Essentials in the theory of framed structures . + 28P8 + 2P9<2oPio + 34^11 + 40P12. There are two positions of the train, when moving to the left,which satisfy this criterion; namely, wheel 11 at ^2 and wheel 8at Lg. The maximum shear, occurring when the train is in thelatter position, is — lb.; as found by taking the sum of theproducts of each floor beam load and its corresponding value may be closely approximated by the proportionatemethod, as follows: Since the influence line jklmnop (Fig. 197)has its longest ordinate at the center of the arm, it will becompared with th
Essentials in the theory of framed structures . + 28P8 + 2P9<2oPio + 34^11 + 40P12. There are two positions of the train, when moving to the left,which satisfy this criterion; namely, wheel 11 at ^2 and wheel 8at Lg. The maximum shear, occurring when the train is in thelatter position, is — lb.; as found by taking the sum of theproducts of each floor beam load and its corresponding value may be closely approximated by the proportionatemethod, as follows: Since the influence line jklmnop (Fig. 197)has its longest ordinate at the center of the arm, it will becompared with the influence line abc (Fig. 198), which also hasits longest ordinate at the center of the arm. The latterinfluence line is for the moment at U3 for Case III, and themoment is 7,057. The ratio of the sum of the ordinates 312 THEORY OF FRAMED STRUCTURES Chap. VIII jklmnop (Fig. 197) to the sum of the ordinate abc (Fig. 198) = — and 7)057 X — = — = shear in panel o-i. Ui Uz IJ3 U4. Us Ufe Uj Ur Ufl Uio Uii. FIG. 200 This quantity represents also the maximum negative reactionat Lo when the right arm is loaded, from which all the stresses Sec. I SWING BRIDGES 313 may be determined as given in the designated column of Table I. 191. Shear in Panel 1-2.—The influence lines are shown inFig. 199. The stresses in UiL2 for Case III, as given in TableI, are —11 and +140; from which the stresses for Case IV may-be found as follows: ^ +140 X °if+°-°^ t °-^ t °° = +113 + + + stresses for Case IV, determined by the exact method, are — 15 and +113 respectively. 192. Shear in Panel 2-3.—The influence lines are shown inFig. 200. The stresses in LiUs for Case IV, determined by theproportiorfate method are +39 X °°7 + ^ ^.^ + -82 X °-4°6 + o-24i+o-i03 = + + The stresses for Case IV, found by the exact method, are +48 and —60 respectively. 193. Shear in Panel 3-4.—The
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