Plane stress slip-line field solutions, which provide the modes of yielding and the corresponding yield loads, are presented for the plastic bending of end-loaded thin cantilevers of rectangular cross-section containing rectangular holes. The theoretical results obtained from these solutions are compared with some experimental results and those obtained from plane strain slip-line fields and lower bound estimates, all presented previously by the authors (1)‡. It is observed that the correlation of the experimental results was much better with the plane stress solutions than with either the plane strain or lower bound results.
The effect of adjacent holes and possible lateral or local buckling on the ultimate strength of the cantilevers is also examined.
Get full access to this article
View all access options for this article.
References
1.
RanshiA. S.ChitkaraN. R.JohnsonW.‘Limit loads for the plastic bending in plane strain of cantilevers containing rectangular holes under end shear’, Int. J. Mech. Sci., 1973, 15, 15–35.
2.
RanshiA. S.ChitkaraN. R.JohnsonW.‘Plane strain plastic yielding due to bending of end-loaded cantilevers containing circular, triangular or diamond-shaped holes’, Int. J. Mech. Sci., 1973, 15, 329–343.
3.
SavinG. N.‘Stress concentration around holes’, Pergamon Press, New York (1961), Edited by JohnsonW., 430.
4.
DeresiewiczH.‘Stresses in beams having holes of arbitrary shape’, 1968, Proc. A.S.C.E., 94, J. Eng. Mech. Div., 1183–1214.
5.
HellerS. R.Jr‘The stresses around a small opening in a beam subjected to pure bending’, J. App. Mech., 1950, 17, 353.
6.
HellerS. R.JrBrockJ. S.BartR.‘The stresses around a rectangular opening with rounded corners in a beam subjected to bending with shear’, Proc. 4th U.S. Nat. Congr. App. Mech., Berkeley, Calif., 1962, 489–496.
7.
BowerJ. E.‘Elastic stresses around holes in wide-flange beams’, Proc. A.S.C.E., 1966, 92, J. Structural Div., No. ST2, 85–101.
8.
BowerJ. E.‘Experimental stresses in wide-flange beams with holes’, Proc. A.S.C.E., 1966, 92, J. Structural Div., No. ST5, 167–186.
9.
BowerJ. E.‘Ultimate strength of beams with rectangular holes’, Proc. A.S.C.E., 1968, 94, J. Structural Div., No ST6, 1315–1337.
10.
RedwoodR. G.MccutcheonJ. O.‘Beam tests with unreinforced web openings’, Proc. A.S.C.E., 1968, 94, J. Structural Div., No ST1, 1–17.
11.
HillR.‘The mathematical theory of plasticity’, Oxford University Press, 1950.
12.
JohnsonW.ChitkaraN. R.RanshiA. S.‘Plane stress yielding of cantilevers in bending due to combined shear and axial load’, J. Strain Anal., 1974, 9, 67–77.
13.
RanshiA. S.ChitkaraN. R.JohnsonW.‘Plane stress plastic collapse loads for tapered cantilevers and haunched beams’, Int. J. Mech. Sci., 1974, 16, 867–886.
14.
GreenA. P.‘A theory of plastic yielding due to the bending of can tilevers and fixed ended beams’, J. Mech. Phy. Solids, 19543, 1–15 and 143–155.
15.
MuskhelishviliN. I.‘Some basic problems of the mathematical theory of elasticity’, 1953, P. Noordhoff, Groningen, Article 84.
16.
DruckerD. C.‘The effect of shear on the plastic bending of beams’, Trans. A.S.M.E., 1956, 78, J. App. Mech., 509–514.
17.
GreenA. P.‘The plastic yielding of metal junctions due to combined shear and pressure’, J. Mech. Phy. Solids, 1954, 2, 197–211.
18.
BowerJ. E.‘Design of beams with web openings’, Proc. A.S.C.E., 94, J. Structural Div., 1968, No ST3, 783–807.
WorleyW. J.‘Inelastic behaviour of aluminium alloy I-beams with web cutouts’, Bulletin No 448, Engineering Experiment Station, University of Illinois, Urbana, Illinois, April 1958.
21.
TimoshenkoS. P.GereJ. M.‘Theory of elastic stability’, 1961, McGraw-Hill Book Co., New York.
22.
BleichF.‘The buckling strength of metal structures’, 1952, McGraw-Hill Book Co., New York.
23.
GalambosT. V.‘Structural members and frames’, 1968, Prentice-Hall, Englewood Cliffs, N.J.
24.
NealB. G.‘Lateral instability of yielded mild steel beams of rectangular cross-section’, Phil. Trans. Roy. Soc., 1950, 242, Series A, 199–242.
25.
ClarkJ. W.HillH. N.‘Lateral buckling of beams’, Proc. A.S.C.E. July 1960, 86, J. Structural Div., 175–196.
26.
HorneM. R.‘The full plastic moments of sections subjected to shear force and axial loads’, Brit. Welding J., 1958, 170–178.
27.
LongbottomE.HeymanJ.‘Experimental verification of the strengths of plate girders designed in accordance with the revised British Standard 153: Tests on full size and model plate girders’, Proc. Inst. Civ. Engrs., Aug. 1956, 5, Part III.
28.
HosainM. V.SpeirsW. G.‘Experiments on castellated steel beams’, Welding Journal, Welding Research Supplement, Aug. 1973, 329s–342s.
29.
HorneM. R.MerchantW.‘The stability of frames’, 1965, Pergamon Press.
30.
RankineW. J. M.‘Useful rules and tables’, 1866, London.
31.
MerchantW.‘The failure load of rigidly jointed frameworks as influenced by stability’, Structural Engineers, 1954, 32, 185.
32.
MerchantW.‘Frame instability in the plastic range’, British Welding Journal, 1956, 3, 366.
