# Correspondence. The Behaviour and Strength of Prestressed Concrete and Rectangular Beams Subjected to Combined Bending and Torsion

*Dr. G. S. Pandit: The tests reported by the authors have made an invaluable contribution to the understanding of the problem of combined bending and torsion of prestressed concrete beams. The tests have further corroborated the generally accepted view that the bending moment can increase the torsional strength only if the prestressing is eccentric and that the effect of bending moment of whatever magnitude is to reduce the torsional strength of concentrically prestressed beams. The line of thrust (or the centre of compression) of an unloaded prestressed concrete beam coincides with the centroid of the prestressing steel. The effect of
bending moment is only to shift the line of thrust through a distance em = Mb / P where P is the total effective prestressing force. If the bending moment Mb is of such
magnitude that em equals the eccentricity of prestressing force e, then the line of thrust coincides with the centroid of the cross-section producing uniform compressive
stress over the entire cross-section. Hence the optimum bending moment for maximum torsional strength would appear to be Mb, opt = Pe. For the Series E,P =1/2 x 1820 x 5 x 8 = 36400 Ib and e = 8/6 = 1.33 in. Hence Mb,opt = 36 400 x 1.33 = 48 533 Ib in or 48.5 kips in. This value of optimum bending moment is in close agreement with authors' test results for beams of Series EW of Part 2 with p = 1.0 per cent and 1.6 per cent as can be seen from the interaction diagrams of Fig 18 by scaling out the bending moment corresponding to the maximum torque. The agreement is not so good for the beams of Series E, Fig 9, in which the optimum bending moment appears to be about 80 kips in. The shape of the interaction diagram for Series E in Fig 9 does not agree with the theoretical shape and I wonder, therefore, whether this could be attributed to the usual scatter and the possible errors of observation. It may be pointed out that the theoretical interaction diagram of Fig 8 is in contradiction with authors' own observations regarding the increase and decrease in torsional strength due to bending moment for eccentrically and concentrically prestressed beams respectively. Thus the authors' theory would appear to be conservative for eccentrically prestressed beams and errs on the unsafe side for concentrically prestressed beams in the range Mb < Mboc.*