陳 國,周 通,于云飛,談 闖,楊文琪,徐振東
竹集成材釘節(jié)點力學(xué)性能的試驗研究
陳 國,周 通,于云飛,談 闖,楊文琪,徐振東
(南京林業(yè)大學(xué)土木工程學(xué)院,南京 210037)
為研究現(xiàn)代竹構(gòu)建筑中釘節(jié)點的受力性能和變形性能,對85個竹集成材釘連接節(jié)點試件進行單調(diào)加載試驗,研究不同釘子端距、中距、邊距、行距對釘節(jié)點的承載性能、變形特性和破壞機理的影響。試驗結(jié)果表明,節(jié)點的力學(xué)性能主要取決于端距和中距,而邊距和行距的影響較小。加載初期的釘孔間隙導(dǎo)致節(jié)點初期的剛度較低。當(dāng)端距和中距小于6(為釘子直徑)時,節(jié)點的承載力隨著端距和中距的增加而呈增大趨勢,當(dāng)端距和中距大于等于6時,節(jié)點的承載力將不再增大。釘節(jié)點的破壞形態(tài)與釘子的布置密切相關(guān)。當(dāng)端距或中距小于6時,分別以端部剪切破壞和縱向劈裂破壞為主;當(dāng)邊距小于4或行距小于3時,分別以劈裂和塊剪破壞為主。當(dāng)釘子的端距、中距、邊距和行距布置滿足最小容許要求時,釘節(jié)點以銷槽承壓破壞模式為主,表現(xiàn)出較好的延性特征。試驗結(jié)果的回歸分析表明,F(xiàn)olz模型能較好地反映釘節(jié)點在各個受力階段的荷載-位移本構(gòu)關(guān)系,而基于Foschi和Hassanieh模型預(yù)測的彈塑性階段的釘節(jié)點荷載-本構(gòu)關(guān)系結(jié)果偏于保守,但明顯高估了破壞階段的受力變形性能。研究結(jié)果可為竹集成材釘節(jié)點的設(shè)計與應(yīng)用提供參考。
竹;釘子;竹集成材;釘連接;構(gòu)造要求;荷載-位移模型
中國擁有極其豐富的竹材資源,種類、蓄積量和產(chǎn)量均居世界首位。對竹子進行改性并應(yīng)用于工程領(lǐng)域有利于降低對不可再生建筑材料的依賴[1-3]。竹集成材(Laminated Bamboo Lumber,LBL)是以3~5年生的毛竹為原料,加工成一定規(guī)格的矩形竹片,再經(jīng)干燥、蒸煮、炭化、涂膠、組坯后熱壓而成的一種型材[4-5]。與圓竹相比,LBL克服了原竹的材料缺陷和尺寸變異性,力學(xué)性能明顯優(yōu)于速生木材[6],目前主要應(yīng)用于家具、地板和裝飾等非結(jié)構(gòu)領(lǐng)域。盡管LBL在橋梁[7]和房屋[8-9]結(jié)構(gòu)中也有一定的應(yīng)用,但其設(shè)計和建造主要采用國內(nèi)外的木結(jié)構(gòu)設(shè)計標準,嚴重制約了LBL在土木工程領(lǐng)域的推廣應(yīng)用。突破LBL的局限性,拓展其應(yīng)用范圍,在國內(nèi)具有重要的現(xiàn)實意義。
節(jié)點是影響竹木結(jié)構(gòu)抗震性能的重要部件,直接關(guān)乎結(jié)構(gòu)的安全。常見的節(jié)點形式包括榫卯節(jié)點[10-12]、齒板節(jié)點[13]、螺栓節(jié)點[14-16]和釘節(jié)點[17]等。其中,釘連接具有施工方便、安全可靠、價格低廉的特點,是一種最常見的連接方式。國內(nèi)外學(xué)者對木結(jié)構(gòu)釘節(jié)點的力學(xué)性能進行了大量的試驗研究和理論分析。Porteous等[18]研究了端距、邊距、中距、行距等對木材-鋼夾板釘節(jié)點力學(xué)性能的影響并提出了設(shè)計計算方法。Meghlat等[19-20]認為釘節(jié)點的破壞形態(tài)與釘子間距影響密切,其中端距和中距的影響最顯著。GB 50005-2017《木結(jié)構(gòu)設(shè)計標準》[21]和Breyer等[22]對木結(jié)構(gòu)釘節(jié)點的構(gòu)造要求進行了嚴格限制,并提出了相應(yīng)的設(shè)計計算方法。
木結(jié)構(gòu)釘節(jié)點承載力低,不適合應(yīng)用于大跨度和重型木結(jié)構(gòu)中;另一方面,中國實施了數(shù)十年的天然林保護工程,木材的采伐和利用嚴重受限,迫切需要尋找另一種可持續(xù)綠色建材。為解決上述問題,研究人員[23-26]提出了“以竹代木”,并成功將其應(yīng)用于工程領(lǐng)域。Ramirez等[27-28]認為主材和側(cè)材的銷槽承壓強度對釘節(jié)點力學(xué)性能有著顯著的影響的影響,竹集成材的銷槽承壓強度明顯優(yōu)于木材。Li等[29]對膠合竹-木釘連接節(jié)點進行了有益的探索,但未考慮釘子間距對組合節(jié)點的影響。更為重要的是,迄今為止國內(nèi)外尚未有結(jié)構(gòu)用LBL的相關(guān)規(guī)范或標準,且LBL釘節(jié)點的研究亦未見文獻報道。
已有研究表明[21],竹木材料順紋方向的力學(xué)強度最高,斜紋次之,橫紋向最低。因而,實際工程中主要選擇其順紋方向使用。本文設(shè)計了85個LBL釘節(jié)點順紋向受力的試件,進行單調(diào)加載試驗,研究其破壞機理和抗剪性能,討論釘子端距、中距、邊距和行距對受力性能的影響,在試驗的基礎(chǔ)上,研究釘節(jié)點荷載-位移本構(gòu)模型,為此類LBL釘節(jié)點的設(shè)計和有限元分析提供技術(shù)依據(jù)。
本研究涉及的材料包括LBL和釘子。其中LBL由東莞湘楠竹木制品有限公司提供,材性試驗依據(jù)ASTM D143-14[30]和ASTM D5764-97a[31]進行,測得其抗拉強度為107.7 MPa,抗壓強度為56.3 MPa,彈性模量為11 GPa,密度為870 kg/m3,含水率為9.2%。銷槽承壓強度是衡量LBL在銷類連接件作用下抵抗自身破壞的能力,銷槽承壓強度與銷類連接件的直徑密切相關(guān)[32],當(dāng)銷直徑為2.5 mm時,LBL順紋向銷槽承壓強度為73.71 MPa。根據(jù)GB 50005-2017《木結(jié)構(gòu)設(shè)計標準》[21]規(guī)定和當(dāng)前工程實踐,釘連接常采用直徑為2.5 mm、長度D為50 mm的普通光圓鐵釘,參照ASTM F1575-17測得其抗彎強度平均值為705.2 MPa。
參照目前國內(nèi)外常見木結(jié)構(gòu)釘節(jié)點的尺寸,設(shè)計的LBL釘節(jié)點試件[17-18]由兩塊側(cè)材和一塊主材組成,側(cè)材和主材通過釘子按一定間距連接。主材和側(cè)材的厚度分別為40和20 mm,截面寬度均為40 mm,同組試件的主材和側(cè)材長度相等,不同組主材和側(cè)材的截面示意圖參見圖1。釘節(jié)點的受力性能、變形性能和破壞機理主要取決于釘子的端距、中距、邊距和行距等構(gòu)造參數(shù)。85個LBL釘節(jié)點試件,分為4個組共17個系列,每系列5個重復(fù)試件。各組分別考慮端距、中距、邊距和行距對釘節(jié)點荷載-位移曲線、承載力和延性的影響,如表1所示。已有研究表明[24],直接釘入竹集成材易發(fā)生劈裂破壞,因而采用預(yù)鉆孔的方式釘入釘子,鉆孔深度約等于釘子長度的90%,鉆孔直徑約為釘子直徑的80%。為消除主材和側(cè)材間的摩擦力對節(jié)點抗剪性能的影響[33],試件制作時,首先在主材和側(cè)材之間嵌入1 mm厚的薄鋼片,然后從節(jié)點側(cè)面垂直釘入鐵釘,直至釘帽與側(cè)材表面平齊,最后再拔出薄鋼片,試件制作完畢后10 min內(nèi)開始進行單調(diào)加載試驗。
注:e1為端距,mm;e2為邊距,mm;s為中距,mm;r為行距,mm;l為主(側(cè))材長度,mm。下同。
表1 釘節(jié)點試件參數(shù)
注:為釘節(jié)點行數(shù);為釘節(jié)點列數(shù);為釘子直徑。下同。
Note:is number of rows of nails;is number of lines of nails;is diameter of nails. Same as below.
1.3.1 加載方案與量測內(nèi)容
單調(diào)加載試驗在DDL5電子萬能試驗機上進行,試驗機的最大加載值為50 kN。試驗加載裝置和測點如圖2所示,側(cè)材底部與40 mm × 40 mm × 150 mm的竹間隔塊通過M20螺栓連接以形成夾持段,主材頂部和竹間隔塊底部的夾持段分別通過M 20螺栓和U型夾具相連。試驗時拉力荷載使用萬能試驗機上的剛性夾頭在試件兩端的U型夾具加載,確保試件始終處于軸心受力狀態(tài)。加載過程中,在試件側(cè)面布置2個位移計實時監(jiān)測主材和側(cè)材的豎向相對位移值,通過試驗機高精度力傳感器實測荷載。所有的位移和荷載均由東華DH3820靜態(tài)應(yīng)變測量系統(tǒng)自動采集并存入電腦記錄,采樣頻率為1 Hz。
參照《木質(zhì)結(jié)構(gòu)材料用銷類連接件連接性能試驗方法》LY/T 2377-2014[34],正式加載前進行預(yù)加載,從而消除試件和夾具之間的縫隙并檢驗儀器設(shè)備是否工作正常,初始加載為預(yù)估極限承載力的15%。正式加載采用位移加載,速度為2 mm/min,保證試件在10 min左右達到極限荷載,當(dāng)荷載降至極限荷載的85%左右時,認為試件破壞,結(jié)束加載。
1.3.2 參數(shù)計算
屈服荷載y采用“5%釘子直徑”法[34]確定,如圖3所示。對照實測的荷載-位移曲線線性段,沿橫坐標向右平移釘子直徑5%的位移,再繪制一條與其平行的直線,取該直線和荷載-位移曲線交點與起始點之間的極限荷載作為屈服荷載y。如果該直線未與荷載-位移曲線相交,則取曲線極限荷載m作為y。由于釘連接節(jié)點的初始剛度較低,根據(jù)Zheng等[20]的研究成果,取0.1m和0.4m對應(yīng)位移量的斜率作為剛度0。試件發(fā)生破壞時的位移與屈服位移Δ之比值為其延性系數(shù)[35]。
式中Δ為相應(yīng)于y的屈服位移,mm;Δ為試件最終發(fā)生破壞時的位移,取荷載下降至85%m時對應(yīng)的位移值,mm。
注:Fy為屈服荷載,kN;Fm為極限荷載,kN。下同。
2.1.1 荷載-位移曲線
以dj3試件的荷載-位移曲線為例(圖4),分析試件的相對變形過程,其大致可分為4個階段:1)初始滑移階段,荷載從0到10%m,釘節(jié)點發(fā)生了較大滑移,但荷載增長非常緩慢,這主要是因為釘子和孔壁間存在間隙,使得釘子未能充分發(fā)揮其承載能力,類似的現(xiàn)象也發(fā)生在木結(jié)構(gòu)釘連接試驗中[19];2)彈性階段,當(dāng)荷載不大于40%m時,荷載-位移曲線保持較好的線性關(guān)系,節(jié)點處于彈性工作階段;3)彈塑性階段,荷載繼續(xù)增加,但增速明顯變緩,節(jié)點破壞緩慢發(fā)展,荷載-位移曲線出現(xiàn)多個峰值;4)破壞階段,荷載達到m后,進入破壞加速階段,曲線開始顯著下降,試件喪失承載力,試驗結(jié)束。
圖4 dj3試件荷載-位移曲線
2.1.2 承載能力
試件的主要試驗結(jié)果取平均值及變異系數(shù)V如表2所示,試件的極限荷載和屈服荷載與釘子的端距1、中距、邊距2和行距密切相關(guān)。
當(dāng)1<6(dj1和dj2)或<6(zj1、zj2和zj3)時,屈服承載力和極限承載力隨釘子端距和中距的增大而增加,但屈服荷載的增長幅度明顯低于極限荷載的增長幅度。但當(dāng)1≥6(dj3、dj4和dj5)或≥6(zj4和zj5)時,承載能力不再增大,趨于恒定值。當(dāng)2<4(bj1)或<3(hj1)時,承載力隨釘子邊距和行距的增大而增加,但當(dāng)2≥4(bj2和bj3)或≥3(hj2、hj3和hj4)時,承載能力將不再增大。邊距和行距對試件承載能力的影響較小,這主要是因為邊距2和行距為橫向的釘間距,垂直于LBL的受力方向。因此,LBL釘節(jié)點的最小端距1和中距應(yīng)取6,最小邊距2和行距的構(gòu)造要求分別取4和3。LBL順紋向受力的釘子最小間距,應(yīng)符合表3的要求。GB 50005-2017《木結(jié)構(gòu)設(shè)計標準》對木結(jié)構(gòu)釘節(jié)點的最小容許距離做出了嚴格的限制,但未充分考慮釘子的釘入方式對釘子最小距離的影響,釘間距采用統(tǒng)一的要求。Breyer等[22]認為端距和中距的最小容許距離隨著主(側(cè))材密度的增大而呈減小的趨勢,而邊距和行距的容許距離與主(側(cè))材的密度沒有必然的聯(lián)系。當(dāng)木材的密度大于600 kg/m3,應(yīng)采用預(yù)鉆孔的方式以避免木材劈裂,因而釘子的最小距離應(yīng)細分為預(yù)鉆孔和非預(yù)鉆孔兩種情況,采用預(yù)鉆孔加工的釘間距略小于非預(yù)鉆孔。LBL的密度大于木材的密度,因而LBL釘節(jié)點的端距1和中距的要求均小于國內(nèi)外木材的要求,而LBL的最小邊距2要求大于國內(nèi)外木結(jié)構(gòu)的要求,最小行距要求則介于《木結(jié)構(gòu)設(shè)計標準》[21]和Breyer等[22]的要求之間。
表2 釘節(jié)點主要試驗結(jié)果
表3 釘子的最小容許距離
2.1.3 位移延性
延性是指結(jié)構(gòu)或構(gòu)件抵抗彈塑性變形的能力,一般可用延性系數(shù)來衡量。在承載力保持不變的前提下,結(jié)構(gòu)或構(gòu)件的變形能力越強,說明其延性就越好。Smith[36]依據(jù)延性系數(shù)的大小將木結(jié)構(gòu)銷連接節(jié)點的延性劃分為4種類型,即脆性(≤2),低延性(2<≤4),中等延性(4<≤6)和高延性(>6)。如表2所示,釘節(jié)點的延性系數(shù)隨著端距的增大而增大。當(dāng)端距1大于6時,釘節(jié)點表現(xiàn)出高延性的特性,這與試件破壞前釘子發(fā)生明顯的彈塑性變形是一致的。中距小于6的試件發(fā)生了過早的脆性破壞,破壞前無明顯征兆,因而其延性系數(shù)較小。邊距2和行距對試件的延性系數(shù)影響較小,大部分試件表現(xiàn)出中等的延性,試件發(fā)生最終破壞前LBL的銷槽和釘子破壞前發(fā)生較大的變形所致。
2.1.4 試驗現(xiàn)象
LBL釘節(jié)點的破壞現(xiàn)象與釘子的布置密切相關(guān),主要觀察到4種:①端部竹材剪切破壞;②銷槽承壓破壞;③劈裂破壞;④塊剪破壞。
端距1<6的試件dj1和dj2的破壞形態(tài)為端部剪切破壞,如圖5a所示,由于端部竹材對釘子的約束不足,因此靠近邊緣的竹材發(fā)生過早的剪切破壞并帶出竹屑,試件隨即喪失承載力,但其他截面無破壞現(xiàn)象。隨著端距1的逐漸增大,試件dj3、dj4和dj5均表現(xiàn)為孔壁銷槽承壓破壞(圖5b)。
試件zj1~zj3的中距<6,裂縫首先在靠近端部的釘子孔洞處產(chǎn)生,隨著荷載的增大,裂縫變寬變長并伴隨著不斷加劇的撕裂聲,相鄰釘子處的竹材裂縫隨即發(fā)展成一條通縫,導(dǎo)致試件劈裂破壞(圖5c)。中距≥6的試件zj4和zj5的破壞形態(tài)以銷槽承壓破壞為主,破壞始于靠近端部的銷槽,靠近中部的銷槽無可見破壞。
圖5 試件主要破壞形態(tài)
邊距和行距對節(jié)點的抗剪性能具有類似的破壞特征,對于邊距2<4或行距<3的試件,加載初期,荷載增加,但滑移不明顯,當(dāng)加載至屈服荷載后,釘子孔洞出現(xiàn)輕微的銷槽承壓破壞并伴有順紋向微裂縫,相鄰釘子之間的裂縫逐漸匯合。當(dāng)達到極限荷載后,隨著裂縫變寬,荷載稍有下降,滑移愈發(fā)明顯,最終發(fā)生塊剪破壞(圖5d)。對于邊距2≥4或行距≥3的試件,當(dāng)加載至屈服荷載后,靠近兩端的銷槽處首先發(fā)生了承壓破壞伴隨竹材的撕裂聲,之后荷載呈波浪形變化,銷槽從兩端向中間逐個發(fā)生破壞。當(dāng)達到極限荷載后,銷槽承壓破壞加劇,相鄰孔洞間出現(xiàn)微裂縫。
銷連接的荷載-位移的本構(gòu)關(guān)系主要有Foschi[37]、Folz[38]和Hassanieh[39]模型。Foschi等[37]于1974年首先提出了簡化的指數(shù)模型公式,其表達式為
式中0為屈服后漸近線在軸上的截距,kN;1為屈服后剛度與彈性階段的剛度之比(0<1<1),0為彈性階段的剛度,kN/mm。
基于Foschi表達式,F(xiàn)olz提出了改進的表達式:
式中2為退化剛度與初始剛度之比(2<0);和分別為極限位移和破壞位移,mm。
Hassanieh于2016年提出了鋼夾板-木結(jié)構(gòu)銷連接節(jié)點的荷載-位移本構(gòu)模型:
式中K和K分別為節(jié)點屈服后和破壞前漸近線的剛度,kN/mm;1為破壞前漸近線在軸上的截距,kN;1和2為常系數(shù)。
選取4個典型的釘節(jié)點試件dj5、zj4、bj2和hj2進行數(shù)據(jù)擬合,獲得了理論擬合曲線和試驗曲線的對比結(jié)果,如圖6所示。結(jié)果表明,由于釘節(jié)點初始加載階段發(fā)生了滑移,F(xiàn)ochi、Hassanieh和Folz的表達式均不能很好的模擬此階段的荷載-位移關(guān)系。但3個理論表達式擬合的曲線能夠真實的反映釘節(jié)點彈性段的受力變形性能,F(xiàn)ochi和Hassanieh預(yù)測值低估了釘節(jié)點彈塑性階段的荷載-位移性能,但明顯高估了破壞階段的行為。
圖6 荷載-位移關(guān)系的試驗值和理論值對比
綜上所述,在忽略初始滑移階段的前提下,F(xiàn)ochi、Hassanieh和Folz提出的理論表達式均能如實地反映釘節(jié)點在彈性階段的荷載-位移性能,而Folz模型能更加精確的反映LBL釘節(jié)點在各個受力階段的荷載-位移本構(gòu)關(guān)系,但表達式形式較復(fù)雜,不適合用于手算分析。相對于其他理論本構(gòu)關(guān)系表達式而言,F(xiàn)oschi提出的指數(shù)表達式的形式簡單,因而被廣泛地應(yīng)用于模擬木結(jié)構(gòu)銷類連接的變形滑移性能。本構(gòu)關(guān)系的分析研究可為竹集成材釘節(jié)點的設(shè)計與有限元分析提供有益的參考。
通過85個LBL釘節(jié)點試件的單調(diào)加載試驗,研究了端距1、中距、邊距2和行距對釘節(jié)點力學(xué)性能的影響,得到以下結(jié)論:
1)LBL釘節(jié)點的屈服承載力和極限承載力隨釘子端距和中距的增大而增加,但屈服承載力的提高幅度明顯低于極限承載力的增幅,當(dāng)端距或中距大于6(為釘子直徑)時,承載能力將不再增加。而邊距和行距對承載力的影響較小。
2)采取預(yù)鉆孔方式的LBL釘節(jié)點的最小容許端距和中距應(yīng)取6,最小邊距和行距的最小容許構(gòu)造要求分別為4和3。
3)當(dāng)端距和中距小于6時,表現(xiàn)出低延性的破壞特征。當(dāng)端距大于6時,釘節(jié)點表現(xiàn)出高延性的特性,邊距和行距對試件的延性系數(shù)影響較小。
4)釘節(jié)點的破壞形態(tài)有4種:端部竹材剪切破壞、釘孔壁承壓破壞、劈裂破壞和塊剪破壞。LBL釘節(jié)點的破壞形態(tài)與釘子間距密切相關(guān)。
5)LBL釘節(jié)點的荷載-位移關(guān)系可分為4個階段:初始滑移階段、彈性段、彈塑性段和破壞段。在忽略滑移階段的前提下,F(xiàn)olz模型能真實的反映LBL節(jié)點受力全程的荷載-位移本構(gòu)關(guān)系。
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Experimental study on mechanical performance of laminated bamboo lumber nailed connections
Chen Guo, Zhou Tong, Yu Yunfei, Tan Chuang, Yang Wenqi, Xu Zhendong
(,,210037,)
In recent years, the building industry of China has expanded rapidly, however, construction materials such as the steel and cement are extensive used, which leads to serious environmental issues and energy consumption. As one of the fast-growing plants in the world, bamboo has been applied in civil engineering field for thousands of years. However, some disadvantages are exposed during the practice, such as thin-walled hollow and the diameter of bamboo culm decreases from the bottom to top. More importantly, the service life of bamboo structures generally does not exceed 3 years when the untreated bamboo exposure to natural environment. Recently, more and more attention are paid on the laminated bamboo lumber (LBL), which is considered as an alternative to wood because of its advantage of higher ration of strength to weight. Dowel connections including bolt, nail, screw and dowel are common types of connections in timber engineering for a large range of structural applications. Among them, nail connection is simple to produce and can be used for small as well as for large forces. Over the last decade, the use of LBL for modern bamboo structure has become increasing popular in China. LBL nailed connection which consisted of one middle member and two side members were introduced. A total of 85 specimens were tested in order to investigate the effect of parameters on capacity, deformation and failure modes of nailed connections, including end distance (1), center-to-center distance (), row spacing () and edge distance (2). It was found that the mechanical performance of nailed connections was mainly determined by the end distance and center-to-center distance of nails, and the influence of row spacing and edge distance was relative small. The initial gap between the lead hole and nails tended to result in lower stiffness. Four failure modes were recorded, including compression failure at the nail hole, splitting, shear failure at the end and block shear. For1orless than 6 times the diameter of nails (), the nailed connections failed in shear failure at the end and splitting, respectively. Forless than 3or2less than 4the connections failed in splitting and block shear, respectively. When nail spacing meet the minimum structural requirement, the nailed connections failed in compression failure of nail holes in the middle or side members, showing good ductile behavior. The ultimate load and yield load of specimens increased with the increase of nail spacing and kept constant as the nails spacing satisfied the minimum structural requirement. Many models had been proposed to quantify the load-displacement relationship of wood nailed connections, such as Folz’s, Foschi’s and Hassanieh’s model. Using the regression analysis for comparing the three theoretical models, it was found that the Folz’s model was more objectively reflected the load- displacement relationship of LBL nailed connections loaded parallel to grain. A good agreement could be observed between the Foschi’s or Hassanieh’s model and experimental results in the elastic stage, but great deviation of the theoretical results in the post-yielding stage increased gradually. The results provided useful information for modeling various bamboo structures containing LBL nailed connections.
bamboo; nails; laminated bamboo lumber (LBL);nailed connection; structural requirement;load-displacement model
陳國,周通,于云飛,等. 竹集成材釘節(jié)點力學(xué)性能的試驗研究[J]. 農(nóng)業(yè)工程學(xué)報,2020,36(13):291-298.doi:10.11975/j.issn.1002-6819.2020.13.034 http://www.tcsae.org
Chen Guo, Zhou Tong, Yu Yunfei, et al. Experimental study on mechanical performance of laminated bamboo lumber nailed connections[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2020, 36(13): 291-298. (in Chinese with English abstract) doi:10.11975/j.issn.1002-6819.2020.13.034 http://www.tcsae.org
2019-12-01
2020-06-01
國家自然科學(xué)基金資助項目(51408312);江蘇省自然科學(xué)基金資助項目(BK20130982);住房和城鄉(xiāng)建設(shè)部資助項目(2018-K5-003)
陳 國,博士,副教授,主要從事現(xiàn)代竹木結(jié)構(gòu)研究。Email:chenguo@njfu.edn.cn
10.11975/j.issn.1002-6819.2020.13.034
TU366.1
A
1002-6819(2020)-13-0291-08