# Sample Column Design

**Symbols**

**A _{c }**= Gross cross-section area of the column or wall end region

**A**= Core concrete area within the measure taken outside of the confinement reinforcement

_{ck}**A**= Along the height corresponding to the transverse reinforcement range, the cross-sectional area values of all hoops and crossties in the column are taken into account. sum of projections in perpendicular direction

_{sh}**b**= Cross-section dimension of column or wall end zone core (distance between outermost transverse reinforcement axes) for each of the horizontal directions perpendicular to each other

_{k}**b**= Width of the column in the direction of transverse reinforcement calculation

_{w }**f**= Characteristic cylinder compressive strength of concrete

_{ck }**f**= Design tensile strength of concrete

_{ctd}**f**= Characteristic yield strength of the transverse reinforcement

_{ywk}**N**= Axial force calculated under the combined effect of vertical loads and earthquake loads multiplied by load coefficients

_{d}**N**= defined for live loads in TS 498 Considering the live load reduction coefficients,

_{dm}*G*and

*Q*joint effect of vertical loads and

*E*earthquake effect

*G*+

*Q*+

*E*, the largest axial pressure forces calculated under

**s**= Transverse reinforcement spacing, spiral / winding reinforcement pitch

_{ }**ρ**= Reinforcement ratio

_{ }**ρ**= Volumetric ratio of spiral reinforcement in the column

_{s}**ϕ**= Reinforcement diameter

_{ }**E**= Earthquake load

**Q**= Live load

**G**= Dead load

As an example, the S02 column on the 11

^{th}floor of the building will be shown. The S02 column is a structural element containing C35 B420C reinforcement with a cross section of 80 * 80 and the concrete cover is determined as 4 cm. The material model used in the calculation is as follows.

#### Column Axial Force Control

According to TBDY 7.3.1.2, the gross cross-section area of the column, N

_{dm}, taking into consideration the live load reduction factor defined in TS 498, is the maximum of the axial compression forces calculated under the joint effect of vertical loads G and Q and E earthquake effect in case of G + Q + E loading. It should satisfy the condition Ac≥N_{dm}/(0.40f_{ck}) using the larger one. It should also be provided under the control of TS 500 7.4.1.

In the program, in the reinforced concrete design - columns tab, all loading combinations for the 11

^{th}floor S02 column under the heading Forces-Reinforcement areas are examined, and it is determined that the greatest axial compression force occurred for the G+Q +E case and 1.4G+1.6Q for all loading combinations.We can check whether the forces we get from the program meet the conditions as follows.

In the column report obtained from the program below, the control included in TS 500 7.4.1 is summarized as well as the TBDY 7.3.1.2 control.

Within the TS 500, the largest axial compressive force will be selected from among loading combinations. For TS 500, there is no requirement that the load combination contain an earthquake.

It can be seen that the calculated values are compatible with the report.

#### Determination of Column Transverse and Longitudinal Reinforcement

In accordance with TBDY 7.3, the minimum longitudinal reinforcement and transverse reinforcement of the column element we consider as an example will be determined first. The element strengths obtained with these reinforcements will be compared with the design forces obtained from the calculation. If the strength values are smaller than the design forces, the required reinforcement will be revised and the required element strength will be obtained.

In accordance with TBDY 7.3.4.1b article, in the case of N

_{d}> 0.20A_{c}f_{ck}(compression), the minimum total transverse reinforcement area in the confinement zones is calculated in such a way that the unfavorable conditions given below.Below are the calculations for the S1102 column.

Transverse reinforcement required in the coiling area max (A_{sh,1} , A_{sh, 2} ) = 4.50 cm ^{2}

4 arms in the projected transverse reinforcement plan 12 = 4.52 cm^{2}

The stirrup spacing selected on the vertical is 100 mm (TBDY 7.3.4.1a)

The minimum area of longitudinal reinforcement in columns cannot be less than 1% of the gross section. (TBDY 7.3.2.1)

-Predicted longitudinal reinforcement 20Φ22 = 76 cm2, pursantage ρ = 1.18%

The suitability of the recommended reinforcement for minimum transverse and longitudinal reinforcement has been checked below.

#### Column Transverse Reinforcement Control

According to TBDY 7.3.7.5, the shear force Ve, which will be taken as basis in the calculation of the transverse reinforcement of the columns, is used as the Resistance Excess Coefficient, D together with the vertical loads, and the shear force calculated from the earthquake Vd and must also meet the following conditions.

In the calculation of the column transverse reinforcement according to the shear force, V

_{c}, contribution of concrete to the shear strength will be determined according to TS 500. However, in accordance with TBDY 7.3.7.6, in the calculation of the transverse reinforcement in the column confinement regions, if the shear force consisting only of seismic loads is greater than half of the total shear force in seismic condition and at the same time , if the condition N_{d}≤0.05A_{c}f_{ck is}fulfilled, the contribution of concrete to shear strength is V_{c}= 0 is taken.The following values are obtained from reinforced concrete design - column -11th FLOOR S02 column.

-V_{G'+Q' }=14.2145 kN

-D * V _{E} = 80.8336 kN

-V _{G '+ Q} + D * V _{E} + 0.3E _{z} (G) = 98.1566 kN

-V _{E} / Ve = 80.8336 / 98.1566 = 0.82> 0.50

-Nd=1031.67 kN

As a result of the above conditions, V

_{c}= 0 and shear contribution of concrete will not be used in calculations.

As a result of the calculations made above in accordance with TBDY 7.3.4.1b, it is seen that the amount of transverse reinforcement provides the shear safety of the columns.

The column reports in the table above are from the shear reinforcement section. Manual control matches the report.

#### Column Reinforcement Control

M2-M3 interaction diagram was obtained against the normal force obtained for each load combination under the joint effect of vertical and earthquake loads in the design on the yield surface created for the projected column longitudinal reinforcements. It is checked whether the moment values obtained at the lower and upper ends of the column remain in this diagram. The amount of longitudinal reinforcement foreseen in accordance with TBDY 2018 7.3.2.1 provides the design values obtained from the calculations.

Below are the results of the capacity diagrams section obtained from the program.

P-M2-M3 diagrams can be checked under all loading combinations on the program interface. The moment values obtained at the upper and lower ends of the column remain in the diagram.

In the column report, reinforcement areas are given with the relevant forces in the reinforced concrete section.