Calculation of concrete beams

Unlike other ordinary construction materials, such as steel or timber, the characteristics of concrete render calculations – particularly in the case of statically undetermined structures – complicated. The main difficulty lies in cracking and the ensuing changes in stiffness. Non-linearity at higher strains, as well as long-time effects like creep, all contribute to the complexity. 

Calculation principles

The calculation uses member stiffness values calculated from a comprehensive and potentially non-linear section analysis. The method could be viewed as an iterative estimate of secant stiffness.

The calculation interprets non-linear behaviour from cracking into strain and curvature data, which influence the iteration as a load between the nodes corresponding to thermal load. Non-linear strain from creep and shrinkage are likewise converted to loads between nodes corresponding to thermal load. As the magnitude of creep and curvature depends on the distribution of section forces, the calculation of creep values also requires iteration.

Remaining deflection from earlier loadcases may also be added.

Effective stiffness

Inelastic strain at cracking

Inelastic strain and curvature of creep and shrinkage

Inelastic strain and curvature from previous loadcase

Creep and shrinkage mean that deflections remain in the beam after unloading. During the calculation, these deflections are stored for all relevant loadcases, and can be re-activated through Dependency. In other words, a current loadcase calculation may be influenced by a previous loadcase calculation. This way, the effect of a long-time load in one load combination can be made to influence another. When calculating the new loadcase, the inherited deflections will be treated as added deflections. 

Cracking in previous loadcase

Possible cracking in a load combination is stored during a calculation. Through the use of Dependency (more information can be found here: Guide to load combinations), the cracking from a previous load combination can be inherited, which may affect the analysis of the current load combination. 

Design theory

Bending reinforcement

Shear reinforcement

Flange reinforcement

End zone reinforcement

Recess beam

Control theory

Section properties

Stresses and strains at linear section analysis

Stresses and strains at non-linear section analysis

Elongation and curvature

Ultimate moment capacity

Shear capacity with shear reinforcement

Shear capacity of the shear reinforcement

Shear capacity of concrete

Rules for shear reinforcement

Resistance to spalling (hollowcore elements)

Control of splitting

Eigenfrequency calculations

Fire theory

References