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Prediction of lateral stiffness and fundamental period of concentrically braced frame buildings

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Abstract

In this paper, a simple hand calculation method to predict lateral stiffness and fundamental period of concentrically braced frame buildings with either fixed or pin base, which can also be used for unbraced frame buildings, is theoretically derived. To verify the reliability of the developed equations, the estimated lateral stiffness and fundamental periods are compared with the corresponding values obtained from pushover and Eigenvalue analyses for a wide range of low to medium rise buildings (i.e. up to ten storeys) with varying geometrical configurations. Systematic investigation of parameters affecting the fundamental period of frame buildings is also carried out. Although the basic formulation considers X and chevron brace configurations explicitly, its applicability to other types of brace configurations is also investigated. The suitability of the proposed equation for the braced frames with linear variation of section properties along the building height and pin beam-column connections is also scrutinized. Reliability of the developed hand calculation method is verified using the experimental test and numerical analysis results available in the literature. Finally, a flowchart and two worked examples are provided to explain the sequence of steps to calculate the fundamental period of concentrically braced frame buildings.

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Authors and Affiliations

  1. Department of Civil and Natural Resources Engineering, University of Canterbury, Christchurch, New Zealand

    Pavan K. Aninthaneni & Rajesh P. Dhakal

Authors
  1. Pavan K. Aninthaneni
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  2. Rajesh P. Dhakal
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Correspondence to Pavan K. Aninthaneni.

Appendix

Appendix

1.1 Flow chart to calculate the fundamental period of braced frames with fixed and pin bases

The sequence of steps in the application of the proposed method to calculate the fundamental period of a braced frame building with either fixed or pin base is shown in Fig. 19. For the definitions of symbols, refer the paper or Appendix “Step by step calculation to arrive at fundamental period: examples”.

1.2 Step by step calculation to arrive at fundamental period: examples

Description A six storey frame (n s equal to 6) with five bays (n b equal to 5) in each direction is used to show the calculation process. Two cases are considered for the demonstration purpose; (1) a reinforced concrete (RC) frame building with X brace and fixed base, (2) a steel frame with chevron brace and pin base as shown in Fig. 20. Both buildings have a storey height h of 3.6 m and span length l of 6 m. In the two buildings, it is assumed that braces are provided in respectively two and three bays (out of the five bays) only in the two perimeter frames, resulting in n r equal to 2 and 3. It is assumed that all beam column connections of the RC frame building are rigid, whereas for the steel frame building the perimeter frames have rigid beam column connections and the internal frames are provided with pin beam column connections. The material and cross section properties of the RC and steel frame buildings considered for the demonstration purpose are reported in Table 11. The step by step calculation for both cases is shown in Table 12; note the formulas for each step implemented in Table 12 are given in Fig. 19. Eigenvalue analyses are also performed for the two example buildings and the analytically obtained natural periods are listed in the last row of Table 12 for comparison. The subscripts “o” and “i” in Table 11 and 12 represent the corresponding variable for the perimeter (outer) and internal frames. It is important to note that in both cases, it is assumed that the effect of axial shortening of columns is neglected (i.e. τ = 0).

Fig. 20
figure 20

Building frame configurations considered for detailed calculation as examples. a Case 1: RC frame building with X brace, b Case 2: steel frame building with chevron brace

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Table 11 Cross sectional and material properties of case study buildings
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Table 12 Step by step calculation of fundamental period of the two example buildings
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Aninthaneni, P.K., Dhakal, R.P. Prediction of lateral stiffness and fundamental period of concentrically braced frame buildings. Bull Earthquake Eng 15, 3053–3082 (2017). https://doi.org/10.1007/s10518-016-0081-7

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  • DOI: https://doi.org/10.1007/s10518-016-0081-7

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