Structural Load Modeling and Combination for Performance and Safety Evaluation

1. Introduction. Benefit versus risk of engineering facilities. Uncertainties in demand and capacity of engineering facilities. Treatment of uncertainty in design of engineering facilities. Objectives and emphasis. Organization of subject materials. 2. Basic Random Variable and Random Process Models. Commonly used load occurrence models. Bernoulli sequence. Poisson process. Renewal process. Polya process. Multi-variate point process. Commonly used load intensity models. Uni- and multi-variate normal distribution. Lognormal distribution. Gamma and exponential distribution. Extreme value distribution. Continuous Gaussian process. Point process with deterministic shape response function. Generation of random load intensity and random load process on digital computer and Monte-Carlo method. Generation of random variables. Generation of random processes. Convergence of Monte-Carlo method. 3. Modeling of Time Varying Load and Load Effect. Fluctuation of load and load effect. Loadings with macro-scale time variability only. Loadings with both macro- and micro-time variability. Pulse process. Poisson pulse process. Generalization. Other pulse process. Intermittent continuous process. Examples of load and load effect as pulse and intermittent processes. Appendix 3-A: Input-Output relationship of linear systems. Under dynamic random excitation. 4. Combination of Loads and Load Effects. Linear combination. Load coincidence (L.C.) method. Method of point crossing. Method of upcrossing rate. Other methods. Nonlinear combination. Outcrossing rate analysis. Resistance uncertainty. Load coincidence method. First and second order methods. Point crossing method. 5. Modeling and Effect of Load Dependencies. Within-load dependencies. Dependence between intensity and duration. Occurrence dependence (clustering). Intensity dependence. Between-load dependencies. Occurrence clustering among loads. Intensity dependence between loads. General case. Duration of coincidence of dependent loadings. Appendices: Monte-Carlo simulation and combination of dependent pulse processes. Sum of two independent Gauss-Markov processes. Derivation of function h 12 (3) (t,t'). Integration of Eq. 5.50. 6. Load Combination Rules. Risk consistency of current rules. Load reduction factor method (LRF). SRSS rule. Companion action factor method (CAF). Turkstra's rule (TR). Accuracy of load combination rules. Appendices: Derivation of joint distribution function of lifetime maximum value, R, and arbitrary-point-in-time value, S, of a pulse or intermittent process. Derivation of nonexceedance probability according to Turkstra's rule. Index.