. Engineering and Contracting. CaFt. Excayat/on .^ x .50 Total27/3 /lax L pad on Toe -/70 ^per saF/11—Comparison of Three Designs of Concrete Retaining Walls. 174 ENGINEERING-CONTRACTING Vol. XXXIII. No. 8. zontal lines in the table represent beams andthe cross lines the various supports. Abovethis line are given the bending moment factorsat center and at the supports of any span in anumber of spans. Below this hne is given the /^distance between this formula as a rule—The average of moment factors at the sup-ports (disregarding negative sign) phis mo-ment factor
. Engineering and Contracting. CaFt. Excayat/on .^ x .50 Total27/3 /lax L pad on Toe -/70 ^per saF/11—Comparison of Three Designs of Concrete Retaining Walls. 174 ENGINEERING-CONTRACTING Vol. XXXIII. No. 8. zontal lines in the table represent beams andthe cross lines the various supports. Abovethis line are given the bending moment factorsat center and at the supports of any span in anumber of spans. Below this hne is given the /^distance between this formula as a rule—The average of moment factors at the sup-ports (disregarding negative sign) phis mo-ment factor at center equals — 1/8. of continuity is to consider the ends of thebeam cantilevering out to the point of inflec-tion and the span of beam between the pointsof inflection as a simple beam. This ideaaffords an independent way of proving the. fn^.-Conf^. Fig. 1—Diagram for Theorem of Three Moments for Computing Reinforced Concrete Slabs. Formulas—Theorem of three moments. Spansequal and loads equal and uniform. Starting atany support: (1) M, -I- 4 M: -I- M3 = — wl=, M™ 4- 4 M3 +M, = — wl-, etc. Mo—Ml wl (2) V, = -t- — 1 2 (3) M = Ml -h Vix (4) Mc = Ml + Vi % w combine 2 X ~ :l\\ = 1-Dl. 1 % WX-. Mc = mom. at center x — and 4 (make Vi =: Vi).M,-|-M2 (5) h Mc = ^i w 1=. 2 Substituting in (3) values of Mi and Vi andplacing M = o X = distance out of point of in-flection in terms of ^ For M = 12wl Vi = 2 NOTES. Above.—Moment factors for wl-. Below.—Vertical shear factors for wl. (1st) From formula (5) average of sum offactors at supports in any span (disregardingsign) plus factor at center = ^ = .125. (2d) Sum of vertical shear factors in a span=: 1 and sum of factors at a support multipliedby wl equals the reaction. (3d) The maximum distance out of point ofinflection = 1-5 1 in the ctise of a beam perfe
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