User:Dpetlicki/Reinforced Concrete Column

=Introduction= Reinforced Concrete Columns refer to columns, structural members designed to carry compression loads, composed of concrete with an embedded steel frame to provide reinforcement. For design purposes, the columns are separated into two categories: short columns and slender columns.

Short Columns
The strength of short columns is controlled by the strength of the material and the geometry of the cross section. Reinforcing rebar is placed axially in the column to provide additional axial stiffness. Accounting for the additional stiffness of the steel, the nominal loading capacity Pn for the column in terms of the maximum compressive stress of the concrete fc', the yield stress of the steel fy , the gross cross section area of the column Ag, and the total cross section area of the steel rebar Ast
 * $$\begin{align}

P_\mathrm{n} &= 0.85f'_\mathrm{c}(A_\mathrm{g} - A_\mathrm{st}) + A_\mathrm{st}f_\mathrm{y}\\ \end{align}$$ where the first term represents the load carried by the concrete and the second term represents the load carried by the steel. Because the yield strength of steel is an order of magnitude larger than that of concrete, a small addition of steel will greatly increase the strength of the column.

Design Load
To give a conservative estimate and build redundancies into the final structural system, the ACI Building Code Requirements give a maximum reduced design load of $$\mathrm{{\phi}P_\mathrm{n}}\,\!$$ where $$\mathrm{\phi}\,\!$$ is an appropriate safety factor for the type of column used. For spiral columns
 * $$\begin{align}

{\phi}P_\mathrm{n(max)} &= 0.85\phi[0.85f'_\mathrm{c}(A_\mathrm{g} - A_\mathrm{st}) + A_\mathrm{st}f_\mathrm{y}]\\ \end{align}$$ where $$\mathrm{\phi} = 0.75\,\!$$. For tied columns
 * $$\begin{align}

{\phi}P_\mathrm{n(max)} &= 0.80\phi[0.85f'_\mathrm{c}(A_\mathrm{g} - A_\mathrm{st}) + A_\mathrm{st}f_\mathrm{y}]\\ \end{align}$$ where $$\mathrm{\phi} = 0.65\,\!$$. The additional reduction past the safety factor is to account for any eccentricities in the loading of column. Distributing a load toward one end of the column will produce produce a moment in the column and prevent the entire cross section from carrying the load, thus producing high stress concentrations towards that end of the column.

Spiral Columns
Spiral columns are cylindrical columns with a continuous helical bar wrapping around the column. The spiral acts to provide support in the transverse direction and prevent the column from barreling. The amount of reinforcement is required to provide additional load-carrying capacity greater than or equal to that attributed from the shell as to compensate for the strength lost when the shell spalls off. With further thickening of the spiral rebar, the axially loaded concrete becomes the weakest link in the system and the strength contribution from the additional rebar does not take affect until the column has failed axially. At that point, the additional strength from spiral comes into play and prevents catastrophic failure, instead giving rise to a much slower ductile failure.

The ACI Building Code Requirements put the following restrictions on amount of spiral reinforcement. ACI Code 7.10.4.2: For cast-in-place construction, size of spirals shall not be less than 3/8 in. diameter. ACI Code 7.10.4.3: Clear spacing between spirals shall not exceed 3 in., nor be less than 1in. Section 10.9.3 adds an additional lower limit to the amount of spiral reinforcement via the volumetric spiral reinforcement ratio ρs.


 * $${\rho}_{s}=0.45(\frac{A_g}{A_{ch}}-1)\frac{f'_c}{f_{yt}}$$

where Ach is the shell area, the total area between the outside of the column and the transverse reinforcement.

Tied Columns
Tied columns have closed lateral ties spaced approximately uniformly across the column. The spacing of the ties is limited in that they must be close enough to prevent barreling failure between them, and far enough apart that they do not interfere with the setting of the concrete. The ACI codebook puts an upward limit on the spacing between ties. ACI Code 7.10.5: Vertical spacing of ties shall not exceed 16 longitudinal bar diameters, 48 tie bar or wire diameters, or lease dimension of the compression member. If the ties are spaced too far apart, the column will experience sheer failure and barrel in between the ties.

Slender Columns
Columns qualify as being slender when their cross sectional area is very small in proportion to their length. Unlike Short Columns, Slender Columns are limited by their geometry and will buckle before the concrete or steel reinforcement yields.

Column