ABSTRACT
The elastic analysis of a reinforced concrete section, by the modular ratio method, is applicable to the behaviour of the section under service loads only. The strength of the concrete in tension is neglected, and a linear stress-strain relationship is assumed for both concrete and reinforcement. The strain distribution across the section is also assumed to be linear. Thus, the strain at any point on the section is proportional to the distance of the point from the neutral axis and, since the stress-strain relationship is linear, the stress in the concrete is also proportional to the distance from the neutral axis. This gives a triangular distribution of stress, ranging from zero at the neutral axis to a maximum at the outermost point on the compression face. Assuming no slipping occurs between the reinforcement and the surrounding concrete, the strain in both materials is the same, and the ratio of the stresses in the two materials depends on the ratio of the modulus of elasticity of steel and concrete, known as the modular ratio α e. The value of E s is taken as 200 kN/mm2, but the value of E for concrete depends on several factors, including the aggregate type, the concrete strength, and the load duration. Commonly adopted values for sustained loads, are 15 for normal-weight concrete and 30 for lightweight concrete. The geometrical properties of reinforced concrete sections can be expressed in equivalent concrete units, by multiplying the reinforcement area by α e.
