under concentrated loads

*Abstract*

Bridge engineers have encountered difficulty in designing and assessing reinforced concrete bridge cantilevers against accidental wheel loads from deviated vehicles. This is because of the lack of understanding of the behaviour of reinforced concrete cantilever slabs under concentrated loads.

This dissertation examines both the elastic and collapse behaviour of
reinforced concrete cantilevers under concentrated loads.

To study the elastic behaviour, a patch load is transformed into a number
of point loads so that Jaramillo's elastic solution, which has been incorporated
in four Matlab programs, can be used to compute the deflections, bending
moments and twisting moments due to a patch load applied on an infinitely
long cantilever. The results from elastic analysis are plotted in graphs
which provide a general view of the elastic behaviour of cantilevers under
patch loads. Engineers can use the proposed Matlab programs in the design
of cantilevers.

To investigate the flexural failure of reinforced concrete cantilevers
under concentrated loads, both upper-bound and lower-bound flexural strengths
are assessed. Yield-line analysis is performed to evaluate the upper-bound
flexural strength. Five new yield-line mechanisms are proposed which
aim to improve the flexural strength predictions. Engineers can apply
these new yield-line mechanisms in the assessment of bridge cantilevers.
The lower-bound flexural strength is computed using *discontinuity-line
analysis*, a state-of-the-art lower-bound method. New techniques
to postulate discontinuity-line patterns are proposed for improving the lower-bound
flexural strength predictions and for analysing edge-stiffened cantilevers.
A lower-bound method is proposed for use by engineers to calculate
the effective length of a reinforced concrete cantilever resisting concentrated
loads. Key parameters influencing the lower-bound flexural strength
predictions from the discontinuity-line analysis are discussed. The
discontinuity-line method gives engineers an insight into the possible load-carrying
mechanisms in bridge cantilevers and hence allows them to obtain flexural
strength predictions with an adequate safety margin.

The shear behaviour of reinforced concrete cantilevers under concentrated
loads is also studied, and two empirical methods which relate the topology
of critical sections for shear to the schematic load paths are proposed.

An experimental program is carried out to investigate the effect of slab
reinforcement ratios, the presence of an edge beam and the load configuration
on the elastic and collapse behaviour of reinforced concrete cantilevers.
Non-linear finite element analysis is performed to model the behaviour
of the cantilevers tested for verifying its applicability. Modelling
techniques are recommended and the limitations are also discussed.

Finally, all the theoretical, empirical and numerical methods mentioned
above are used to predict the collapse load of all the cantilevers tested
and the results compared. Guidelines are provided for engineers to
design and assess bridge cantilevers.

[Cambridge University | CUED | Structures Group | Geotechnical Group]