Info Hxe
which is less than the allowable upper limit, thus deflection requirements are likely to be satisfied. The theory and design requirements for shear were covered in chapter 5 and the relevant design equations were derived based on the requirements of EC2 using the Variable Strut Inclination Method. The shear reinforcement will usually take the form of vertical links or a combination of links and bent-up bars. Shear reinforcement may not be required in very minor beams such as door or window...
Determine The Area Of Tension Reinforcement
The designer is concerned however with the maximum crack width which has an acceptably low probability of being exceeded. For design purposes the design maximum crack width, iv , can be based on the maximum spacing. .vr.TOX. Hence the design crack width at any level defined by y in a member will thus be given by The expression for the design crack width given in EC2 is of the above form and is given as V.max the maximum crack spacing esin the mean strain in the reinforcement allowing for the...
Biaxial bending of short columns
For most columns, biaxial bending will not govern the design. The loading patterns necessary to cause biaxial bending in a building's internal and edge columns will not usually cause large moments in both directions. Corner columns may have to resist significant bending about both axes, but the axial loads are usually small and a design similar to the adjacent edge columns is generally adequate. A design for biaxial bending based on a rigorous analysis of the cross-section and the strain and...
Info Jme
The moments in slabs spanning in two directions can also be determined using tabulated coefficients. Slabs which are not rectangular in plan or which support an irregular loading arrangement may be analysed by techniques such as the yield line method or the Hilleborg strip method, as described in section 8.9. Concrete slabs are defined as members where the breadth is not less than 5 times the overall depth and behave primarily as flexural members with the design similar to that for beams,...
Why Is Strut Angle Between 22 Degrees And 45 Degrees Used In Shear Design In Ec2
0.5 sin 20 see proof in the Appendix which alternatively can be expressed as fl O-Ssin-'i ' 1 lt 45 5.8b where Vnr is the shear force at the face of the support and the calculated value of the angle 9 can then be used to determine col 9 and calculate the shear reinforcement AiW s from equation 5.9 below when 22 lt lt 45 . 2 The vertical shear reinforcement As previously noted, all shear will be resisted by the provision of links with no direct contribution from the .shear capacity of the...
Reinforced Concrete
Bill Mosley, John Bungey and Ray H lse Other titles of interest to civil engineers Civil Engineering Materials, fifth edition edited by n. iackson amp r. k. dhir Civil Engineering Quantities, sixth edition l.H. seeley Design of Structural Elements W. M.C. McKenzie Design of Structural Timber to EC5, second edition w. M. c. Mckenzie amp b. zhang Design of Structural Masonry w. m. c. Mckenzie Design of Structural Steelwork w. m.c. Mckenzie Engineering Hydrology, fourth edition e. m. wilson...
Info Klh
2 0459 k lt 4'45 gt Once we know the properties of the stress block, the magnitude and position of the resultant compressive force in the concrete can be determined, and hence the moment of resistance of the section calculated using procedures similar to those for the rectangular stress block. Comparison of the rectangular-parabolic and the rectangular stress blocks provides rectangular-parabolic k bx ss 0.459 5 rectangular 0.567 k x 0.8 .v 0.454 ii Lever arm, z rectangular parabolic d Kv ss d...
Info Xur
The provision of shear links to resist vertical shear in a flanged beam is identical to that previously described for a rectangular section, on the assumption that the web carries all of the vertical shear and that the web width. bw, is used as the minimum width of the section in the relevant calculations. Longitudinal complementary shear stresses also occur in a Hanged section along the interface between the web and flange as shown in figure 5.6. This is allowed for by providing transverse...
M Wou
6.3.2 Creep and shrinkage effects Creep The effect of creep will be to increase deflections with time and thus should be allowed for in the calculations by using an effective modulus. CiCff. using the equation c,eff W l lt KoO,f0 6-8 where is a creep coefficient equal to the ratio of creep strain to initial elastic strain. Serviceability, durability and stability requirements Table 6.12 Final creep coefficient of normal weight concrete Class C25 30
A Hkf
curtailment described in section 7.9. The application of these nilcs establishes the cutoff points beyond which the bars must extend at least a curtailment anchorage length. It should be noted that at the external columns the reinforcement has been bent to give a full anchorage bond length. The shear-force envelope and the arrangement of the shear reinforcement for the same continuous beam are shown Is figure 7.18. On the shear-force envelope the resistance of the minimum stirrups has been...
Info Gdv
Transverse reinforcement for lapped bars Notwithstanding the above requirements, the absolute minimum lap length is given as Transverse reinforcement must be provided around laps unless the lapped bars are less than 20 mm diameter or there is less than 25 per cent lapped bars. In these cases minimum transverse reinforcement provided for other purposes such as shear links will be adequate. Otherwise transverse reinforcement must be provided, as shown in figure 5.13, having a total area of not...
Info Qee
Cracked section - strain and stress distribution Section transformed section Strain Section transformed section Strain The assumed elastic strain and stress distribution for a cracked section is shown in figure 6.5. This is identical to that shown in figures 4.27 and 4.28. and equation 4.48 or figure 4.29 can be used to determine the neutral-axis depth. Alternatively, moments of area can be taken to establish the neutral-axis depth directly. The second moment of area of the cracked section can...
Ray Hulse
formerly faculty of engineering and computing c W.H. Hosley and J.H. Bungey 1976, 1982, 1987, 1990 i W.H. Mosley, J.H. Bungey and R. Hulse 1999, 2007 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence...
I 1
As the coefficients of thermal expansion of steel and concrete a-r.s and qt,c are similar, differential movement between the steel and concrete will only be very small and is unlikely to cause cracking. The differential thermal strain due to a temperature change T may be calculated as and should be added to the shrinkage strain lt S if significant. The overall thermal contraction of concrete is, however, frequently effective in producing the first crack in a restrained member, since the...
Yield line and strip methods
For cases which are more complex as a result of shape, support conditions, the presence i openings, or loading conditions it may be worthwhile adopting an ultimate analysis ethod. The two principal approaches are the yield line method, which is particularly litable for slabs with a complex shape or concentrated loading, and the strip method hich is valuable where the slab contains openings. These methods have been the subject of research, and are well documented although hey are of a relatively...
Ribbed and hollow block floors
Cross-sections through a ribbed and hollow block floor slab are shown in ligure 8.15. The ribbed floor is formed using temporary or permanent shuttering while the hollow block floor is generally constructed with blocks made of clay tile or with concrete containing a lightweight aggregate. If the blocks are suitably manufactured and have adequate strength they can be considered to contribute to the strength of the slab in the design calculations, but in many designs no such allowance is made....
I Ksg
so that the roof's external connection Ma 0.54 x - x 60 1.6 kN m As a check at each joint, Mr Y Mq. The bending moments due to characteristic wind loads in all the columns and beams of this structure are shown in figure 3.21. 3.5 Shear wall structures resisting horizontal loads A reinforced concrete structure with shear walls is shown in figure 3.22 . Shear walls are very effective in resisting horizontal loads such as Fz in the figure which act in the direction of the plane of the walls. As...
Stair slabs
The usual form of stairs can be classified into two types 1 those spanning horizontally in the transverse direction, and 2 those spanning longitudinally. Stairs of this type may be supported on both sides or they may be cantilevered from a supporting wall. Figure 8.17 shows a stair supported on one side by a wall and on the other by a stringer beam. Each step is usually designed as having a breadth b and an effective depth of d D 2 as shown in the ligurc a more rigorous analysis of the section...
Concrete Drop Panel
Moments in a continuous two-way slab The panel considered is an edge panel, as shown in figure 8.9 and he uniformly distributed load, n 1.35 k I.5i k 10kN nr. The moment coefficients are taken from table 8.5. Ma lianl 0.045 x 10 x 52 11.25 kN m in direction , WS gt . 0.028 x 10 x 52 7.0 kN m in direction ly Support ad. A x 0.059 x 10 x 52 14.75 kN m Supports ab and dc. ,Wy 0.037 x 10 x 52 9.25 kN m The moments calculated are for a metre width of slab. The design of reinforcement to resist these...
Chapter Introduction Kas
Many buildings are constructed with a steel framework composed of steel beams and steel columns but mostly with a concrete floor slab. A much stiffer and stronger structure can be achieved by ensuring that the steel beams and concrete slabs act together as composite and so, effectively, monolithic units. This composite behaviour is obtained by providing shear connections at the interface between the steel beam and the concrete slab as shown in ligure 12.1. These shear connections resist the...
H Lan
Strip footing with bending reinforcement In tlie transverse direction the maximum moment can he calculated on the assumption that the 2.2 m wide looting is acting as a 1.1 ni long cantilever for the purposes of calculating the design moment 0.87 x 500 x 0.95 x 720 497 mm m Minimum As 0.15 x 1000 x 1080 mnr m Provide H20 bars at 250mm centres, area 1260 mnr m. bottom steel. 5. Normal shear will govern as the punching perimeter is outside the fooling. The critical section for shear is taken l.fW...
Info Dkh
EXAMPLE 6.3 Adjustment of basic span to effective depth ratio Determine Ihe appropriate basic ratio for a cantilever beam supporting a uniform load and a concentrated point load at its tip as shown in figure 6.9. Assume that the concrete is C30 35 and is highly stressed. Basic ratio from table 6.10 6.0 for u.d.l. From table 6.14 k for cantilever with u.d.l. over full length 0.25 k for cantilever with point load at tip 0.33 Thus, for the point load only, adjusted basic ratio equals An adjusted...
Example Gmo
Design of a section with moment redistribution applied and A 0 8 The section shown in figure 4.17 is subject to an ultimate design moment of 230 kN m after a 20 reduction due to moment redistribution. The characteristic material strengths are yk 500N mm2 and ck 25 N mm2. Determine the areas of reinforcement required using the constants k and ki from a the EC2 and b the UK annex to EC2. Limiting neutral axis depth, Abai J f gt - k d kj From EC2 clause 5.5 k, 0.44 and k2 1.25. therefore .tM - 0.8...
Chapter Introduction Cpf
This chapter deals with the theory and derivation of the design equations for shear, bond and torsion. Some of the more practical factors governing the choice and arrangement of the reinforcement are dealt with in the chapters on member design, particularly chapter 7, which contains examples of the design and detailing of shear and torsion reinforcement in beams. Punching shear caused by concentrated loads on slabs is covered in section 8.1.1 of the chapter on slab design. Figure 5.1 represents...
Info Mta 1
AB and CD. and equation 10.7 can be modified to give required area o reinforcement in each truss - 4 0.87fyk 4d x 0.87 yk and this reinforcement should be provided in both directions in the bottom face of the pile-cap. The truss theory may be extended to give the tensile force in pile caps with other configurations of pile groups. Table 10.4 gives the force for some common cases. The shear capacity of a pile cap should be checked at the critical section taken to be 20 per cent of the pile...
I Slx
b Design of main tension reinforcement From equation 10.8, the required area of reinforcement in each truss is _ T 2 N x 's 0.87 yk 4d x 0.87 yk _ 5000 x 103 x 1350 2 4 x 875 x 0.87 x 500 2216mm2 The total area of reinforcement required in each direction 2 x A, 2x2216 4432 mm2. As the piles are spaced at three times ilic pile diameter this reinforcement may be distributed uniformly across the section. Hence provide fifteen H20 bars, area 4710 mm2, at 140 mm centres in both directions Shear...
Info Dol
These equations ure not suitable for direct solution and the design of a column with symmetrical reinforcement in each face is best carried out using design charts as illustrated in figure 9.8. Sets of these charts can be found in the Concise Eurocode rcf. 21 , the Manual for the Design of Concrete Structures rcf. 23 and the website www.eurocode2.info. f EXAMPLE 9.2 Column design using design charts Figure 9.9 shows a frame of a heavily loaded industrial structure for which the centre columns...
Info Pjv
Increase of concrete strength with age. Typical curve for a concrete made with a class 42.5 Portland cement with a 28 day compressive strength of 30 N mm2 used in design to be varied according to the age of the concrete when it supports the design load. European Codes, however, do not permit the use of strengths greater than the 28-day value in calculations, but the modulus of elasticity may be modified to account for age as shown later. In the United Kingdom, compressive stress has...
Preface
The purpose of this book is to provide a straightforward introduction to the principles and methods of design for concrelc structures. It is directed primarily at students and young engineers who require an understanding of the basic theory and a concise guide to design procedures. Although the detailed design methods are generally according to European Standards Eurocodes , much of the theory and practice is of a fundamental nature and should, therefore, be useful to engineers in countries...
Concrete Interaction Diagram
M-N interaction diagram or a non-symmetrical section Non-rectangular M N interaction example EXAMPLE 4.11 M-N interaction diagram for a non-rectangular section Construct the interaction diagram for the equilateral triangular column section in figure 4.23 with i 25N mm2 and gt k 500N mm2. The bending is about an axis parallel to the side AA and causes maximum compression on the corner adjacent to the steel area A'. Non-rectangular M N interaction example
Pile Cap Truss Analogy
Therefore, substituting for y and .vn P, 166.7 - 35.4 x 1.67 33.3 x 1.0 - 140.9kN P2 166.7 - 35.4 x 1.67 - 33.3 x 1.0 74.3 kN Pi 166.7 35.4 x 0.33 33.3 x 1.0 211.7 kN P4 166.7 35.4 x 0.33 - 33.3 x 1.0 145.1 kN Ps 166.7 35.4 x 1.33 33.3 x 1.0 247.1 kN P6 166.7 35.4 x 1.33 - 33.3 x 1.0 180.5 kN When a pile group is unsymmetrieal about both co-ordinate axes it is necessary to consider the theory of bending about the principal axes which is dealt with in most textbooks on strength of materials. In...
Chapter Introduction Jcc
A reinforced concrete structure is a combination of beams, columns, slabs and walls, rigidly connected together to form a monolithic frame. Each individual member must be capable of resisting the forces acting on it, so that the determination of these forces is an essential part of the design process. The full analysis of a rigid concrete frame is rarely simple but simplified calculations of adequate precision can often be made if the basic action of the structure is understood. The analysis...
Combined footings
Where two columns are close together it is sometimes necessary or convenient to combine their footings to form a continuous base. The dimensions of the footing should he chosen so that the resultant load passes through the centroid of the base area. This may be assumed to give a uniform bearing pressure under the footing and help to prevent differential settlement. For most structures the ratios of permanent and variable loads carried by each column are similar so that if the resultant passes...
Moment Redistribution
Additional moments diagram Hinges at A and C Elastic BMD Collapse loads Final Collapse BMD Figure 3.28 Moment redistribution, one-span beam Additional moments diagram Hinges at A and C Elastic BMD Collapse loads Final Collapse BMD I- - is the load to cause the first plastic hinge thus the beam may carry a load of with redistribution. m the design point of view, the elastic bending-moment diagram can be obtained la required ultimate loading in the ordinary way. Some of these moments may then ....
Info Hud
c Forces acting on one lace of the section c Forces acting on one lace of the section As q is the shear force per unit length of the circumference of the box section, the force produced by the shear How is the product of q and the circumference 0 of the area Ak. Hence, if it assumed that this force is resisted by the truss action of the concrete compressive struts acting at an angle. 0. together with tension in the longitudinal steel, from figure 5.16b the force F in the longitudinal tension...
F Kqm
he the compressive force developed in the concrete and acting through ti. centroid of the stress block l c be the compressive force in the reinforcement area A' and acting through centroid l be the tensile or compressive force in the reinforcement area and actin through its centroid. i Basic equations and design charts The applied force N must be balanced by the forces developed within the cros-section, therefore In this equation, h will be negative whenever the position of the neutral axis is...
J Wlg
4.6.3 Flanged section with compression reinforcement With x 0.45f in figure 4.16 and taking moments about A,, the maximum resistance moment of the concrete is 0.16 Ub d2 0.567 ck fcf - bw d - if 2 4.24 Note that the value of 0.167 was derived in equation 4.10 for the rectangular section. e applied design moment. W gt A bai- compression reinforcement is required. In tte e the area of compression steel can be calculated from 4id . msidering the equilibrium of forces on the section r - cl Fc2 F.C...
Info Src
Modular ratio 8. 94-8. 139. 343 Modulus of elasticity see Elastic modulus Moment coefficients 37, 210, 224, 227, 230 Moment redistribution 53-7. 79, 178-82 Neutral-axis depth 61-4. 81 Nominal reinforcement 106. 131. 188. 397 Pad footings 285-91 Parabola, properties of 92 Partial safety factors 18, 19, 59, 282, 283 Permissible bearing pressures 284 Permissible stresses 97, 330 Piled foundations 300-8 Prestressed concrete analysis and design 319-68 cable zone 340-2 deflections 347-50 end block...
Hhmmm
common practice to use a raft foundation in conjunction with a more flexible superstructure. The simplest type of raft is a flat slab of uniform thickness supporting the columns. Where punching shears are large the columns may be provided with a pedestal at the base as shown in figure 10.15. The pedestal serves a similar function to the drop panel in a fiat slab floor. Other, more heavily loaded rafts require the foundation to be strengthened by beams to form a ribbed construction. The beams...
ireircri ooac
From table 6.11 the cracking strength of the concrete, fam, is given as 2.6 N mnr. Hence from elastic bending theory and considering the uncrackcd concrete section, the moment that will just cause cracking of the section. M , is given by 2.6 x 300 x 7002 6 x 10 6 63.7 kNm i I-P MJM 2 I - 0.5 x 63.7 200 2 0.95 ii Calculate the 'average' curvature 0.95 x 3.08 x Itr6 I - 0.95 x 2.86 x 10 fi 3.07 x I0-6 mm S Ai d-x 2450 600 - 329 664 x I03 mm3 and from table 6.13. ecs 470 x 10'' because 2AJu 210,...
Info Vif
This value is greater than the yield strain of 0.00217 from section 4.1.2. c Check ultimate moment of resistance Taking moments about the centre of compression Mu 123 275 - 0.40a 4- 68.3 245 - 0.40 123 275 - 0.40 x 88 68.3 245 - 0.40 x 88 lO'3 43.8 kN m If it had been found in b that either the prestressing steel or unlensioned steel had not yielded, then a rial and error approach similar to example 11.10 would have been necessary. Shear in prestressed concrete is considered at the ultimate...
Info Oki
chloride-induced corrosion . Detailed requirements for mix specification and compliance are given by BS EN206 'Concrete - Performance. Production, Placing and Compliance Criteria' and BS8500 'Concrete - Complementary British Standard to BS EN206' Table 1.3 lists the characteristic design strengths of some of the more common types of reinforcement currently used in the UK. Grade 500 50 N mnr characteristic strength has replaced Grade 250 and Grade 460 reinforcing steel throughout Europe. The...
Counterfort Wall
Such walls are usually required to resist a combination of earth and hydrostatic loadings. The fundamental requirement is that the wall is capable of holding the retained material in place without undue movement arising from deflection, overturning or sliding. Concrete retaining walls may be considered in terms of three basic categories I gravity. 2 counterfort, and 3 cantilever. Within these groups many common variations exist, for example cantilever walls may have additional supporting ties...
Info Das
lightly stressed when p equals 0.5 per cent, p is given by l 0Aymi l gt d where i4s,rCq i the area of tension reinforcement required in the section. Interpolation between the values of p indicated is permissible. In the case of slabs it is reasonable to assume lha they are lightly stressed. Since the value of allowable span-effective depth ratio is affected by both reinforcement ratio and concrete strength it may be more convenient to use the char in figure 6.3 which is for a simply supported...
Moment Capacity
ultimate moment of resistance 253 x 123 x 10 3 31.1 kNm Untensioned steel is therefore required to permit the beam to support an ultimate moment of 40 kNm. Additional moment capacity to be provided 40-31.1 8.9kNm Effective depth of additional steel 245 mm lever arm to additional steel 220 mm and
Strut And Tie Models
Parabolic tendon profile eccentric at ends of beam If the prestrcss force does not lie at the centroid of the section at the ends of the beam, but at an eccentricity lt o as shown in figure 11.17, the expression for deflection must be modified. It can he shown that the deflection is the same as that caused by a force P acting at a constant eccentricity c0 throughout the length of the member, plus a force P following a parabolic profile with mid-span eccentricity e as shown in figure 11.17. The...
Xf Lzg
1. Freeze-thaw resisting aggregates to be specified. 1. Freeze-thaw resisting aggregates to be specified. a gt cno ib lt w 2 Figure 6.1 a gt cno ib lt w 2 Figure 6.1 6.1.2 Minimum member dimensions and cover fire resistance In order that a reinforced concrete member is capable of withstanding Hre for a specified period of time, it is necessary to ensure the provision of minimum dimensions and cover here defined as nominal minimum concrete surface to main bar axis dimension as illustrated in...
X Ubu
A partial factor of safety of 7g 1 0 is applied to the permanent load Gk if its effect is 'favourable' i.e. contributes to the sliding resistance and the 'unfavourable' effects of the permanent earth pressure loading at the rear face of the wall arc multiplied by a partial factor of safety of 7f 1.35. The 'unfavourable' effects of the variable surcharge loading are multiplied by a partial factor of safety of 7f 1.5. Thus, if the coefficient of friction between base and soil is .i, the total...
I Cqq
Idealised link frame for a structure with shear walls and structural frames links of large cross-sectional area pinned at their ends whereas this would normally be of a secondary magnitude. To overcome this the cross-sectional areas of all he beams in the model may be increased say to 1000 m2 and this will virtually remove the effects of axial shortening in the beams. In the computer output the member forces for type A frames would need to be divided by a factor of four and those for type B...
Shear Crack In Concrete Beam
VRd.c the design shear resistance of the section without shear reinforcement lsi - the area of tensile reinforcement that extends beyond the section being considered by at least a full anchorage length plus one effective depth id bw the smallest width of the section in the tensile area mm Some typical values of the corresponding shear stress capacities rRd.c Vri,c bvd arc given in chapter 8 table 8.2 . 5.1.2 The variable strut inclination method for sections that do require shear reinforcement...