Introduction

The behaviour of reinforced concrete is not linear-elastic, even with loads within working stress limits, and it is therefore necessary to adjust either E or I depending on the magnitude of the applied load. In addition concrete is subjected to significant long term strains due to creep and shrinkage, which will affect the curvature and stiffness of a reinforced concrete structures.This chapter describes how the curvature and stiffness of a reinforced concrete section is calculated.

Stiffness presentation command is used for presentation of calculated stiffness. The procedure for calculation of stiffness is based on the requirements mentioned in chapter 7.4.3 from EN 1992-1-1. Generally, two states of cross-section are considered:

• I) uncracked cross-section - which is loaded below the level when tensile strength of concrete is reached, here the cross-section with tensile strength is used
• II) fully cracked cross-section - which is loaded above the level when tensile strength of concrete is reached, here the cross-section without tensile strength is used

The stiffness is decreased when the load achieve cracking moment (M_y,cr). The dependency of stiffness on cracking moment is visible from the following figure. The curve is not linear due to tensile stiffening which partly higher then cross-section completely without tensile strength

The behaviour of the reinforced cross-section can be also expressed in term of moment and strain (deformation) diagram. The final value of stiffness is calculated using interpolation formula between state (I) deformation for uncracked concrete section (ξ = 0) and state (II) deformation for fully cracked concrete section (no tension carries) (ξ = 1) dependently on the ratio of stress in reinforcement from cracking load and acting load.The dependency of cracking moment on strain in concrete is visible from the following figure.

The distribution of the reinforcement stress in crack and between cracks can be graphically expressed on the following figure. Reinforcement stress is higher in crack and concrete stress is zero in crack. The final values of stiffness is dependent on the tension stiffening of concrete in cracks based on distribution coefficient.

The plane of the equilibrium is calculated for particular state of cross-section using method described in chapter "Theoretical background" . There are used different stress-strain diagram towards the Capacity-response (ULS). Stress-strain diagram based on the serviceability limit state are used for the finding of the plain of the equilibrium. Generally, this command uses the iterative method for the interaction of the normal force (N) with uni-axial or bi-axial bending moments (M_y + M_z). Additionally, there is possibility to calculate short-term or long-term stiffness which is applied via modified stress-strain diagram.