A treatise on concrete, plain and reinforced : materials, construction, and design of concrete and reinforced concrete; 2nd ed. . isting Forces in a Re-inforced Chimney. (See p. -J66.) kD fs+nf. whence k = .A (l) APPENDIX III 767 CENTRE OFTENSION By this formula the position of the neutral axis may be determined for anycombinations of /^, f^, and n. If now, as shown in Fig. 244, a represents half the angle subtended at thecenter by the portion in compression, we have cos a = (i â 2 k) from which, for any given value of z, cos a becomes known as well as aand sin a. Thus having locatedthe neutra
A treatise on concrete, plain and reinforced : materials, construction, and design of concrete and reinforced concrete; 2nd ed. . isting Forces in a Re-inforced Chimney. (See p. -J66.) kD fs+nf. whence k = .A (l) APPENDIX III 767 CENTRE OFTENSION By this formula the position of the neutral axis may be determined for anycombinations of /^, f^, and n. If now, as shown in Fig. 244, a represents half the angle subtended at thecenter by the portion in compression, we have cos a = (i â 2 k) from which, for any given value of z, cos a becomes known as well as aand sin a. Thus having locatedthe neutral axis for any given com-binations of /g, fg and n and bear-ing in mind that the stress at anypoint of the shell is proportionalto the distance of that point fromthe neutral axis, it is now possibleto determine the total force on thecompression side, the total forceon the tension side, and also thelocation of the center of compres-sion and the center of tension. Considering a small radial ele-ment subtending an angle dd, asshown in Fig. 244, we have in thiselement, since the length of an arc is its radius times the angle,. CENTREOF COM-PRESSION CONCRETE IN COM-PRESSION STEEL INCOMPRESSION STEEL INTENSION Fig. 244.âDistribution of Stresses in theSteel of a Reinforced Chimney. (^Seep. 767.) area of concrete = t/ddarea of steel = t/dd The distance of the element from the neutral axis is r(cos d â cos a),while the distance from the neutral axis to the point of extreme stress /^ isr\^i â cos a). Therefore the intensity of stress on this elemental area is and r (cos d â cos a) . f in the concrete ^ (i â cos a) r (cos d â cos a)fc n ; ^ in the steel. r (1 â cos a) 768 A TREATISE ON CONCRETE Assuming these intensities at the mean circumference to represent theaverage for the entire element, we have the total force on the elemental area(concrete and steel) /. r (cos d â cos a) dP= {t^+nQrdd -^ z -- * ^ (i â cos a) The total force P on the compression side of the section is the
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Keywords: ., bookcentury1900, bookdecade1910, bookpublishernewyo, bookyear1912
