# Shear Strength of Columns

**ICONS**

**A _{w }=** Effective body area of column cross-section

**f**Characteristic cylinder compressive strength of concrete

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

_{cd}=**f**Design yield strength of longitudinal reinforcement

_{yd}=**L**Free height of column between beams, free span of beam between column or curtain faces

_{n }=**M**Moment at the lower end of the column's free height, based on the column shear calculation

_{a }=**M**At the upper end of the column's free height, the moment

_{ü }=**M**moment at the upper end of the column is the moment at the work floor.

_{hü (i) }= The**M**is the moment at the lower end of the column at the work floor.

_{ha (i) }= It**M**is the moment at the lower end of the column in the upper floor of the studied floor.

_{ha (i + 1)}= It**M**the moment at the upper end of the column in the lower floor of the studied floor.

_{hü (i-1)}= It is**M**The moment of bearing strength calculated according to f

_{ra}=_{cd}and f

_{yd}at the lower end of the free height of the column or curtain

**M**The moment of bearing strength calculated according to f

_{rü}=_{cd}and f

_{yd}at the upper end of the free height of the column or curtain

**M**The moment of positive or negative bearing strength calculated according to f

_{ri}=_{cd}and f

_{yd}on the column or wall face at the left end i of the beam

**M**Negative or positive moment of bearing strength calculated according to f

_{rj}=_{cd}and f

_{yd}on the column or wall face at the right end j of the beam

**V**Contribution of the concrete to the shear strength

_{c }=**V**Shear force based on column transverse reinforcement calculation

_{e }=**7.3.7. Shear Safety of Columns**

**7.3.7.1 -** Shear force *V *_{e to} be taken as basis for transverse reinforcement calculation in columns , **Eq. It will** be calculated with **(7.5)** .

*V *_{e} = ( *M *_{a} + M _{ü} ) **/** l _{n } **(7.5)**

**For** the calculation of *M *_{a} and *M *_{u} in **Eq. (7.5)** , if **Equation (7.3)** is fulfilled at the lower and / or upper ends of the column , **7.3.7.2** will be applied , and if not, **7.3.7.3** will be applied ( **Figure 7.5** ). The sum of the shear force calculated from the earthquake increased with *D* with the vertical loads , **Eq. If ***V *_{e} calculated by **(7.5)** is smaller than *V *_{e} , this shear force will be used instead.

**Figure 7.5 7.3.7.2 - The** moment *M *_{p,} which is the sum of the moment capacities at the ends of the beams joining to the **joint point where Equation (7.3)** is provided, will be calculated:

∑ *M *_{p }**= ***M *_{pi} + *M *_{pj } **(7.6)**

In cases where a more precise calculation is not made, *M *_{pi} ≈1.4 *M *_{ri} and *M *_{pj} ≈1.4 *M *_{rj} can be taken. ∑ The moment *M *_{p} will be distributed to the columns in proportion to the moments obtained according to **Section 4** at the joining ends of the columns, and the moment obtained at the lower or upper end of the relevant column as a result of the distribution will be considered as *M *_{a} or *M *_{u} in **Equation (7.5)** . **Equation (7.6)** will be applied separately for both directions of the earthquake and the maximum obtained in each direction ∑ *M *_{p}** **its value will be based on distribution.

**Eq. (7.3)** 'provided that although **Eq. (7.5)** ' one of *M *_{a} or *M *_{ü} 'are calculation, to stay on the safe side, **7.3.7.3** ' to be made to.

** 7.3.7.3 - The** moments at the ends of the columns joining the node point where **Equation (7.3)** cannot be provided **shall** be calculated as the moment capacities of the columns and **Equation. (7.5)** 't *M *_{a} and / or *M *_{ü} will be used. Torque capacities, in cases where a more accurate analysis is performed, *M *_{pa} ≈1.4 *M *_{ra} and *M *_{pi} ≈1.4 *M *_{r} can be taken. *In the* calculation of *M *_{pa} and *M *_{pü} moments, in accordance with the direction of the earthquake, *N *_{d} axial forces will be taken into account.

**7.3.7.4 -** Moment *M *_{a} at the lower end of columns connected to the foundation _{shall} also be calculated as moment capacities according to **7.3.7.3** .

**7.3.7.5 -** Shear force calculated by **Equation (7.5)** , *V *_{e} , the shear force calculated under the combined effect of vertical loads and earthquake loads multiplied by the load coefficients **shall** not be taken less than *V *_{d} and will also **meet** the conditions given in **Eq. (7.7).** . **In** case the second condition in **Equation (7.7) is** not fulfilled, the earthquake calculation will be repeated by increasing the cross-section dimensions as necessary.

**7.3.7.6 - In the calculation of the** column transverse reinforcement according _{to the} shear force *V *_{e} , the contribution of the concrete to the shear strength, *V *_{c} , will be determined according to TS 500. However, in the calculation of the transverse reinforcement in the column confinement zones defined in **7.3.4.1** , if the shear force consisting only of seismic loads is greater than half of the total shear force under seismic condition and at the same time the condition *N *_{d} ≤ 0.05 *A *_{c} f _{ck} is met, the contribution of concrete to shear strength is *V *_{c} = 0 will be taken.

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