Service Limit State Control of Permanent Deflection for Steel Sections in Flexure

The service limit state control of permanent deflection for steel sections in flexure has serious implications for both design and evaluation of steel bridges. These provisions are found in Article 6.10.3 of the American Association State Highway and Transportation Officials (AASHTO) LRFD Bridge Design Specifications [AASHTO, 1998]. Load combination Service II of LRFD Table 3.4.1-1 is the specified combination for this limit state. This uncalibrated limit state/load combination governs the design of compact steel sections in flexure, as demonstrated by several published deign examples. Since the vast majority of modern steel sections in positive flexure qualify as compact sections in the LRFD Specifications, the implications of this governing, uncalibrated limit state are significant. The limit state is also suggested in the proposed AASHTO Manual for Condition Evaluation and Load and Resistance Factor Rating of Highway Bridges for the review of permit issuance. These provisions were first introduced with Load Factor Design in the 1970's, based upon limited experimental results from the earlier AASHTO test road bridges [HRB, 1962]. Herein, the basis of these provisions is reviewed and discussed, along with the questions that must be answered to calibrate this important limit state for rational use in both design and evaluation of steel bridges. Introduction The AASHTO LRFD Bridge Design Specifications [AASHTO, 1998] specify four sets of limit states for the design of highway bridges: the service, strength, fatigue-andfracture, and extreme-event limit states, in Article 1.3.2. Of these limit states, the service limit states, which ensure serviceability of the structural components, are material dependent. Load combinations for all of the limit states are specified in Table 3.4.1-1. The service I and III load combinations are applied in the design of concrete components only. The service I load combination is applied when checking cracking of reinforced-concrete components, and when checking compressive stresses in prestressed-concrete components. The service III load combination is applied when checking tensile stresses in prestressed-concrete components. The subject of this discussion, the service II load combination, is applied only to steel components: slip-critical bolted connections and compact sections in flexure. The Service II Load Combination The service II load combination basically combines 130% of the nominal notional live load with 100% of the dead load. Slip-critical bolted connections shall not slip, and the Copyright ASCE 2004 Structures 2000 2 extreme fiber of compact steel sections in flexure shall not yield under the service II load combination. This discussion concentrates on the “Service Limit State Control of Permanent Deflection,” as this compact-section check is termed in Article 6.10.6. While the LRFD Specifications do not specifically state that this load combination only applies to compact sections, a quick comparison of load combinations specified in Table 3.4.1-1 reveals that the criterion for the control of permanent deflection does not govern for composite non-compact sections. The load factors for this load combination were not calculated based upon a reliabilitybased calibration of the limit state, as the control of permanent deflection is not well defined with significant performance data. The load factors were developed to produce designs of comparable proportions to those of compact sections design to the recently archived AASHTO Standard Specifications for Highway Bridges [AASHTO, 1996]. The Control of Permanent Deflection This deflection control states that flange stresses of composite steel sections in both positive and negative flexure shall not exceed 95% of the “effective” yield strength of the flange (“effective” yield strength being the author’s term). The “effective” yield strength is the minimum specified yield strength of the flange modified by reduction factors for load-shedding from the web from bend-buckling and under-strength webs of hybrid girders. A similar relationship is specified for non-composite steel section, but as modern steel sections should only be constructed as composite girders, non-composite sections will not be considered in this discussion. As stated in the commentary to the provisions, the limit state is “intended to prevent objectionable permanent deflections due to expected severe traffic loadings that would impair rideability.” The limit state was originally developed as the overload check of Article 10.57 of the Standard Specifications. The AASHTO test road bridges [HRB, 1962] suggested that repetitive stress excursions near, but below, the yield strength produced permanent set approaching potentially undesirable roadway profiles. Thus, the limit state limits computed stress to approximately 95% of the yield strength under an overload, of 130% of the nominal notional live load in the case of the LRFD Specifications. Design Implications The implications of the service II load combination for control of permanent deflection are evident in the sample, state-of-the-art and cost-effective LRFD designs developed by HDR Engineering, Inc. for the American Iron and Steel Institute (AISI), and published by the National Steel Bridge Alliance (NSBA) [NSBA, 1997]. These examples illustrate that the service II load combination governs the design of composite compact steel sections. Further, they illustrate that virtually all composite steel sections in positive flexural regions can be considered to be compact sections. Thus, again virtually all Copyright ASCE 2004 Structures 2000 3 composite steel sections in positive flexure will be governed by this uncalibrated limit state. Table 1 shows a comparison of the performance ratios, the factored loads divided by the factored resistances for the strength I and the service II limit states. The performance ratio closer to unity is the more governing of the two for each design component. Table 1 Comparisons of Strength I and Service II Performance Ratios Example Flexural Region Limit-State Load Combination Performance Ratio strength I 0.88 No. 1 simple-span plate girder positive service II 1.01 strength I 0.81 positive service II 1.00 strength I 0.94 No. 2 two-span continuous plate girder negative service II 0.98 strength I 0.63 positive service II 0.69 strength I 0.99 No. 3 three-span continuous plate girder negative service II na strength I 0.91 positive service II 0.99 strength I 0.98 No. 4 three-span continuous box girder negative service II na As the table illustrates, compact steel sections are governed by the service II limit-state load combinations, not the strength I limit-state load combinations which are calibrated to produce uniform safety through reliability theory. In all cases, except the negativemoment regions of examples no. 3 and 4 which are non-compact sections and the positive-moment region of example 3 which is governed by the fatigue-and-fracture limit state, the flexural resistance of the steel sections are governed by the control of permanent deflection represented by the service II load combination. Copyright ASCE 2004 Structures 2000 4 The service II limit-state load combination is also suggested in the proposed AASHTO Manual for Condition Evaluation and Load and Resistance Factor Rating of Highway Bridges for the review of permit issuance, and has implications on the evaluation of existing steel bridges. The fact that an uncalibrated limit state governs bridge design is not exclusive to steel bridges. The design of prestressed-concrete girders is also governed by service limit states, either the service I or III limit state, not the strength limit states calibrated through reliability theory to yield uniform safety. In other words, the design of prestressedconcrete girders is governed by allowable stresses not ultimate capacity. The Calibration of the Service II Load Combination? The service II load combination should be reviewed, including the limit test results from the AASHTO test road bridges [HRB, 1962], and calibrated as it has great implications on the design of modern steel bridges. To accomplish this calibration, several questions must be answered: · what degree of kinking of the vertical alignment of the roadway is objectionable, in terms of rideability, · can this kinking be quantified, perhaps in terms of a percentage of flange yielding as suggested by the current provisions, and · if so, what degree of flange yielding corresponds to the objectionable degree of kinking? While the word “kinking” is used here, the reader must remember that such plastic deformations are finite in length and thus the “kink” occupies a certain length of the girder.