RC Design question

[Enhineyero]

I was thinking, The Strength design is governed by the servicibility and the material strength. Then Why do we allow/design beams to crack at the tension fiber? (because if you can check, when we design using USD method the stress at the tension fiber exceeds the Modulus of Rupture of concrete).

Since the tension fiber will crack even if it has not reached the design moment, then in terms of serviciblity the beam has already failed? because it would be an eyesore for the occupants (if there is no ceiling finish to cover it). Please enlighten me....

 

[hokie66]

Many cracks do not present a serviceability issue, even if visible to occupants. That depends on the width of the cracks.

 

[Teguci]

I've never used strength design to check servicability. For instance, in a pretensioned beam, servicability is checked against unfactored loads. Typically the design is initially controlled at release when the concrete is not yet up to 28 day strength and checked against some factor of rupture. The strength design is checked (factored loads) for final bending at mid span.

 

[dtoli]

SLS design, in terms of crack control, put limitations in crack width not only for occupants good feeling but mostly for structure durability. In many codes you would see a dependence on these.

Cracks in R.C. are unavoidable due to low concrete tensile strength and the way that reinforcement is calculated.

 

[TXStructural]

If you did not allow concrete to (theoretically) crack at service loads, you would be limited to the tensile strength of the concrete at the extreme fiber. You can design a member or project as unreinforced, using reinforcement to simply provide ductility, but it is not economical and severely limits options (think ancient Rome.)

And when we design with the notion that the concrete will crack, the cracks will be very small, until the steel yields. Current design practice limits strain in the reinforcement to 0.003 in./in. at ultimate loads, which are approximately 40% above service. This translates to a crack width at maximum service loads of 0.026", or less than 1/32 inch per foot.

That said, grade 40 or 60 steel reinforcement sized for strength will typically restrain crack widths very well at service loads. Grade 75/80 also provides good crack control. Flexural members reinforced with grades above will begin to have excessive crack widths, primarily because of the very low reinforcement ratios required to reach strength. Crack width is a function of the stress in a given area of steel crossing a crack, i.e., dL=P*L/(As*E). In a well-developed steel reinforcing bar the "L" length is short, and even shorter in welded wire mesh.