144 Mechanics of Materials 2 §5.3 For such sections egns.(5.1)and(5.2)may be re-written in the form TT tmax kidb=Zi (5.7) T and T L=kadbG JegG (5.8) where Z'is the torsion section modulus =Z'web +Z'flanges kidib+kid2b2+...etc. =∑k1db2 and Jeg is the "effective"polar moment of area or"equivalent J"(see $5.7) J eq web Jeg fianges k2dib+k2d2b+...etc. =∑k2db3 T i.e. tmax三 ∑k1db2 (5.9) 0 T and L=G∑kdb (5.10) and for d/b ratios in excess of 10,k=k2=.so that 3T Tmax= ∑db2 (5.11) 8 3T L=G∑ab (5.12) To take account of the stress concentrations at the fillets of such sections,however,Timo- shenko and Young'suggest that the maximum shear stress as calculated above is multiplied by the factor 6 Aa (Figure 5.3).This has been shown to be fairly reliable over the range 0<a/b<0.5.In the event of sections containing limbs of different thicknesses the largest value of b should be used. b Fig.5.3. S.Timoshenko and A.D.Young.Strength of Materials.Van Nostrand.New York.1968 edition.144 Mechanics of Materials 2 $5.3 For such sections eqns. (5.1) and (5.2) may be re-written in the form T kldb2 Z’ - T Tmax = and T ~- - - T - I9 L k2db3G J,,G _- where Z’ is the torsion section modulus = Z’ web + Z’ flanges = kldlbt + kld2b; + . . . etc. = Ckldb2 and J,, is the “effective” polar moment of area or “equivalent J” (see $5.7) = J,, web + J,, flanges = k2dl b: + k2d2b: + . . . etc. = Ck2db3 T kldb2 i.e. Tmax = and l and for d/b ratios in excess of 10, kl = k:! = 3, so that 3T Tmax = ~ db2 3T - e - L GCdb3 (5.9) (5.10) (5.11) (5.12) To take account of the stress concentrations at the fillets of such sections, however, Timo￾shenko and Young? suggest that the maximum shear stress as calculated above is multiplied bv the factor (Figure 5.3). This has been shown to be fairly reliable over the range 0 < a/b < 0.5. In the event of sections containing limbs of different thicknesses the largest value of b should be used. Fig. 5.3 ‘S. Timoshenko and AD. Young, Strength offuteritrls, Van Nostrand. New York. 1968 edition