土木专业外文翻译---关于钢筋混凝土板桥活荷载简化的研究.doc

investigation of aashto live load reduction inreinforced concrete slab bridgesf. el me sk i 1; m. mabsout 2 ; and k. tarhini3journal of bridge engineering.submitted july 30,2010;accepted februray 24,2011;posted ahead of print march 2,2011;doi:10.1061/(asce)be.1943-5592.00002371phd candidate, dept. of civil and environmental engineering, american univ. of beirut; formerly, project engineer at khatib and alami, beirut, lebanon. email: .lb 2dept. of civil and environmental engineering, american univ. of beirut, lebanon. email: .lb 3dept. of civil engineering, us coast guard academy, new london, ct 06320 email: kassim.m.t abstract: this paper presents the results of a 3d finite element study that investigated the effect of multi-presence factor of load reduction factors used in the aashto bridge design specifications. typical one-span, two-equal-span continuous, simply supported, three- and four-lane reinforced concrete slab highway bridges were selected for this study. aashto hs20 design truck loads are first placed transversally in all lanes, positioned side-by-side and close to one edge of the bridge slab; this fully loaded condition served as a reference case. reduced loading patterns are then investigated using 3d fea, with design loads in two out of three lanes (reduced 2/3), three out of four lanes (reduced 3/4), and two out of four lanes (reduced 2/4). the longitudinal bending moments and deflection results obtained for the fea reduced and fully loaded bridges are directly compared. furthermore, a correlation between the reduced load cases and aashto reduction factors or multiple presence factors is made for concrete slab bridges. for the three- and four-lane bridge cases, aashto standard specifications generally correlate well with or overestimate the fea reduced maximum moments and edge beam moments by up to 15% and 30%, respectively. this over-estimation is more pronounced in short-span bridges. it is recommended that a reduction factor of 25% be applied only for reinforced concrete slabs with span lengths greater than 12 m (40 ft) and a reduction factor of 10% be applied for spans less than 12 m (40 ft). the aashto lrfd overestimated the maximum longitudinal moments and edge beam moments by up to 15% and 40%, respectively. this over-estimation by aashto lrfd, which is larger for longer spans, is increased to 40% and 55% when compared to the fea results due to reduced moments. this research supports the current aashto lrfd multiple-presence factors of 0.85 for three lanes and 0.65 for four lanes in estimating longitudinal bending moments in concrete slab bridges. the fea results highlight the importance of considering span length in determining the multi-presence factors when designing three-lane or more concrete slab bridges. thispaper will assist bridge engineers in quantifying the adjustment factors used in analyzing and designing multi-lane reinforced concrete slab bridges. keywords: concrete slab bridges; load reduction; multi-lane multi-span bridges; finite element analysis; aashto standard specifications and lrfd. introduction according to the u.s. federal highway administration.s (fhwa) national bridge inventory data, 23.7% of the nation.s 597,787 bridges are structurally deficient or functionally obsolete as reported in better roads magazine 2009. also, the portland cement association (pca) 2008 reported that out of the 139,031 reinforced concrete bridges, 29.3% are considered structurally deficient or functionally obsolete. the high number of deficient bridges means that a considerable number of bridges are being recommended for weight limiting posting, rehabilitation, or decommissioning and replacement. reinforced concrete slab bridges offer economic alternatives for short-span bridges in the united states and particularly in developing countries where cast-in-place concrete is common practice. the main advantage of cast-in-place concrete slab bridges is the ability to field adjustment of the roadway profile during construction. typically, the design of highway bridges in the united states must conform to the american association of state highway and transportation officials (aashto) standard specifications for highway bridges (2002) or aashto load and resistance factor design (lrfd) bridge design specifications (2007). the analysis and design of any highway bridge must consider truck and lane loading. however, truck loading provisions govern for short-span structures when considering aashto standard specifications. aashto specifies a distribution width for highway loading to reduce the twoway bending problem into a beam or one-way bending problem. alternately, an empirical expression for live-load bending moment is provided. therefore, reinforced concrete slab bridges are designed as a series of beam strips. aashto standard specifications design procedures were originally developed in the early to mid 1900s based on research work by westergaard (1926, 1930), jensen (1938, 1939), and newmark (1948). the goals of aashto lrfd bridge design specifications were to develop comprehensive specification and achieve more uniform margin of safety for all bridge structures. aashto lrfd procedures specify hl93 live load which is a combination of hs20 trucks or design tandem with lane loading. aashto permits a reduction in live-load intensity on a bridge deck due to the improbability of having all lanes of bridge superstructure loaded simultaneously. these live-load reduction factors are used to account for the probability of having all lanes loaded at the same time and at locations along the bridge deck producing the maximum bending moment in an element of a bridge superstructure. aashto standard bridge specifications and lrfd procedures specify that results obtained from analyses of three- and four-lane bridge decks where all lanes are loaded simultaneously are to be multiplied by reduction factors. sanders (1984) summarized and dated the various changes in the aashto standard specifications over the years and noted that these reduction factors were originally introduced in 1941 in the third edition. however, sanders (1984) also reported that the greatest confusion appears to be in the appropriateness of using the provisions of reduction in load intensity for determining the design bending moments in a girder. some engineers permit the reduction of live load, while others do not. taly (1996) reported that bridge designers disagree on the correct interpretation of aashto regarding the reduction of live load in longitudinal beams for bridges carrying more than two traffic lanes. the load reduction on steel girder bridges was investigated by mabsout et al. (2002). in this study, a parametric study was conducted to assess the effect of multiple-presence design trucks on wheel-load distribution for bending moments and deflections in three- and four-lane bridges. the results of bridge cases with reduced truck loading were compared to fully-loaded bridges and assessed with aastho procedures. mabsout et al. (2004) reported the results of a parametric investigation using the 3d finite element analysis (fea) of straight, single-span, simply supported reinforced concrete slab bridges. the study considered various span lengths and slab widths, varied number of lanes, and varied live loading conditions for bridges with and without shoulders. longitudinal bending moments and deflections in the concrete slab were evaluated and compared with procedures specified by aashto. further, awwad et al. (2008) reported the fea results of a preliminary parametric study of the effect of continuity on wheel load distribution in simply supported, twoequal-span, one- and two-lane straight reinforced concrete slab bridges. the study considered various span lengths, number of lanes (one and two), and live loading conditions for bridges without shoulders. this paper presents the results of a deterministic parametric study investigating the effect of multiple-presence of hs20 trucks on bending moments and deflections in three- and four-lane reinforced concrete slab bridges using the general computer program sap2000 (2007). a total of 60 distinct bridge cases were modeled using three-dimensional (3d) finite element analysis subject to static wheel loading. various bridge parameters investigated in this study were span length, single span, continuous two-equal-spans, and design live loads in all three lanes, two out of three lanes, all four lanes, three out of four lanes, and two out of four lanes positioned to produce the maximum longitudinal bending moments. these parameters were varied within practical ranges in order to investigate their effect on wheel-load distribution. the maximum moments and deflections were calculated using the 3d finite element analysis and the effect of load reduction was assessed by comparing 3d bridge cases with full and reduced loading, and results were compared with 2d aashto standard specifications and lrfd procedures. aashto standard specifications for highway bridges for simply supported concrete slab bridges, aashto standard specifications (2002) suggest three approaches in determining the live-load bending moment for hs20 design truck loading. one simple approach used by aashto (section ) provides empirical equations for the design moment in the slab and will be adopted in this study as described below: in si units: m = 13,500 x s for s 15 m (1a) m = 1,000(19.5 x s - 90) for s 15 m (1b) which, in us units, are equivalent to: m = 900 x s for s 50 ft (2a) m = 1,000(1.30 x s - 20) for s 50 ft (2b) where s = span length m for eq. (1) or ft for eq. (2); and m = longitudinal bending moment per unit width n-m/m eq. (1) or lb-ft/ft eq. (2). furthermore, aashto section 3.24.8 requires edge beams along the free edges of the concrete slab bridges. the live-load bending moment in an edge beam is specified by the expression: 0.1ps (where p=72 kn or 16 kips for hs20 truck). aashto does not specify a width for the edge beam. however, some departments of transportation (such as ohio) suggest the use of an edge beam width of 450 mm (18 inches). for continuous spans, according to aashto (section ), the edge beam moment calculated for simple spans may be reduced by 20% to yield 0.08ps, unless a greater reduction results is obtained from a more refined analysis. the concrete slab thickness was calculated to control the live-load deflection according to aashto section 8.9.2; the minimum slab thickness h (mm) for bridges with main reinforcement parallel to traffic is 1.2(s+3,000)/30, which is equivalent, in us units (ft), to 1.2(s+10)/30. the maximum fea live-load deflection was compared with the aashto section deflection criterion of s/800. finally, aashto section 3.12.1 specifies that results obtained from the analyses of three- and four-lane bridge decks where all lanes are loaded simultaneously can be reduced by 10% and 25% (i.e. multiplied by 0.90 and 0.75), respectively. aashto lrfd bridge design specifications aashto lrfd (2007) section provides an equivalent strip width to design reinforced concrete slab bridges similar to the aashto standard specifications. this simplistic approach is to divide the total statical moment by the equivalent width to achieve a moment per unit width. the moments are determined by establishing the structural width per design lane. the equivalent width e of longitudinal strips per lane for both shear and moment is determined using the following formulas: width for one lane loaded is: e = 250 + 0.42(l1 x w 1) 1 /2 (3a) e = 10 + 5(l1 x w 1) 1 /2 (3b) width for mult i-lanes loaded is: e = 2,100 + 0.12(l1 x w 1) 1 /2 (4a) e = 84 + 1.44(l1 x w1)1 / 2 (4b) where “e” is in mm in eqs. (3a) and (4a) inches in eqs. (3b) and (4b); l1= span length in mm (or ft), the lesser of the actual span or 18,000 mm (60 ft); w1=edge-to-edge width in mm (or ft) of bridge taken to be the lesser of the actual width or 18,000 mm (60 ft) for multi-lane loading, or 9,000 mm (30 ft) for single-lane loading. aashto lrfd section live load hl93 requires the consideration of lane loading plus hs20 design truck or lane loading plus tandem. the design lane loading consists of a uniformly distributed load in the longitudinal direction of 9.3 kn/m (0.64 kip/ft) and occupying 3 m (10 ft) transversally. the bending moment is determined for the design lane and is then divided by the width e to determine the design moment per unit width. aashto lrfd edge beam moment (section .4b) shall be assumed to support one line of wheel load and a tributary portion of the design lane load. the effective width is considered to be the sum of the distance between the edge of the deck and the inside face of barrier (assumed equal to 30 cm or 1 ft), plus 30 cm (1 ft), plus one quarter of the strip width calculated above, but shall not exceed either one-half the full strip width 1.8 m or (6 ft). aashto lrfd table .3-1 provides the minimum slab thickness “h” for deflection control to be 1.2(s +3,000)/30, where “h” and “s” are in mm, which is similar to the aashto standard specifications equation 1.2(s+10)/30 (ft). the same criterion of s/800 will be used to assess live load deflections. according to aashto lrfd section 2, the extreme live-load force effect shall be determined by placing live loads in all lanes and then reduced by using multiple-presence factors of 0.85 and 0.65 for three and four lanes respectively, to account for the probability of simultaneous lane loading. （美国国家公路与运输协会）关于钢筋混凝土板桥活荷载简化的研究作者：f. el me sk i 1; m. mabsout 2 ; and k. tarhini3出处：桥梁工程杂志 提交于2010年7月30日，审批于2011年2月24日；2011年3月2日头条出版；标识符：10.1061/asce(美国土木工程协会).be(教育部).1943-5592.00002371.博士候选人，贝鲁特美国大学，土木与环境工程专业；前黎巴嫩首都贝鲁特khatib 和alami项目工程师；邮箱地址：.1b2.黎巴嫩贝鲁特美国大学，土木与环境工程专业；邮箱地址：.1b3.新伦敦美国海岸警卫学院，土木工程专业，建筑水电安装06320，邮箱地址：kassim.m.t摘要：本文章主要介绍美国国家公路与运输协会桥梁设计规范中，分析调查影响活载折减系数的多方面因素的一个三维有限元分析研究结果。典型的单跨体系，两跨（等跨）连续体系，简支体系，三车道以及四车道钢筋混凝土公路板桥均被收录到本研究。美国国家公路与运输协会hs20（半强度）设计中车辆荷载首先被横向并排分布在所有车道，且贴近于桥面板边缘，这样的完全加载条件可作为一个参考方案。荷载简化模式是将设计荷载分别加载到三分之二车道（减少2 / 3），四分之三车道（减少3/4）以及四分之二车道（减少2/4）上，然后利用三维有限元分析。简化模式下的有限元分析可得到桥的纵向弯矩和挠度结果，并且与桥梁满载情况进行了直接对比。此外，荷载折减工况和（美国国家公路与运输协会）设计规范中的折减系数或者多方面因素之间的相关性也被考虑到混凝土板桥设计当中。对于三车道和四车道桥的情况，（美国国家公路与运输协会）标准规范中通常将（荷载折减模式下）有限元分析最大弯矩值跟边梁弯矩值分别偏高估算15%和30%，或者掌握好两者间的相关性。这样的偏高估算在短跨桥中体现的更为明显。建议（荷载）折减（系数）25%的工况仅在钢筋混凝土板桥跨径超过12米（40英尺）时被采用，而折减10%的工况则在跨径小雨12米（40英尺）时被采用。美国国家公路与运输协会荷载及阻力因子设计规范中分别将纵向弯矩最大值和边梁弯矩值偏高估算15%和40%。这一估算会随桥梁跨径的增大而增加，当与有限元分析结果对比时会由于弯矩减小的原因增大到40%甚至55%。本研究支持现行的美国国家公路与运输协会荷载及阻力因子设计规范在估算混凝土板桥纵向弯矩时对于三车道桥0.85、四车道桥0.65的多方面因素。有限元分析的结果（重点）冲突在设计三车道或者更多车道的混凝土板桥时考虑桥跨长度对确定多方面因素影响的重要性。本篇文章将有助于桥梁工程师在研究设计和分析多车道钢筋混凝土板桥时定量那些可变因素。关键词：混凝土板桥；简化荷载；多车道、多跨桥；有限元分析；美国国家公路与运输协会标准规范、荷载及阻力因子设计介绍：根据美国美国联帮公路管理署（fhwa）国家桥梁数据库显示，正如杂志better roads 在2009年的报道一样，全美597787座桥梁中有23.7%的桥存在结构缺陷或者功能过时（现象）。同时，波特兰水泥协会(pca)在2008年报道139031座钢筋混凝土桥中的29.3%被认为存在结构缺陷或者功能过时。大量存在缺陷的桥梁意味着有相当数量的桥要被责令限制载重、修复、拆除或者新建。在美国，钢筋混凝土板桥是短跨桥经济型的选择，尤其对于那些把衬砌混凝土当做常用方法的发展中国家。衬砌混凝土板桥的主要优点在于施工过程中可以现场调整桥形。一般来说，美国公路桥梁的设计必须遵循美国国家公路与运输协会公路桥梁标准规范2002，或者遵循桥梁荷载及阻力因子设计规范2007。任何公路桥的设计及分析都必须考虑车道荷载和车辆荷载。但是，当考虑美国国家公路与运输协会标准规范时，车辆荷载适用于短跨桥。规范中指定一个公路桥荷载的分布宽度以减小存在于梁体中的单向或者双向弯曲问题。间接地，就证明了一个活荷载弯矩经验表达式。因此，钢筋混凝土板桥也就被设计成为一系列带状梁体。美国国家公路与运输协会标准规范设计程序在20世纪初期到中期基于westergaard (1926, 1930)，jensen (1938, 1939)，以及newmark (1948)的调查研究工作，得到初步发展。美国国家公路与运输协会荷载及阻力因子桥梁设计规范的目标是发展全面的规定，并且为所有桥梁结构制定出更加统一的安全限度。介于不可能在桥梁上部结构所有车道同时加载，美国国家公路与运输协会允许降低加载到桥面的活荷载强度。这些活荷载减小因素被用于解释在同一桥梁结构元素下所有车道同时加载并且沿桥面位置产生最大弯矩的可能性。美国国家公路与运输协会桥梁标准规范和荷载及阻力因子设计程序规定，由全部车道同时加载的三车道以及四车道桥面板分析所得公认结果，须得乘以折减系数。sanders (1984)总结并列举了近年来美国国家公路与运输协会标准规范的一系列变更，同时还提到折减系数这一概念最初是在1941年第三版中产生。然而，sanders (1984)也同样报道：最大的疑惑似乎是确定主梁设计弯矩时如何适度应用规定的荷载强度折减。有工程师支持活荷载折减的同时，也有工程师在反对。据taly (1996)报道：桥梁设计者不同意美国国家公路与运输协会关于为桥梁可承载多于两车道时纵向梁活载折减提出的合理解释。mabsout et al. (2002)研究了钢梁桥的荷载折减，在这个研究中，为估算三车道、四车道桥梁在多重存在的设计车辆轮压分布对其弯矩和挠度的影响而进行了一项参数研究。这一车辆荷载折减的桥梁实例，由美国国家公路与运输协会设计程序计算得到结果兵与满载作用下的桥做比较。mabsout et al. (2004)报道了利用三维有限元分析单跨钢筋混凝土简支板直桥变量研究现结果。这项研究被认为是集各种桥跨长度以及桥面板宽度，多种车道数量和各种加载条件于一桥（有路肩和没有路肩的）。混凝土板的纵向弯矩和挠度得到了估算，并且与美国国家公路与运输协会所规定的设计程序进行了对比。此外，awwad et al. (2008)还报道了一项影响轮压在简支体系、两跨体系、单车道和双车道钢筋混凝土板直桥上连续分布的初步变量研究有限元分析结果。这项研究被认为是集各种跨径长度、车道数（单车道和双车道）以及活荷载条件于一桥（没有路肩的）。本文章介绍用一般计算机程序sap2000 (2007)计算的三车道和四车道钢筋混凝土板桥，在多重汽车荷载（hs20）作用下，对其弯矩以及挠度的影响这一确定性参数研究。共列举了60个不同的桥梁实例，均以静态轮压为条件进行三维有限元分析。诸如跨径长度、单跨体系、两跨等跨连续体系以及在三车道、三分之二车道、四车道、四分之三车道、四分之二车道上布置设计活荷载产生的最大纵向弯矩。为了它们对轮压分布的影响，这些参数均被列入实用范围。最大弯矩和挠度用三维有限元分析计算得到，对荷载分布的影响从满载和荷载折减（两种情况）的三维桥梁实例对比中得到，且这些结果会同美国国家公路与运输协会标准规范（二维）及荷载及阻力因子设计程序进行对照。美国国家公路与运输协会公路桥梁标准规范对于简支混凝土板桥，美国国家公路与运输协会标准规范（2002）中建议了确定活荷载（hs20设计车辆荷载）弯矩时的三种方法。aashto规范（章节3.24.