Accuracy
The calculation of deflection in Eurocode 2 using the rigorous method presented here is more advanced than that in BS 8110 It can be used to take account of early-age construction loading by considering reduced early concrete tensile strengths. However, the following influences on deflections cannot be accurately assessed Tensile strength, which determines the cracking moment. Therefore any calculation of deflection is only an estimate, and even the most sophisticated analysis can still result...
Introduction Scope
P 1 Eurocode 2 applies to the design of buildings and civil engineering works in plain, reinforced and prestressed concrete. It is subdivided into various separate parts, see 1.1.2 and 1.1.3. P 2 This Eurocode is only concerned with the requirements for resistance, serviceability and durability of structures. Other requirements, e.g. concerning thermal or sound, insulation, are not considered. P 3 Execution1 is covered to the extent that is necessary to indicate the quality of the construction...
Hazard Identification
A hazard is a set of circumstances, possibly occurring within a given system, with the potential for causing events with undesirable consequences. For instance the hazard of a civil engineering system may be a set of circumstances with the potential to an abnormal action e.g. fire, explosion or environmental influence flooding, tornado and or insufficient strength or resistance or excessive deviation from intended dimensions. In the case of a chemical substance, the hazard may be a set of...
Discretized Solution
Balance Equilibrium Stiffness matrix Convection Stiffness Matrix Boundary forces Body forces Initial strain Initial stress Table 12.1 Comparison of Scalar and Vector Field Problems, Revisited
Design procedure
A procedure for carrying out the detailed design of beams is shown in Table 1. This assumes that the beam dimensions have previously been determined during conceptual design. Concept designs prepared assuming detailed design would be to BS 8110 may be continued through to detailed design using Eurocode 2. More detailed advice on determining design life, actions, material properties, methods of analysis, minimum concrete cover for durability and control of crack widths can be found in Chapter 2,...
Stiffness of composite sections
In structural elements in which there is concrete in compression, the effective equivalent steel section is calculated assuming that the concrete in compression is uncracked. This is reflected in the value for the modular ratio n EJEcm 7. In structural elements in which the concrete is in tension, the effective equivalent steel section is calculated neglecting the concrete in tension and considering only the reinforcement. As a result, the stiffness of the section can be different, depending on...
Design for high beam shear support B
As uniformly distributed load predominates consider at d from face of support VEd 1098 - 350 2 0.689 x 1.35 x 46.0 1.5 x 633 1098 - 0.864 x 157.1 962.3 kN By inspection, shear reinforcement required and cot 0 lt 2.5. Check VRd max to determine 9 Check maximum shear resistance As before 6 0.5 sin-1 0.20 fck 1 - fck 250 gt cot-12.5 where 962.3 x 103 350 x 0.9 x 687 4.45 MPa 6 0.5 sin-1 4.45 0.20 x 30 1 - 30 250 gt cot-12.5 0.5 sin-1 0.843 gt cot-12.5 0.5 x 57.5 gt 21.8 28.7 cot 6 1.824 i.e. gt...
Flexural design span BC and CD similar
beff, 0.2b 0.1 0 lt 0.2 0 lt b1 where 7500 - 1000 - 550 2 2975 mm 0 0.70 x 2 0.7 x 7500 5250 mm beff1 0.2 x 2975 0.1 x 5250 lt 0.2 x 5250 lt 2975 1120 lt 1050 lt 2975 1050 mm bw 2000 mm bf2 0.2b2 0.1 0 lt 0.2 0 lt b2 where beff2 0.2 x 3725 0.1 x 5250 lt 0.2 x 5250 lt 3725 1270 lt 1050 lt 3725 1270 mm b 1050 2000 1270 4320 mm assuming 10 mm link and H25 in span fck 30 K 393.2 x 106 4320 x 2522 x 35 0.041 By inspection, K lt K' .'. section under-reinforced and no z d 2 1 1 - 3.53K 05 lt 0.95d 252...
Simplified design of frames with decoupled diagonal bracings
The structural behaviour of decoupled diagonal bracings is similar to that of X bracings, but as there are two braced zones, each containing one diagonal instead of two, the problem of overstrength described above for X bracings takes place differently, as twice as many columns are involved in the bracing. For this reason, clause 6.7.3 2 states that no lower bound value of slenderness restricts the possible dimensions of the diagonals in this case. However, to be complete the design must also...
Example Stress Transformation
Show that the transformation tensor of direction cosines previously determined transforms the original stress tensor into the diagonal principal axes stress tensor. Solution
Systems of large lightly reinforced walls
Eurocode 8 is unique among international codes in that it includes special provisions for systems consisting of a fairly large number of large but lightly reinforced concrete walls which are designed to sustain seismic demands not by dissipating kinetic energy through hysteresis in plastic hinges but by converting part of this energy into potential energy of the masses and returning part to the ground through radiation from their foundation. To qualify for the special design provisions of...
Limit states
The following ultimate limit states ULS should be satisfied for geotechnical design they each have their own combinations of actions. For an explanation of Eurocode terminology please refer to Chapter 1, originally published as Introduction to Eurocodes5. EQU Loss of equilibrium of the structure. STR Internal failure or excessive deformation of the structure or structural member. GEO Failure due to excessive deformation of the ground. Loss of equilibrium due to uplift by water pressure. HYD...
Controllability and Observability of the DiscreteTime Structural Model
Consider now a structure in modal coordinates. Similar to the continuous-time grammians the discrete-time grammians in modal coordinates are diagonally dominant, where Wci and W0i are 2 x 2 blocks, such that Wci wCiI2 and W0i w0iI2, see 98 , where IK II2 2 1 - cos fflj At 2 1 - cos fflj At wci TT--Y- wci cont-Yl-- 4.8 Q In the above equations Bmi is the ith block of Bm in modal coordinates, and Cmi is the ith block of Cm in modal coordinates, where Cm CmqQ_1 Cmv , see 2.42 for Zs0. In the...
Columns 1
1 P In primary seismic columns the design values of shear forces shall be determined in accordance with the capacity design rule, on the basis of the equilibrium of the column under end moments Mi d with ' 1,2 denoting the end sections of the column , corresponding to plastic hinge formation for positive and negative directions of seismic loading. The plastic hinges should be taken to form at the ends of the beams connected to the joints into which the column end frames, or if they form there...
Structural types and behaviour factors Structural types 1
1 P Composite steel-concrete structures shall be assigned to one of the following structural types according to the behaviour of their primary resisting structure under seismic actions a Composite moment resisting frames are those with the same definition and limitations as in 6.3.1 1 a, but in which beams and columns may be either structural steel or composite steel-concrete see Figure 6.1 b Composite concentrically braced frames are those with the same definition and limitations as in 6.3.1...
Limiting equilibrium methods
Limiting equilibrium methods are commonly used to assess the required penetration of embedded retaining walls, associated shear forces and bending moments in their cross-sections, and the forces in any props or anchors used to support them. Limiting equilibrium methods assume that the full strength of the ground is mobilized uniformly around the wall, so that the wall is at the point of collapse or 'limiting equilibrium' . Cantilever walls and walls propped near their top are statically...
A Mass of disturbed soil for testing
1 The minimum masses of disturbed soil required for testing are summarised in Table A.4.1. Where the minimum mass depends on the size of the largest particles present in significant quantity, this is related to the minimum mass required for sieving denoted by MMS which is given below Table A.4.1. 2 The required mass listed in Table A.4.1 allows for the preparation of one test specimen, with some allowance for wastage but not for the inclusion of over-size particles. When only the fine fraction...
Vacuum Filtration
We have already discussed this important technology in Chapter 5, but a review may be helpful in placing its importance to sludge processing into perspective. The vacuum filter for dewatering sludge is a drum over which is laid the filtering medium consisting of a cloth of cotton, wool, nylon, dynel, fiber glass or plastic, or a stainless steel mesh, or a double layer of stainless steel coil springs. The drum with horizontal axis is set in a tank with about one quarter of the drum submerged in...
Info Wnn 1
b Edge and end distances Fig. 10.11. Fastener spacings and distances. to allow fixings to be formed in dense timber and this is a requirement for nails driven in timber with a characteristic density greater than 500 kg m3 EC5,8.3.1.1 and for all screws in hardwood EC5,10.4.5 . The above and other related requirements in EC5 are summarised in the notes accompanying Tables 10.8 and 10.9. EC5 rules for spacing, edge and end distances for joints formed with nails and or staples are summarised in...
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...
Introduction To Advanced Elasticity Theory
Any element of material may be subjected to three independent types of stress. Two of these have been considered in detai previously, namely direct stresses and shear stresses, and need not be considered further here. The third type, however, has not been specifically mentioned previously although it has in fact been present in some of the loading cases considered in earlier chapters these are the so-called body-force stresses. These body forces arise by virtue of the bulk of the material,...
Column splices ends prepared for contact in bearing Fig
25 Column splice ends prepared for contact in bearing Splices should be designed for full contact bearing to resist the vertical loads. In addition, the following recommendations should be followed a the projection of the flange cover plates beyond the ends of the column members should be equal to the width of the flange of the upper column or 225 mm, whichever is greater b the thickness of the flange cover plates should be half the thickness of the flange of the upper column or 10 mm,...
Stiffened walls
1 Walls may be considered as stiffened at a vertical edge if and its stiffening wall is not expected, i.e. - both walls are made of materials with approximately similar deformation behaviour, - are approximately evenly loaded - are erected simultaneously and bonded together - and differential movement between the walls for example, due to shrinkage, loading etc., is not expected, the connection between a wall and its stiffening wall, is designed to resist developed tension and compression...
Chlorine
Chlorine is familiar to most people as it is used to treat virtually all municipal water systems in the United States. Chlorine has a number of problems when used for field treatment of water. When chlorine reacts with organic material, it attaches itself to nitrogen containing compounds ammonium ions and amino acids , leaving less free chlorine to continue disinfection. Carcinogenic trihalomethanes are also produced, though this is only a problem with long-term exposure. Trihalomethanes can...
Chlorination Systems
Water chlorination is carried out by using both free and combined residuals. The latter involves chlorine application to produce chloramine with natural or added ammonia. Anhydrous ammonia is used if insufficient natural ammonia is present in the wastewater. Although the combined residual is less effective than free chlorine as a disinfectant, its most common application is as a post-treatment following free residual chlorination to provide initial disinfection. Free residual chlorination...
Division of moments between column and middle strips
The design moments obtained from analysis of the frames or from Table 5.4 should be divided between the column and middle strips in the proportions given in Table 5.5. Table 5.5 Distribution of design moments of flat slabs For the case where the width of column strip is taken as equal to that of the drop and the middle strip is thereby increased in width, the design moments to be resisted by the middle strip should be increased in proportion to its increased width. The design moments to be...
Design procedure
a Calculate the factored load 1.6 x imposed 1.4 x dead, and then calculate the maximum factored bending moments Mx and the factored shear forces b Calculate the second moment of area required to satisfy the deflection limitations described in clause 2.6.2. For simply supported beams, use the method described in clause 4.2 b . c Determine the effective length LE from the two cases Beams with lateral restraints at their ends only The effective length LE should be obtained from Table 7 according...
Butt welds
Throat thickness for full penetration welds should be taken as the thickness of member. For partial penetration welds, it should be taken as the minimum depth of weld penetration, except that it should be taken as the actual depth less 3mm for V- or bevel welds. The depth should not be less than 2 f t, where t is the thickness in mm of the thinner connected part. The design strength should be taken as that of the parent metal, provided that the weld is made with a suitable electrode. Any...
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...
A Stage Structural Design of Concrete Cantilever Retaining Wall
As stated in the introduction to this appendix, the second stage of the wall design entails the structural design of the concrete wall, to include the dimensioning of the concrete base slab the toe and heel elements and stem, and the detailing of the reinforcing steel. All reinforced-concrete hydraulic structures must satisfy both strength and serviceability requirements. In the strength design method, this is accomplished by multiplying the service loads by appropriate load factors and by a...
Residual strength of soil
In an investigation concerning the stability of a clay slope, the normal procedure is to take representative samples, conduct shear tests, establish the strength parameters c' and lt gt ' from the peak values of the tests, and conduct an effective stress analysis. For this analysis the shear strength of the soil can be expressed by the equation There have been many cases of slips in clay slopes which have afforded a means of checking this procedure. Obviously when a slope slipped its factor of...
An Alternative Analysis The Forgotten Method Of Dimensional Analysis
I often refer to dimensional analysis as lost art - because it is usually not heavily emphasized in engineering education today. However, for well over 100 years its has provided simply a wealth of practical design correlations that are still relied upon in virtually all aspects of chemical engineering, ranging from classes of problems dealing with heat and mass transfer, reaction kinetics, momentum exchanges in flow dynamics. Much of sedimentation theory, and indeed the basis for more...
Design for beam shear support A
VEd 646 - 350 2 0.689 x 1.35 x 46.0 1.5 x 63.3 646 - 0.864 x 157.1 Check maximum shear resistance v 0.6 1 - fck 250 0.6 1 - 30 250 0.528 fd 30 1.5 20.0 MPa 0 angle of inclination of strut. 0.5 sin-1 vEd2 0.20 fCk 1 - fCk 250 gt cot-12.5 where VEd bz VEd b x 0.9d 510.3 x 103 350 x 0.9 x 689 2.35 MPa 0 0.5 sin-1 2.35 0.20 x 30 1 - 30 250 gt cot-12.5 0.5 sin-1 0.445 gt cot-12.5 0.5 x 26.4 gt 21.8 21.8 1.0 x 350 x 0.90 x 689 x 0.528 x 20.0 2.5 0.4 790 kN lt 6.2.3 amp NA gt lt 6.2.3 1 gt lt 6.2.3 3...
Materials
4.1 Introduction 4 3 4.1.1 Standards and codes of practice 4 3 4.2.4 Concrete mix design 4 8 4.2.5 Properties of hardened concrete 4 9 4.2.7 Concreting in hot, arid climates 4 14 4.2.8 Reinforcement and prestressed steel 4 14 4.3.1 Workability tests 4 14 4.3.3 Accelerated strength tests 4 16 4.3.5 Nondestructive strength tests 4 16 4.3.6 Tests on aggregates 4 16 4.3.7 Measurement of entrained air 4 17 4.3.8 Analysis of fresh concrete 4 17 4.3.9 Analysis of hardened concrete 4 17 4.4 Plastics...
Vertical component of the seismic action
1 If avg is greater than 0,25 g 2,5 m s2 the vertical component of the seismic action, as defined in 3.2.2.3, should be taken into account in the cases listed below - for horizontal or nearly horizontal structural members spanning 20 m or more - for horizontal or nearly horizontal cantilever components longer than 5 m - for horizontal or nearly horizontal pre-stressed components - for beams supporting columns 2 The analysis for determining the effects of the vertical component of the seismic...
Design of anchorages
The design of anchorages is covered by Section 8 of Eurocode 7 Part 1, 'Anchorages', whose contents are as follows 8.1 General 12 paragraphs 8.2 Limit states 1 8.3 Design situations and actions 2 8.4 Design and construction considerations 15 8.5 Ultimate limit state design 10 8.6 Serviceability limit state design 6 8.7 Suitability tests 4 8.8 Acceptance tests 3 8.9 Supervision and monitoring 1 Section 8 of EN 1997-1 applies to prestressed and non-prestressed anchorages both temporary and...
Design strength py
This Manual covers the design of structures fabricated from steels supplied to BS 4360, and the design strengths, py, should be obtained from Table 2. Other steels may be used provided that their design strengths are obtained in a similar manner as in BS 4360.
Kinetics
5.2.1 Force, Traction and Stress Vectors 38 There are two kinds of forces in continuum mechanics body forces act on the elements of volume or mass inside the body, e.g. gravity, electromagnetic fields. dF pbdVol. surface forces are contact forces acting on the free body at its bounding surface. Those will be defined in terms of force per unit area. 39 The surface force per unit area acting on an element dS is called traction or more accurately stress vector. f tdS if txdS jf tydS kf tzdS 5.37...
Commentary Eurocode
Copyright European Concrete Platform ASBL, June 2008 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the European Concrete Platform ASBL. Published by the European Concrete Platform ASBL Editor Jean-Pierre Jacobs All information in this document is deemed to be accurate by the European Concrete Platform...
Field Vane Test FVT
1 Examples of correction factors to obtain the undrained shear strength from the measured value are shown in figures G.1 and G.2, based on local experience and back calculations of slope failures. 2 Correction factors based on figure G.1 may be used in soft normally consolidated clays. 3 Correction factors based on figure G.2 may be used in overconsolidated clays. 4 If more than one method correcting the measured value is used, the value of the correction factor which will give the lowest...
Iodine
Iodine's use as a water purification method emerged after World War 2, when the U.S. military was looking for a replacement for Halazone tablets. Iodine was found to be in many ways superior to chlorine for use in treating small batches of water. Iodine is less sensitive to the pH and organic content of water, and is effective in lower doses. Some individuals are allergic to iodine, and there is some question about long term use of iodine. The safety of long-term exposure to low levels of...
Figure Centre of compression lever arm z and force distributions for deriving
Figure 6.16 Simplified models for bolted joints with extended end-plates Figure 6.16 Simplified models for bolted joints with extended end-plates 13 Where the members are not prepared for full contact in bearing, splice material should be provided to transmit the internal forces and moments in the member at the spliced section, including the moments due to applied eccentricity, initial imperfections and second-order deformations. The internal forces and moments should be taken as not less than...
Axial Loading Of Metal Dowel Connection Systems
The strength equations given in the following sub-sections assume that the tensile strength of fasteners will always exceed their withdrawal capacity from the connection. If, however, there is a need to evaluate the tensile strength of the fastener, it should be carried out in accordance with the requirements of EN 1993-1-1. The withdrawal capacity of nails loaded axially is dependent on the type of nail being used. Smooth round wire nails give the poorest result and with threaded nails the...
isolator units
elements constituting the isolation system. The devices considered in this section consist of laminated elastomeric bearings, elasto-plastic devices, viscous or friction dampers, pendulums, and other devices the behaviour of which conforms to 10.1 2 . Each unit provides a single or a combination of the following functions - vertical-load carrying capability combined with increased lateral flexibility and high vertical rigidity - energy dissipation, either hysteretic or viscous - lateral...
Table 1
Bending moment coefficients for flat slabs End support slab connection First Interior Interior End End End End support span support span G.GB6FI -G.G4FI G.G7SFI -G.GB6FI G.G63FI 1 Applicable to slabs where the area of each bay exceeds 30 m2, Qk, lt 1.25 Gk and qk lt 5 kN m2 2 F is the total design ultimate load, l is the effective span 3 Minimum span gt 0.85 longest span, minimum 3 spans 4 Based on 20 redistribution at supports and no decrease in span moments Whichever method of analysis is...
E SLS check
Table E15.2 also shows the results of a serviceability computation by FREW. For this, all partial factors are unity and there is no allowance for 'overdig'. The length of wall gives it fixity at the base, as can be seen in Figure E15.5, and the SLS bending moment is 119 kNm m, only 28 of the design ULS value. Calculations of this type, if done at all, would normally only be used to assess the maximum SLS deflection, which was calculated as 29 mm. This value should be used in assessing effects...
C No faade steel beam concrete cantilever edge strip present Figure Cc
1 When there is a concrete cantilever edge strip but no fa ade steel beam, EN 1994-1-1 2004 applies for the calculation of the moment capacity of the joint. b no concrete cantilever edge strip - no fa ade steel beam - see C.3.1.1. c concrete cantilever edge strip - no fa ade steel beam - see C.3.1.2. d no concrete cantilever edge strip - fa ade steel beam - see C.3.1.3. e concrete cantilever edge strip - fa ade steel beam - see C.3.1.4. A main beam B slab C exterior column D fa ade steel beam...
C Ultimate limit state design
Besides checking the stability and serviceability of individual foundations, it is essential to check the stability of the site, or part of the site on which a structure is to be built. The reader is referred to Section 9 and to D2.2. The basic requirement is represented by the inequality Vd-Rd where Vd is the ultimate limit state design load normal to the foundation, and Rd is the design bearing resistance of the foundation against loads normal to the foundation. This may appear to be a...
Measurement of soil suction
From a geotechnical point of view there are two components of soil suction as follows 1 Matric suction that part of the water retention energy created by the soil matrix. 2 Osmotic suction that part of the water retention energy created by the presence of dissolved salts in the soil water. It should be noted that these two forms of soil suction are completely independent and have no effect on each other. The total suction exhibited by a soil is obviously the summation of the matric and the...
Fundamental Laws of Continuum Mechanics
58 We have thus far studied the stress tensors Cauchy, Piola Kirchoff , and several other tensors which describe strain at a point. In general, those tensors will vary from point to point and represent a tensor field. 59 We have also obtained only one differential equation, that was the compatibility equation. 60 In this chapter, we will derive additional differential equations governing the way stress and deformation vary at a point and with time. They will apply to any continuous medium, and...