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.
 

figure-co4-2b.jpg

 

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

 

Working Stress Analysis for Concrete Beams

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

  1. 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.
  2. Crack Concrete Stage – Elastic Stress range
  3. Ultimate Stress Stage – Beam Failure
wsd-beam-analysis-crack-uncrack.jpg

 

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