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Firmen-Angaben Hinweis! Willkommensnachricht Hier kann die Willkommensnachricht in den 3 Perinorm Sprachen angepasst werden. Klicken Sie dann auf Suchen. Klicken Sie dazu auf Zu Gruppen zuordnen. The major changes in the revision were on the following lines: a The concept of limit state which provides a rational approach, taking into account variations in material strengths and loads on semi-probabilistic basis, had been introduced. This, in fact, was a rationalization of the ultimate load method, covered in the earlier version.
Consequently, the Code covered 3 types of structures, the types being associated with the permissible tensile stress in concrete. Limitations on total chloride and sulphate content of concrete had also been given. IS has since been revised as IS : Code of practice for plain and reinforced concrete fourth revision. In IS , major changes have been incorporated in provisions relating to materials, workmanship, inspection and testing, and general design requirements.
In view of the attempt at unification between provisions i 4. Considering this aspect as also the need for a complete review of the provisions of the Code in light of the latest international developments and the improved practices being followed now, a full scale revision of the Code has been brought out.
In this revision, the following major changes have been incorporated: a As mentioned, the provisions have been aligned with the revised IS It should be noted that the effective height of a column in the two plan directions may be different.
In Table 3. Increase in this scale corresponds to a decrease in end fixity. An appropriate value can be assessed from 3. 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. Where the column is connected to a foundation structure, this should be of a form specifically designed to carry moment. The end of the column is connected monolithically to beams or slabs on either side which are shallower than the overall dimension of the column in the plane considered.
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.
The end of the column is unrestrained against both lateral movement and rotation e. The considerations of deflection see 3. An allowance for them is made in the design requirements for slender columns see 3. Sub-clause 3. When a column is subject only to an axial load with no significant applied moment, as in the case of columns supporting a symmetrical arrangement of approximately equally loaded beams, only the design ultimate axial force need be considered in design together with a design moment representing a nominal allowance for eccentricity, equal to that recommended in 3.
Where biaxial bending is considered, it is only necessary to ensure that the eccentricity exceeds the minimum about one axis at a time. The appropriate values of K may be found iteratively, taking an initial value of 1. It may be assumed that the initial moment at the point of maximum additional moment i. Assuming the column is bent in double curvature, M1 should be taken as negative and M2 positive.
It will be seen from Figure 3. The initial moment Mi is the maximum moment at the critical section calculated for the ultimate limit state. These additional moments are then combined with the appropriate initial moments to obtain total design moments in the two directions. The critical section is then designed to withstand the design ultimate axial load, N, plus the total design moments in the two directions. The additional moment referred to in 3. The moment will act in a direction such that it increases the absolute magnitude at the critical section.
In such cases, an average ultimate deflection may be applied to all the columns. Where there are columns both above and below a joint, the beams or slabs should be designed to withstand the sum of the additional design moments at the ends of the two columns. They are based on Figure 2. Within the recommended limits of slenderness no specific check is necessary. Where no finishes susceptible to damage as a result of deflection are present, an unbraced column within the recommended limits of slenderness see 3.
If checks are needed, guidance on appropriate limits is given in section 3 of BS A more lightly-loaded column subject to bending should be considered as a beam for the purpose of crack control. Ac gross area of concrete at a cross-section. Asc area of compression reinforcement, per unit length of wall. The supports should be able to transmit forces assumed equal in magnitude to the sum of the following: a the simple static reactions to the sum of the applied design ultimate horizontal forces at the point of lateral support; and b 2.
When construction is designed to be simply supported by the wall, the eccentricity may be assessed as for plain walls see 3. When a shear connection is assumed between vertical edges of adjacent walls, an appropriate elastic analysis may be used provided the shear connection is designed to withstand the design forces.
The cross-section of the wall should be designed to resist the appropriate design ultimate axial load and transverse moment. The assumptions made in the analysis of beam sections apply see 3. Considering only axial forces and in-plane moments, the distribution of force along the wall is calculated by elastic analysis, assuming no tension in the concrete see 3. The transverse moments are calculated see 3. At various points along the wall, effects a and b are combined and checked using the assumptions of 3.
The effects should be assessed in stages as follows. Considering only axial forces and in-plane moments the distribution of force along the wall is calculated by elastic analysis, assuming no tension in the concrete see 3.
Effects a and b are combined and each unit length is considered as a slender column and designed as such in accordance with 3. Appropriate allowance for this is made by considering such walls as slender columns bent about the minor axis see 3. NOTE For gable walls to pitched roofs, lo may be measured mid-ways between eaves and ridge.
In the case of a slender wall further eccentricity can arise as a result of deflection under load. Procedures allowing for this are given in 3. Where there is an in situ concrete floor on either side of the wall, the common bearing area may be assumed to be shared equally on each floor.
NOTE For concrete of grades lower than 25 and lightweight aggregate concrete, the figure of 0. Guidance is given in 3. Wherever provided, the quantity of reinforcement should be in each direction at least: a for grade 0.
It should consist of small diameter bars, relatively closely spaced, with adequate cover near the exposed surface. When provided it should be dispersed half near each face. It needs to be provided only in the area of wall found to be in tension under design service loads. It should be arranged in two layers and conform to the spacing rules given in 3. When, however, staircases surrounding open wells include two spans that intersect at right angles, the load on the areas common to both spans may be assumed to be divided equally between the two spans.
When staircases or landings that span in the direction of the flight are built at least mm into walls along part or all of their length, a mm strip adjacent to the wall may be deducted from the loaded area. AB total cross-sectional area of reinforcement parallel to the shorter side of a slab. No redistribution of moments should be made.
See 3. Use 3. The lower nodes of the truss lie at the intersections of the centre-lines of the piles with the tensile reinforcement. The whole of the force from the piles with centres lying outside this line should be considered to be applied outside this line. The maximum shear capacity may also be limited by the provisions of 3. BS gives guidance on accuracy and permissible deviations.
The partial safety factors will, on a design based on nominal dimensions, provide for all normal permissible deviations. When large permissible deviations are allowed for small highly-stressed members, it may be necessary to base the design on net dimensions after allowance for the maximum specified permissible deviation; this would occur rarely.
However, when reinforcement is located in relation to more than one face of a member, e. However, where the permissible deviation on member size is greater than 5 mm, 5 mm, 10 mm and 10 mm for the four categories respectively, larger deductions should be made or the cover increased. This may lead to reductions in resistance moments exceeding the percentage allowed for in the normal value of the partial safety factors.
In the design of a particularly critical member, therefore, appropriate adjustment to the effective depth assumed may be necessary. They should generally be at right angles to the direction of the member. If special preparation of the joint faces is required, it should be specified.
In general, movement joints in the structure should pass through the whole structure in one plane. Information on various types of movement joints is given in section 8 of BS Where a building is divided by expansion joints into structurally independent sections, each section should have an appropriate tying system.
Reinforcement provided for other purposes may be regarded as forming part of, or the whole of, these ties. At re-entrant corners or at substantial changes in construction, care should be taken to ensure that the ties are adequately anchored or otherwise made effective. They should be effectively continuous throughout their length and should be anchored to the peripheral ties at each end unless continuing as horizontal ties to columns or walls.
They may, in whole or in part, be spread evenly in the slabs or may be grouped at or in beams, walls or other appropriate positions, but at spacings generally not greater than 1. In walls they should be within 0. Whenever walls occur in plan in one direction only e. The length which may be considered lost should be taken as the length between adjacent lateral supports or between a lateral support and a free edge.
Further information is given in 2. Where the peripheral tie is located within the wall, only such horizontal tying as is required to anchor the internal ties to the peripheral ties needs to be provided see 3. The tie should be capable of resisting a tensile force equal to the maximum design ultimate dead and imposed load received by the column or wall from any one storey. The design load is that assessed in accordance with 2. Where a column or a wall at its lowest level is supported by an element other than a foundation, a general check for structural integrity should be made in accordance with 3.
Where this is done, the bundle or pair should be treated as a single bar of equivalent area for all purposes in section 3. In no situation, even at laps, should more than four bars be arranged in contact.
Where reinforcement is to fit between two concrete faces, the permissible deviations recommended in 3. The minimum quantities recommended in 3. Ac total area of concrete. As minimum recommended area of reinforcement. Asc area of steel in compression. Ast area of transverse steel in a flange.
The minimum number of longitudinal bars in a column should be four in rectangular columns and six in circular columns, and the size of bar should be not less than 12 mm. No bar within a compression zone should be further than mm from a restrained bar. The size and spacing of the ties should be in accordance with 3. These horizontal bars should be evenly spaced and be not less than one-quarter of the size of the vertical bars and not less than 6 mm.
The spacing of links should not exceed twice the wall thickness in either the horizontal or vertical direction. In the vertical direction it should be not greater than 16 times the bar size. All vertical compression bars should be enclosed by a link. Provided this is done, local bond stress may be ignored. It may be taken as the force in the bar divided by its effective surface anchorage area see 3.
It should not exceed the appropriate value obtained from 3. For bars in tension in slabs or in beams where minimum links have been provided in accordance with Table 3. This does not apply to slabs. Values for anchorage lengths are given in Table 3. When condition b is not satisfied, the anchorage bond stress should be taken as that appropriate to the individual bars or wires in the sheet.
They should be placed, if possible, away from points of high stress and should preferably be staggered. Laps in fabric may be layered or nested to maintain the lapped bars in one plane. At the lap the links should be at least one-quarter the size of the smaller bar and the spacing should not exceed mm. Lap lengths for unequal size bars or wires in fabric may be based upon the smaller bar.
The following provisions also apply: a where a lap occurs at the top of a section as cast and the minimum cover is less than twice the size of the lapped reinforcement, the lap length should be increased by a factor of 1. Values for lap lengths are given in Table 3.
The concrete cover for the sleeve should be not less than that specified for normal reinforcement. If a longer length of weld is required, it should be divided into sections and the space between runs made not less than five times the size of the bar.
Any length of bar in excess of four bar-diameters beyond the end of the bend and which lies within the concrete in which the bar is to be anchored may also be included for effective anchorage. In addition for a bar in the tension zone, one of the following distances for all arrangements of design ultimate load should be considered: c an anchorage length appropriate to its design strength 0. Simplified rules for curtailment are also given in 3. Where a cantilever forms an extension beyond the end support of a continuous beam or slab, care should be taken to ensure that the top steel in the adjacent span extends beyond the point of contraflexure.
To control this, an amount of reinforcement equal to half the area of bottom steel at mid-span but not less than the minimum given in 3. It should have a full effective tensile anchorage into the support and extend not less than 0. Bottom reinforcement may be detailed: a as indicated in Figure 3. Where other conditions apply see BS Sub-clauses 3. The bar size should be in accordance with 3. In addition, unless crack widths are checked by direct calculation, the following rules will ensure adequate control of cracking for slabs subjected to normal internal and external environments: a no further check is required on bar spacing if either.
Design and detailing: prestressed concrete NOTE In this section the design strengths of materials are expressed in all tables and equations in terms of the characteristic strength of the material. As it is not possible to assume that a particular limit state will always be the critical one, design methods are given for the ultimate limit state and the serviceability limit states.
For lightweight aggregate concrete, design should be with reference to section 5 of BS The prestress losses will, in general, be greater than those for dense aggregate concrete; specialist literature gives guidance. This section gives methods of analysis and design which will in general ensure that, for prestressed concrete construction, the design requirements given in section 2 are met.
Other methods may be used proved they can be shown to be satisfactory for the type of structure or member considered. The design of class 3 members is usually controlled by ultimate limit state conditions or by deflection. Recommendations are given in 4. Fire test results or other evidence may be used to ascertain the fire resistance of a member or reference may be made to section 4 of BS The design loads to be used for the serviceability limit states see 4.
Consideration should be given to the construction sequence and to the secondary effects due both to the construction sequence and to the prestress particularly for the serviceability limit states.
Grades C35 and C40 are the minimum recommended for post-tensioning and pre-tensioning respectively. Redistribution involving a reduction of moment in columns will generally be ruled out, unless the design ultimate axial load and the prestress in the column are small.
Particular attention should be paid to possible instability during construction as well as when under load in their final positions. Members may collapse by tilting about a longitudinal axis through the lifting points. This initial tilting, which may be due to imperfections in beam geometry and in locating the lifting points, could cause lateral bending moments and these, if too high, could result in lateral instability.
The problem is complex and experience is the best guide. The following factors may require consideration: a beam geometry, i.
The design stresses due to the combined effects of lateral bending, dead load and prestress may need to be assessed; if cracking is possible the lifting arrangements should be changed or the beam should be provided with adequate lateral support.
The design loads should be those relating to the limit state considered see 2. The arrangements of load are: a alternate spans loaded with the maximum design load and all other spans loaded with the minimum design load; b all spans loaded with the maximum design load. Redistribution of the moments obtained by this method may be carried out for the ULS only, within the limits recommended in 4. In direct compression the stress should not exceed 0.
Elsewhere stresses should not exceed the following for different classes. No tensile stress. The design tensile stresses should not exceed the design flexural tensile strength of the concrete for pre-tensioned members nor 0. The limiting tensile stresses are 0. Values are given in Table 4. Similar provisions apply in later sub-clauses. Table 4. When the stresses in Table 4. Although cracking is allowed it is assumed that the concrete section is uncracked and that design hypothetical tensile stresses exist at the limiting crack widths in 4.
The design hypothetical tensile stresses for use in these calculations for members with either pre-tensioned or grouted post-tensioned tendons are given in Table 4. The cracking in prestressed concrete flexural members is dependent on the member depth and the design stress given in Table 4.
For composite construction when the flexural stresses given in Table 4. When additional reinforcement is contained within the tension zone, and is positioned close to the tension faces of the concrete, these modified design hypothetical tensile stresses may be increased by an amount that is in proportion to the cross-sectional area of the additional reinforcement expressed as a percentage of the cross-sectional area of the concrete in the tension zone.
For other percentages of additional reinforcement, the stresses may be increased in proportion up to a limit of 0. When a significant proportion of the design service load is transitory see 3.
Members with pre-tensioned tendons should have some tendons or additional reinforcement well distributed throughout the tensile zone of the section. Members with post-tensioned tendons should, if necessary, have additional reinforcement located near the tension face of the member. The design tensile stress should not, in general, exceed the appropriate value for a class 2 member.
Where this stress is exceeded, the section should, in design, be considered as cracked. For reinforced concrete, in all normal cases, deflections are controlled by limiting the ratio of span to effective depth. In general, this approach is not possible for prestressed concrete, because of major influence of the level of prestress. When it is considered necessary to calculate deflections, the methods outlined in 4.
In other cases, more rigorous calculations based on the moment-curvature relationship for cracked sections should be carried out. Suitable levels of design loading and design criteria should be selected from section 3 of BS where values for the relevant material properties may also be obtained.
In determining the effective modules of elasticity for the calculation of long term deflections, values for the creep coefficient may be determined from either 4. NOTE In both cases the strain at the outermost compression fibre is taken as 0. An alternative approach for obtaining the stress in the tendons is given in 4.
Aps area of prestressing tendons in the tension zone. As area of reinforcement. Mu design moment of resistance of the section. For bonded tendons, values of fpb and x may be obtained from Table 4. These values have been derived from the assumptions in 4. For unbonded tendons, values of fpb and x may be obtained from equations 52 and The value of fpb should not be taken as greater than 0.
The length l should normally be taken as the length of the tendons between end anchorages. This length may be reduced in the case of continuous multi-span members when an analysis is carried out to determine the minimum number of zones of inelasticity associated with each arrangement of design load.
Asv cross-sectional area of the two legs of a link. NOTE Where a duct occurs in a rib, the value of bv should be reduced by the size of the duct if ungrouted and two- thirds of the size if grouted. Mo moment necessary to produce zero stress in the concrete at the extreme tension fibre; in this calculation only 0.
V and M design shear force and bending moment values at the section due to the particular ultimate load condition. Vc design ultimate shear resistance of the concrete. Vco design ultimate shear resistance of a section uncracked in flexure.
Vcr design ultimate shear resistance of a section cracked in flexure. If necessary, shear reinforcement should be provided in accordance with 4. In the calculation of Vco, the design value of the prestress at the centroidal axis should be taken as 0.
In flanged members where the centroidal axis occurs in the flange the principal tensile stress should be limited to 0. For a section uncracked in flexure and with inclined tendons or compression zones, the design shear forces produced should be combined algebraically with the external design load effects.
The prestress development length should be taken as either the transmission length see 4. For a section cracked in a flexure and with inclined tendons or compression cords, the design shear forces produced should be combined with the external design load effects where these effects are increased.
A link should extend as close to the tension and compression faces as possible, with due regard to cover. The links provided at a cross-section should between them enclose all the tendons and additional reinforcement provided at the cross-section and should be adequately anchored see 3. When V exceeds 1. The lateral spacing of the individual legs of the links provided at a cross-section should not exceed dt.
The method adopted for reinforced concrete beams in 2. The methods of analysis described in 3. The design for shear should be in accordance with 4. The additional reinforcement may usually be assumed to be acting at its design stress 0.
Attention should also be paid to the effect of any frictional forces that may occur. If experimental evidence on performance is not available, account should be taken of the properties of the steel and of the concrete in calculating the losses of prestress, from these causes.
For a wide range of structures the simple recommendations given in 4. However, these recommendations are necessarily general and approximate.
A better estimate may often be obtained from experience, particularly with factory-produced units, where both the properties of the materials and of the units themselves are known and checked on a regular basis. The initial force should be taken as the value immediately after stressing in the case of pre-tensioning and immediately after transfer in the case of post-tensioning.
The relaxation factors given in Table 4. In the absence of the UK Certificate of Approval the 1 h relaxation value should be taken as the maximum value for the appropriate initial load stated in the British Standard for the product, BS for high tensile HT bars and BS for HT wire and strand. Specialist literature should be consulted in these cases.
In making these calculations it may usually be assumed that the tendons are located at their centroid. This should be calculated on the basis of half the product of the modular ratio and the stress in the concrete adjacent to the tendons averaged along their length; alternatively, the loss of prestress may be exactly computed on the basis of the sequence of tensioning.
Any method may be adopted that can be demonstrated to be appropriate for the particular problem being considered e. However, when the design relies on the torsional resistance of a member, the recommendations given in 2. As area of longitudinal reinforcement Asv area of two legs of closed links at a sectiona C torsional constant equals half the St. Venant value for the plain concrete section fyv characteristic strength of the links G shear modulus hmax larger dimension of a rectangular section hmin smaller dimension of a rectangular section sv spacing of the links T torsional moment due to ultimate loads vt torsional shear stress vt,min minimum torsional shear stress, above which reinforcement is required see Table 2.
Venant value calculated for the plain concrete section. The St. Venant torsional stiffness of a non-rectangular section may be obtained by dividing the section into a series of rectangles and summing the torsional stiffness of these rectangles. The division of the section should be arranged so as to maximize the calculated stiffness.
This will generally be achieved if the widest rectangle is made as long as possible. T-, L- or I- sections are divided into their component rectangles; these are chosen in such a way as to maximize h3 h in the following expression. Box and other hollow sections in which wall thicknesses exceed one-quarter of the overall thickness of the member in the direction of measurement may be treated as solid rectangular sections.
NOTE For other sections, specialist literature should be consulted. Recommendations for reinforcement for combinations of shear and torsion are given in Table 2. The links should be a closed shaped with dimensions x1 and y, as above. The clear distance between these bars should not exceed mm and at least four bars, one in each corner of the links, should be used. Additional longitudinal reinforcement required at the level of the tension or compression reinforcement may be provided by using larger bars than those required for bending alone.
The torsion reinforcement should extend a distance at least equal to the largest dimension of the section beyond where it theoretically ceases to be required.
Where the torsional shear stress in a minor component rectangle does not exceed vt,min, no torsion reinforcement need be provided in that rectangle. Where a more accurate assessment is desired, the equations given in 2. I second moment of area of the section le effective height of a column in the plane of bending considered lo clear height between end restraints! There may, however, be cases where there are key elements as defined in 2.
Details of such cases are given in 2. A horizontal member, or part of a horizontal member that provides lateral support vital to the stability of a vertical key element, should also be considered a key element. For the purposes of 2. The reaction should be the maximum that might reasonably be transmitted having regard to the strength of the attached component and the strength of its connection.
At each storey in turn, each vertical load-bearing element, other than a key element, is considered lost in turn. The design should be such that collapse of a significant part of the structure does not result. If catenary action is assumed, allowance should be made for the horizontal reactions necessary for equilibrium. The length of wall considered to be a single load-bearing element should be taken as the length between adjacent lateral supports or between a lateral support and a free edge see 2.
For the purposes of this subclause, a lateral support may be considered to occur at: a a stiffened section of the wall not exceeding 1.
Serviceability calculations 3 3. The purpose of this section is to provide further guidance when the first of these approaches is adopted. In addition this information will be of use when it is required not just to comply with a particular limit state requirement but to obtain a best estimate of how a particular structure will behave, for example when comparing predicted deflections with on-site measurements.
If a best estimate of the expected behaviour is required, then the expected or most likely values should be used. In contrast, in order to satisfy a serviceability limit state, it may be necessary to take a more conservative value depending on the severity of the particular serviceability limit state under consideration, i. Failure here means failure to meet the requirements of a limit state rather than collapse of the structure. It is clear that serviceability limit states vary in severity and furthermore what may be critical in one situation may not be important in another.
Guidance on the assumptions regarding loads and material values are given in 3. This shortcoming can in many cases be at least partially overcome by providing an initial camber. If this is done, due attention should be paid to the effects on construction tolerances, particularly with regard to thicknesses of finishes. This shortcoming is naturally not critical if the element is not visible. NOTE These values are indicative only. These values also apply, in the case of prestressed construction, to upward deflections.
All elements should be detailed so that they will fit together on site allowing for the expected deflections, together with the tolerances allowed by the specification. Loss of performance includes effects such as excessive slope and ponding. Where there are any such specific limits to the deflection that can be accepted, these should be taken account of explicitly in the design. Excessive accelerations under wind loads that may cause discomfort or alarm to occupants should be avoided.
NOTE For guidance on acceptable limits, reference should be made to specialist literature. Unless partitions, cladding and finishes, etc. NOTE For further guidance reference should be made to specialist literature. For members that are visible, cracking should be kept within reasonable bounds by attention to detail. As a guide the calculated maximum crack width should not exceed 0.
For members in aggressive environments, the calculated maximum crack widths should not exceed 0. Where cracking may impair the performance of the structure, e. For prestressed members, limiting crack widths are specified in section 2 of BS Generally, for best estimate calculations, expected values should be used. For calculations to satisfy a particular limit state, generally lower or upper bound values should be used depending on whether or not the effect is beneficial.
The actual values assumed however should be a matter for engineering judgement. For loads that vary with time, e. Generally, in serviceability calculations both best estimate and limit state it will be sufficient to take the characteristic value. When calculating deflections, it is necessary to assess how much of the load is permanent and how much is transitory.
The proportion of the live load that should be considered as permanent will, however, depend on the type of structure. Where a single value of stiffness is used to characterize a member, the member stiffness may be based on the concrete section.
In this circumstance it is likely to provide a more accurate picture of the moment and force fields than will the use of a cracked transformed section, even though calculation shows the members to be cracked.
Where more sophisticated methods of analysis are used in which variations in properties over the length of members can be taken into account, it will frequently be more appropriate to calculate the stiffness of highly stressed parts of members on the basis of a cracked transformed section.
The modulus of elasticity may be corrected for the age of loading where this is known. Attention is, however, drawn to the large range of values for the modulus of elasticity that can be obtained for the same cube strength.
It may therefore be appropriate to consider either calculating the behaviour using moduli at the ends of the ranges given in Table 7. Reference may be made to Section 7 for appropriate values for creep and shrinkage in the absence of more direct information. Item a corresponds to the case where the section is cracked under the loading considered, item b applies to an uncracked section.
Under short-term loading the modulus of elasticity may be taken as that obtained from 3. Assessment of the stresses by using a requires a trial-and-error approach.
Calculation by means of a computer or programmable calculator is straightforward. In assessing the total long-term curvature of a section, the following procedure may be adopted. NOTE In assessing the transformed steel area, the modular ratio should be as defined above. Ss is the first moment of area of the reinforcement about the centroid of the cracked or gross section, whichever is appropriate.
These are as follows. Because the dead load is known to within quite close limits, lack of knowledge of the precise imposed load is not likely to be a major cause of error in deflection calculations. Imposed loading is highly uncertain in most cases; in particular, the proportion of this load which may be considered to be permanent and will influence the long-term behaviour see 3.
Considerable differences will occur in the deflections depending on whether the member has or has not cracked. Finishes and rigid partitions added after the member is carrying its self-weight will help to reduce the long- term deflection of a member.
As the structure creeps, any screed will be put into compression, thus causing some reduction in the creep deflection. The screed will generally be laid after the propping has been removed from the member, and so a considerable proportion of the long-term deflection will have taken place before the screed has gained enough stiffness to make a significant contribution.
If partitions of blockwork are built up to the underside of a member and no gap is left between the partition and the member, creep can cause the member to bear on the partition which, since it is likely to be very stiff, will effectively stop any further deflection along the line of the wall. If a partition is built on top of a member where there is no wall built up to the underside of the member, the long-term deflection will cause the member to creep away from the partition.
The partition may be left spanning as a self-supporting deep beam that will apply significant loads to the supporting member only at its ends. Thus, if a partition wall is built over the whole span of a member with no major openings near its centre, its mass may be ignored in calculating long-term deflections.
A suitable approach for assessing the magnitude of these effects is to calculate a likely maximum and minimum to their influence and take the average. Deflections may be calculated directly from this equation by calculating the curvatures at successive sections along the member and using a numerical integration technique. Alternatively, the following simplified approach may be used: equation 11 where l is the effective span of the member; 1 is the curvature at mid-span or, for cantilevers, at the support section; rb K is a constant that depends on the shape of the bending moment diagram.
As the calculation method does not describe an elastic relationship between moment and curvature, deflections under complex loads cannot be obtained by summing the deflections obtained by separate calculation for the constituent simpler loads. A value of K appropriate to the complete load should be used.
Table 3. The usual formulae for the end deflection of cantilevers assume that the cantilever is rigidly fixed and is therefore horizontal at the root. In practice, this is by no means necessarily so, because the loading on the cantilever itself, or on other members to which the cantilever connects, may cause the root of the cantilever to rotate. There are two sources of root rotation which may occur. First, rotation of the joint in the frame to which the cantilever connects see Figure 3.
This problem will require attention only when the supporting structure is fairly flexible. Secondly, even where the cantilever connects to a substantially rigid structure, some root rotation will occur. This is because the steel stress, which is at a maximum at the root, should be dissipated into the supporting structure over some length of the bar embedded in the support.
To allow for this, it is important to use the effective span of the cantilever as defined in 3. If Table 3. The problem of estimating the deflection of two-way spanning slabs is not simple.
Before they crack, slabs will behave substantially as elastic, isotropic slabs. As soon as cracking occurs, the slabs become anisotropic, the amount of this anisotropy varying continuously as the loading varies, and so a reliable determination of the moment surface for the slab under any particular load is not normally practicable.
Deflections of slabs are therefore probably best dealt with by using the ratios of span to effective depth. However, if the engineer feels that the calculation of the deflections of a slab is essential, it is suggested that the following procedure be adopted. A strip of slab of unit width is chosen such that the maximum moment along it is the maximum moment of the slab, i.
The deflection of the strip is then calculated as though it were a beam. This method will be slightly conservative. This will be particularly true for fairly shallow members.
Figure 3. Equation 12 in 3. It should be remembered that cracking is a semi-random phenomenon and that an absolute maximum crack width cannot be predicted. The formula is designed to give a width with an acceptably small chance of being exceeded, thus an occasional crack slightly larger than the predicted width should not be considered as cause for concern.
However, should a significant number of cracks in a structure exceed the calculated width, reasons other than the statistical nature of the phenomenon should be sought to explain their presence. Alternatively, as an approximation, it will normally be satisfactory to calculate the steel stress on the basis of a cracked section and then reduce this by an amount equal to the tensile force generated by the stress distribution defined in 3. In assessing the strains, the modulus of elasticity of the concrete should be taken as half the instantaneous values.
NOTE This approach makes a notional allowance for long-term effects. In pours that are subjected to either internal or external restraint, thermal stresses may develop which can cause cracking. Cracking can occur through two different mechanisms. Cracking due to differential temperature changes is most common in massive pours.
Since the low thermal conductivity of concrete prevents rapid heat dissipation, the temperature in the mass of concrete increases.
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