畢繼紅,王照耀,趙?云,霍琳穎,王光宇
基于延性剪切破壞模式的SFRC無(wú)腹筋梁受剪承載力分析
畢繼紅1, 2,王照耀1,趙?云1,霍琳穎1,王光宇1
(1. 天津大學(xué)建筑工程學(xué)院,天津 300354;2. 濱海土木工程結(jié)構(gòu)與安全教育部重點(diǎn)實(shí)驗(yàn)室(天津大學(xué)),天津 300354)
鋼纖維混凝土(SFRC)無(wú)腹筋梁受剪承載力是結(jié)構(gòu)設(shè)計(jì)時(shí)的關(guān)鍵指標(biāo),準(zhǔn)確預(yù)測(cè)其受剪承載力具有重要意義.大量SFRC無(wú)腹筋梁受剪性能試驗(yàn)發(fā)現(xiàn)由于鋼纖維的加入,其破壞模式由脆性的剪切破壞轉(zhuǎn)變?yōu)檠有约羟衅茐模赟FRC無(wú)腹筋梁延性剪切破壞模式及其抗剪機(jī)理,提出一種新的受剪承載力計(jì)算模型,其中包括骨料咬合力、縱筋銷(xiāo)栓作用、斜裂縫截面鋼纖維及受壓區(qū)混凝土的貢獻(xiàn).根據(jù)理論分析分別推導(dǎo)了各抗剪機(jī)制的計(jì)算公式,并通過(guò)SFRC無(wú)腹筋梁變形協(xié)調(diào)及受力平衡條件將這些抗剪機(jī)制有效結(jié)合,給出了SFRC無(wú)腹筋梁受剪承載力計(jì)算的具體步驟.為了方便工程設(shè)計(jì),在提出的受剪承載力計(jì)算模型的基礎(chǔ)上根據(jù)各抗剪機(jī)制的受力特點(diǎn)及對(duì)于受剪承載力的貢獻(xiàn)提出了簡(jiǎn)化計(jì)算公式,簡(jiǎn)化計(jì)算公式力學(xué)概念清晰且形式簡(jiǎn)單.采用提出的計(jì)算模型、簡(jiǎn)化計(jì)算公式和5種已有計(jì)算模型對(duì)收集到的217根SFRC無(wú)腹筋梁受剪承載力進(jìn)行預(yù)測(cè)并與試驗(yàn)結(jié)果進(jìn)行對(duì)比.計(jì)算結(jié)果表明,斜裂縫截面鋼纖維在SFRC無(wú)腹筋梁抗剪中發(fā)揮重要作用,提出的計(jì)算模型與簡(jiǎn)化計(jì)算公式均能夠準(zhǔn)確地預(yù)測(cè)SFRC梁受剪承載力,且變異系數(shù)小,在不同的剪跨比、軸心抗壓強(qiáng)度、纖維特征系數(shù)及縱筋配筋率時(shí)均能保證較高的計(jì)算精度,為SFRC無(wú)腹筋梁抗剪設(shè)計(jì)與分析提供參考.
鋼纖維混凝土;無(wú)腹筋梁;受剪承載力;骨料咬合力;縱筋銷(xiāo)栓作用
鋼筋混凝土梁受剪性能是鋼筋混凝土結(jié)構(gòu)最基本的研究課題之一,因?yàn)槠淇辜魴C(jī)理的復(fù)雜性,受到研究者們的廣泛關(guān)注.許多研究認(rèn)為混凝土抗拉強(qiáng)度是影響受剪承載力的主要因素,并將其作為重要的設(shè)計(jì)參數(shù),如我國(guó)《混凝土結(jié)構(gòu)設(shè)計(jì)規(guī)范》(GB50010—2010)[1].而鋼纖維混凝土(SFRC)由于纖維的橋接作用,使得SFRC抗拉強(qiáng)度,尤其是開(kāi)裂后抗拉強(qiáng)度有較大的提升,同時(shí)也提高了混凝土的韌性和抗裂性能[2-7],因此SFRC梁相比普通混凝土梁的受剪性能有較大的改善,在實(shí)際工程中已有廣泛的應(yīng)用.
由于鋼纖維的加入會(huì)顯著提高SFRC梁的抗剪強(qiáng)度,根據(jù)梁的位置不同鋼纖維可替代部分甚至全部箍筋[8-9],大大減少箍筋的配置,這使得SFRC無(wú)腹筋梁有更廣泛的工程應(yīng)用.由于混凝土構(gòu)件抗剪機(jī)理的復(fù)雜性,一般分別研究無(wú)腹筋梁和有腹筋梁的受剪性能,以此確定腹筋在梁抗剪機(jī)制中的貢獻(xiàn),因此研究SFRC無(wú)腹筋梁的受剪性能具有非常重要的意義.
許多研究者對(duì)SFRC無(wú)腹筋梁受剪性能進(jìn)行了試驗(yàn)和理論研究[8-13],其中提出的受剪承載力計(jì)算模型大多都是基于試驗(yàn)數(shù)據(jù)回歸的經(jīng)驗(yàn)公式,難以解釋SFRC無(wú)腹筋梁復(fù)雜的抗剪機(jī)理.通過(guò)分析可知SFRC梁主要的抗剪機(jī)制包括:縱筋銷(xiāo)栓作用、裂縫間纖維橋接作用、縱筋銷(xiāo)栓作用、骨料咬合和它們之間的復(fù)合作用,而已有的SFRC受剪承載力計(jì)算模型只考慮部分影響,很難同時(shí)反映這些抗剪機(jī)制的貢獻(xiàn).
我國(guó)《混凝土結(jié)構(gòu)設(shè)計(jì)規(guī)范》(GB50010—2010)[1]根據(jù)剪跨比不同將受剪破壞分為斜壓破壞、剪壓破壞和斜拉破壞,而SFRC相比普通混凝土韌性更強(qiáng),許多研究者發(fā)現(xiàn)鋼纖維的加入會(huì)使剪跨比較大(一般認(rèn)為大于等于2)的混凝土梁由脆性剪切破壞轉(zhuǎn)變?yōu)橛幸欢ㄑ有缘募羟衅茐腫8-13],即發(fā)生剪切破壞時(shí)部分或者全部縱筋已經(jīng)屈服,梁的變形性能更好,而目前對(duì)于這種破壞模式下SFRC梁受剪承載力的研究還較少.
本文基于SFRC無(wú)腹筋梁延性剪切破壞模式提出了一種新的受剪承載力計(jì)算模型,其中包括骨料咬合力、縱筋銷(xiāo)栓作用、斜裂縫截面鋼纖維及受壓區(qū)混凝土對(duì)受剪承載力的貢獻(xiàn),并通過(guò)變形協(xié)調(diào)條件及受力平衡將這幾種抗剪機(jī)制有效結(jié)合.為方便工程應(yīng)用,在分析受剪承載力計(jì)算模型的基礎(chǔ)上提出簡(jiǎn)化計(jì)算公式,采用提出的計(jì)算模型、簡(jiǎn)化計(jì)算公式和5種已有計(jì)算模型對(duì)收集到的217根SFRC梁試驗(yàn)數(shù)據(jù)進(jìn)行驗(yàn)算,并分析了受剪承載力模型中設(shè)計(jì)參數(shù)的影響,驗(yàn)證了本文計(jì)算模型及簡(jiǎn)化計(jì)算公式的準(zhǔn)確性和合理性.
對(duì)大量SFRC無(wú)腹筋梁受剪性能試驗(yàn)現(xiàn)象總結(jié)可知,其典型的破壞模式為延性剪切破壞,即:加載初期純彎段首先出現(xiàn)豎向彎曲裂縫,隨著荷載增加,剪跨區(qū)段中部的豎向裂縫開(kāi)始傾斜,之后豎向裂縫和斜裂縫均向上發(fā)展,部分斜裂縫合并,直到形成一條臨界斜裂縫,臨界斜裂縫迅速加寬,此時(shí)其他裂縫基本沒(méi)有變化,直到加載至峰值荷載,此時(shí)梁內(nèi)部分縱筋已經(jīng)屈服,剪壓區(qū)混凝土被壓碎,荷載超過(guò)峰值荷載之后,臨界斜裂縫快速向加載點(diǎn)延伸,試件發(fā)生受剪破壞.基于上述試驗(yàn)現(xiàn)象,本文提出的SFRC無(wú)腹筋梁的受剪承載力計(jì)算模型見(jiàn)圖1,將混凝土受壓區(qū)分為剪壓區(qū)和斜拉區(qū),剪壓區(qū)混凝土在剪力和壓力共同作用下被壓碎,斜拉區(qū)混凝土被斜裂縫貫穿而發(fā)生斜拉破壞.受剪承載力由臨界斜裂縫控制,達(dá)到受剪承載力之后臨界斜裂縫向上發(fā)展,剪壓區(qū)混凝土被壓碎,斜裂縫迅速貫穿斜拉區(qū),試件發(fā)生受剪破壞.
本文提出的受剪承載力計(jì)算模型首先需要確定臨界斜裂縫的位置及其傾角,如圖1所示,斜裂縫與縱筋交點(diǎn)距支座距離為a.雖然鋼纖維的加入可以有效限制裂縫的發(fā)展并減小裂縫寬度,但是裂縫發(fā)展模式與普通混凝土梁相似,式(1)為Cavagnis等[14]采用先進(jìn)的測(cè)量?jī)x器進(jìn)行受剪性能試驗(yàn)得到臨界斜裂縫傾角的計(jì)算公式,認(rèn)為與剪跨比相關(guān),即
式中為剪跨比,,a為剪跨長(zhǎng)度,h0為截面有效高度.
式中:為梁的高度;為中性軸至截面上邊緣的?距離.
圖1中,要求得斜裂縫水平開(kāi)裂寬度,需先確定斜裂縫間距,SFRC中由于加入了鋼纖維,其斜裂縫間距和普通混凝土差異較大,需要考慮鋼纖維對(duì)斜裂縫間距的影響,根據(jù)Dupont等[15]的研究,鋼纖維長(zhǎng)徑比可以顯著影響斜裂縫間距,斜裂縫間距近似取為
則可求得臨界斜裂縫水平開(kāi)裂寬度為
如圖2所示,本文提出的受剪承載力計(jì)算模型主要由4部分組成,即斜裂縫截面鋼纖維的貢獻(xiàn)f、骨料咬合力的貢獻(xiàn)a、縱筋銷(xiāo)栓作用的貢獻(xiàn)d和受壓區(qū)混凝土的貢獻(xiàn)c.
圖2?受剪承載力組成
假定混凝土基體開(kāi)裂后不承擔(dān)拉應(yīng)力,鋼纖維為三維隨機(jī)亂向分布,開(kāi)裂后拉應(yīng)力全部由鋼纖維承擔(dān),由鋼纖維提供的垂直臨界斜裂縫截面的拉力為
式中c為臨界斜裂縫截面面積.
而臨界斜裂縫截面鋼纖維數(shù)量根據(jù)臨界斜裂縫面積及單位面積鋼纖維根數(shù)確定,即
式中w為單位面積鋼纖維數(shù)量.根據(jù)Soroushian 等[17]的研究,w計(jì)算式為
式中:b為與鋼纖維形狀系數(shù),帶端鉤鋼纖維取0.8,波紋形鋼纖維取0.6,平直鋼纖維取0.4;c表示混凝土軸心抗壓強(qiáng)度.
由于混凝土基體開(kāi)裂后退出工作,則臨界斜裂縫處開(kāi)裂后混凝土受拉作用對(duì)梁受剪承載力的貢獻(xiàn)即為鋼纖維的貢獻(xiàn).圖2中,SFRC沿臨界斜裂縫截面受力呈均勻分布,開(kāi)裂后抗拉強(qiáng)度按照式(13)計(jì)算,則鋼纖維對(duì)受剪承載力的貢獻(xiàn)為
骨料咬合力是最早被研究人員發(fā)現(xiàn)的鋼筋混凝土梁的抗剪機(jī)制之一,因?yàn)镾FRC中鋼纖維可以很好地限制斜裂縫的發(fā)展,臨界斜裂縫在達(dá)到峰值荷載時(shí)仍處于一個(gè)較小的寬度,因此骨料咬合力在SFRC梁受剪承載力計(jì)算中必須考慮.
目前廣泛認(rèn)同的骨料咬合力計(jì)算模型是Walraven[19]基于兩相模型提出的剪力傳遞理論,該模型是一種基于幾何學(xué)考慮裂縫表面骨料和水泥砂漿基體之間接觸的力學(xué)模型.骨料和水泥漿基體之間的接觸面積主要取決于裂縫張開(kāi)及裂縫滑移,Walraven[19]基于試驗(yàn)結(jié)果回歸得到裂縫處應(yīng)力-變形關(guān)系(模型1)如式(15)、(16)所示:
Gambarova等[20]在混凝土開(kāi)裂模型的基礎(chǔ)上考慮裂縫的動(dòng)力學(xué)特征,并對(duì)原模型進(jìn)行改良和修正,得出的裂縫處應(yīng)力-變形關(guān)系(模型2)如式(17)、(18)所示:
Ulaga[21]基于Walraven[19]的兩相模型,考慮裂縫張開(kāi)及裂縫滑移與加載角度之間的關(guān)系,提出一種新的骨料咬合力計(jì)算模型(模型3),根據(jù)式(19)、(20)進(jìn)行計(jì)算.
在混凝土梁承受剪切荷載時(shí),開(kāi)裂截面往往處于裂縫張開(kāi)和裂縫滑移同時(shí)進(jìn)行的混合模式,Jacobsen等[22]通過(guò)雙軸試驗(yàn)機(jī)對(duì)有雙側(cè)凹槽的試件同時(shí)施加受拉和剪切荷載,得到了混合模式下裂縫截面應(yīng)力及變形,其中為裂縫張開(kāi)和裂縫滑移之間的夾角.為了驗(yàn)證3種骨料咬合力計(jì)算模型的準(zhǔn)確性,采用模型1、模型2和模型3分別對(duì)Jacobsen等[22]的試驗(yàn)進(jìn)行驗(yàn)證.計(jì)算結(jié)果和試驗(yàn)結(jié)果的對(duì)比見(jiàn)圖3,可以看出模型1和模型2的計(jì)算結(jié)果高估了裂縫截面的剪應(yīng)力,而且在峰值后隨著裂縫張開(kāi)和裂縫滑移的增大沒(méi)有明顯的軟化現(xiàn)象,而模型3計(jì)算結(jié)果在峰值前的剛度與試驗(yàn)吻合較好,且在峰值后有明顯的軟化,可以較好地預(yù)測(cè)混合模式下裂縫截面骨料咬合作用,故本文選用模型3計(jì)算骨料咬合力對(duì)受剪承載力的貢獻(xiàn).
圖3?3種計(jì)算模型計(jì)算結(jié)果與試驗(yàn)結(jié)果對(duì)比(w=0.04 mm)
利用式(21)對(duì)臨界斜裂縫截面正應(yīng)力和剪應(yīng)力進(jìn)行積分,可得臨界斜裂縫處骨料咬合作用貢獻(xiàn)的受剪承載力為
將式(19)和(20)代入式(21),可得
當(dāng)剪切面發(fā)生錯(cuò)動(dòng)時(shí)縱筋銷(xiāo)栓作用開(kāi)始參與到SFRC梁的抗剪中來(lái),為了保證試件發(fā)生剪切破壞,在試驗(yàn)設(shè)計(jì)時(shí)縱筋配置往往較多;由于混凝土基體中加入了鋼纖維,使得SFRC與縱筋的黏結(jié)性能更好,SFRC良好的力學(xué)性能使得保護(hù)層對(duì)于縱筋的約束作用更強(qiáng)[23],故在SFRC無(wú)腹筋梁抗剪設(shè)計(jì)中縱筋銷(xiāo)栓作用往往不能忽略.許多研究者對(duì)縱筋銷(xiāo)栓作用進(jìn)行了研究,目前廣泛認(rèn)同且求解精度較高的方法是彈性地基梁理論,即將包裹鋼筋的混凝土視為地基,將鋼筋視為梁,通過(guò)梁的變形及地基剛度之間的關(guān)系建立縱筋銷(xiāo)栓力計(jì)算公式.
彈性地基梁理論中最重要的是地基剛度s的確定,Moradi等[24]根據(jù)試驗(yàn)中縱筋曲率分布和曲率影響區(qū)域得到地基剛度和變形之間的關(guān)系為
最終求得縱筋銷(xiāo)栓力計(jì)算公式為
根據(jù)大量的SFRC梁受剪性能試驗(yàn)現(xiàn)象可知,SFRC梁達(dá)到受剪承載力時(shí)加載點(diǎn)處剪壓區(qū)混凝土被壓碎,而臨界斜裂縫頂部受壓區(qū)混凝土沒(méi)有被壓碎.如圖4所示,受剪承載力模型剪壓區(qū)和臨界斜裂縫頂部受壓區(qū)混凝土通過(guò)一系列斜向壓桿傳力(即拱作用),但是斜向壓桿與水平方向夾角很小,故假定臨界斜裂縫截面受壓區(qū)混凝土的壓應(yīng)力為均勻分布,根據(jù)平衡條件知,其水平壓力應(yīng)與加載處受壓混凝土所受水平壓力相等,即
由于本文研究的SFRC無(wú)腹筋梁剪跨比均偏大,其加載處的縱筋往往已經(jīng)達(dá)到或者接近屈服.故本文計(jì)算模型采用的SFRC梁加載處的正截面受力分析如圖5所示.
圖5?正截面受力分析
根據(jù)水平力衡可得
式中表示等效矩形受壓區(qū)高度,趙國(guó)藩等[16]及高丹盈[26]對(duì)等效矩形受壓區(qū)高度與中性軸至截面上邊緣距離之間的關(guān)系進(jìn)行了大量研究并認(rèn)為鋼纖維的加入對(duì)其影響不大,為簡(jiǎn)化計(jì)算,取/=0.8.則受壓區(qū)高度為
本文提出的受剪承載力計(jì)算模型由4個(gè)部分組成,可以準(zhǔn)確地表達(dá)出各個(gè)部分對(duì)于受剪承載力的貢獻(xiàn),總的受剪承載力為
圖6?計(jì)算流程
由上述分析可知本文討論的4種抗剪機(jī)制都與臨界斜裂縫有著密切聯(lián)系,受剪承載力計(jì)算的迭代過(guò)程也是緊密?chē)@臨界斜裂縫進(jìn)行的,由此得到的每一種抗剪機(jī)制對(duì)于受剪承載力的貢獻(xiàn)都不是獨(dú)立的,計(jì)算結(jié)果各部分中既包括該抗剪機(jī)制的貢獻(xiàn)也包括其他抗剪機(jī)制對(duì)其產(chǎn)生的影響的貢獻(xiàn),故計(jì)算的受剪承載力中包含4種抗剪機(jī)制的復(fù)合作用.
為驗(yàn)證本文提出的SFRC梁受剪承載力計(jì)算模型的適用性和準(zhǔn)確性,對(duì)收集到的217根SFRC無(wú)腹筋梁受剪性能試驗(yàn)數(shù)據(jù)[8,9,11-13,27-52]進(jìn)行計(jì)算,計(jì)算結(jié)果如圖7所示.由于本文討論的主要是延性剪切破壞模式下SFRC梁的受剪承載力,考慮鋼纖維對(duì)于SFRC梁延性的提升,故選取的SFRC梁受剪性能試驗(yàn)數(shù)據(jù)中剪跨比均大于等于2.
由圖7計(jì)算結(jié)果可知,本文計(jì)算模型的計(jì)算值u與試驗(yàn)值ex之比的平均值為0.98,變異系數(shù)為0.17.可以看出,按照本文的計(jì)算模型計(jì)算的受剪承載力與試驗(yàn)結(jié)果吻合較好,且變異系數(shù)小,說(shuō)明本文提出的受剪承載力計(jì)算模型的合理性和準(zhǔn)確性.
由計(jì)算結(jié)果分析可得,骨料咬合力、縱筋銷(xiāo)栓作用、受壓區(qū)混凝土及臨界斜裂縫截面鋼纖維占受剪承載力的比例根據(jù)具體的試件設(shè)計(jì)參數(shù)變化而改變,近似的比例可以取為0.35∶0.15∶0.3∶0.2,可以看出鋼纖維是SFRC無(wú)腹筋梁抗剪機(jī)制中非常重要的組成部分.分析可知,由于本文是基于延性剪切破壞模式討論SFRC無(wú)腹筋梁受剪承載力,主要針對(duì)剪跨比較大的情況,此時(shí)受壓區(qū)混凝土拱機(jī)制作用不顯著,且鋼纖維在抗剪過(guò)程中具有關(guān)鍵性作用,故和普通混凝土梁相比,受壓區(qū)混凝土在受剪承載力中所占比重相對(duì)較??;因?yàn)殇摾w維混凝土良好的受拉性能,縱筋周?chē)腟FRC對(duì)縱筋有很好的約束能力,且鋼筋與SFRC黏結(jié)性能也較普通混凝土有較大的提升,故縱筋銷(xiāo)栓作用在抗剪設(shè)計(jì)中不能忽略.由于纖維的橋接作用可以有效限制裂縫寬度,故骨料咬合力及裂縫截面鋼纖維在SFRC梁抗剪機(jī)制中發(fā)揮重要作用.
圖7?試驗(yàn)結(jié)果與計(jì)算模型計(jì)算結(jié)果對(duì)比
上述受剪承載力計(jì)算模型雖然能夠較好地反映各部分對(duì)于抗剪承載力的貢獻(xiàn),具有較高的計(jì)算精度,但是由于其計(jì)算過(guò)程較為繁瑣,在實(shí)際工程中難以應(yīng)用.為了簡(jiǎn)化計(jì)算過(guò)程,需要在上述模型的基礎(chǔ)上提出受剪承載力簡(jiǎn)化計(jì)算公式.
骨料咬合力和受壓區(qū)混凝土均為混凝土對(duì)受剪承載力的貢獻(xiàn),因此本文簡(jiǎn)化計(jì)算公式主要將受剪承載力分為3部分,其計(jì)算式為
受剪承載力計(jì)算模型中受壓區(qū)混凝土和骨料咬合力對(duì)抗剪強(qiáng)度的貢獻(xiàn)與式(35)計(jì)算結(jié)果見(jiàn)圖8,可看出式(35)與提出計(jì)算模型的計(jì)算結(jié)果吻合良好.
縱筋銷(xiāo)栓作用對(duì)受剪承載力的貢獻(xiàn)主要與縱筋的配筋率、縱筋周?chē)炷量箟簭?qiáng)度和相對(duì)豎向位移相關(guān),而相對(duì)豎向位移根據(jù)計(jì)算模型中臨界斜裂縫的基本概念主要受剪跨比影響,并與剪跨比呈反比.參照上述因素與d之間的關(guān)系,提出d的簡(jiǎn)化公式為
根據(jù)式(36)的計(jì)算結(jié)果與提出的受剪承載力計(jì)算模型中Vd/(bh0)的計(jì)算結(jié)果如圖9所示,可以看出式(36)與原模型的計(jì)算結(jié)果吻合較好.
鋼纖維對(duì)抗剪強(qiáng)度的貢獻(xiàn)根據(jù)式(14)計(jì)算,即
將式(35)、(36)和(37)代入式(34)可以得到最終的受剪承載力簡(jiǎn)化計(jì)算公式為
采用簡(jiǎn)化計(jì)算公式(38)并選取有代表性的5種已有計(jì)算模型對(duì)搜集到的217根SFRC無(wú)腹筋梁的受剪承載力進(jìn)行預(yù)測(cè),計(jì)算結(jié)果見(jiàn)圖10和表1.
根據(jù)圖10及表1的計(jì)算結(jié)果可知,簡(jiǎn)化計(jì)算公式的計(jì)算值sp與試驗(yàn)值ex之比的平均值為0.94,變異系數(shù)為0.24;Narayanan模型[9]計(jì)算結(jié)果為0.91,變異系數(shù)為0.24;Gandomi模型[10]計(jì)算結(jié)果為1.24,變異系數(shù)為0.21;Swamy模型[11]計(jì)算結(jié)果為0.76,變異系數(shù)為0.25;Imam模型[53]計(jì)算結(jié)果為1.14,變異系數(shù)為0.33;Khuntia模型[54]計(jì)算結(jié)果為0.74,變異系數(shù)為0.24.可以看出本文簡(jiǎn)化計(jì)算公式計(jì)算的受剪承載力最接近試驗(yàn)結(jié)果,其平均值為0.94,小于1,且變異系數(shù)較?。f(shuō)明簡(jiǎn)化計(jì)算公式計(jì)算結(jié)果可靠,在設(shè)計(jì)中稍偏于保守,保證有一定的安全度,為SFRC無(wú)腹筋梁抗剪設(shè)計(jì)提供參考.
圖10?試驗(yàn)結(jié)果與簡(jiǎn)化計(jì)算公式計(jì)算結(jié)果對(duì)比
表1?已有SFRC無(wú)腹筋梁受剪承載力計(jì)算模型
Tab.1 Calculation model of shear capacity of SFRC without web reinforcements
圖11為采用本文計(jì)算模型和簡(jiǎn)化計(jì)算公式的計(jì)算結(jié)果與試驗(yàn)結(jié)果的比值隨著不同的剪跨比、軸心抗壓強(qiáng)度、纖維特征系數(shù)及縱筋配筋率的變化情況,可以看出比值均在1.0上下波動(dòng),且波動(dòng)幅度較小,說(shuō)明本文提出的受剪承載力計(jì)算模型及簡(jiǎn)化計(jì)算公式均有較高的計(jì)算精度,可以應(yīng)用于各種類(lèi)型的SFRC無(wú)腹筋梁.
圖11?不同計(jì)算參數(shù)對(duì)受剪承載力計(jì)算精度的影響
根據(jù)SFRC無(wú)腹筋梁延性剪切破壞模式及其抗剪機(jī)理建立了受剪承載力計(jì)算模型,分別討論了骨料咬合力、縱筋銷(xiāo)栓作用、受壓區(qū)混凝土和斜裂縫截面鋼纖維對(duì)受剪承載力的貢獻(xiàn),通過(guò)變形協(xié)調(diào)及受力平衡條件將4種抗剪機(jī)制其有效結(jié)合,并給出了具體的計(jì)算步驟.為了便于工程設(shè)計(jì),在受剪承載力計(jì)算模型的基礎(chǔ)上提出了簡(jiǎn)化計(jì)算公式,可以準(zhǔn)確反映各部分對(duì)受剪承載力的貢獻(xiàn)且形式簡(jiǎn)單.
采用本文提出的受剪承載力計(jì)算模型、簡(jiǎn)化計(jì)算公式及5種已有計(jì)算模型對(duì)SFRC無(wú)腹筋梁受剪性能試驗(yàn)數(shù)據(jù)進(jìn)行驗(yàn)算,通過(guò)對(duì)比可得本文提出的計(jì)算模型及簡(jiǎn)化計(jì)算公式能夠準(zhǔn)確地預(yù)測(cè)SFRC無(wú)腹筋梁受剪承載力,與試驗(yàn)結(jié)果相近且變異系數(shù)小,在不同的設(shè)計(jì)參數(shù)下均能保證較高的計(jì)算精度,為SFRC無(wú)腹筋梁抗剪設(shè)計(jì)提供參考.
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Analysis on Shear Bearing Capacity of SFRC Beams Without Web Reinforcements Based on Ductile Shear Failure Mechanism
Bi Jihong1, 2,Wang Zhaoyao1,Zhao Yun1,Huo Linying1,Wang Guangyu1
(1. School of Civil Engineering,Tianjin University,Tianjin 300354,China;2. Key Laboratory of Coast Civil Structure Safety of Ministry of Education(Tianjin University),Tianjin 300354,China)
The shear bearing capacity of steel fiber reinforced concrete(SFRC)beams without web reinforcements is a critical parameter in building structure design. Therefore,it is significant to accurately predict the shear capacity accurately. Several experimental studies on the shear behavior of SFRC beams have found that the failure mode of SFRC beams changes from brittle shear failure to ductile shear failure due to the effect of steel fibers. Herein,a novel calculation model is proposed based on the ductile shear failure mechanism to calculate the shear bearing capacity. The model includes the contribution of aggregate interlock,dowel action,steel fibers at the diagonal crack section and the concrete in compressive zone. The formulas corresponding to each shear mechanism are derived respectively based on the theoretical analysis. These shear mechanisms are effectively combined through the deformation and stress conditions of SFRC beams,and the specific steps for calculating the shear bearing capacity are given. Moreover,a simplified formula is proposed for the design of practical projects based on the stress characteristics and the contribution of each shear mechanism to the shear bearing capacity. The shear bearing capacities of 217 SFRC beams without web reinforcements are predicted using the calculation model,the simplified formula,and five existing calculation models,respectively. The results indicate that steel fibers play an important role in the shear resistance of SFRC beams without web reinforcements. The proposed calculation model and the simplified formula can accurately predict the shear bearing capacity with a small coefficient of variation,and ensure high accuracy for different calculation parameters.
steel fiber reinforced concrete;beam without stirrups;shear bearing capacity;aggregate interlock;dowel action
TU375.1
A
0493-2137(2021)05-0497-11
10.11784/tdxbz202003003
2020-03-02;
2020-05-19.
畢繼紅(1965—??),女,博士,教授.
畢繼紅,jihong_bi@163.com.
國(guó)家自然科學(xué)基金資助項(xiàng)目(51227006).
Supported by the National Natural Science Foundation of China(No. 51227006).
(責(zé)任編輯:樊素英)