What is the fundamental period formula used in CBC for estimating seismic forces on regular buildings?
Correct Answer
C) T = Ct × hn^x
CBC uses T = Ct × hn^x where Ct and x are building type coefficients and hn is the height above base to the highest level of the structure.
Why This Is the Correct Answer
T = Ct × hn^x is the CBC approximate fundamental period formula per ASCE 7, which CBC adopts. Here, Ct is a coefficient based on structural system type (e.g., 0.028 for moment frames, 0.02 for other systems), hn is the structural height above the base, and x is an exponent also dependent on structural system (typically 0.8). This general form covers all building types with variable coefficients.
Why the Other Options Are Wrong
Option A: T = hn/100
T = hn/100 is an oversimplified rule-of-thumb sometimes used for rough estimates but is not the CBC/ASCE 7 code formula. It lacks the building-type adjustment coefficients (Ct and x) that differentiate steel moment frames from concrete shear wall buildings, making it inaccurate for design.
Option B: T = Ct × hn^0.75
T = Ct × hn^0.75 is a partial version of the formula that fixes the exponent at 0.75. While 0.75 is one valid value of x for certain building types (concrete moment frames), the general CBC formula keeps x as a variable because different structural systems have different exponents. The fixed exponent version is not the complete general formula.
Option D: T = 0.1 × N
T = 0.1 × N is an older simplified approximation where N = number of stories, sometimes cited for steel moment frames as T ≈ 0.1N. However, this is not the CBC code formula — it does not account for structural height directly or differentiate between building types, and has been superseded by the Ct × hn^x formulation.
Memory Technique
Think of T = Ct × hn^x as 'Coefficients Times Height to the X power.' The 'C' in Ct stands for the structural system's Characteristic, and 'x' is the eXponent that varies. This formula has two blanks (Ct and x) because buildings are not all the same — the formula adapts to the system type.
More California Questions
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