. Strength of materials: a practical manual of scientific methods of locating and determining stresses and calculating the required strength and dimensions of building materials . ) acts. By center of gravity of a plane area of any sha|)e we meanthat point of it wliich corresj)oiHls to tlie center of iii-;i\itv of apiece of tin when tlu^ latter is cut out in tlie sli:i|)(> of llio center of gravity of a (piite iii-cgular area can lie foiiiid nn)strciadily by balancing a piece of tin oi still pajHT cut in tlie sliajieof the area. But when an area is sinipK in sliajtc, ov consists of
. Strength of materials: a practical manual of scientific methods of locating and determining stresses and calculating the required strength and dimensions of building materials . ) acts. By center of gravity of a plane area of any sha|)e we meanthat point of it wliich corresj)oiHls to tlie center of iii-;i\itv of apiece of tin when tlu^ latter is cut out in tlie sli:i|)(> of llio center of gravity of a (piite iii-cgular area can lie foiiiid nn)strciadily by balancing a piece of tin oi still pajHT cut in tlie sliajieof the area. But when an area is sinipK in sliajtc, ov consists ofparts which are simple, the center of gra\ ity of tlu whole can l»e 44 STKEXGTH OF MATEEIALS found readily Dy computation, and such a method will now bedescribed. 48. Principle of rioments Applied to Areas. Let Fig. 21represent a piece of tin which has been divided off into any num-ber of parts in any way, the weight of the being AV, andthat of the parts Wj, W^, ^^, etc. Let Oj, C,, Cg, etc., be thecenters of gravity of the parts, C that of the whole, and c^, c.,, c^,etc., and c the distances from those centers of gravity respectivelyto some line (L L) in the plane. Ficr. 21. of the sheet of tin. Wlien thetin is lying in a horizontal posi-tion, the moment of the weio-htof the entire piece about L L isW^, and the moments of theparts are Wi^i, Wg^^g, etc. Sincethe weight of the whole is theresultant of the weights of theparts, the moment of the weightof the whole equals the sum of the moments of the weio-hts of theparts; that is, ■Vrc=^V,^etc . .. Xow let Aj, A2, etc. denote the areas of the parts of the piecesof tin, and A the area of the whole; then since the weio-hts areproportional to the areas, we can replace the ^\s in the precedingequation by corresponding As, thus: Ar=A/i-L A/.-,-f-etc (4) If we call the product of an area and the distance of itscenter of gravity from some line in its plane, the moment of thearea with respect to that line, then the precedin
Size: 2033px × 1229px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1900, bookpublisherchicagoamericansch
