P(1) This Appendix sets out the procedures to be adopted when calculating deformations and describes a simplified calculation method suitable for use in the design of members such as frames, beams or slabs. P(2) The deformation of reinforced and prestressed concrete members is influenced by a great many factors, none of which are known with certainty. The calculated result is not regarded as an accurate prediction of the deflection which will be expected to occur. For this reason, the use of excessively sophisticated calculation methods is avoided.
A4.2 Requirements for the calculation of deformations
P(1) The calculation method adopted shall represent the true behaviour of the structure to an accuracy appropriate to the objectives of the calculation. In particular, where elements are expected to be cracked, the influence of the cracks on the deformations of the tension chord and of the corresponding compression chord shall be taken into account.
P(2) Where appropriate, the following shall be considered:
— Effects of creep and shrinkage
— Stiffening effect of the concrete in tension between the cracks.
— Cracking resulting from previous loadings
— The influence of indirect actions such as temperature
— Type of loading: static or dynamic
— The appropriate value of modulus of elasticity of the concrete, taking account of the aggregate type and maturity at time of loading.
P(3) It should be noted that, if cracking is expected under the actions considered, the principle of superposition is invalid for the calculation of deformations.
(4) Simplified methods may be used provided their degree of approximation is acceptable in the particular case considered.
(5) In buildings, it will normally be satisfactory to consider the deflections under the quasi-permanent combination of loading and assuming this load to be of long duration.
(6) It may occasionally be necessary to take into account deformations from causes other than flexure, for example shear or torsional deformations, or differential contraction of vertical members in tall buildings. These possibilities will not, however, be covered further in this code.
A4.3 Calculation method
(1) Two limiting conditions are assumed to exist for the deformation of concrete sections.
— the uncracked condition.
In this state, steel and concrete act together elastically in both tension and compression.
— the fully cracked condition.
In this state, the influence of the concrete in tension is ignored.
(2) Members which are not expected to be loaded above the level which would cause the tensile strength of the concrete to be exceeded anywhere within the member will be considered to be uncracked. Members which are expected to crack will behave in a manner intermediate between the uncracked and fully cracked conditions and, for members subjected dominantly to flexure, an adequate prediction of behaviour is given by Equation (A4.1) below.
where a is the parameter considered which may be, for example, a strain, a curvature, or a rotation. (As a simplification, a may also be taken as a deflection — see (3) below)
aI and aII are, respectively, the values of the parameter calculated for the uncracked and fully cracked conditions.
M is a distribution coefficient given by Equation (A4.2) below:
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