The strength of I-beams in flexure

The Engineering Experiment Station was established by act of the Board of Trustees, December 8, 1903. It is the purpose of the Station to carry on investigations along various lines of engineering and to study problems of importance to professional engineers and to the manufacturing, railway, mining, constructional, and industrial interests of the State.

The control of the Engineering Experiment Station is vested in the heads of the several departments of the College of Engineering. These constitute the Station Staff, and with the Director, determine the character of the investigations to be undertaken. The work is carried on under the supervision of the Staff, sometimes by research fellows as graduate work, sometimes by members of the instructional staff of the College of Engineering, but more frequently by investigators belonging to the Station corps.

The results of these investigations are published in the form of bulletins, which record mostly the experiments of the Station's own staff of investigators. There will also be issued from time to time in the form of circulars, compilations giving the results of the experiments of engineers, industrial works, technical institutions, and governmental testing departments.

The volume and number at the top of the title page of the cover are merely arbitrary numbers and refer to the general publications of the University of Illinois; above the title is given the number of the Engineering Experiment Station bulletin, or circular, which should be used in referring to these publications.

For copies of bulletins, circulars or other information address the Engineering Experiment Station, Urbana, Illinois.

Introduction. The mathematical theory of the resistance of materials in flexure has been extensively developed, but much less has been done in the experimental study of the phenomena of flexural stress. A striking fact brought out in the tests which have been made is the tendency of metal beams to fail by reason of column action in fibers which are under compressive stress. This tendency is especially strong in I-beams, channel-beams, and other forms of beams having tension and compression flanges connected by a comparatively thin web. The tests of Marburg, Christie, and Burr and Elmore show that this column action in I-beams may cause failure of test pieces by sidewise buckling or on account of excessive stresses in the web. These tests emphasize the importance of taking into account of stresses other than the direct flexure stresses in the flanges.

The wide-spread use of I-beams as flexural members makes the subject of their flexural strength a matter of general engineering interest. To obtain experimental data on the action of I-beams under load, several series of tests of I-beams were carried out in the Laboratory of Applied Mechanics of the University of Illinois. This bulletin records and discusses the results of these tests and of others of similar kind. A formula is deduced for the flexural strength of I-beams which are not restrained against sidewise buckling. There also is given a discussion of the stiffness of I-beams, a discussion of the action of I-beams restrained against sidewise buckling and restrained against twisting at the ends of the beams, and a discussion of web failure of I-beams.

3. Phenomena of Flexural Failure. The formulas commonly used for computing the stresses and deflections in beams are based on the assumptions (1) that a plane cross-section of a beam remains plane during flexure and (2) that the moduli of elasticity of the beam material for tension and for compression are equal and constant. For low stresses and for beams of medium or long spans these assumptions are very nearly exact. They become rough approximations when a beam is loaded to a point near failure.

The failure of beams of brittle material usually occurs by snapping of the extreme tension fibers at a computed fiber stress higher than the tensile strength of the material as determined by tension tests of specimens. Brittle material is nearly always much weaker in tension than in compression. As the fiber stress in beams of such material increases with increasing load, by reason of the change which takes place in the values of the moduli of elasticity, the tension side of the beam stretches more readily than the compression side shortens. The effect is to shift the neutral axis of the beam toward the compression side. This, together with the difference in strength, causes the actual tensile fiber stress to be less than the computed tensile fiber stress.

The failure of beams of ductile material may take place in one of a number of ways:

(1) The beam may fail by direct flexure. Under increasing load the usual flexure formulas are very nearly exact up to a load which stresses the extreme fibers of the beam to the yield-point strength of the material. When the yield point is reached in the extreme fibers, the deflection of the beam increases more rapidly with respect to an increase of load; and if the beam is of a thick, stocky section or is firmly held so that it cannot twist or buckle, failure takes place by a gradual sagging which finally becomes so great that the usefulness of the beam as a supporting member is destroyed.,

(2) In a beam of long span, the compression fibers act somewhat as do the compression fibers of a column, and failure may take place by buckling. Buckling failure, in general occurs in a sidewise direction. Sidewise buckling may be either the primary or the secondary cause of failure. In a beam in which excessive flexural stress is the primary cause of failure and in which the beam is not firmly held against sidewise buckling, the primary overstress may be quickly followed by the collapse of the beam due to sidewise buckling. The sidewise resisting strength of a beam is greatly lessened if its extreme fibers are stressed to the yield point. Sidewise buckling may in some cases be a primary cause of beam failure, in which cases the computed fiber stress, in general, does not reach the yield-point strength of the material. Sidewise buckling not infrequently limits the strength of narrow, deep beams, especially beams of I-section or channel-section with tension and compression flanges connected by a thin web. Whether it is a primary cause of failure or a final manner of failure, sidewise buckling results in a clearly marked and generally quite sudden failure of a beam.

(3) Failure in an I-beam or a channel-beam may occur by excessive shearing stress in the web, or by buckling of the web under the compressive stresses which always accompany shearing stress. If the shearing fiber stress in the web reaches a value as great as the yield-point strength of the material in shear, beam failure may be expected and the manner of failure will probably be by some secondary buckling or twisting action. The inclined compressive stress always accompaning shear may reach so high a value that the buckling of web of the beam is a primary cause of failure. Danger of web failure as a primary cause of beam failure exists, in general, only for short beams with thin webs.

(4) In the parts of beams adjacent to bearing blocks which transmit concentrated loads or reactions to beams, high compressive stresses may be set up, and in I-beams or channel-beams the local stress in that part of the web nearest a bearing block may become excessive. If this local stress exceeds the yield-point strength of the material at the junction of web and flange, the beam may fail primarily on account of the yielding of the overstressed part and finally by a resulting twisting action of the beam.