sample_load_profile contains the default residential load profile.
It can be invoked via sample_load_profile.
Its parameters can be modified with sample_load_profile["parameterName"].
sample_load_profileAn object of class data.frame with 1 rows and 13 columns.
- The load is defined as $$\tau(t)=\phi R_o\frac{\gamma{D}_d + {D}_s(t) + {D}_e(t)}{\gamma\alpha_d + \alpha_l}$$
- Following the National Building Code of Canada (NBCC) standards document CAN/CSA-O86, assume that \(\gamma\) = 0.25, \(\alpha_d\) = 1.25, \(\alpha_l\) = 1.5.
- \(R_o\) is the characteristic value depending on the lumber population. By default, \(R_o\) = 2722psi.
- \(\phi\) is the performance factor.
- According to Foschi, Folz, and Yao(1989)
1. \(D_d\) is the normalized dead load for the weight of the structure, and \(D_d\) ~ N(load_d_mean, load_d_sd). By default, load_d_mean = 1, load_d_sd = 0.01.
2. \(D_s(t)\) is the sustained load. \(D_e(t)\) is the extraordinary load. \(D_s(t)\) and \(D_e(t)\) are two independent processes.
3. The sizes of the loads are modelled using gamma distributions \(G(k,\theta)\) where k and \(\theta\) represent the shape and scale parameters. The random times between and during live load events are modeled using exponential distributions \(Exp(\lambda)\) with mean \(\lambda^{-1}\). Parameters for these models were previously fitted using survey data.
4. The process \(D_s(t)\) consists of a sequence of successive periods of sustained occupancy each with iid duration \(T_s\) ~ Exp(1 / mean_Ts).
During these periods of occupancy \(D_{ls}\) ~ G(load_s_shape, load_s_scale) iid. By default, mean_Ts = 10, load_s_shape = 3.122, and load_s_scale = 0.0481.
5. The process \(D_e(t)\) consists of brief periods of extraordinary loads, separated by longer periods with no load \(T_e\) ~ Exp(mean_Te) of expected duration 1 year.
When extraordinary loads occur, they last for iid periods of random duration \(T_p\) ~ Exp(1 / mean_Tp). The normalized loads \(D_{le}\) during these brief periods
are iid with gamma distribution \(D_{le}\) ~ G(load_p_shape, load_p_scale). By default, mean_Te = 1, mean_Tp = 0.03835, load_p_shape = 0.826, and load_p_scale = 0.1023.
Foschi, R. O., Folz, B., and Yao, F. (1989), Reliability-Based Design of Wood Structures (Vol. 34), Vancouver, BC: Department of Civil Engineering, University of British Columbia.
Corotis, R. B., and Doshi, V. A. (1977), <U+201C>Probability Models for Live-Load Survey Results,<U+201D> Journal of the Structural Division, 103, 1257<U+2013>1274.
Chalk, P. L., and Corotis, R. B. (1980), <U+201C>Probability Model for Design Live Loads,<U+201D> Journal of the Structural Division, 106, 2017<U+2013>2033.
Harris, M. E., Bova, C. J., and Corotis, R. B. (1981), <U+201C>Area-Dependent Pro-cesses for Structural Live Loads,<U+201D> Journal of the Structural Division, 107,857<U+2013>872.
Yang, C. H., Zidek, J. V., & Wong, S. W. (2019). Bayesian analysis of accumulated damage models in lumber reliability. Technometrics, 61(2), 233-245.