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"l is a coefficient which takes account of the bond properties of the bars = 1 for high bond bars = 0.5 for plain bars.

"2 is a coefficient which takes account of the duration of the loading or of repeated loading = 1 for a single short-term loading

= 0.5 for sustained loads or many cycles of repeated loading Bs is the stress in the tension steel calculated on the basis of a cracked section.

Bsr is the stress in the tension steel calculated on the basis of a cracked section under the loading which will just cause cracking at the section being considered.

(Note: Bs/Bsr can be replaced by M/Mcr for flexure or N/Ncr for pure tension). M is zero for uncracked sections.

The critical material properties required to enable deformations due to loading to be assessed are the tensile strength and the effective modulus of elasticity of the concrete.

Table 3.1 indicates the range of likely values for tensile strength. In general, a best estimate of the behaviour will be obtained if fctm is used.

An estimate of the modulus of elasticity of the concrete may be obtained from Table 3.2. Creep may be allowed for by using an effective modulus calculated from Equation (A4.3):

where

0 is the creep coefficient (see Table 3.3)

Shrinkage curvatures may be assessed by using Equation (A4.4)

where

1/rcs is the curvature due to shrinkage ecs is the free shrinkage strain (see Table 3.4)

S is the first moment of area of the reinforcement about the centroid of the section

1 is the second moment of area of the section ae is the effective modular ratio = Es/Ecef

S and I should be calculated for the uncracked condition and the fully cracked condition, the final curvature being assessed by use of Equation (A4.1).

(3) The most rigorous method of assessing deflections using the method given in (2) above is to compute the curvatures at frequent sections along the member and then calculate the deflection by numerical integration. The effort involved in this is not normally justified and it will be acceptable to compute the deflection twice assuming the whole member to be in the uncracked and fully cracked condition in turn and then employ Equation (A4.1). The approach given in a) above is not directly applicable to cracked sections subjected to significant normal force.

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