Rogers' Designed and detailed BS 8110 1985 i4 . Calculations are, wherever possible, given in the same order as those in Higgins and Rogers enabling a direct comparison to be made between BS 8110 2 gt and EC2 1 gt designs. For the same reason, a concrete grade C32 40 is used. This is not a standard grade recognized by EC2 or ENV 206 6 ,...
Twoway spanning solid slabs
EC2 1 permits the use of elastic analysis, with or without redistribution, or plastic analysis for ultimate limit state design. Elastic analyses are commonly employed for one-way spanning slabs and for two-way spanning slabs without adequate provision to resist torsion at the corners of the slab and prevent the corners from lifting. Plastic analyses are commonly used in other situations. Tabulated results for moments and shears from both types of analysis are widely available. Care is necessary...
Info Qqy
Width of base required - 2.96 say 3.0 m Use 7.2 m x 3.0 m x 0.75 m deep base For ground conditions other than non-aggressive soils, particular attention is needed to the provisions in ENV 206 and the National Foreword and Annex to that document for the country in which the concrete is required. In the UK it should be noted that the use of ISO 9690 15 and ENV 206 may not comply with the current British Standard, BS 8110 Part 1 1985 Table 6.1 2 where sulphates are present. Class 2 a has been...
Info Arh
lt 0.0015 x 1000 x 81 122 mm2 Check minimum area of reinforcement for crack control 0.4 x 0.8 x 3.0 x 52.5 x 103 460 110 mm2 No further check for crack control Is necessary as h 105 lt 200 mm. Maximum bar spacing 3h 315 lt 500 mm The reinforcement details are shown in Figure 8.5. Figure 8.5 Nib reinforcement details Figure 8.5 Nib reinforcement details Check shear in nib, taking into account the proximity of the concentrated load 4.3.2.3 to the support. 0 2.5dlx 2 5 X 81 1.69 Eqn 4.17
Calculation method 1
Requirements for the control of cracking are given in EC2 Section 4.4.2. Crack control is normally achieved by the application of simple detailing rules. The procedure for the calculation of crack widths is first to calculate the stress and hence the strain in the reinforcement, taking into account the bond properties of the bars and the duration of loading. Next, the average final crack spacing dependent on the type, size and disposition of the reinforcement and the form of strain distribution...
Info Rfi
The resistance moment is inadequate at support 2 and additional reinforcement is required. d 0421 lt 0593 OK Additional area of reinforcement required Fs 2630 - 2285 103 _ , - --- 863 mm2 2T16 and 2T20 gives 1030 gt 863 mm2 OK Use 2T16 top and bottom throughout beam with additional 2T20 top at support 2
K A
Basic span effective depth ratios for flat slabs are lightly stressed p 0.5 30 nominally reinforced p 0.15 41 Span reinforcement is typically T12 250 mm crs. 452 mm2 m 100 x 452 By interpolation p 0.26 , basic span effective depth ratio 37.5 29.7 lt 37.5 x 0.87 32.6 OK Use method without direct calculation. 4.4.2.3 Estimate service stress, a amp , under quasi-permanent loads as follows 4.4.2.3 3 G. Q G 0.3Q. 6.4 0.3 x 5 7.9 kN m2 2.3.4 Ratio of quasi-permanent to ultimate design loads 7.9 16.2...
Concrete grades
EC2 1 uses the cylinder strength, fck, to define the concrete strength in design equations, although the cube strength may be used for control purposes. The grade designations specify both cylinder and cube strengths in the form C cylinder strength cube strength, for example C25 30. It may occasionally be necessary to use cube strengths which do not exactly correspond to one of the specified grades. In such instances a relationship is required between cylinder and cube strength in order to...
Symmetrically reinforced rectangular columns
Figures 13.2 a to e give non-dimensional design charts for symmetrically reinforced columns where the reinforcement can be assumed to be concentrated in the corners. The broken lines give values of K in Eqn 4.73 of EC2. Eqn 4.73 Where the reinforcement is not concentrated in the corners, a conservative approach is to calculate an effective value of d' as illustrated in Figure 13.3.
Load cases example
Fundamental load combination to be used is 2.3.2.2P 2 ZyGpKs 7aiQM YQAiQk,i Ecn 2-7 lt a As the stability will be sensitive to a possible variation of dead loads, it will be necessary to allow for this as given in EC2 Section 2.3.2.3 P3 . g,in, -9. Yg,uP 135 Table 2.2 Treat the wind load as the primary load see Figure 12.2 .
Comparison with spaneffective depth ratio
The procedure for limiting deflections by use of span effective depth ratios is set out in EC2 Section 4.4.3. 100 4 100 x 2410 o _ UU 0.37 Therefore the concrete is lightly stressed, p lt 0.5 The NAD 1 introduces a category of nominally reinforced concrete corresponding to p 0.15 Basic span effective depth ratio for a simply supported beam, interpolating for p 0.37 For flanged beams where M gt w gt 3.0 the basic span effective depth ratio should be multiplied by a factor of 0.8 The span...
Example Xlf
A proposed arrangement of walls and columns is shown in Figure 11.1. Loading details are presented in Figure 11.2. It is intended to justify a design using the Simple Rules of Section 2 of the CIRIA Guide. The beam is a flat vertical plate and the thickness is small compared with other CIRIA There are two loads which may be defined as concentrated and no indirect Cl.2.1.1 4 In EC2 a beam is classified as a deep beam if the span is less than twice the 2.5.2.1 2 depth. CIRIA Guide 2 classifies...
References
1. british standards institution. Eurocode 2 Design of concrete structures. Part 1. General rules and rules for buildings together with United Kingdom National Application Document . DD ENV 1992-1-1 1992. London, BSI, 1992. 254 pp. 2. British standards institution. Structural use of concrete. Part 1 Code of practice for design and construction. Part 2 Code of practice for special circumstances. Part 3 Design charts for singly reinforced beams, doubly reinforced beams and rectangular columns. BS...
Info Mur
K is a factor dependent upon the shape of the being moment diagram. For a simply supported beam with uniformly distributed load Total curvature at mid-span, from Section 10.1.3.2 Therefore maximum deflection at mid-span Again this is close to the rigorously assessed value.
Flanged beams
For beams with flanges on the compression side of the section, the formulae for rectangular sections may be applied provided For beams where the neutral axis lies below the flange, it will normally be sufficiently accurate to assume that the centre of compression is located at mid-depth of the flange. Thus, for singly reinforced beams, approximately The neutral axis depth is given approximately by xld 1.918 blb o gt - 1.25 b b - 1 hjd where b is the rib width and the definition of w is...