Symbols
D = Excess of strength coefficient
R = Coefficient of behavior of the carrier system
θII,i (X) = (X) second order indicator value defined for each i'th floor in the earthquake direction
θII,max (X) = (X) defined in the earthquake direction maximum second order indicator value
Vi(X) = (X) reduced storey shear force at ith floor in earthquake direction [kN]
hi = height of ith floor [m]
∆i,avg (X) = (X) average reduced relative story drift [m]
wk = total weight acting on the kth story [kN]
βII (X) = Second order amplification coefficient
βtE (X) = Equivalent base shear force amplification coefficient
For each direction, the second order indicator value θII,i is calculated according to TBDY 4.9.2 for all floors . If maximum θ II,max satisfies the condition given below; Second-order effects are not taken into account in determining the internal forces based on the design.
Ch is a coefficient calculated depending on the non-linear hysteretic behavior of the carrier system and is taken as 1 for steel structures as per TBDY 2018 4.9.2.2.
If the condition given in Equation 4.36 is not satisfied , the internal forces obtained from the horizontal earthquake effects are increased with the β II coefficient determined by the equation below .
This value calculated for all floors is used only to increase the internal forces of the upper section elements as per TBDY 4.9.2.4.
For manual calculation, V i and w k values are obtained from the Floor Parameters section in the upper toolbar Analysis and Design tab of the program.
The above table from floor X direction forces, Vi , for FX; FY columns are used for the Y direction storey forces. Since the values in the FX column are only the force acting on the relevant floor, they are added down and the total shear force diagram is created for the building. The following table V i values indicated in the column were obtained in this way.
wk is for the total weight affecting the floor, and the values in the G and Q columns from the table above are combined to be G+0.3Q. Here, 0.3 is the live load participation coefficient and 0.3 was chosen for this building.
Average storey displacement values are used directly as values in the program report. Equation 4.36 is used for limit value calculation. The values of the building used in the calculation are as follows:
The result of the calculation for the building is given in the earthquake regulation report.
βII =1 for the building . There is no increase. If it is greater than 1, it can go to increase the stiffness.
The excel table for the manual part of the account can be obtained here.