C-F13F13 Proportions of beams and girders

F13.1 Strength Reductions for Members with Bolt Holes in the Tension Flange

Historically, provisions for proportions of rolled beams and girders with bolt holes in the tension flange were based upon either a percentage reduction independent of material strength or a calculated relationship between the tensile rupture and tensile

yield strengths of the flange, with resistance factors or safety factors included in the calculation. In both cases, the provisions were developed based upon tests of steel with a specified minimum yield stress of 36 ksi (250 MPa) or less.

More recent tests (Dexter and Altstadt, 2004; Yuan et al., 2004) indicate that the flexural strength on the net section is better predicted by comparison of the quantities $F_{y} A_{f g}$ and $F_{u} A_{f n}$, with a slight adjustment when the ratio of $F_{y}$ to $F_{u}$ exceeds 0.8 . If the bolt holes remove enough material to affect the member strength, the critical stress is adjusted from $F_{y}$ to $F_{u} A_{f n} / A_{f g}$ and this value is conservatively applied to the elastic section modulus, $S_{x}$.

The resistance factor and safety factor used throughout this chapter, $\phi=0.90$ and $\Omega=1.67$, are those normally applied for the limit state of yielding. In the case of rupture of the tension flange due to the presence of bolt holes, the provisions of this chapter continue to apply the same resistance and safety factors. Because the effect of Equation F13-1 is to multiply the elastic section modulus by a stress that is always less than the yield stress, it can be shown that this resistance and safety factor always give conservative results when $Z / S \leq 1.2$; it can also be shown to be conservative when $Z / S>1.2$ and a more accurate model for the rupture strength is used (Geschwindner, 2010a).

F13.2 Proportioning Limits for I-Shaped Members

The provisions of this section were taken directly from Appendix G, Section G1, of the 1999 AISC LRFD Specification (AISC, 2000b) and have been the same since the 2005 AISC Specification (AISC, 2005b). They have been part of the plate girder design requirements since 1963 and are derived from Basler and Thürlimann (1963). The web depth-to-thickness limitations are provided to prevent the flange from buckling into the web. Equation F13-4 was slightly modified from the corresponding Equation A-G1-2 in the 1999 AISC LRFD Specification to recognize the change in the definition of residual stress from a constant 16.5 ksi (110 MPa) to 30% of the yield stress in the 2005 AISC Specification, as shown by the following derivation:

(C-F13-1)

F13.3 Cover Plates

Cover plates need not extend the entire length of the beam or girder. The end connection between the cover plate and beam must be designed to resist the full force in the cover plate at the theoretical cutoff point. The end force in a cover plate on a beam whose required strength exceeds the available yield strength, $\phi M_{y}=\phi F_{y} S_{x}$ (LRFD) or $M_{y} / \Omega=F_{y} S_{x} / \Omega$ (ASD), of the combined shape can be determined by an elastic-plastic analysis of the cross section but can conservatively be taken as the full yield strength of the cover plate for LRFD or the full yield strength of the cover plate divided by 1.5 for ASD. The forces in a cover plate on a beam whose required strength does not exceed the available yield strength of the combined section can be determined using the elastic distribution, $M Q / I$.

The requirements for minimum weld lengths on the sides of cover plates at each end reflect uneven stress distribution in the welds due to shear lag in short connections.

The requirement that the area of cover plates on bolted girders be limited was removed for the 2016 AISC Specification (AISC, 2016) because there was no justification to treat bolted girders any differently than welded girders when considering the size of the cover plate.