. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. 1840.] THE CIVIL ENGINEER AND ARCHITECrS JOURNAL. S3 other dimensions being taken from the transverse section given Journal, page 433, Vol. II in the Evample 2.âOther dimensions remaining the same as in the last Lample, what is the value of * when d and k' are each equal to 7 ft. exam From equation (5) /.â = V- 12,500â17x (2X 17x 7 + 7=) â33x7^ 7x33 + 7x171^ 17 7x33h 7x 17 17 V- .12500-2499-1617 350 17 350 V'493-2 + 424-3 â 20-G = V/ 917 17 17 17 ~ â 20-G = 30-3 â -20-6 = 9-7
. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. 1840.] THE CIVIL ENGINEER AND ARCHITECrS JOURNAL. S3 other dimensions being taken from the transverse section given Journal, page 433, Vol. II in the Evample 2.âOther dimensions remaining the same as in the last Lample, what is the value of * when d and k' are each equal to 7 ft. exam From equation (5) /.â = V- 12,500â17x (2X 17x 7 + 7=) â33x7^ 7x33 + 7x171^ 17 7x33h 7x 17 17 V- .12500-2499-1617 350 17 350 V'493-2 + 424-3 â 20-G = V/ 917 17 17 17 ~ â 20-G = 30-3 â -20-6 = 9-7 feet. 3.âOther dimensions remaining the same as those in ex- ample 1, what is the value of i' when d= 7 feet and *= 9 feet ? From equation (6) we have k' =: V IG 12500 ⢠16 X (7= + 126) â 9 = V- 12,500 â 2800 17 V- ,9700 17 17 â 16= v/570-6â16 23-9 - 16 = 7-9 feet. When/=/' and also i=i', we find from equation (4) by a few easy reductions dâ^' m c3 (6-y)AV (/ + 6) X /' (')⢠6 6 6 also from the general equation of equilibrium, 2A^/+ 2k/d + h\f + -2kdb + bd'- x/i-2 = OTC^ = 4A=/+ 2h/d + 2hdb + bd^, from bd- , and by quadratics, , . , , bd + db mc which /i- + â k = 2/ 4/ '-^Tf + 47â (i f)d 4/ (8). Example 4.âRequired the width of the main dam in fig. 6, the depth of water being 30 feet, and the other dimensions as follows, viz. t'=*=8 feet,/=/'= 15 feet, and 6 = 34 feet. ,12,500 , (34 From equation (7) a â =z v â + 15)11= (34 + 15) 8 34 34 1'2,500 23,104 392 34 = V367-7 + 20â11-5 = V387-7 â 11-5= 19-7 â 11-5 = 8-2 feet, the width required. Example 5.âWhat is the value of i=i' when the depth of water is 27 feet/= 15 feet, 6 = 30 feet, and i=6 feet? From equation (8) A =: V- 9 M X 27' 30 â 15 X 6> 45 x ' ,91,125 = ^-600" ^ 4 60 60 4-5 = V151-9 + 2-2â 4-5 : 60 VIsFl â 4-5 = 12-4 â 45 = 7-9. Example 6.âWhat width shall vpe adopt for the main dam, the depth of the water being IS feet, when /{â¢= i'= 5 feet,/=/'= 12 feet, and 6 = 21
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