Essentials in the theory of framed structures . at any distance d from the same support. E is themodulus of elasticity in pounds per square inch, and I is themoment of inertia of the constant cross-section of the beamabout the neutral axis, measured in inches*. 142. Point of Maximtun Deflection.—^The maximum deflec-tion occurs in the longer segment of Fig. 131 where c is greaterthan k, and at the point where the tangent through T is hori-zontal; hence the value of c for A^^x- may be found by equatingthe expressions for ts and h, whence c= i-V(i-P)/3 The values of c and the corresponding values
Essentials in the theory of framed structures . at any distance d from the same support. E is themodulus of elasticity in pounds per square inch, and I is themoment of inertia of the constant cross-section of the beamabout the neutral axis, measured in inches*. 142. Point of Maximtun Deflection.—^The maximum deflec-tion occurs in the longer segment of Fig. 131 where c is greaterthan k, and at the point where the tangent through T is hori-zontal; hence the value of c for A^^x- may be found by equatingthe expressions for ts and h, whence c= i-V(i-P)/3 The values of c and the corresponding values of F for Amai-are also given in Table I. Since the limits of k are o and , all values of c for maximumdeflection will fall between and Hence the pointof maximum deflection for a single load is between the load Sec. II DEFLECTION OF BEAMS 219 and the center of the span, and always relatively near thecenter. The most eccentric loading which a simple beam ofuniform cross-section and span / can experience, occurs when a ^S. ^ao7. as 06y^/ues of c Pig. 132. single load is adjacent to one of the supports, and jfe is on thepoint of becoming zero. Under this condition the point ofmaximum deflection cannot be at a distance greater than the center of the span. Any second load apphed to the 220 THEORY OF FRAMED STRUCTURES Chap. V beam must necessarily throw the point of maximum deflectionnearer the center. Hence the point of maximum deflection of asimple beam of uniform cross-section, loaded in any manner,will be near the center and not more than of its lengthfrom the center. 143. A 20-in. 6s-lb. I-beam supports two loads of 30,000 (Fig. 133). Since the loads are symmetrically placed,the elastic curve and M-diagram are symmetrical about thecenter. The tangent to the elastic curve at the center, drawn
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