VM146
VM146
Bending of a Reinforced Concrete Beam
Test Case
A concrete beam reinforced with steel rods (of cross-sectional
area A) is subjected to a pure bending load M. Determine the depth
of the crack δck from the bottom
surface, the maximum tensile stress σt in the steel, and the maximum compressive stress σc in the concrete, assuming the cracking tensile strength
of concrete σct to be zero.
Analysis Assumptions and Modeling Notes
The bottom concrete element is lined with two spar elements
to match the assumption given in the reference of discrete (rather
than smeared) reinforcement. A zero Poisson's ratio and an infinite
crushing strength are also assumed for the concrete to match the reference
assumptions. An element width (in the X-direction) of 1.5 in. is
arbitrarily selected. Constraint equations are used along the beam
depth to conveniently apply the load and match the reference assumption
that cross-sections remain plane. Dummy PIPE288 pipe elements are used to "line" the constraint equation region
to provide the necessary rotational degrees of freedom at the nodes.
Up to five substeps are specified with automatic load stepping to
allow convergence of the crack nonlinearity.
Results Comparison
Five sets of integration points
(each set consisting of 4 points parallel to the X-Z plane) below
3.49 in. crack open, including one set at 3.32 in. from the bottom.
Three sets of integration points above 3.32 in. remain closed, including
one set at 4.18 in. from the bottom. Note that the integration points
are printed only if the element has cracked. A more exact comparison
with theory could be obtained with more elements along the depth of
the beam (and thus a closer spacing of integration points).
Stresst = SAXL in the spars (elements 13 and 14).
Stressc = SX in element 1 at nodes 9, 10, 19, or 20.
