Essentials in the theory of framed structures . / represent the expression in the parenthesis of Eq. (6)then 24EI (7) The values of / for various values of c are given in Table II; inwhich I is the length of the beam in inches, W is the total uni-formly distributed load in pounds and A is the deflection ininches at any distance cl from the nearer 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, expressed in inches.* For Amax-, c = , hence ^max WP ^, 5WP Table II c J c 7
Essentials in the theory of framed structures . / represent the expression in the parenthesis of Eq. (6)then 24EI (7) The values of / for various values of c are given in Table II; inwhich I is the length of the beam in inches, W is the total uni-formly distributed load in pounds and A is the deflection ininches at any distance cl from the nearer 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, expressed in inches.* For Amax-, c = , hence ^max WP ^, 5WP Table II c J c 7 oiS •4S 0,3088 224 THEORY OF FRAMED STRUCTURES Chap. V I4S. Deflection for Load of Uniformly Varying Intensity.— The beam in Fig. 136 supports a load of uniformly varyingintensity. The total load is W lb., and the length of the beamis / in. The bending moment at any distance x from A is Ml = ^,{Px - X?)The bending moment at any distance x from B is. Fig. 136. w. 3^ Mixdx i&oET WP M2xdx = „ „,i8o£/ A = h + cik - h) = (20c — I2C^) (7 — 30C^ + 20c + 15c* — I2cO WP 180EI (7c - loc^ + 3c0 The value of c for A^ax- may be found by equating h and h,whence 15c* - 30c2 = -7c = ^max X = WP 180EI ?^ £/ The intensity of the load in Fig. 137 increases uniformlyfrom each support to the center of the span. The total load is Sec. II DEFLECTION OF BEAMS 225 W lb., and the length of the beam is I in. The bending momentat any distance x between the end and center is The bending moment at any distance x, when x is greaterthan y^l is
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Keywords: ., bookcentury1900, bookdecade1920, booksubjectstructu, bookyear1922
