Article(id=1243226197925146705, tenantId=1146029695717560320, journalId=1242798230522609684, issueId=1243226190786441246, articleNumber=null, orderNo=null, doi=10.7511/jslx20240522001, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1716307200000, receivedDateStr=2024-05-22, revisedDate=1718812800000, revisedDateStr=2024-06-20, acceptedDate=null, acceptedDateStr=null, onlineDate=1774337823610, onlineDateStr=2026-03-24, pubDate=1761580800000, pubDateStr=2025-10-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774337823610, onlineIssueDateStr=2026-03-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774337823610, creator=13701087609, updateTime=1774337823610, updator=13701087609, issue=Issue{id=1243226190786441246, tenantId=1146029695717560320, journalId=1242798230522609684, year='2025', volume='42', issue='5', pageStart='699', pageEnd='888', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1774337821909, creator=13701087609, updateTime=1774338282025, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243228120724128564, tenantId=1146029695717560320, journalId=1242798230522609684, issueId=1243226190786441246, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243228120724128565, tenantId=1146029695717560320, journalId=1242798230522609684, issueId=1243226190786441246, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=839, endPage=845, ext={EN=ArticleExt(id=1243226198877253723, articleId=1243226197925146705, tenantId=1146029695717560320, journalId=1242798230522609684, language=EN, title=Analysis of the deflection of simply supported steel truss web composite box beam considering the shear deformation of the steel truss web, columnId=1243226193193971746, journalTitle=Chinese Journal of Computational Mechanics, columnName=Research Papers, runingTitle=null, highlight=null, articleAbstract=

To study the influence of steel truss web shear deformation on the deflection of steel truss web composite box beams, the beams were first decomposed into a laminated structure composed of top and bottom flanges and a steel truss. A steel truss web shear deformation angle function was introduced to establish an analytical model, and the flexural deformation of a simply supported beam was analyzed as an example. The effective stiffness of the cross-section was determined by combining Euler beam theory and the analytical solution, and the mid-span deflection was calculated using this effective stiffness. The flexural characteristics under different load conditions were analyzed and compared with the Euler beam theory. The influence of structural parameters such as steel truss web diameter, steel truss web wall thickness, and steel truss web inclination angle on the effective stiffness was also examined. The results show that considering steel truss web shear deformation provides an analytical solution closer to the finite element results, with a maximum error of 6.24%. Using the effective stiffness can effectively predict the mid-span deflection, with a maximum error of 3.64% compared with the analytical solution. Among the structural parameters affecting the effective stiffness, steel truss web wall thickness has the greatest influence, followed by steel truss web diameter and steel truss web inclination angle. Additionally, the effective stiffness is positively correlated with steel truss web diameter and steel truss wall thickness but negatively correlated with steel truss web inclination angle.

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为研究腹杆剪切变形对钢桁腹组合箱梁挠度的影响,首先将钢桁腹组合箱梁分解为由上下翼板和钢桁架组成的叠层梁,引入腹杆剪切变形转角函数建立钢桁腹组合箱梁在荷载作用下的解析模型,以简支梁为例求解挠曲变形解析解;其次为简便计算组合箱梁跨中挠度,结合初等梁理论及解析解求得截面有效刚度,并利用有效刚度求解跨中挠度;最后分析了组合箱梁在不同荷载工况下的挠曲特性,并与初等梁理论进行对比;在此基础上分析了腹杆直径、腹杆壁厚、腹杆倾角等构造参数对有效刚度的影响。结果表明,腹杆变形对钢桁腹组合箱梁挠度的影响不可忽略,采用初等梁理论计算组合箱梁挠度的最大误差达到了13.61%,考虑腹杆剪切变形得到的解析解计算结果与有限元更接近,最大误差为6.24%;利用截面有效刚度可有效预测跨中挠度,与解析解最大误差为3.64%;构造参数对有效刚度的影响中,腹杆壁厚影响最大,其次是腹杆直径、腹杆倾角;此外,有效刚度与腹杆直径及腹杆壁厚呈正相关,而与腹杆倾角呈负相关。

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吕向明*(1979-),男,硕士,副教授(E-mail:).

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吕向明*(1979-),男,硕士,副教授(E-mail:).

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Effective stiffness method for calculating deflection of corrugated web girder[J]. Engineering Mechanics, 2012, 29(8): 71-79. 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ArticleFig(id=1243226254535667776, tenantId=1146029695717560320, journalId=1242798230522609684, articleId=1243226197925146705, language=CN, label=图13, caption=腹杆倾角变化对λζ的影响, figureFileSmall=zuCq7sDQs2eg3GI7lmVXuw==, figureFileBig=kGtaSODOm5AIIMJ0aKaw7Q==, tableContent=null), ArticleFig(id=1243226254653108290, tenantId=1146029695717560320, journalId=1242798230522609684, articleId=1243226197925146705, language=EN, label=Tab. 1, caption=

Comparison of mid-span deflection

, figureFileSmall=null, figureFileBig=null, tableContent=
荷载 wi/ρ计算方法
EulerANSYSEq.(38)/(50)Eq.(63)/(64)
均布 wi/mm-1.633-1.835-1.946-2.012
ρ/%11.016.059.65
集中 wi/mm-2.133-2.469-2.623-2.713
ρ/%13.616.249.88
), ArticleFig(id=1243226254728605764, tenantId=1146029695717560320, journalId=1242798230522609684, articleId=1243226197925146705, language=CN, label=表1, caption=

跨中挠度对比

, figureFileSmall=null, figureFileBig=null, tableContent=
荷载 wi/ρ计算方法
EulerANSYSEq.(38)/(50)Eq.(63)/(64)
均布 wi/mm-1.633-1.835-1.946-2.012
ρ/%11.016.059.65
集中 wi/mm-2.133-2.469-2.623-2.713
ρ/%13.616.249.88
), ArticleFig(id=1243226254846046281, tenantId=1146029695717560320, journalId=1242798230522609684, articleId=1243226197925146705, language=EN, label=Tab. 2, caption=

Parameter value of steel truss web

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参数变化直径/mm壁厚/mm倾角/(°)
3311460.10
3411664.34
3511867.00
3612069.24
3712271.07
), ArticleFig(id=1243226255005429836, tenantId=1146029695717560320, journalId=1242798230522609684, articleId=1243226197925146705, language=CN, label=表2, caption=

腹杆参数取值

, figureFileSmall=null, figureFileBig=null, tableContent=
参数变化直径/mm壁厚/mm倾角/(°)
3311460.10
3411664.34
3511867.00
3612069.24
3712271.07
), ArticleFig(id=1243226255110287438, tenantId=1146029695717560320, journalId=1242798230522609684, articleId=1243226197925146705, language=EN, label=Tab. 3, caption=

Significance index

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 腹杆直径腹杆壁厚腹杆倾角
λ0.4994.5460.320
ζ1.59221.7260.975
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显著性指标

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 腹杆直径腹杆壁厚腹杆倾角
λ0.4994.5460.320
ζ1.59221.7260.975
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考虑腹杆剪切变形的简支钢桁腹组合箱梁挠度分析
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吕向明 1 , 王方旭 1, 2 , 王鑫 1
计算力学学报 | 研究论文 2025,42(5): 839-845
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计算力学学报 | 研究论文 2025, 42(5): 839-845
考虑腹杆剪切变形的简支钢桁腹组合箱梁挠度分析
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吕向明1 , 王方旭1, 2, 王鑫1
作者信息
  • 1.天水师范大学 土木工程学院,天水 741000
  • 2.兰州交通大学 土木工程学院,兰州 730070
  • 吕向明*(1979-),男,硕士,副教授(E-mail:).

Analysis of the deflection of simply supported steel truss web composite box beam considering the shear deformation of the steel truss web
Xiangming LÜ1 , Fangxu WANG1, 2, Xin WANG1
Affiliations
  • 1.School of Civil Engineering, Tianshui Normal University, Tianshui 741000, China
  • 2.School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
出版时间: 2025-10-28 doi: 10.7511/jslx20240522001
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为研究腹杆剪切变形对钢桁腹组合箱梁挠度的影响,首先将钢桁腹组合箱梁分解为由上下翼板和钢桁架组成的叠层梁,引入腹杆剪切变形转角函数建立钢桁腹组合箱梁在荷载作用下的解析模型,以简支梁为例求解挠曲变形解析解;其次为简便计算组合箱梁跨中挠度,结合初等梁理论及解析解求得截面有效刚度,并利用有效刚度求解跨中挠度;最后分析了组合箱梁在不同荷载工况下的挠曲特性,并与初等梁理论进行对比;在此基础上分析了腹杆直径、腹杆壁厚、腹杆倾角等构造参数对有效刚度的影响。结果表明,腹杆变形对钢桁腹组合箱梁挠度的影响不可忽略,采用初等梁理论计算组合箱梁挠度的最大误差达到了13.61%,考虑腹杆剪切变形得到的解析解计算结果与有限元更接近,最大误差为6.24%;利用截面有效刚度可有效预测跨中挠度,与解析解最大误差为3.64%;构造参数对有效刚度的影响中,腹杆壁厚影响最大,其次是腹杆直径、腹杆倾角;此外,有效刚度与腹杆直径及腹杆壁厚呈正相关,而与腹杆倾角呈负相关。

组合箱梁  /  腹杆  /  剪切变形  /  挠度分析  /  有效刚度

To study the influence of steel truss web shear deformation on the deflection of steel truss web composite box beams, the beams were first decomposed into a laminated structure composed of top and bottom flanges and a steel truss. A steel truss web shear deformation angle function was introduced to establish an analytical model, and the flexural deformation of a simply supported beam was analyzed as an example. The effective stiffness of the cross-section was determined by combining Euler beam theory and the analytical solution, and the mid-span deflection was calculated using this effective stiffness. The flexural characteristics under different load conditions were analyzed and compared with the Euler beam theory. The influence of structural parameters such as steel truss web diameter, steel truss web wall thickness, and steel truss web inclination angle on the effective stiffness was also examined. The results show that considering steel truss web shear deformation provides an analytical solution closer to the finite element results, with a maximum error of 6.24%. Using the effective stiffness can effectively predict the mid-span deflection, with a maximum error of 3.64% compared with the analytical solution. Among the structural parameters affecting the effective stiffness, steel truss web wall thickness has the greatest influence, followed by steel truss web diameter and steel truss web inclination angle. Additionally, the effective stiffness is positively correlated with steel truss web diameter and steel truss wall thickness but negatively correlated with steel truss web inclination angle.

composite box beam  /  steel truss web  /  shear deformation  /  deformation calculation  /  effective stiffness
吕向明, 王方旭, 王鑫. 考虑腹杆剪切变形的简支钢桁腹组合箱梁挠度分析. 计算力学学报, 2025 , 42 (5) : 839 -845 . DOI: 10.7511/jslx20240522001
Xiangming LÜ, Fangxu WANG, Xin WANG. Analysis of the deflection of simply supported steel truss web composite box beam considering the shear deformation of the steel truss web[J]. Chinese Journal of Computational Mechanics, 2025 , 42 (5) : 839 -845 . DOI: 10.7511/jslx20240522001
钢桁腹组合箱梁由混凝土翼板、钢桁架及节点组成[1],钢桁架可有效解决混凝土腹板开裂[2]、减轻结构自重[3]、增加抗风性能[4];组成钢桁架的钢腹杆拉压交替,在受压腹杆中填充混凝土可提高弯曲[5]和压缩性能[6],有助于避免受压腹杆的局部屈曲[7],提升钢桁腹组合箱梁的抗弯刚度[8];此外钢桁架具有出色的轴向[9]和弯曲强度[10];利用PBL节点将腹杆与翼板连接可增强两者之间的界面剪切[11],保证结构整体受力。组合箱梁如图1所示。
近年来,众学者对钢桁腹组合箱梁的弯曲行为进行了深入研究。Chen等[12]提出反三角钢桁架弯曲刚度最佳。Feng等[13]提出多平面反三角钢桁架的最优设计参数。Huang等[14]研究了界面缺陷的钢桁架的变形行为。Zhou等[15]研究了钢桁架不同位置的变形行为。Huang等[16]提出钢桁架弯矩承载力设计的估算方程。虽然众多学者对钢桁腹组合箱梁变形性能研究已取得丰硕的成果,但腹杆作为不连续的腹板结构,轴向变形会引起箱梁产生竖向剪切附加挠度,现有研究大多采用拟平截面法,因其忽略剪切变形[17],在特定条件下将低估主梁挠度,设计时安全系数偏低。
本文将钢桁腹组合箱梁的抗弯行为分解为上下翼板之间的桁架抗弯和上下翼板抗弯两者叠加,建立了一个能够考虑腹杆剪切变形的梁理论模型,以简支梁为例推导了组合箱梁在不同荷载类型下的挠曲变形解析解。通过引入有效刚度简化了考虑腹杆剪切变形的组合箱梁跨中挠度计算。在此基础上,分析了腹杆直径、腹杆壁厚和腹杆倾角对有效刚度折减参数和折减系数的影响。
钢桁腹组合箱梁挠曲变形时,做如下假定:
(1)假定上下翼板的挠曲位移相同;
(2)上下翼板各自满足平截面假定,忽略剪力滞效应;
(3)材料均为理想弹性;
(4)忽略翼板自身的剪切变形;
(5)假定压杆稳定性满足要求。
参见文献[17],钢桁腹组合箱梁可分解为由上下翼板和钢管桁架组成的叠层梁,将钢桁腹组合箱梁的抗弯行为分解为上下翼板之间的桁架抗弯和上下翼板抗弯两者叠加,如图2所示。
引入直角坐标系{oxyz},在竖向荷载作用下,中间层桁架发生剪切变形,顶底板中性轴产生相对转角ϕ,组合箱梁产生竖向挠曲位移w,如图3所示。
在线弹性范围内,钢桁腹组合梁截面上任意一点的纵向位移由组合梁的纵向位移、上下翼板之间的相对转角引起的相对纵向位移、上下翼板和桁架自身弯曲变形引起的纵向位移叠加,即
式中u为组合箱梁固有的纵向位移,huhL为组合箱梁截面中性轴分别到上下翼板中性轴的距离,zu为上翼板上任意一点相对于上翼板中性轴的z向坐标值,zL为下翼板上任意一点相对于下翼板中性轴的z向坐标值。
在竖向荷载下截面轴力为0,则u=0,可得
式中εu为组合箱梁上翼板任意一点的正应变,εL为组合箱梁下翼板任意一点的正应变,huL为上下翼板中性轴之间的距离,hw为钢管桁架的高度。
梁段微元体模型如图4所示。
式中NuNL为上下翼板所受轴力,(EAu、(EAL为上下翼板轴向刚度,MuML为上下翼板所受弯矩,(EIu、(EIL为上下翼板抗弯刚度。
组合箱梁承受横向荷载作用时,截面轴力为
由式(6)可得
组合箱梁截面弯矩为
式中M为组合箱梁截面总弯矩,Mb为上下翼板弯曲作用提供的总抵抗弯矩,Mt为上下翼板桁架作用提供的抵抗弯矩。
根据材料力学知识,截面剪力可表示为
图4可得
式中Vw为腹杆提供的截面剪力。
整理式(11~14),可得到组合箱梁内力平衡控制微分方程为
式中B1为桁架提供的抗弯刚度,B2为翼板提供的抗弯刚度,C为中间层桁架的有效抗剪刚度。
钢桁腹组合截面,Vw常见计算方法为求解腹杆轴力的竖向分量或根据剪切变形相等将腹杆换算为钢腹板,通过剪应变求解。本文考虑剪切变形,且微分运算需截面连续,故采用等效换算。
图5所示,基于剪切变形相等原则将不连续的钢腹杆换算为钢腹板。假设斜腹杆长为l1,其竖向高度与水平投影长度分别为h3b3,钢桁腹杆竖向夹角为β
钢桁腹杆在剪力VV的作用下,假设节点X2相对于节点X1的位移为η1
等效钢腹板在VV作用下,η2
式中Gs为钢材剪切模量,Aw为等效钢腹板的横截面积,Aw=h3twtw为等效钢腹板的厚度。
根据剪切变形相等原则,可得等效钢腹板厚度的计算公式为
式中μs为钢材的泊松比。
腹杆的等效剪应变γw
腹杆提供的剪力及有效抗剪刚度为
结合式(15,19),便可进行后续计算。
简支钢桁腹组合箱梁跨度为L,满跨作用均布荷载q,如图6所示。
弯矩和剪力为
边界条件为
通过顶底板中性轴产生相对转角ϕ,引入中间层桁架发生的剪切变形,联立式(19,20)可得
解方程(28)可得
将式(29)代入式(15),可得解析解为
式中
利用边界条件式(27),可求得C1~C5
C1~C5代入式(30)可得跨中挠度为
同理可得简支钢桁腹组合箱跨中集中荷载为P时,
参考材料力学可得,忽略剪切变形时,简支梁在均布荷载和跨中集中荷载下的跨中挠度为
式中B为采用拟平截面法计算得到的组合梁截面刚度。
由于简支梁跨中挠度为工程设计中重点控制指标,而式(35,37)过于复杂,故参见文献[17]结合式(38),对式(35,37)进行有效简化,将采用拟平截面法得到的组合梁截面刚度B利用考虑腹杆剪切变形得到的截面有效刚度Bz代替,即得
式中λ为有效刚度折减系数,ζ为有效刚度折减参数。
选取某工程实例为背景,主梁为单箱单室,跨径35 m,顶板宽8.5 m,底板宽4.8 m,梁高2.3 m,混凝土C50,钢桁腹杆Q345C级钢管,规格ϕ351×16,水平倾角为67°,节间距为1.95 m,横截面如图7所示。
采用ANSYS建立三维有限元分析模型,钢腹杆均为空心,选用SOLID187单元模拟,未考虑受压腹杆中填充混凝土的影响,顶板、底板选用SOLID185单元模拟,各组件的连接采用节点自由度耦合,混凝土弹性模量Ec=3.45×104 MPa,泊松比μc=0.2,钢材弹性模量Es=2.06×105 MPa,泊松比μs=0.3,有限元模型如图8所示。
选取简支梁受均布荷载(工况Ι)、集中荷载(工况Ⅱ)。根据《公路桥涵设计通用规范》(JT-GD60-2015),按公路-Ι级车道荷载取值,均布荷载q=10.5 kN/m,集中荷载P=300 kN。以本文解析解与Euler梁及ANSYS计算结果作对比,其中ANSYS结果取其顶板几何中心处。对比结果如图9图10所示。
图9图10可知,采用Euler梁理论将低估主梁挠度,均布荷载时误差为11.01%,集中荷载时误差为13.61%;本文解析解计算结果更接近实际状态,承受均布荷载时的跨中误差为6.05%,承受集中荷载时的跨中误差为6.24%,从而验证了本文方法的正确性。
选取不同工况下解析解及按截面有效刚度计算的跨中挠度与有限元进行对比,计算百分比时以有限元结果为参考,百分比差值表示为ρ,结果列入表1
表1可知,采用简化的截面有效刚度计算的跨中挠度与有限元最大误差为9.88%,组合箱梁在承受均布荷载时的跨中误差为3.6%,承受集中荷载时的跨中误差为3.64%;由此说明跨中挠度计算时可采用截面有效刚度简化处理。
采用截面有效刚度计算钢桁腹组合箱梁变形时,与λζ相关的tw采用等效换算,现取与tw相关的腹杆直径、腹杆壁厚及腹杆倾角3个参数进行分析,研究各参数对λζ的影响,各参数均取5个变化值,列入表2,各参数影响结果如图11~图13所示。
图11~图13可知,λζ随着腹杆直径及腹杆壁厚的增加而增加,随着腹杆倾角的增加而减小;由此说明λζ与腹杆直径及腹杆壁厚正相关,而与腹杆倾角负相关。
为综合衡量不同参数对λζ的影响,选取相对增量比来区分各影响因素的显著性,令显著性为
式中Δpmax为不同参数百分比最大差值,Δkmax为对应参数指标变化百分比。
腹杆直径、腹杆壁厚及腹杆倾角的显著性指标列入表3。由表3可知,腹杆壁厚对λζ的影响最大,其次为腹杆直径、腹杆倾角。
(1)腹杆变形对钢桁腹组合箱梁挠度的影响不可忽略,与有限元相比,采用初等梁理论计算时组合箱梁在承受均布荷载时的跨中误差为11.01%,承受集中荷载时的跨中误差为13.61%,考虑腹杆剪切变形得到的解析解计算结果更接近实际状态,承受均布荷载时的跨中误差为6.05%,承受集中荷载时的跨中误差为6.24%;
(2)利用解析解结合初等梁理论求得截面有效刚度可简化跨中挠度计算,与解析解相比,组合箱梁在承受均布荷载时的跨中误差为3.6%,承受集中荷载时的跨中误差为3.64%;
(3)影响有效刚度的构造参数中,腹杆壁厚影响最大,其次是腹杆直径、腹杆倾角;此外,有效刚度与腹杆直径及腹杆壁厚呈正相关,而与腹杆倾角呈负相关。
  • 国家自然科学基金(52068063)
  • 2022年度甘肃省高等学校创新基金(2022A-107)
  • 天水师范学院2023年科研创新平台建设专项(PTJ2023-07)
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2025年第42卷第5期
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doi: 10.7511/jslx20240522001
  • 接收时间:2024-05-22
  • 首发时间:2026-03-24
  • 出版时间:2025-10-28
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  • 收稿日期:2024-05-22
  • 修回日期:2024-06-20
基金
国家自然科学基金(52068063)
2022年度甘肃省高等学校创新基金(2022A-107)
天水师范学院2023年科研创新平台建设专项(PTJ2023-07)
作者信息
    1.天水师范大学 土木工程学院,天水 741000
    2.兰州交通大学 土木工程学院,兰州 730070
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2种不同金属材料的力学参数

Family
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genus
种数
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species
占总种数比例
Percentage of
total species (%)

Genus
种数
Number of
species
占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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