Continuous deep beams - Reinforced Concrete Deep Beams - page 105

ratio of test to calculated strength ranged from 0.94 to 1.02 (mean 1.00 and
standard deviation 0.03). For the other beams, the prediction accuracy
depended upon the truss model used because the beams were not always
ductile enough fully to redistribute forces in accordance with the truss
model. If the model assumed full yield of the top reinforcement over the
support when in fact it did not yield, unconservative predictions resulted.

4.4 Truss models for continuous deep beams

This section reviews truss models in detail and describes specific models
suitable for continuous deep beams. These are discussed at some length
because the selection of truss model has a significant impact on capacity
predictions.
Truss models are based on the lower-bound theorem of plasticity which
states that:

If an equilibrium distribution of stresses can be found which balances the applied load and is
everywhere below yield or at yield, the structure will not collapse. Since the structure can
carry at least this applied load, it is a lower bound to the load carrying capacity of the
structure.
While the theorem has a rigorous mathematical basis, it is obvious to most
designers that if one can find a safe load path through the structure, it will be
a conservative lower bound to the true capacity. The structure will
undoubtedly find other more complex load paths with greater capacity. With
truss models, one produces a simple load path in the form of a truss and
checks or designs the components of the truss for the required load.
Truss models assume or require that:

i) equilibrium is satisfied
ii) concrete resists compression stresses only and has an effective
strength less than the specified design strength
iii) steel is required to resist all tensile forces
iv) the centroids of each truss member and the lines of actions of all
externally applied loads must coincide (this ensures that local
equilibrium is satisfied)
v) failure of the truss model occurs when a concrete compression
member crushes or when a sufficient number of steel tension
members reach yield to produce a mechanism.
Truss models are composed of three elements
i) steel tension members which are permitted to reach and sustain

yield stresses; collapse of the beam does not necessarily occur with
yielding of a single tension member; collapse occurs when
sufficient tension members yield to convert the truss into a
mechanism