What is the Cracking Moment?
The Cracking Moment, also known as Mcr is the moment that when exceeded causes concrete to begin cracking. This moment is necessary to find out which Moment of Inertia should be used when calculating Deflection.
Find the Cracking Moment:
- Find the Modulus of rupture (fr):
f_{r} = 7.5\sqrt{f'_c}
where:
f'c = The compression strength of the concrete (e.g. 4 ksi, 6 ksi)
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Note: If lightweight concrete is being used then fr should be factored by 0.75 (reduced by 25%). |
- Find yt:
yt is the distance from the center of gravity of the beam to the extreme fiber of the tension side (this neglects reinforcement).Therefore for a rectangular section, yt = {h\over 2}
- Find Ig:
Ig is the gross Moment of Inertia for the beam.
Note: For a rectangular section, Ig = {bh^3\over 12}
where:
b = the width of the concrete beam
h = the height of the beam
- Find Mcr:
M_{cr} = {f_rI_g\over y_t}