. Graphical and mechanical computation. 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 = 0
. Graphical and mechanical computation. 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 transversaljoining the zero points of thescales. The complete chart is given inFig. 36^, and the index lines showthat when W = 130,000 pounds,/ = 1000 inch units, and L = 25ft., then A = Fig. 36a. 37. Deflection of beams under various methods of loading and sup-porting. A = =77-.—Here A is the deflection of the beam in ^ * 192 aEI inches, W is the total load on beam in pounds, L is the length of beam infeet, E is the modulus of elasticity of material in inch units, and / is themoment of inertia in inch units; a is a quantity whose value determinesthe method of loading and supporting, thus (i) a = I —beam fixed at ends and loaded at center; (2) a = 2 — uniformly; (3) ^ =«*¥ — one end and loaded at other; (4) a =5^ — uniformly; (5) ^ = 4 — supported at ends and loaded at center; (6) a = § — uniformly. 72 NOMOGRAPHIC OR ALIGNMENT CHARTS Chap. IV These six cases may be represented by six charts similar to those dis-cussed in Arts. 35 and 36, for the equation can be written v^ = — -^, L^ a/ LENGTH OF BEAM (L) IN FEET II M I 1 I L__J \ \ I L /.500-
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