This section is from the book "Safe Building", by Louis De Coppet Berg. Also available from Amazon: Code Check: An Illustrated Guide to Building a Safe House.
As a rule the angles are made in one piece from end to end, as they can easily be obtained of great length, and are awkward to splice. Angles should be used as heavy as possible, but if very thick they are difficult to straighten, and besides reduce greatly the value of flange rivets, owing to the bending-moment.
In determining the thickness of web it has to have sufficient area of vertical cross-section at all points to resist the vertical cross-shearing, and must be stiff enough not to buckle under its load, which will be equal to the vertical cross-shearing at each point of web.
Angles in one piece.
As this vertical cross-shearing is always greatest at one or both supports, we should have for thickness of web:
b = p/d.(g/f)
Where b = the required thickness of web, in inches, (should never be less than 1/4" thick).
Where d = the depth of web, in inches, this should be the net depth d, that is depth less all rivet holes coming on any vertical section at or near reaction.
Where p = the reaction, in pounds, at either end, (Formulae 14 to 17). The larger reaction should be used, where they are unequal.
If web is not to be of uniform thickness throughout, use, in place of p, the amount of vertical shearing-strain, in pounds, at the point for which thickness of web is being calculated.
Where (g/f ) = the safe cross-shearing stress of the material, in pounds, per square inch.
In many plate girders the web will be so thin in comparison to its depth, that there will be serious danger of the web buckling, particularly towards the ends where the vertical cross-shearing (except in case of single concentrated loads) is always greatest.
To avoid this danger the web is stiffened by riveting upright angle irons, or T-irons to same, between the flanges. The ends of these stiffeners should always he planed and bear truly against each flange. At the very ends of girders there should always be stiffeners over the reactions, of sufficient strength, as columns, to carry the amount of reaction, less the amount of bearing of web on reaction. As the length of these columns will be only equal to the depth of girder, and the column will generally consist of the hearing amount of web, plus two angles, they, the stiffeners, can safely be considered as short columns and the full safe compression stress, per square inch, allowed on them. The number of rivets connecting any of the stiffeners to web, should equal the amount of cross-shearing being carried by the stitffener, that is vertical cross-shearing at the stiffener, less the amount borne by web. This latter amount at the ends is the safe load on a column or section of web, equal to its bearing on reaction; between reactions a section of web equal to its depth is taken as assisting or being assisted by the stiffener, that is as acting together with the stiffener. While the web really receives its load from the flanges by pin-connected ends - rivets-it is, nevertheless, assumed by most engineers to have planed ends, presumably to avoid too many stiffeners, the whole calculation, as it is, being but very theoretical anyhow.
Danger of buckling.
Use of stiffeners.
We should have, then, amount of strain on end stiffeners,
Strain on end stiffeners.
s = p - 12000.b.x/1+0,0003.d2/b2
(125) and amount of strain on intermediate stiffeners,
Strain on intermediate stiffeners.
s = y - 12000.b.d/1+0,0003.d2/b2
Where s = the total compression strain on stiffeners in pounds; the stiffeners should have sufficient area of cross-section to resist this strain, considered as short columns, and sufficient rivets connecting them to web to ==s in value.
Where p = the greater reaction, in pounds, where the reactions are unequal; or either reaction where they are equal, see Formulas (14 to 17).
Where y = the amount of vertical cross-shearing, in pounds, at the point of girder, see Formula (11), at which stiffener is applied.
Where x = the distance, in inches, that girder rests on (selected) reaction p.
Where b = the thickness of web, in inches, at end or at point y, as the case may be.
Where d - the depth of web, in inches, at end or point y, as the case may be.
To deride whether the web needs or does not need stiffeners, and if so, at what points, use the following formula.
Where stiffeners are necessary.
y = 12000.b.d/1+0.0003.d2/b2
Where b and d same as in Formulas (125 and 126). Should y be larger than the greater reaction p no stiffeners are required, except at the very end.
Should y be less than either reaction, stiffeners will be required up to the point of web where the vertical shearing - (as found by Formula 11) -just equals y.
At this point place stiffeners a distance apart equal to the depth of web.
Stiffeners should always be placed under concentrated loads. At end of web place stiffeners and again just inside of reaction, and between end and point where y equals shearing place stiffeners, not less than the depth of web apart, and gradually diminishing the distance between them towards end ; this distance should be regulated by the amount of increase in vertical shearing towards end.
In regard to the deflection of plate girders, the same rules apply, as for beams, that is FormulŠ (36) to (42), Table VII, and FormulŠ (95) to (97). It should be noted, however, that owing to more or less imperfections in riveting, fitting of parts, etc., the plate girders will deflect very much more than if calculated by these rules, with a modulus of elasticity same as for perfectly rolled beams.
To allow for these imperfections in manufacture a lower modulus of elasticity should be used, to be varied according to the care exercised in manufacturing the girder. Experiments on riveted girders have given moduli of elasticity for steel as low as 5000000 pounds-inch.