Ductility of Concrete Beam-Column

[DTS419]

In reinforced concrete beam design, ACI sets limits on the concrete compressive strain to ensure a ductile failure (steel reinforcing yields before the concrete fails in compression). However, if a beam-column experiences both flexure and compressive axial load at the same time, the axial load will increase the compressive stress in the concrete compression block while at the same time decreasing the tension in the steel. How is a ductile failure ensured since the concrete compression block will reach its limit sooner?

 

[KootK]

Your design would transition to column design procedures in which case:

1) You don't necessarily ensure that the rebar yields first but;

2) Your phi factor (resistance side safety factor) is placed on a sliding scale wherein your capacity is reduced for more compression dominated members.

In this way, we attempt to achieve similar reliability for columns as we do for beams, albeit via a different strategy.

 

[DTS419]

Koot, makes sense.

Wouldn't it be appropriate to account for the axial compression stress when computing the moment strength of the beam? For example,

Mn = (As * Fy - P/2) * (d - a/2) where P = the axial load on the beam-column acting above the neutral axis

In this equation, the moment capacity is reduced by lowering the limit of the compression that can be applied by the internal couple of the tension in the steel (As * Fy) and the theoretical compression block (0.85 * f'c *a * b) by the amount of compressive stress applied from the axial load.

 

[KootK]

Wouldn't it be appropriate to account for the axial compression stress when computing the moment strength of the beam? For example,

Yes, and that's precisely what is done when you used column design procedures.

 

[DTS419]

Yes, and that's precisely what is done when you used column design procedures.

True, but could my proposed method above be used as a simple procedure to analyze an existing beam-column if you know the axial load and moment without having to developing an interaction diagram?

 

[KootK]

True, but could my proposed method above be used as a simple procedure to analyze an existing beam-column if you know the axial load and moment without having to developing an interaction diagram?

I don't believe so. By reducing calculated moment capacity, your proposal would encourage designers to add more rebar. And that would tend to reduce ductility. Something of that sort may well be better done by adjusting the equation for rho-max rather than the equation for moment capacity.

For what it's worth, one does not need to create a complete interaction diagram in order to design a basic beam column. The procedure for evaluating P-M pairs simplifies in a hurry when one avails themselves of the following:

1) Uniaxial bending.

2) Symmetry.

3) No compression reinforcement relied upon.

3) A single lager of reinforcement at the extreme tension face assumed to yield.

It pretty much boils down to just including the axial force in the determination of the compression block depth.