. Concrete bridges and culverts, for both railroads and highways . )oint .r may be selected, so thecurve on the left will fall within the middle third,or tangent to it. It will be seen that this line ofresistance shown dotted, falls outside of the middlethird in two places and intersects the outer verticalthrough c at 3. This curve cuts the center lineof arch at /. See if it is possible to draw anotherline of resistance, so that it will cut the center ofthe span at the point / and pass through the point P draw a line parallel to / y intersectingAB at D, and from D draw another line DP p
. Concrete bridges and culverts, for both railroads and highways . )oint .r may be selected, so thecurve on the left will fall within the middle third,or tangent to it. It will be seen that this line ofresistance shown dotted, falls outside of the middlethird in two places and intersects the outer verticalthrough c at 3. This curve cuts the center lineof arch at /. See if it is possible to draw anotherline of resistance, so that it will cut the center ofthe span at the point / and pass through the point P draw a line parallel to / y intersectingAB at D, and from D draw another line DP parallelto ty. The new pole will lie on the line DP. Alsotlirough P draw a line parallel to xy intersectingthe load line in Q. and from Q draw another line QPparallel to .n, intersecting the line DP at P. Thepoint will be the correct position of the pole, inorder to have the line of resistance pass throughthe three points, .r, / and y. The distance 11 in thr^force polygon may be verified analytically as fol-lows :—. u « ID m 0) o CI t> o hf ■^ H c3 d 13 a j^ ^ rt d -^ X a 3 Oj O 1—1 -£ d p H rC .s M :3 , CI o; jA Ll -^ C2 <V rt =1 hn +^ o n ; ^ tC VJ cc i) —I ^ a: d pi ^ ^^^ U o a S ^ J ^ b 12 -tJ o coyo tg ©-^ J ^ •^ S dHoc »3 ^ S O CU (V, ot^ S t^ 3-5 o c ^ •^ •= ^ I 5 S „ <fH =2 -4 r^ ■^ 1« !D •- 2 CO v- ,a S S <ft o s J3 O ^ *^ en ^ .S Ti • ^ u % I ^^ 2 o -2 -- 5 5 .2 y *2 <i-i S ^ -t= oO U c3 c3 « PLAIN COXCRETE ARCH BRIDGES. 49 HX^A; = Hx/A:.From this equation the value of II may be found,and the point P will lie on the line QP at a distanceII from the load line. The line of resistance xfy istangent to the line of middle third in the strip point where lines become tangent might havelieen taken as the required point through whicli,with .r and f, it was desired to pass a line of re-sistance. The corresponding line would hav
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Keywords: ., bookcentury1900, bookdecade1900, bookidconcretebrid, bookyear1909
