[ { "page": 1, "items": [ { "page": 1, "type": "TITLE", "location": { "l": 81.5753, "t": 832.8917, "r": 400.439, "b": 791.3791 }, "text": "Bridge Building Challenge", "reading_order": 0, "level": 1 }, { "page": 1, "type": "FIGURE", "location": { "l": 427.5508, "t": 829.7722, "r": 577.0256, "b": 782.7406 }, "text": "", "reading_order": 1 }, { "page": 1, "type": "TEXT", "location": { "l": 29.2712, "t": 777.4615, "r": 517.0437, "b": 719.8718 }, "text": "Goal: Design and build a model bridge that spans a given distance and holds the maximum load possible using the provided materials. Your bridge must be strong, stable, and efficient!", "reading_order": 2 }, { "page": 1, "type": "TEXT", "location": { "l": 30.9506, "t": 705.9543, "r": 99.5699, "b": 688.4374 }, "text": "Materials:", "reading_order": 3 }, { "page": 1, "type": "TEXT", "location": { "l": 40.0679, "t": 686.0378, "r": 146.8356, "b": 669.4808 }, "text": "Popsicle sticks", "reading_order": 4 }, { "page": 1, "type": "TEXT", "location": { "l": 41.0276, "t": 668.281, "r": 121.1634, "b": 650.0442 }, "text": "Wood glue", "reading_order": 5 }, { "page": 1, "type": "LIST_ITEM", "location": { "l": 40.5477, "t": 650.7641, "r": 148.995, "b": 633.2472 }, "text": "String or tape", "list_id": "L1", "level": 0, "reading_order": 6 }, { "page": 1, "type": "LIST_ITEM", "location": { "l": 39.828, "t": 633.9671, "r": 214.4952, "b": 616.4502 }, "text": "Cardboard base (supports)", "marker": "•", "list_id": "L1", "level": 0, "reading_order": 7 }, { "page": 1, "type": "LIST_ITEM", "location": { "l": 39.588, "t": 616.4502, "r": 228.6509, "b": 606.492 }, "text": "Small weights (for testing)", "marker": "-", "list_id": "L1", "level": 0, "reading_order": 8 }, { "page": 1, "type": "LIST_ITEM", "location": { "l": 39.588, "t": 606.492, "r": 228.6509, "b": 596.5338 }, "text": "The bridge must span 30 cm between the supports.", "marker": "-", "list_id": "L1", "level": 0, "reading_order": 9 }, { "page": 1, "type": "TITLE", "location": { "l": 258.162, "t": 704.7545, "r": 336.6183, "b": 687.7175 }, "text": "Constraints:", "reading_order": 10, "level": 2 }, { "page": 1, "type": "TEXT", "location": { "l": 264.1602, "t": 668.7609, "r": 544.3954, "b": 651.484 }, "text": "Only the provided materials may be used.", "reading_order": 11 }, { "page": 1, "type": "TEXT", "location": { "l": 263.9202, "t": 651.484, "r": 556.1519, "b": 634.687 }, "text": "The bridge must be no wider than 10 cm.", "reading_order": 12 }, { "page": 1, "type": "TEXT", "location": { "l": 263.9202, "t": 633.9671, "r": 436.1882, "b": 617.89 }, "text": "Build time: 60 minutes.", "reading_order": 13 }, { "page": 1, "type": "TEXT", "location": { "l": 262.4807, "t": 617.65, "r": 571.5073, "b": 582.1363 }, "text": "Testing will be done by placing weights at the center of the bridge until it fails.", "reading_order": 14 }, { "page": 1, "type": "TITLE", "location": { "l": 24.2327, "t": 566.7791, "r": 189.0629, "b": 546.3827 }, "text": "Think Like an Engineer!", "reading_order": 15, "level": 2 }, { "page": 1, "type": "TEXT", "location": { "l": 24.7125, "t": 540.8637, "r": 302.3086, "b": 506.5498 }, "text": "A bridge must resist different types of forces and distribute the load to the supports.", "reading_order": 16 }, { "page": 1, "type": "TEXT", "location": { "l": 30.2309, "t": 492.8722, "r": 215.6948, "b": 474.6355 }, "text": "Compression: squishing force", "reading_order": 17 }, { "page": 1, "type": "TEXT", "location": { "l": 30.4708, "t": 474.3955, "r": 173.4676, "b": 458.0784 }, "text": "Tension: pulling force", "reading_order": 18 }, { "page": 1, "type": "TEXT", "location": { "l": 29.9909, "t": 457.8385, "r": 286.9533, "b": 442.0013 }, "text": "Shear: forces sliding across each other", "reading_order": 19 }, { "page": 1, "type": "TEXT", "location": { "l": 29.2712, "t": 441.0415, "r": 301.3489, "b": 407.2075 }, "text": "Bending: caused by the load pushing down on the bridge", "reading_order": 20 }, { "page": 1, "type": "TEXT", "location": { "l": 318.3838, "t": 566.2991, "r": 458.5014, "b": 546.6226 }, "text": "Common Bridge Shapes", "reading_order": 21 }, { "page": 1, "type": "FIGURE", "location": { "l": 321.9827, "t": 541.3436, "r": 393.4811, "b": 509.1893 }, "text": "", "reading_order": 22 }, { "page": 1, "type": "TEXT", "location": { "l": 405.7174, "t": 535.1047, "r": 493.7707, "b": 518.5476 }, "text": "Triangular Truss", "reading_order": 23 }, { "page": 1, "type": "TEXT", "location": { "l": 409.3163, "t": 519.0276, "r": 538.1573, "b": 503.4303 }, "text": "→ strong and stable", "reading_order": 24 }, { "page": 1, "type": "FIGURE", "location": { "l": 321.7427, "t": 494.5519, "r": 391.8016, "b": 466.9568 }, "text": "", "reading_order": 25 }, { "page": 1, "type": "FIGURE", "location": { "l": 315.2647, "t": 457.5985, "r": 402.8382, "b": 418.7254 }, "text": "", "reading_order": 26 }, { "page": 1, "type": "TEXT", "location": { "l": 406.4371, "t": 494.7919, "r": 473.3769, "b": 478.7147 }, "text": "Howe Truss", "reading_order": 27 }, { "page": 1, "type": "TEXT", "location": { "l": 411.7156, "t": 477.9949, "r": 548.7141, "b": 459.0382 }, "text": "→ good for heavy loads", "reading_order": 28 }, { "page": 1, "type": "TEXT", "location": { "l": 406.4371, "t": 446.5605, "r": 534.3185, "b": 413.4464 }, "text": "Arch Bridge\n→ compression only", "reading_order": 29 }, { "page": 1, "type": "TITLE", "location": { "l": 25.1924, "t": 392.5701, "r": 219.5336, "b": 371.6938 }, "text": "Load and Strength (Algebra)", "reading_order": 30, "level": 2 }, { "page": 1, "type": "TEXT", "location": { "l": 23.033, "t": 366.8947, "r": 264.4001, "b": 319.3831 }, "text": "Load (L) is the total weight the bridge holds. If the bridge holds 5 weights and each weight is 20 g:", "reading_order": 31 }, { "page": 1, "type": "DISPLAY_FORMULA", "location": { "l": 56.6229, "t": 317.2235, "r": 104.1285, "b": 304.5058 }, "text": "L = 5w", "reading_order": 32 }, { "page": 1, "type": "TEXT", "location": { "l": 23.273, "t": 303.5459, "r": 202.0189, "b": 270.4318 }, "text": "where w = weight of one mass\nL = 5(20) = 100 g", "reading_order": 33 }, { "page": 1, "type": "TEXT", "location": { "l": 275.6767, "t": 389.2107, "r": 464.9795, "b": 374.0934 }, "text": "Stress (σ) is the force on a material", "reading_order": 34 }, { "page": 1, "type": "TEXT", "location": { "l": 277.5961, "t": 372.1737, "r": 491.3715, "b": 355.6167 }, "text": "divided by the area (A) of the material.", "reading_order": 35 }, { "page": 1, "type": "DISPLAY_FORMULA", "location": { "l": 306.6273, "t": 350.0976, "r": 369.2484, "b": 317.4635 }, "text": "σ = F/A", "latex": "\\sigma = \\frac{F}{A}", "reading_order": 36 }, { "page": 1, "type": "TEXT", "location": { "l": 382.9243, "t": 352.4972, "r": 593.8205, "b": 325.862 }, "text": "If a stick has a cross-sectional area of 0.2 cm2 and the force on it is 12 N:", "reading_order": 37 }, { "page": 1, "type": "DISPLAY_FORMULA", "location": { "l": 394.4408, "t": 324.6622, "r": 541.7562, "b": 299.4667 }, "text": "σ = 12/0.2 = 60N/cm2", "latex": "\\sigma=\\frac{12}{0.2}=60N/c m^{2}", "reading_order": 38 }, { "page": 1, "type": "TEXT", "location": { "l": 276.3965, "t": 295.1474, "r": 492.811, "b": 267.3124 }, "text": "Stronger designs spread the load across more members, reducing stress.", "reading_order": 39 }, { "page": 1, "type": "TEXT", "location": { "l": 31.4305, "t": 263.4731, "r": 204.6581, "b": 227.9594 }, "text": "Your goal is to MAXIMIZE L (the load) before failure!", "reading_order": 40 }, { "page": 1, "type": "TEXT", "location": { "l": 19.1942, "t": 209.7226, "r": 134.1195, "b": 192.2058 }, "text": "Example Calculation:", "reading_order": 41 }, { "page": 1, "type": "TEXT", "location": { "l": 18.2345, "t": 187.1667, "r": 243.2865, "b": 158.1318 }, "text": "If your bridge holds 8 weights (20 g each) and the span is 30 cm:", "reading_order": 42 }, { "page": 1, "type": "DISPLAY_FORMULA", "location": { "l": 45.1064, "t": 156.2122, "r": 165.55, "b": 140.375 }, "text": "L = 8(20) = 160g", "reading_order": 43 }, { "page": 1, "type": "TEXT", "location": { "l": 17.7546, "t": 138.6953, "r": 218.0941, "b": 121.1784 }, "text": "Convert to Newtons (1 g ≈ 0.0098 N)", "reading_order": 44 }, { "page": 1, "type": "DISPLAY_FORMULA", "location": { "l": 18.2345, "t": 119.7387, "r": 192.9017, "b": 102.2218 }, "text": "P = 160g×0.0098 ≈ 1.57N", "latex": "P=160g\\times0.0098\\approx1.57N", "reading_order": 45 }, { "page": 1, "type": "DISPLAY_FORMULA", "location": { "l": 17.7546, "t": 94.5432, "r": 218.334, "b": 76.3064 }, "text": "M = 7.5P = 7.5(1.57) ≈ 11.78N· cm", "latex": "M=7.5P=7.5(1.57)\\approx11.78N\\cdot c m", "reading_order": 46 }, { "page": 1, "type": "TEXT", "location": { "l": 276.1565, "t": 263.2331, "r": 497.1297, "b": 233.9583 }, "text": "Bending Moment (M) at the center of a simply supported beam with a center load:", "reading_order": 47 }, { "page": 1, "type": "TEXT", "location": { "l": 391.5616, "t": 232.9985, "r": 477.6956, "b": 219.5609 }, "text": "where P = load", "reading_order": 48 }, { "page": 1, "type": "DISPLAY_FORMULA", "location": { "l": 289.3525, "t": 226.9996, "r": 347.8948, "b": 197.0049 }, "text": "M = PL/4", "latex": "M=\\frac{P L}{4}", "reading_order": 49 }, { "page": 1, "type": "DISPLAY_FORMULA", "location": { "l": 427.3108, "t": 219.8009, "r": 513.4448, "b": 204.9235 }, "text": "L = spanlength", "reading_order": 50 }, { "page": 1, "type": "TEXT", "location": { "l": 377.4059, "t": 203.9637, "r": 542.716, "b": 187.8865 }, "text": "For our bridge, L = 30 cm", "reading_order": 51 }, { "page": 1, "type": "TEXT", "location": { "l": 252.8836, "t": 165.3306, "r": 314.5449, "b": 56.8699 }, "text": "Good design\nBalance of Strength, Stability, and Efficiency!", "reading_order": 52 }, { "page": 1, "type": "DISPLAY_FORMULA", "location": { "l": 376.6861, "t": 185.487, "r": 571.0274, "b": 161.2513 }, "text": "S0,M = (P(30))/4 = 7.5P(N· cm)", "latex": "S_{0},M=\\frac{P(30)}{4}=7.5P(N\\cdot c m)", "reading_order": 53 }, { "page": 1, "type": "LIST_ITEM", "location": { "l": 347.6549, "t": 151.413, "r": 448.9043, "b": 134.1361 }, "text": "Testing Procedure:", "list_id": "L2", "level": 0, "reading_order": 54 }, { "page": 1, "type": "LIST_ITEM", "location": { "l": 349.5743, "t": 131.2566, "r": 550.8735, "b": 116.3793 }, "text": "Place the bridge on the supports.", "marker": "1.", "list_id": "L2", "level": 0, "reading_order": 55 }, { "page": 1, "type": "LIST_ITEM", "location": { "l": 349.0945, "t": 116.3793, "r": 591.1813, "b": 101.9818 }, "text": "Add one weight at a time to the center.", "marker": "2.", "list_id": "L2", "level": 0, "reading_order": 56 }, { "page": 1, "type": "LIST_ITEM", "location": { "l": 349.3344, "t": 102.4618, "r": 495.9301, "b": 89.0241 }, "text": "Record the total load.", "marker": "3.", "list_id": "L2", "level": 0, "reading_order": 57 }, { "page": 1, "type": "LIST_ITEM", "location": { "l": 348.8546, "t": 89.2641, "r": 547.2746, "b": 75.3466 }, "text": "Continue until the bridge fails.", "marker": "4.", "list_id": "L2", "level": 0, "reading_order": 58 }, { "page": 1, "type": "LIST_ITEM", "location": { "l": 348.6146, "t": 75.3466, "r": 580.6245, "b": 59.5094 }, "text": "The team with the highest load wins!", "marker": "5.", "list_id": "L2", "level": 0, "reading_order": 59 }, { "page": 1, "type": "TEXT", "location": { "l": 49.1851, "t": 41.9925, "r": 511.5254, "b": 16.797 }, "text": "☆ Plan carefully. Build strong. Test fairly. Improve together! ☆", "reading_order": 60 } ] } ]