. The strength of materials; a text-book for engineers and architects. int, we must get anew theory if we wish to calculate the stresses. These so-called discrepancies between theoretical and actualstrengths of beams point to the desirability of choosing theworking stresses for ductile metals in terms of the stress at theelastic limit, and not of the breaking stress—as we pointed outin Chap. III.—because if the working stress in a beam is,say, one-half of the stress at the elastic limit in tension, thentwice the load on the beam will cause the elastic limit in the STRESSES IN BEAMS 209 beam; i
. The strength of materials; a text-book for engineers and architects. int, we must get anew theory if we wish to calculate the stresses. These so-called discrepancies between theoretical and actualstrengths of beams point to the desirability of choosing theworking stresses for ductile metals in terms of the stress at theelastic limit, and not of the breaking stress—as we pointed outin Chap. III.—because if the working stress in a beam is,say, one-half of the stress at the elastic limit in tension, thentwice the load on the beam will cause the elastic limit in the STRESSES IN BEAMS 209 beam; if, however, the workmg stress be taken as one-fourthof the breaking stress in tension, four times the load will notcause failure, the exact load to do this being more, anddepending on the shape of the section. Cast-Iron Beams.—The discrepancy in the case of cast-iron beams is due to the fact that the stress-strain diagram isnot a straight line except for very low stresses and that forgiven strain the stress is appreciably less in tension than in Tension. Fig. 101. compression. The result of this is that the stress diagrambecomes more like that shown in Fig. 101; the neutral axisbecomes raised above the centroid and the diagram is this figure the actual stress is shown about one-half of thecalculated stress. This effect will be most marked in sectionssuch as rounds or diagonal squares with a large amount ofmetal in the web; it is least in I sections with the com-pression flange smaller than the tensile, i. e. the discrepancybetween theory and practice is least in a well-designed section.* Diagonal Square Sections.—It is an interesting factthat we can obtain as follows the apparently paradoxical I 210 THE STRENGTH OF MATERIALS result that by cutting away part of a beam of diagonal squaresection we increase it strength. Referring to Fig. 101a and the table on p. 185 1^, of whole section = (V 2) _ ^ ~48 .. Z of whole section = .o -=~ o = o^ 48
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