The flexural strength (fr) of concrete measured from the bending test is always higher than the direct tensile strength (ft). In reality, the stress in the cracked part of the concrete is lower than ft. Also, failure may occur on the compressive side. Assuming 1) there is no tension softening in the cracked zone, i.e., tensile stress stays at ft; and 2) infinitely large compressive strength, draw the stress distribution over the depth of the beam at ultimate failure when the curvature of the section is approaching infinity. With this stress distribution, show that the upper bound of fr/ft is equal to 3.
The flexural strength (fr) of concrete measured from the bending test is always higher
than the direct tensile strength (ft). In reality, the stress in the cracked part of the
concrete is lower than ft. Also, failure may occur on the compressive side. Assuming
1) there is no tension softening in the cracked zone, i.e., tensile stress stays at ft; and 2)
infinitely large compressive strength, draw the stress distribution over the depth of the
beam at ultimate failure when the curvature of the section is approaching infinity. With
this stress distribution, show that the upper bound of fr/ft is equal to 3.
(Hint: On rotating the section, because the compressive stress can increase well beyond
ft, the neutral axis will continue to shift towards to the compression side.)
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