Supported at ends, loaded in middle, e = W元 / 48 EI. The three most common conditions only are given below, reference to the handbook being necessary if other conditions must be satisfied: The formula for transverse deflection, deduced from mechanics, varies with the system of loading. 01 inch per foot of length is a common allowance but it is impossible to fix any general limit, as in many case this figure, if exceeded, would do no harm, while in others - such as heavily loaded or high-speed bearings - even the figure given might be fatal to good operation. Transverse deflection of shafts, however, rarely exists up to the point of limiting fiber stress, because before that point is readied the alignment of the shaft is so disturbed that it is not practicable as a device for transmitting power. It may therefore exist alone or in conjunction with angular deflection. Transverse deflection occurs when the shaft is subjected to a bending moment. per square inch), thus indicating that the relation of one degree to twenty diameters is well within the limit of strength.įor a hollow shaft the above formula becomes : In fact, in calculations for strength, even for reversing stresses, the usual figure is 8,000 (lbs. This in a safe value for shearing fiber stress in steel. The shearing modulus of elasticity of ordinary shaft steel runs from 10,000,000 to 13,000,000, giving as an average about 12,000,000.īy the well-known relation of "Hooke's law" (stresses proportional to strains within the elastic limit of the material), we have:Ī / 366 = SL / πGd or S = AπGd /360 L (46)Ī twist of one degree in a length of twenty diameters is a usual allowance. The equation worked out from mechanics for this condition, is: ao = 584 TL / Gd4, (45) which at once gives the number of degrees of angular deflection for a shaft whose modulus of elasticity, torsional moment, and length are known. 26, the angular deflection due to the load may be carried to a certain point before the limit of working fiber stress is exceeded. For a shaft subjected to pure torsion, as in Fig.
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