Machinery's Handbook, 31st Edition
Size of Rail to Carry Load 277 effect. From the table on page 275, the K factors are 1.20 and 0.85 for points A and B, respectively, derived from R / c = 200 ∕ 50 = 4. Thus, the actual stress due to bending at point B is 1.20 3 38.4 = 46.1 N/mm 2 (46.1 MPa) in tension; and the stress at point A is 0.85 3 38.4 = 32.6 N/mm 2 (32.6 MPa) in compression. To these stresses at A and B must be added, algebraically, the direct stress at section AB due to the 4 kN clamping force. The direct stress on section AB will be a tensile stress equal to the clamping force divided by the section area. Thus, 4000 ∕ 5000 = 0.8 N/mm 2 . The maximum unit stress at A is, therefore, 32.61 − 0.8 = 31.8 N/mm 2 (31.8 MPa) in compression, and the maximum unit stress at B is 46.1 + 0.8 = 46.9 N/ mm 2 (46.9 MPa) in tension. Size of Rail Necessary to Carry a Given Load.— The following formulas may be em- ployed for determining the size of rail and wheel suitable for carrying a given load. Let A = the width of the head of the rail in inches; B = width of the tread of the rail in inches; C = the wheel-load in pounds; D = the diameter of the wheel in inches.
B A
” 5 16
R
Then the width of the tread of the rail in inches is found from the formula:
C 1250 =
B
(1)
D
8 inch. The diameter D of the smallest track wheel
The width A of the head equals B + 5 ∕ that will safely carry the load is found from the formula:
D A K C # =
(2)
in which K = 600 to 800 for steel castings; K = 300 to 400 for cast iron. As an example, assume that the wheel-load is 10,000 pounds; the diameter of the wheel is 20 inches; and the material is cast steel. Determine the size of rail necessary to carry this load. From Formula (1): . B 1250 20 10,000 0 4 inch # = = The width of the rail required equals 0.4 + 5 ∕ 8 inch = 1.025 inch. Determine also whether a wheel 20 inches in diameter is large enough to safely carry the load. From Formula (2): . D 1025 600 10,000 16 4 1 inches # = = This is the smallest diameter of track wheel that will safely carry the load; hence a 20-inch wheel is ample. American Railway Engineering Association Formulas.— The American Railway En- gineering Association recommends for safe operation of steel cylinders rolling on steel plates that the allowable load p in pounds per inch of length of the cylinder should not exceed the value calculated from the formula
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