Essentials in the theory of framed structures . Fig. 17. Sec. VI EQUILIBRIUM OF COPLANAR FORCES 33 ZV=-A+B-C + D•ZH = +F + G- E SMp = -{a + h)A + (6 + h)B - (c + h)C + {d + h)D -{f + k)F-(g + k)G+{e + k)EHMo = -aA +bB -cC +dD -JF -gG +eE•2Mp - l^Mo = K-A + 5 - C + D) + k{-F -G + E) = {kX IV) - (kX IH)If 2H = o (i) and ZF = o (2) then IMp — IMo = o or IMp = 7:Mo for any value of A or ^. Hence, if the vertical magnitudes are balanced and the hori-zontal magnitudes are balanced, the algebraic sum of themoments of the forces is the same for all points chosen as thecenter of moments; in which case
Essentials in the theory of framed structures . Fig. 17. Sec. VI EQUILIBRIUM OF COPLANAR FORCES 33 ZV=-A+B-C + D•ZH = +F + G- E SMp = -{a + h)A + (6 + h)B - (c + h)C + {d + h)D -{f + k)F-(g + k)G+{e + k)EHMo = -aA +bB -cC +dD -JF -gG +eE•2Mp - l^Mo = K-A + 5 - C + D) + k{-F -G + E) = {kX IV) - (kX IH)If 2H = o (i) and ZF = o (2) then IMp — IMo = o or IMp = 7:Mo for any value of A or ^. Hence, if the vertical magnitudes are balanced and the hori-zontal magnitudes are balanced, the algebraic sum of themoments of the forces is the same for all points chosen as thecenter of moments; in which case if 2M = o (3) for any point, the moments are balanced about all points,equilibrium is assured; and there will be one and only oneindependent If-equation as illustrated in Article 24. 26. Four Groups.—The three statements or Eqs. (i), (2)and (3) are the necessary and sufl&cient conditions for insuringthe equilibrium of a body, when acted upon by any system ofcoplanar non-concurrent forces; and any fourth equation will bedependent on
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Keywords: ., bookcentury1900, bookdecade1920, booksubjectstructu, bookyear1922
