Cracking Moment of a Concrete Section
Mediumcracking-momentserviceability
An uncracked concrete section has modulus of rupture fr = 3.2 MPa, gross second moment of area Ig = 4.5×10⁹ mm⁴, and distance yt = 300 mm from the gross centroid to the extreme tension face. Assume linear elastic behavior with no axial force. Find the cracking moment Mcr.
- A24.0 kN·m
- B96.0 kN·m
- C48.0 kN·m
- D48,000 kN·m
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Answer: C. 48.0 kN·m
Equation: at first cracking fr = Mcr·yt/Ig, so Mcr = frIg/yt. Inputs: fr = 3.2 N/mm², Ig = 4.5×10⁹ mm⁴, yt = 300 mm. Substitution: Mcr = 3.2(4.5×10⁹)/300 = 48×10⁶ N·mm = 48.0 kN·m (1 kN·m = 10⁶ N·mm). Wrong: 24.0 kN·m divides by 600 mm (twice yt, e.g. the full depth); 96.0 kN·m divides by 150 mm (half of yt); 48,000 kN·m converts N·mm to kN·m with 10³ instead of 10⁶. The gross Ig is correct before cracking; cracked I and fy are not used.
N·mm kN·m
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