Jcss Model Code -

def compute_form_beta(self): # Transform correlated variables to independent space dists = [self.get_distribution(v, self.vars[v]["nominal"]) for v in self.vars] # Perform FORM (HL-RF algorithm) beta, alpha, x_star = form_hlrf(self.limit_state_function, dists, self.corr) return beta, alpha

| Output | Description | |----------------------------|-------------| | Reliability index ( \beta ) | FORM result | | Failure probability ( P_f ) | ( \Phi(-\beta) ) | | Target ( \beta_target ) | Based on CC & ref. period | | Compliance verdict | PASS / FAIL | | Sensitivity factors ( \alpha ) | Importance of each random variable | | Partial factors (implied) | Equivalent to ( \gamma_m, \gamma_q ) | 5. Pseudo-Code Implementation (Python-like) class JCSSModelCode: def __init__(self, input_json): self.ls = input_json["limit_state"] self.ref_period = input_json["reference_period_years"] self.cc = input_json["consequence_class"] self.vars = input_json["variables"] self.corr = input_json.get("correlations", []) def get_distribution(self, var_name, nominal): """Return scipy distribution based on JCSS Model Code.""" model = self.vars[var_name]["jcss_model"] if model == "steel_yield_strength": mean = nominal * 1.05 cov = 0.08 scale = mean * np.sqrt(np.log(1 + cov**2)) shape = np.sqrt(np.log(1 + cov**2)) return stats.lognorm(s=shape, scale=mean) elif model == "imposed_load_office_50yr_max": # Gumbel parameters from JCSS: mu, beta mu = nominal * 0.6 # example beta = nominal * 0.2 return stats.gumbel_r(loc=mu, scale=beta) # ... others else: return stats.norm(loc=nominal, scale=nominal*0.10) jcss model code

def get_target_beta(self): targets_50yr = "CC1": 3.1, "CC2": 3.8, "CC3": 4.3 if self.ref_period == 50: return targets_50yr[self.cc] elif self.ref_period < 50: # Annual beta ~ sqrt(50) relation approx return targets_50yr[self.cc] * np.sqrt(self.ref_period / 50) else: return targets_50yr[self.cc] * np.sqrt(self.ref_period / 50) others else: return stats

def limit_state_function(self, x): Z, f_y, G, Q = x M_R = Z * f_y M_E = (G + Q) * 2.5 # simplified span/4 return M_R - M_E others else: return stats.norm(loc=nominal