Civil Engineering Reference
In-Depth Information
transferred to the building core by a tiered series of strut-and-tie brackets, each sharing
the total shear force equally, Figure 3.22. This adaptability of reinforced concrete is
due to the ductility described in
3.7
. However, concrete is only ductile in this sense if
it cracks due to extension of the reinforcement before it fails in concrete compression,
emphasising the importance of ensuring that the compressive members of the truss are
adequately dimensioned.
Although concrete is adaptable and a variety of strut-and-tie models may be used
to solve any particular problem, the model that mirrors most closely the elastic fl ow
of forces is least likely to suffer prejudicial cracking, although it may not be the most
economical or buildable option. Choosing the most appropriate model requires some
experience.
The designer of reinforced and prestressed concrete structures will be faced with
many examples of these special areas, such as bridge deck diaphragms, brackets and
halving joints, sudden changes in section or the zones immediately behind concentrated
loads such as the attachment of stay cables to a bridge deck.
3.11.2 Limits of elastic analysis
The stresses in an elastic material may be analysed using elastic methods, such as fi nite
element analysis. However reinforced concrete is not an elastic material, such as steel
for instance, but a composite and such methods are not strictly applicable. An example
is the analysis of a deep beam loaded with two concentrated loads, Figure 3.23 (a).
An elastic analysis of the beam would show a stress diagram that had a very deep
compression zone, and a shallow tensile zone, yielding a lever arm that did not exploit
the full depth of the beam. If the beam was to be reinforced in accordance with this
elastic stress diagram, it would require an area of tensile reinforcement spread over the
bottom quarter of the beam.
Figure 3.23
Stress diagrams for deep beam
