Strength of webs of I-beams and girders

1. Preliminary. In designing beams and girders it is usual to consider that the bending action is resisted by the flanges, and the shearing stress by the web. There is a tendency, however, for webs of deep girders to fail by buckling; and there are complex stresses set up at the junction of the web and flange. There are also crushing stresses in the web over the supports of the girder or under the points of application of concentrated loads.

When a girder is subjected to flexure the material on one side of the neutral axis is subjected to longitudinal tensile stresses and the material on the other side is subjected to longitudinal compressive stresses. The material at any point in the girder is also subjected to longitudinal and to transverse shearing stresses of equal intensity. The longitudinal tensile and compressive stresses are equal to zero at the neutral axis and increase to a maximum at the outer edges of the flanges. The shearing stresses are equal to zero at the outer edges of the flanges and increase to a maximum at the neutral axis. Since the shearing stress is equal to zero at the outer edge of the girder the flange carries little and the web practically all of the shear on a transverse section.

In the design of a girder the longitudinal stress in the outer edge of the flange is limited to a safe value for the material in tension or compression, and the average shearing stress in the web (obtained by dividing the maximum total shear upon a transverse section by the cross-sectional area of the web) is kept within safe limits for the material in shear. Although, according to the elastic theory of beams, points intermediate between the neutral axis and the outer edge of the flange are subjected to both longitudinal tension or compression and to transverse and longitudinal shear, and although it is known that these combined stresses result in diagonal tensile (or compressive) and shearing stresses which are greater than the component stresses producing them, these diagonal stresses are not considered in the design of the girder. The view has been held that the diagonal tensile or compressive stresses do not materially exceed the simple longitudinal stress at the outer edge of the flange, and that the diagonal shearing stress does not materially exceed the shearing stress at the neutral axis.

It has been shown by tests that a tensile (or compressive) stress produces a strain in a direction at right angles to the line of action of the stress, the term strain being here used to designate deformation and not stress which is used to designate an internal resisting force. Recent tests, notably those of Dr. Becker, indicate that the tendency of a material to fail depends, within certain limits, upon the strain, and that a stress in one direction, while it does not set up lateral stress, does set up lateral strain, and affects the strength of the material. An analysis of diagonal stresses in a girder shows that, in general, a load which sets up a stress in a diagonal direction sets up a second stress at right angles to that direction. Hence, in considering the strength of a girder to resist a diagonal stress any stress at right angles to that diagonal stress must be taken into account.

The tests reported in this bulletin were made to study the web strains in I-beams and girders so designed that the primary failure would be a web failure. The test data obtained were used in conjunction with a mathematical analysis made to determine the importance of the diagonal strains and the methods of failure of girders.

2. Previous Tests of the Web Strength of I-Beams and Girders. Not many tests of I-beams and girders in which the primary failure was web failure have been made. Table 1 (reprinted from bulletin 68 of the Engineering Experiment Station of the University of Illinois) gives the results of a few such tests.

3. Acknowledgment. This Investigation was a part of the re- search work of the Department of Theoretical and Applied Mechanics and of the Department of Civil Engineering, and was conducted under the general supervision of Professor A. N. Talbot, of the Department of Theoretical and Applied Mechanics, and Professor I. 0. Baker, of the Department of Civil Engineering. Wherever reference has been made to the work of other investigators, credit has been given in the text.