Strength of Materials: Parts 1-2, Volume 2American School of Correspondence, 1907 - Strength of materials |
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12 feet long 12 inches breaking load butt joint cast-iron column coefficient of elasticity compressive stress compressive unit-stresses Compute the greatest Compute the safe dangerous section deflection denote elastic limit elongation end pulls end supports equals equation Euler's formula EXAMPLES FOR PRACTICE factor of safety fibre strength fibre stress flat ends flexural foot-pounds greatest shearing unit-stress greatest tensile hence inch-pounds inches in cross-section inches in diameter inertia lap joint length lower fibre material maximum bending moment of inertia Neglecting the weight neutral axis parabola formula pounds per square preceding example pulleys radius of gyration Rankine's formula ratio represented in Fig rests on end revolutions per minute S₁ safe load section modulus shearing stress solid shaft solve square inch straight-line formula substitute sustains a load Table temperature stress tensile and compressive tensile stress timber beam twisting uniform load unit-fibre stress upper fibre wooden beam wrought iron
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Page 77 - Also, in any crosssection the slippage is least between the upper two and lower two boards, and is greatest between the middle two. These facts indicate that the shearing unit-stress on horizontal sections of a solid beam is greatest in the neutral surface at the supports. It can be proved that at any place in a beam the shearing unit-stresses on a horizontal and on a vertical section are equal. Fig. 41. Fig. 42. It follows that the horizontal shearing unit-stress is greatest at the neutral axis...
Page 79 - 2 = 229; or, a — 15.1 (practically 16) inches. If, again, we let 5 = 6, then a2 = 152.7; or a = 12.4 (practically 13) inches. Either of these sizes will answer so far as fibre stress is concerned, but there is more " timber " in the second. The maximum external shear in the beam equals 1,556 pounds, neglecting the weight of the beam (see example 3, Art. 87; and example 2, Art. 38). Therefore, for a 4 X 16-inch beam. * See
Page 85 - The results indicated in Art. 75 must therefore in this case also be regarded as only approximate, the value of the greatest unitfibre stress (Sc) being too small. For beams loaded in the middle or with a uniform load, the following formulas, which take into account the flexural effect of the end forces, may be used : M denotes bending moment at the middle section of the beam; I denotes the moment of inertia of the middle section with respect to the neutral axis; •5 S,, S2, c, and c.2 have the...
Page 97 - Zir for a column with hinged ends, for example, is less than 150, the parabola formula should be used to compute the safe load, factor of safety, etc.; but if the ratio is greater than 150, then Euler's formula should be used. The line AB, Fig. 51, represents the parabola formula; and the line BC, Euler's formula. The two lines are tangent, and the point of tangency corresponds to the "limiting value
Page 95 - Ans. 8.9 3. A steel Z-bar column (see Fig. 46, a) is 24 feet long and has square ends; the least radius of gyration of its cross-section is 3.1 inches; and the area of the cross-section is 24.5 square inches. What is the safe load for the column with a factor of safety of 4? Ans.
Page 90 - When the resultant of the loads does not act through the center of gravity of the top section, the column is said to be eccentrically loaded. All the following formulas refer to columns centrally loaded. 83. Rankine's Column Formula. When a perfectly straight column is centrally loaded, then, if the column does not bend and if it is homogeneous, the stress on every cross-section is a uniform compression.
Page 117 - B, page 55, Part I, are given formulas for deflection in certain cases of beams and different kinds of loading. In those formulas, d denotes deflection; I the moment of inertia of the cross-section of the beam with respect to the neutral axis, as in equation 6; and E the coefficient of elasticity of the material of the beam (for values, see Art. 95). In each case, the load should be expressed in pounds, the length in inches, and the moment of inertia in biquadratic inches; then the deflection will...
Page 88 - Wooden columns are usually solid, square, rectangular, or round in section; but sometimes they are "built up" hollow. Cast-iron columns are practically always made hollow, and rectangular or round in section. Steel columns are made of single rolled shapes — angles, zees, channels, etc.; but the larger ones are usually " built up" of several shapes. Fig. 46, a, for example, represents a cross -section of a «Z-bar
Page 62 - If the beam is 4 X 12 inches in cross-section (the long side vertical as usual), compute the maximum tensile and compressive unit-stresses. The section modulus of a rectangle whose base and altitude are b and a respectively...
Page 92 - ... 36,000. With these values of S and k, P of the formula means the ultimate load, that is, the load causing failure. The safe load equals P divided by the selected factor of safety — a factor of 4 for steady loads, and 5 for moving loads, being recommended by the company referred to. The same unit is to be used for I and r. Cast-iron columns are practically always made hollow with comparatively thin walls, and are usually circular or rectangular in cross-section.