. Graphical and mechanical computation. 400 nisW, t = nii O 80 The following table exhibitsthe limits of the variables, thechoice of moduli, and the equations and approximate lengths of the scales. Fig. 356. Scale Limits Modulus Equation Length 0 to 80 Wi = X = 12 N 0 to 5000 mo = y = N III W 0 to 400 m-A = z = W 12 L 0 rriom^i5 to 5 m,= „,^ = = ¥ 4 In F!g. 356, the x- and c-axes coincide, so that the and IF-scalesare laid ofif on opposite sides of the common axis, and starting from the 70 NOMOGRAPHIC OR ALIGNMENT CHARTS Chap. iV same
. Graphical and mechanical computation. 400 nisW, t = nii O 80 The following table exhibitsthe limits of the variables, thechoice of moduli, and the equations and approximate lengths of the scales. Fig. 356. Scale Limits Modulus Equation Length 0 to 80 Wi = X = 12 N 0 to 5000 mo = y = N III W 0 to 400 m-A = z = W 12 L 0 rriom^i5 to 5 m,= „,^ = = ¥ 4 In F!g. 356, the x- and c-axes coincide, so that the and IF-scalesare laid ofif on opposite sides of the common axis, and starting from the 70 NOMOGRAPHIC OR ALIGNMENT CHARTS Chap. iV same origin; similarly for the N- and L-scales. The index lines, onejoining L and W and the other joining N and intersect on the trans-versal joining the zero points of the scales. The completed chart is given in Fig. 35c, and the index lines show thatwhen L = 2 ft., I^ = 50 pounds, and N = 2000 , then = 38. CD^^ K. 36. Deflection of beam fixed at ends and loaded at center. A = WL^ 1728 F^ . — Here, A is the deflection of beam in inches, W is the total 192 tl load on beam in pounds, L is the length of beam in feet, E is the modulus Art. 37 DEFLECTION OF BEAMS 71 of elasticity of material in inch units, and / is the moment of inertia ininch units. We shall take E = 30,000,000 for steel, so that the equation may be , which has the form (IV), and gives the written as scales X = wiA, = miU, z = mzW, t = W4 () 7. The following table exhibits the choice of moduli and the equationsof the scales. Scale Limits Modulus Equation Length A up to mi = 8 X = 8 A 12 L 10 to 35 nii = ,224 y = ,224 L^ 10 W up to 300,000 ms = ,04 z = ,04 ^^ 12 I up to 3000 mi W2W3= = ,000,001 12 t = ,735/ 11 mi In Fig. 36a, the x- and z-axesare perpendicular and so are they- and /-axes. The index lines,one joining W and / and theother joining A and L inter-sect on the common
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