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.

Traffic and Highway Engineering

5th Edition

ISBN:9781305156241

Author:Garber, Nicholas J.

Publisher:Garber, Nicholas J.

Chapter20: Design Of Rigid Pavements

Section: Chapter Questions

Problem 12P

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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 NO tension softening (i.e., the stress in the cracked part stays at ft) and infinite compressive strength (i.e., compressive failure will never occur), 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 upwards.)
At what percent of compressive strength of concrete the stress in beam changes from directly proportional to varying with respect to depth.
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