. Steel rails; their history, properties, strength and manufacture, with notes on the principles of rolling stock and track design . t^ = t^ (which isalways the case), showing that at every point in the rail the intensities of thevertical and horizontal shears are equal, and we will hereafter designate themwith the common letter t. The value of t^ has already been deduced in equation(b), namely: t = M -M b Ax ~ X ay- (c) M — MBut the value of = S^, where S, is the total vertical shear at the sec- Ax M — Mtion X. Substituting this value of — in equation (c), there results: S 1/ 250 STEEL RAILS
. Steel rails; their history, properties, strength and manufacture, with notes on the principles of rolling stock and track design . t^ = t^ (which isalways the case), showing that at every point in the rail the intensities of thevertical and horizontal shears are equal, and we will hereafter designate themwith the common letter t. The value of t^ has already been deduced in equation(b), namely: t = M -M b Ax ~ X ay- (c) M — MBut the value of = S^, where S, is the total vertical shear at the sec- Ax M — Mtion X. Substituting this value of — in equation (c), there results: S 1/ 250 STEEL RAILS or the intensity of the shearing stress at any point in the rail is equal to thetotal shearing force on the entire cross section multiplied by the statical momentof the area of the section outside the longitudinal plane of shear in questionabout its axis in the neutral plane, divided by the product of the moment ofinertia of the entire section into the breadth of the section at that point. Fig. 175 shows the intensity of the shearing stress in a 100-pound rail,the total vertical shear at the section being 24,000 Fig. 175. — Shearing Stress in 100-pound A. S. C. E. Rail. There still remains to be considered the horizontal force /, whose valueis given in equation (a), tending either to compress together or pull asunderthe two faces ac and hd (Fig. 174), according as it is on the upper or lower sideof the neutral axis. At the neutral axis where f = 0, t^ and ty are tnen the only stresses, andwe know from mechanics that the resultant action of two equal shears at rightangles to each other, exactly as t^ and t^ are, is equivalent to that of two equaland opposite stresses at right angles to each other, called the principal stressesand making an angle of 45° with the shearing stresses. But at a distance each STRESSES IN THE RAIL 251 side of the neutral axis the third stress, /, now comes in, which evidently givesa new direction to the line of resultant stress, turnin
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Keywords: ., bookcentury1900, bookdecade1910, bookidsteelrailsth, bookyear1913
