{
  "object_id": "c09-enrichment-methods",
  "title": "Scoped mechanical teaching methods and independently checked examples",
  "scope": "Hypothetical inputs, method-specific historical conditions and independently checked educational results; no project acceptance.",
  "methods": {
    "temperature_envelope": {
      "basis": "Selected Celsius branch assumptions: solar50C/winter-40C; dual-service actual endpoints separately evaluated",
      "examples": [
        {
          "metal_C": 200,
          "interval_C": 240
        },
        {
          "metal_C": -60,
          "interval_C": 110
        },
        {
          "dual_service_low_C": -60,
          "dual_service_high_C": 200,
          "interval_C": 260
        }
      ]
    },
    "signed_motion": {
      "units": "in for displacement, nominalin/ft mixed convention for numerical screen",
      "free": [
        0.3,
        0.1,
        0.4
      ],
      "terminal_contribution": [
        0,
        -0.35,
        1.8
      ],
      "combined": [
        0.3,
        -0.25,
        2.2
      ],
      "resultant": 2.234390297150433,
      "screen_q": 0.04137759809537839,
      "free_resultant": 0.5099019513592785,
      "free_screen_q": 0.009442628728875527,
      "screen_inputs": {
        "D_n": 6,
        "L_d_ft": 38,
        "U_ft": 20
      },
      "scope": "Signed authored axes and relative inputs; does not replace earlier2.45in assumed example."
    },
    "local_component_factors": {
      "default_assumed": 2,
      "oblique_branch_twice_default": 4,
      "separate_3_to_4_aspect_category_25_percent_increase": 2.5,
      "scope": "Distinct specifically adopted historical conditions; no combined multiplier or inferred diameter/aspect convention."
    },
    "nozzle_projection": {
      "axes": "Authored x shaft/y vertical/z transverse",
      "F_lbf": [
        250,
        150,
        200
      ],
      "top_normal": [
        0,
        1,
        0
      ],
      "top_parallel_lbf": 320.1562118716424,
      "normal_lbf": 150,
      "three_axis_resultant_lbf": 353.5533905932738,
      "assumed_w_lbf": 500,
      "assumed_D_nominal_in": 4,
      "steel_preliminary_suction_bounds_lbf": [
        800,
        800,
        2000
      ],
      "cast_iron_aluminum_preliminary_suction_bounds_lbf": [
        800,
        200,
        500
      ],
      "scope": "Historical material-specific suction shear comparison only; directional/normal/moment/discharge/actual equipment criteria not established."
    },
    "natural_frequency": {
      "equation": "f_n=(C_o*k/L^2)/sqrt(1+C_p*P/W)",
      "units": {
        "L": "ft",
        "k": "in",
        "P": "lbf",
        "W": "lbf total distributed over span",
        "f_n": "Hz",
        "C_p": "dimensionless",
        "C_o": "embedded inch-foot-Hz empty-carbon-steel numerical convention"
      },
      "coefficient_rows": [
        {
          "boundary": "fixed-free",
          "concentrated_weight_location": "free tip",
          "C_o": 785,
          "C_p": 3.9
        },
        {
          "boundary": "simple-simple",
          "concentrated_weight_location": "midspan",
          "C_o": 2200,
          "C_p": 2.0
        },
        {
          "boundary": "fixed-simple",
          "concentrated_weight_location": "midspan",
          "C_o": 3450,
          "C_p": 2.3
        },
        {
          "boundary": "fixed-fixed",
          "concentrated_weight_location": "midspan",
          "C_o": 5000,
          "C_p": 2.7
        }
      ],
      "k_in_assumed": 0.79,
      "examples": [
        {
          "boundary": "simple-simple",
          "L_ft": 10,
          "P_lbf": 0,
          "W_lbf": 50,
          "f_n_Hz": 17.38
        },
        {
          "boundary": "simple-simple",
          "L_ft": 10,
          "P_lbf": 20,
          "W_lbf": 50,
          "f_n_Hz": 12.954287149648781
        },
        {
          "boundary": "fixed-fixed",
          "L_ft": 10,
          "P_lbf": 20,
          "W_lbf": 50,
          "f_n_Hz": 27.388322188620688
        },
        {
          "boundary": "simple-simple",
          "L_ft": 8,
          "P_lbf": 20,
          "W_lbf": 40,
          "f_n_Hz": 19.20236852659718
        },
        {
          "boundary": "fixed-free",
          "L_ft": 10,
          "P_lbf": 20,
          "W_lbf": 50,
          "f_n_Hz": 3.8759374999999996
        }
      ],
      "scope": "Concentrated position exactlymatchesrow; Co emptyCSnumericalconvention, stainless7percentlower and watercurve distinct. Real contents/stiffness/contact not established."
    },
    "forcing": {
      "assumed_rpm": 360,
      "shaft_Hz": 6,
      "double_acting_single_cylinder_pulsation_Hz": 12,
      "fourth_forcing_harmonic_Hz": 48,
      "five_times_pulsation_Hz": 60,
      "scope": "Distinct conditional procedures and actual forcing spectrum; neither a universal4shaftspeed target."
    },
    "thermowell_wake": {
      "V_ft_s": 10,
      "D_ft": 0.05,
      "nu_ft2_s": 2.5e-05,
      "Re": 20000,
      "Re_scope_max": 100000.0,
      "f_s_Hz": 40,
      "ratio": 1.5,
      "comparison_target_Hz": 60,
      "assumed_natural_frequency_Hz": 70,
      "scope": "Historical circular-cylinder Reynolds-limited frequency screen only; actual pressure/fatigue/geometry/currentstandard qualification separate."
    },
    "fatigue_quantity": {
      "selected_historical_CS_buttweld_range_ksi": 9,
      "full_coverage_amplitude_ksi": 4.5,
      "spot_observation_range_ksi": 4.5,
      "spot_observation_amplitude_ksi": 2.25,
      "scope": "Selected atmospheric/noncorrosive/no significantgeometricconcentration basis, factor2 observation separatefrom fullyreversed range/amplitude conversion; no universal limit or deadline."
    }
  }
}