# Cracking Moment

## Hollow Circular Beam with Known Cracking Moment

**Situation**

A concrete beam with cross section in Figure CO4-2B is simply supported over a span of 4 m. The cracking moment of the beam is 75 kN·m.

1. Find the maximum uniform load that the beam can carry without causing the concrete to crack, in kN/m.

A. 35.2 | C. 33.3 |

B. 37.5 | D. 41.8 |

2. Find the modulus of rapture of the concrete used in the beam.

A. 4.12 MPa | C. 3.77 MPa |

B. 3.25 MPa | D. 3.54 MPa |

3. If the hallow portion is replaced with a square section of side 300 mm, what is the cracking moment of the new section in kN·m?

A. 71.51 | C. 78.69 |

B. 76.58 | D. 81.11 |

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## Working Stress Analysis for Concrete Beams

Consider a relatively long simply supported beam shown below. Assume the load w_{o} to be increasing progressively until the beam fails. The beam will go into the following three stages:

- Uncrack Concrete Stage – at this stage, the gross section of the concrete will resist the bending which means that the beam will behave like a solid beam made entirely of concrete.
- Crack Concrete Stage – Elastic Stress range
- Ultimate Stress Stage – Beam Failure

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