# Sample Shearwall Design

**Symbols**

* D *= Overstrength factor

*=*

**f**_{ck }*Characteristic cylinder compressive strength of concrete*

*=*

**f**_{yk }*Characteristic yield strength of longitudinal reinforcement*

*= Total wall height measured from the top of the foundation or the ground floor slab*

**H**_{w}*=*

**H**_{cr}*Shearwall critical height*

*= Shearwall or coupling-beam shearwall part length in plan*

**l**_{w}**(**

*=*

**M**_{p})_{t}*f*

_{ ck at the}base section of the shearwall, f

_{ yk}and the moment capacity calculated by considering the strength increase of the steel

**(**

*= The moment calculated under the combined effect of the vertical loads and earthquake loads multiplied by the load coefficients in the base section of the wall*

**M**_{d})_{t}*= The Load Bearing System Coefficient*

**R***= The vertical loads and earthquake loads multiplied by the load coefficients Shear force calculated under joint effect*

**V**_{d }*= Shear force taken as basis in transverse reinforcement calculation at column, beam, junction area and shearwall*

**V**_{e }

**β****=**

_{v }*Shear force dynamic magnification coefficient at wall*

*= Gross cross-section area of the wall without a gap, each shearwall piece in a coupling-beam shearwall, slab or each story piece in a hollow story*

**A**_{ch }*= Design tensile strength of concrete*

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

**f**_{ck }*= Transverse design yield strength of reinforcement*

**f**_{ywd}*= shear force taken as basis in transverse reinforcement calculation at column, beam, junction area and shearwall*

**V**_{e }*=*

**V**_{r }*Shear strength of column, beam or shearwall section*

**ρ**= Volumetric ratio of horizontal web reinforcements in the shearwall

_{sh }As an example, the design of the U-shaped shearwall group, which is the core shearwall named P1 on the ground story (first story above the basement) of the building, will be examined.

#### Column Axial Force Control

According to TBDY 7.6.1.1, the net area of the wall after the voids are removed, taking into consideration the live load reduction factor defined in N

_{dm}TS 498, is the result of the axial compressive forces calculated in the case of G+Q+E loading under the joint effect of G and Q vertical loads and E earthquake effect must satisfy the A_{c}≥N_{dm}/(0.35f_{ck}) condition using the largest. In the calculation of A_{c}and N_{dm}values inshearwalls, the entire section of the shearwall (sum of the wall parts) is taken into consideration.

In the program, in the reinforced concrete design - wall group tab, all load combinations for the ground story P01 shearwalls are examined in the forces flange, and the relevant loading and axial compression force for the case of G+Q+E, the largest axial compression force, are determined.

We can check whether the forces we get from the program meet the conditions as follows.

TBDY 7.6.1.1 control is summarized below in the shearwall group report obtained from the program.

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

#### Detection of Wall Cross and Longitudinal Reinforcements

In accordance with TBDY 7.6, the minimum longitudinal reinforcement and transverse reinforcement of the wall element that 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.

TBDY 7.6.2.2 must top foundation or the length of the wall plan from the level where more smaller than 20% of the critical wall height, 2l

_{w}to exceed the value is determined such that the more unfavorable in the following conditions.

If the first three stories above the ground story are determined as the critical shearwall height; H

_{cr}= 11.5 m. The critical wall height from the ground was determined by the program as 11.9 m. Both values are compatible with each other.

##### Shearwall Flange Longitudinal and Transverse Reinforcement Calculation

Since the shearwall to be designed is on the first story on the ground, it is a shearwall located at the critical shearwall height. The plan length of each of the end zones along the critical wall height cannot be less than 20% of the total plan length of the wall and twice the thickness of the wall. (TBDY 7.6.2.3)

The ratio of the total vertical sonata area in each of the wall end zones along the critical wall height shall be at least 0.002 and at least 2/3 of the transverse reinforcement determined by the following condition for the confinement zones of the columns will be placed in the wall end regions. (TBDY 7.6.5.1 -7.6.5.2b)

##### Shearwall web Longitudinal and Transverse Reinforcement Calculation

According to TBDY 7.6.2.3, the total cross-sectional area of the web reinforcements on both sides of the wall, for each longitudinal and transverse reinforcement, can not be less than 0.0025 of the gross cross-section area of the shearwall web remaining between the wall end regions.

According to the above information, projected wall flange length, web longitudinal reinforcement diameter and spacing, web transverse reinforcement diameter and spacing and web vertical reinforcement diameter and spacing are as follows.

In the program interface, the group wall reinforcement placement, the lengths of the flange zone can be controlled and the new reinforcement placement can be followed simultaneously by intervening the reinforcement from this interface.

All reinforcements are summarized in the group wall drawing details below.

#### Shearwall Group Longitudinal Reinforcement Control

M2-M3 interaction diagram is obtained for axial force obtained for each load combination under the joint effect of vertical and seismic loads in the design on the yield surface created for the longitudinal reinforcements of the proposed wall group. It is checked whether the moment values obtained at the lower and upper ends of the shearwall group remain within this diagram. The amount of wall flange and web longitudinal reinforcement stipulated in TBDY 2018 7.6.3 and 7.6.5 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 load combinations on the program interface. The moment values obtained at the upper and lower ends of the shearwall remain in the diagram. In the capacity design tab, the ratio can be controlled.

Group shearwall design bending moments calculation is reported as follows:

In the group shearwall report, reinforcement areas are given together with the relevant forces in the reinforced concrete account section.

#### Group Shearwall Design Bending Moment and Shear Force

According to TBDY 7.6.6.1, the design bending moments for walls meeting the Hw / lw> 2.0 condition are taken as a constant value along the critical wall height, equal to the bending moment calculated at the wall base. Above the section where the critical wall height ends, a linear moment diagram parallel to the line joining the moments calculated at the base and upper end of the wall is applied.

According to TBDY 7.6.6.3, the design shear force, V

_{e}, to be taken as basis in calculating the transverse reinforcement in any section taken into consideration for walls meeting the Hw / lw> 2.0 condition , is calculated by Equation 7.16.

In the calculation, alınır

_{v}= 1.0 is taken as all of the earthquake load is covered by reinforced concrete walls in accordance with the analysis rules of the carrier system including non-beam slab . If the value obtained by increasing the shear force calculated from the earthquake with vertical loads by 1.2D (gapless walls) or 1.4D (hollow walls) is less than V_{e}calculated by equation 7.16 , this shear force is used instead of V_{e}.

V

_{d}and (M_{d})_{t}values shown in TBDY Equation 7.16 are the values of shear force and bending moment calculated under the joint effect of vertical loads and seismic loads multiplied by load coefficients, respectively. In the group shearwall design, the bending moment is calculated at the center of gravity of the wall group, while the shear force is calculated separately for each shearwall arm at their center of gravity. For this reason, the Reinforced Concrete design - group shear dialog can be used for bending moment results and the values read for G, Q, EX loads from the internal forces tab are substituted in the relevant combinations, and the result given in the report as below is reached. However, the results of all load conditions should be read separately for each arm from the perspective screen - analysis display - shearwall results section for shear force.In this case

*V*and_{d}*(M*for the loading combination_{d})_{t}*G '+ Q'-Ex-0.3Ey + 0.3Ez*;*V*= 727.23 kN_{d}*(M*= (-58.655) + (-14.0344) - (2402.4925 - 0.3 × (58310.3313) + 0.3 × (-43.4986) = -19981.33 kNm ._{d})_{t}As a result of the moment curvature analysis made by taking into consideration the axial force and biaxial bending under the G'+Q'-Ey-0.3Ex+0.3Ez loading combination, in the calculation made by taking β

_{v}=1.0, the bearing found by using f_{ck}and f_{yk}material strengths in the base section of the P1 group shear wall. power moment (M_{p})_{t}=233311.193 kNm was found. In this case, the value of V_{e}^{'}found by Equation 7.16;

calculated as.

According to TBDY Article 7.6.6.3, the shear force value V

_{e}^{'}found by Equation 7.16 is obtained by magnifying the shear forces calculated from the earthquake under !G'+Q'-Ex-0.3Ey+0.3Ez load combination by a multiple of 1.4D (shearwall). The shear force value, V_{e}, needs to be compared with the shear force value smaller than V_{e}and V_{e}^{'}is used as the design shear force value.In this case, the shear force value obtained by enlarging the earthquake loads by 1.4D under !G'+Q'-Ex-0.3Ey+0.3Ez load combination,

*V*= (_{e}*!G') + (Q') - (1.4 * 2.5 * Ex) - (1.4 * 2.5 * 0.3Ey) + 0.3Ez = 2385 kN*.*Since V*the design shear force used in the calculation of the transverse reinforcement for the base of the P12 arm of the P1 flange is taken into consideration as_{e}= 2385 kN and V_{e}^{'}= 8491.47 kN,*V*_{e}= 2385 kN.Design shear force V

_{e}in accordance with TBDY 7.6.7 should also meet the conditions given below.

The shear strength of the shearwall sections, V

_{r}, is calculated by equation 7.17.

For P10 and P12 short arms, the wall web horizontal reinforcement foreseen according to the minimum reinforcement area previously required for 2 arms Φ12 / 20;

In this case, the shearwall web horizontal reinforcement is sufficient. At the same time, the shearwall design upper limit condition V

_{e }is met.The shear security of the shearwall arm can be controlled from the program interface, at the same time, the results are available in the shearwall report shear safety section as seen in the image below.

The calculations made are summarized in the group shearwall report shear safety section. It can be seen that the results of the report with manual calculation are consistent.

**Next Topic**