土木專業(yè)外文翻譯---關(guān)于鋼筋混凝土板橋活荷載簡(jiǎn)化的研究

1、<p>　　Investigation of AASHTO Live Load Reduction in</p><p>　　Reinforced Concrete Slab Bridges</p><p>　　F. El Me sk i 1; M. Mabsout 2 ; and K. Tarhini3</p><p>　　Journal of Brid

2、ge Engineering.Submitted July 30,2010;accepted Februray 24,2011;posted ahead of print March 2,2011;doi:10.1061/(ASCE)BE.1943-5592.0000237</p><p>　　1PhD Candidate, Dept. of Civil and Environmental Engineering

3、, American Univ. of Beirut; formerly, Project Engineer at Khatib and Alami, Beirut, Lebanon. Email: fme09@aub.edu.lb </p><p>　　2Dept. of Civil and Environmental Engineering, American Univ. of Beirut, Lebanon

4、. Email: mounir@aub.edu.lb </p><p>　　3Dept. of Civil Engineering, US Coast Guard Academy, New London, CT 06320 Email: Kassim.M.Tarhini@uscga.edu </p><p>　　Abstract: This paper presents the resul

5、ts 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 support

6、ed, 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

7、 the bridge slab; thi</p><p>　　Keywords: Concrete slab bridges; Load reduction; Multi-lane multi-span bridges; Finite element analysis; AASHTO Standard Specifications and LRFD. </p><p>　　Introdu

8、ction </p><p>　　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 repo

9、rted 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

10、 high number of deficient bridges means that a considerable number of bridges are being r</p><p>　　Reinforced concrete slab bridges offer economic alternatives for short-span bridges in the United States and

11、 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 constructi

12、on. Typically, the design of highway bridges in the United States must conform to the American Association of State Highway and Transportation Officials (AASHTO) Standard S</p><p>　　AASHTO permits a reductio

13、n 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 a

14、ll 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 tha

15、t results obtained from analyses of</p><p>　　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 th

16、e 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

17、 a girder. Some engineers permit the reduction of live load, while others do not. Taly (1996) reported that bridge des</p><p>　　The load reduction on steel girder bridges was investigated by Mabsout et al. (

18、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 o

19、f bridge cases with reduced truck loading were compared to fully-loaded bridges and assessed with AASTHO procedures. </p><p>　　Mabsout et al. (2004) reported the results of a parametric investigation using t

20、he 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

21、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 </p><p>

22、;　　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 brid

23、ges 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 inve

24、stigated in this study were span length, single span, continuou</p><p>　　AASHTO Standard Specifications for Highway Bridges </p><p>　　For simply supported concrete slab bridges, AASHTO Standard

25、Specifications (2002) </p><p>　　suggest three approaches in determining the live-load bending moment for HS20 design truck loading. One simple approach used by AASHTO (Section 3.24.3.2) provides empirical eq

26、uations for the design moment in the slab and will be adopted in this study as described below: </p><p>　　In SI units: </p><p>　　M = 13,500 x S for S≤ 15 m (1a) </p><p>　　M = 1,000(

27、19.5 x S - 90) for S > 15 m (1b) </p><p>　　which, in US units, are equivalent to: </p><p>　　M = 900 x S for S ≤ 50 ft (2a) </p><p>　　M = 1,000(1.30 x S - 20) for S > 50 ft (2b

28、) </p><p>　　where S = span length [m for Eq. (1) or ft for Eq. (2)]; </p><p>　　and M = longitudinal bending moment per unit width [N-m/m Eq. (1) or lb-ft/ft Eq. (2)]. </p><p>　　Furt

29、hermore, 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

30、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

31、 (Section 3.24.8.3), the edge beam moment calculated for</p><p>　　The concrete slab thickness was calculated to control the live-load deflection according to AASHTO Section 8.9.2; the minimum slab thickness

32、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 8.9.3.1

33、 deflection criterion of S/800. Finally, AASHTO Section 3.12.1 specifies that results obtained from the analyses of three- and four-lane br</p><p>　　AASHTO LRFD Bridge Design Specifications </p><p

34、>　　AASHTO LRFD (2007) Section 4.6.2.3 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 static

35、al 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

36、 and moment is determined using the following formulas: </p><p>　　Width for one lane loaded is: </p><p>　　E = 250 + 0.42(L1 x W 1) 1 /2 (3a) </p><p>　　E = 10 + 5(L1 x W 1) 1 /2 (3b)

37、 </p><p>　　Width for mult i-lanes loaded is: </p><p>　　E = 2,100 + 0.12(L1 x W 1) 1 /2 (4a) </p><p>　　E = 84 + 1.44(L1 x W1)1 / 2 (4b) </p><p>　　where “E” is in mm in E

38、qs. (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 wid

39、th or 18,000 mm (60 ft) for multi-lane loading, or 9,000 mm (30 ft) for single-lane loading. </p><p>　　AASHTO LRFD Section 3.6.1.2 live load HL93 requires the consideration of lane loading plus HS20 design t

40、ruck 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 de

41、termined for the design lane and is then divided by the width E to determine the design moment per unit width. </p><p>　　AASHTO LRFD edge beam moment (Section 4.6.2.1.4b) shall be assumed to support one line

42、 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)

43、, 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). </p><p>　　AASHTO LRFD Table 2.5.2.6.3-1 provides the mini

44、mum slab thickness “h” for </p><p>　　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 criter

45、ion of S/800 will be used to assess live load deflections. According to AASHTO LRFD Section 3.6.1.12, the extreme live-load force effect shall be determined by placing live loads in all lanes and then reduced by using mu

46、ltiple-presence factors of 0.85 and 0.65 for three and four lanes respectively, to account for the probability</p><p>　?。绹?guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)）關(guān)于鋼筋混凝土板橋活荷載簡(jiǎn)化的研究</p><p>　　作者：F. El Me sk i 1; M. Mabsout 2 ;

47、 and K. Tarhini3</p><p>　　出處：橋梁工程雜志 提交于2010年7月30日，審批于2011年2月24日；2011年3月2日頭條出版；標(biāo)識(shí)符：10.1061/ASCE(美國(guó)土木工程協(xié)會(huì)).BE(教育部).1943-5592.0000237</p><p>　　1.博士候選人，貝魯特美國(guó)大學(xué)，土木與環(huán)境工程專業(yè)；前黎巴嫩首都貝魯特Khatib 和Alami項(xiàng)目工程師

48、；郵箱地址：fme09@aub.edu.1b</p><p>　　2.黎巴嫩貝魯特美國(guó)大學(xué)，土木與環(huán)境工程專業(yè)；郵箱地址：mounir@aub.edu.1b</p><p>　　3.新倫敦美國(guó)海岸警衛(wèi)學(xué)院，土木工程專業(yè)，建筑水電安裝06320，郵箱地址：Kassim.M.Tarhini@uscga.edu</p><p>　　摘要：本文章主要介紹美國(guó)國(guó)家公路與運(yùn)輸協(xié)

49、會(huì)橋梁設(shè)計(jì)規(guī)范中，分析調(diào)查影響活載折減系數(shù)的多方面因素的一個(gè)三維有限元分析研究結(jié)果。典型的單跨體系，兩跨（等跨）連續(xù)體系，簡(jiǎn)支體系，三車(chē)道以及四車(chē)道鋼筋混凝土公路板橋均被收錄到本研究。美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)HS20（半強(qiáng)度）設(shè)計(jì)中車(chē)輛荷載首先被橫向并排分布在所有車(chē)道，且貼近于橋面板邊緣，這樣的完全加載條件可作為一個(gè)參考方案。荷載簡(jiǎn)化模式是將設(shè)計(jì)荷載分別加載到三分之二車(chē)道（減少2 / 3），四分之三車(chē)道（減少3/4）以及四分之二車(chē)道（減少

50、2/4）上，然后利用三維有限元分析。簡(jiǎn)化模式下的有限元分析可得到橋的縱向彎矩和撓度結(jié)果，并且與橋梁滿載情況進(jìn)行了直接對(duì)比。此外，荷載折減工況和（美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)）設(shè)計(jì)規(guī)范中的折減系數(shù)或者多方面因素之間的相關(guān)性也被考慮到混凝土板橋設(shè)計(jì)當(dāng)中。對(duì)于三車(chē)道和四車(chē)道橋的情況，（美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)）標(biāo)準(zhǔn)規(guī)范中通常將（荷載折減模式下）有限元分析最大彎矩值跟邊梁彎矩值分別偏高估算15%和30%，或者掌握好兩者間的相關(guān)性。這樣的偏高估算在短跨橋

51、中體現(xiàn)的更為明顯。建議（荷載）折減（系數(shù)）25%的工況僅在鋼筋混凝土板橋跨徑超過(guò)</p><p>　　關(guān)鍵詞：混凝土板橋；簡(jiǎn)化荷載；多車(chē)道、多跨橋；有限元分析；美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)標(biāo)準(zhǔn)規(guī)范、荷載及阻力因子設(shè)計(jì)</p><p>　　介紹：根據(jù)美國(guó)美國(guó)聯(lián)幫公路管理署（FHWA）國(guó)家橋梁數(shù)據(jù)庫(kù)顯示，正如雜志《Better Roads 》在2009年的報(bào)道一樣，全美597787座橋梁中有23.7

52、%的橋存在結(jié)構(gòu)缺陷或者功能過(guò)時(shí)（現(xiàn)象）。同時(shí)，波特蘭水泥協(xié)會(huì)(PCA)在2008年報(bào)道139031座鋼筋混凝土橋中的29.3%被認(rèn)為存在結(jié)構(gòu)缺陷或者功能過(guò)時(shí)。大量存在缺陷的橋梁意味著有相當(dāng)數(shù)量的橋要被責(zé)令限制載重、修復(fù)、拆除或者新建。</p><p>　　在美國(guó)，鋼筋混凝土板橋是短跨橋經(jīng)濟(jì)型的選擇，尤其對(duì)于那些把襯砌混凝土當(dāng)做常用方法的發(fā)展中國(guó)家。襯砌混凝土板橋的主要優(yōu)點(diǎn)在于施工過(guò)程中可以現(xiàn)場(chǎng)調(diào)整橋形。一般來(lái)說(shuō)，

53、美國(guó)公路橋梁的設(shè)計(jì)必須遵循美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)公路橋梁標(biāo)準(zhǔn)規(guī)范2002，或者遵循橋梁荷載及阻力因子設(shè)計(jì)規(guī)范2007。任何公路橋的設(shè)計(jì)及分析都必須考慮車(chē)道荷載和車(chē)輛荷載。但是，當(dāng)考慮美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)標(biāo)準(zhǔn)規(guī)范時(shí)，車(chē)輛荷載適用于短跨橋。規(guī)范中指定一個(gè)公路橋荷載的分布寬度以減小存在于梁體中的單向或者雙向彎曲問(wèn)題。間接地，就證明了一個(gè)活荷載彎矩經(jīng)驗(yàn)表達(dá)式。因此，鋼筋混凝土板橋也就被設(shè)計(jì)成為一系列帶狀梁體。美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)標(biāo)準(zhǔn)規(guī)范設(shè)計(jì)

54、程序在20世紀(jì)初期到中期基于Westergaard (1926, 1930)，Jensen (1938, 1939)，以及Newmark (1948)的調(diào)查研究工作，得到初步發(fā)展。美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)荷載及阻力因子橋梁設(shè)計(jì)規(guī)范的目標(biāo)是發(fā)展全面的規(guī)定，并且為所有橋梁結(jié)構(gòu)制定出更加統(tǒng)一的安全限度。</p><p>　　介于不可能在橋梁上部結(jié)構(gòu)所有車(chē)道同時(shí)加載，美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)允許降低加載到橋面的活荷載強(qiáng)度。這

55、些活荷載減小因素被用于解釋在同一橋梁結(jié)構(gòu)元素下所有車(chē)道同時(shí)加載并且沿橋面位置產(chǎn)生最大彎矩的可能性。美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)橋梁標(biāo)準(zhǔn)規(guī)范和荷載及阻力因子設(shè)計(jì)程序規(guī)定，由全部車(chē)道同時(shí)加載的三車(chē)道以及四車(chē)道橋面板分析所得公認(rèn)結(jié)果，須得乘以折減系數(shù)。Sanders (1984)總結(jié)并列舉了近年來(lái)美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)標(biāo)準(zhǔn)規(guī)范的一系列變更，同時(shí)還提到折減系數(shù)這一概念最初是在1941年第三版中產(chǎn)生。然而，Sanders (1984)也同樣報(bào)道：最大的

56、疑惑似乎是確定主梁設(shè)計(jì)彎矩時(shí)如何適度應(yīng)用規(guī)定的荷載強(qiáng)度折減。有工程師支持活荷載折減的同時(shí)，也有工程師在反對(duì)。據(jù)Taly (1996)報(bào)道：橋梁設(shè)計(jì)者不同意美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)關(guān)于為橋梁可承載多于兩車(chē)道時(shí)縱向梁活載折減提出的合理解釋。Mabsout et al. (2002)研究了鋼梁橋的荷載折減，在這個(gè)研究中，為估算三車(chē)道、四車(chē)道橋梁在多重存在的設(shè)計(jì)車(chē)輛輪壓分布對(duì)其彎矩和撓度的影響而進(jìn)行了一項(xiàng)參數(shù)研究。這一車(chē)輛荷載折減的橋梁實(shí)例，由美

57、國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)設(shè)</p><p>　　Mabsout et al. (2004)報(bào)道了利用三維有限元分析單跨鋼筋混凝土簡(jiǎn)支板直橋變量研究現(xiàn)結(jié)果。這項(xiàng)研究被認(rèn)為是集各種橋跨長(zhǎng)度以及橋面板寬度，多種車(chē)道數(shù)量和各種加載條件于一橋（有路肩和沒(méi)有路肩的）?；炷涟宓目v向彎矩和撓度得到了估算，并且與美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)所規(guī)定的設(shè)計(jì)程序進(jìn)行了對(duì)比。此外，Awwad et al. (2008)還報(bào)道了一項(xiàng)影響輪壓在簡(jiǎn)支體

58、系、兩跨體系、單車(chē)道和雙車(chē)道鋼筋混凝土板直橋上連續(xù)分布的初步變量研究有限元分析結(jié)果。這項(xiàng)研究被認(rèn)為是集各種跨徑長(zhǎng)度、車(chē)道數(shù)（單車(chē)道和雙車(chē)道）以及活荷載條件于一橋（沒(méi)有路肩的）。</p><p>　　本文章介紹用一般計(jì)算機(jī)程序SAP2000 (2007)計(jì)算的三車(chē)道和四車(chē)道鋼筋混凝土板橋，在多重汽車(chē)荷載（HS20）作用下，對(duì)其彎矩以及撓度的影響這一確定性參數(shù)研究。共列舉了60個(gè)不同的橋梁實(shí)例，均以靜態(tài)輪壓為條件進(jìn)行

59、三維有限元分析。諸如跨徑長(zhǎng)度、單跨體系、兩跨等跨連續(xù)體系以及在三車(chē)道、三分之二車(chē)道、四車(chē)道、四分之三車(chē)道、四分之二車(chē)道上布置設(shè)計(jì)活荷載產(chǎn)生的最大縱向彎矩。為了它們對(duì)輪壓分布的影響，這些參數(shù)均被列入實(shí)用范圍。最大彎矩和撓度用三維有限元分析計(jì)算得到，對(duì)荷載分布的影響從滿載和荷載折減（兩種情況）的三維橋梁實(shí)例對(duì)比中得到，且這些結(jié)果會(huì)同美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)標(biāo)準(zhǔn)規(guī)范（二維）及荷載及阻力因子設(shè)計(jì)程序進(jìn)行對(duì)照。</p><p&g

60、t;　　美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)公路橋梁標(biāo)準(zhǔn)規(guī)范</p><p>　　對(duì)于簡(jiǎn)支混凝土板橋，美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)標(biāo)準(zhǔn)規(guī)范（2002）中建議了確定活荷載（HS20設(shè)計(jì)車(chē)輛荷載）彎矩時(shí)的三種方法。AASHTO規(guī)范（章節(jié)3.24.3.2）中用到的一種簡(jiǎn)便方法為即將安裝的梁板提供了如下所述計(jì)算設(shè)計(jì)彎矩的經(jīng)驗(yàn)公式：</p><p><b>　　國(guó)際制單位：</b></p&g

61、t;<p>　　M=13500×S，其中S ≤ 15 米(1a)</p><p>　　M=1000（19.5×S-90），其中S > 15 米(1b)</p><p>　　用美國(guó)通用單位時(shí)，上式等效于：</p><p>　　M=900 ×S，其中S ≤ 50 英尺 (2a)</p><p>　

62、　M=1000（1.30 ×S-20），其中S > 50 英尺 (2b)</p><p>　　式中S=跨徑長(zhǎng)度（單位為米用式1a，單位為英尺用式2a）；M=單位寬度的縱向彎矩（單位為Nm/m用式1b，單位為bft/ft用式2b）</p><p>　　此外，美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)標(biāo)準(zhǔn)規(guī)范章節(jié)3.24.8還對(duì)混凝土板梁橋沿不受約束的邊界的邊梁做出了要求，邊梁的活荷載彎矩利用如下

63、表達(dá)式確定：0.1PS（對(duì)于HS20車(chē)輛荷載，P= 72 千牛 或者 16 千磅），規(guī)范并未指定邊梁的寬度。然而，一些交通部門(mén)（如在俄亥俄州）卻建議使用邊梁寬度450毫米（18英寸）。對(duì)于連續(xù)多跨的梁橋，根據(jù)美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)標(biāo)準(zhǔn)規(guī)范（章節(jié)3.24.8.3），邊梁彎矩的計(jì)算應(yīng)在簡(jiǎn)單跨徑基礎(chǔ)上減小20%到0.08PS，否則除非從更好詳細(xì)的分析中得到更好的簡(jiǎn)化結(jié)果。</p><p>　　根據(jù)美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)

64、標(biāo)準(zhǔn)規(guī)范（章節(jié)8.9.2）計(jì)算混凝土板的厚度，從而控制活荷載撓度。隨交通量（變化）增大的最小板厚h（單位毫米）按1.2(跨徑+3,000)/30計(jì)算，等效于以英尺為單位1.2(跨徑+10)/30，且將有限元分析活荷載最大撓度值與美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)標(biāo)準(zhǔn)規(guī)范（章節(jié)8.9.3.1）S/800的撓度準(zhǔn)則相對(duì)比。最后，規(guī)范（章節(jié)3.12.1）明確指出，從分析全部車(chē)道同時(shí)加載的三車(chē)道、四車(chē)道橋面板得到的結(jié)果，可分別減少10% and 25%（也

65、即乘以0.90和0.75）。</p><p>　　美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)橋梁荷載及阻力因子設(shè)計(jì)規(guī)范</p><p>　　美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)橋梁荷載及阻力因子設(shè)計(jì)規(guī)范（2007）4.6.2.3章節(jié)中提供了一種類似美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)標(biāo)準(zhǔn)規(guī)范中設(shè)計(jì)鋼筋混凝土板橋等效分解寬度。這種簡(jiǎn)便方法是將總的力矩（彎矩）變量劃分成等效寬度，以得到每單位寬度上的力矩（彎矩）。這個(gè)力矩（彎矩）值通過(guò)建立每

66、個(gè)設(shè)計(jì)車(chē)道結(jié)構(gòu)寬度確定，針對(duì)于剪力和彎矩，每條車(chē)道縱向板條的等效寬度E有以下公式來(lái)確定：</p><p>　　單車(chē)道加載等效寬度是：E = 250 + 0.42(L1 x W 1) 1 /2 (3a) </p><p>　　E = 10 + 5(L1 x W 1) 1 /2 (3b)</p><p>　　多車(chē)道加載等效寬度是：E = 2,100 + 0.12(L1

67、x W 1) 1 /2 (4a) </p><p>　　E = 84 + 1.44(L1 x W1)1 / 2 (4b)</p><p>　　式中：E在公示(3a) 和 (4a)中單位為毫米，在公示(3b) 和 (4b)中單位為英寸；L1=橋跨長(zhǎng)度（單位毫米或英尺），實(shí)際跨徑小于或等于18,000 毫米 (60 英尺)；</p><p>　　W1=多車(chē)道加載時(shí)實(shí)際跨

68、徑小于等于18,000 毫米 (60 英尺)，或者單車(chē)道加載時(shí)實(shí)際跨徑小于等于9,000 毫米(30 英尺)橋梁的橋面凈空，單位毫米（或英尺）。</p><p>　　美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)橋梁荷載及阻力因子設(shè)計(jì)規(guī)范章節(jié)3.6.1.2HL93活荷載要求考慮車(chē)道荷載加上HS20設(shè)計(jì)車(chē)輛荷載或者車(chē)道荷載加上非機(jī)動(dòng)車(chē)荷載。設(shè)計(jì)車(chē)道荷載是由橫向分布3m (10 英尺)，縱向9.3 KN/m (0.64 Kip/ft)的均布

69、荷載組成。為設(shè)計(jì)車(chē)道而確定的彎矩，之后被等效寬度分解，以確定每單位寬度上的設(shè)計(jì)彎矩。</p><p>　　美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)橋梁荷載及阻力因子設(shè)計(jì)規(guī)范（章節(jié)4.6.2.1.4b），邊梁彎矩將被假設(shè)承受一列輪壓和部分設(shè)計(jì)車(chē)道荷載。有效寬度被認(rèn)為是橋面板邊緣到護(hù)欄內(nèi)側(cè)距離（假設(shè)等于30厘米或者1英尺），加上30厘米（1英尺），再加上上面已經(jīng)計(jì)算出的橋面板帶寬度的四分之一得總和，但不應(yīng)超過(guò)板帶全寬的一半1.8米或者

70、6英尺。</p><p>　　美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)橋梁荷載及阻力因子設(shè)計(jì)規(guī)范中表2.5.2.6.3-1為將撓度控制在1.2(S +3,000)/30，而提供了板厚最小值h，這里的“h”和“S”均與美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)標(biāo)準(zhǔn)規(guī)范公式1.2(S+10)/30 (ft)中的相類似，S/800同樣的標(biāo)準(zhǔn)將被用于對(duì)活荷載撓度的評(píng)估。根據(jù)美國(guó)國(guó)家公路與運(yùn)輸協(xié)會(huì)橋梁荷載及阻力因子設(shè)計(jì)規(guī)范章節(jié)3.6.1.12，將三車(chē)道和四車(chē)道