仇建磊+貢金鑫
摘要:基于簡(jiǎn)化修正壓力場(chǎng)理論對(duì)鋼筋混凝土柱抗剪機(jī)理進(jìn)行了分析,并考慮核心混凝土膨脹對(duì)箍筋抗剪承載力貢獻(xiàn)的影響,計(jì)算了骨料咬合作用及受壓區(qū)的抗剪承載力貢獻(xiàn),獲得受拉區(qū)和受壓區(qū)的抗剪強(qiáng)度,從而建立箍筋屈服后柱構(gòu)件抗剪強(qiáng)度計(jì)算方法;結(jié)合傳統(tǒng)截面纖維分析法,同時(shí)引入彎曲變形、剪切變形及滑移變形3種變形分量,在箍筋屈服前對(duì)柱構(gòu)件進(jìn)行抗彎分析,最終得出壓彎剪作用下鋼筋混凝土柱荷載變形曲線,并與所收集的15個(gè)鋼筋混凝土柱低周反復(fù)試驗(yàn)結(jié)果進(jìn)行了對(duì)比。研究結(jié)果表明:采用該方法計(jì)算的荷載變形曲線與試驗(yàn)骨架曲線吻合較好,對(duì)發(fā)生彎曲破壞、彎剪破壞及剪切破壞3種不同破壞類型的鋼筋混凝土柱均有較好的分析效果,可用于壓彎剪作用下鋼筋混凝土柱的荷載變形分析。
關(guān)鍵詞:鋼筋混凝土柱;荷載變形;修正壓力場(chǎng)理論;骨架曲線
中圖分類號(hào):TU375.3文獻(xiàn)標(biāo)志碼:A
Abstract: The shear mechanism of reinforced concrete columns was analyzed based on simplified modified compression field theory. Considering the effect of expansion of core concrete on the shear capacity contribution of stirrups, the shear capacity contribution of aggregate interlock behavior and compressive zone were calculated. The shear strengths of tensile area and compressive area were obtained, and the calculation method of shear strength of column after stirrups yielded was established. Combined with the conventional section fiber analysis method, while three deformation components of bending deformation, shear deformation and slip deformation were introduced, the bending analysis of columns before stirrups yielded was carried out, the loaddeformation curves of reinforced concrete columns under compression bending shear action were obtained, and compared with the low cycle test results of 15 reinforced concrete columns collected. The results show that the loaddeformation curves calculated by the proposed method agree well with the test loaddeformation skeleton curves, and have better analysis effect on the reinforced concrete columns with flexural failure, bending shear failure and shear failure. The proposed method can be used for loaddeformation analysis of reinforced concrete columns under compression bending shear action.
Key words: reinforced concrete column; loaddeformation; modified compression field theory; skeleton curve
0引言
鋼筋混凝土柱作為鋼筋混凝土框架結(jié)構(gòu)和橋梁結(jié)構(gòu)中的主要承重及抗側(cè)力構(gòu)件,其抗震性能的優(yōu)劣對(duì)整體結(jié)構(gòu)有著重要影響。根據(jù)鋼筋混凝土柱在地震作用下的破壞特征,其破壞模式可分為彎曲破壞、彎剪破壞以及剪切破壞3種,其中發(fā)生彎曲破壞的鋼筋混凝土柱延性發(fā)展充分,具備良好的耗能機(jī)制,在地震中的危害相對(duì)較小,可以滿足結(jié)構(gòu)抗震延性設(shè)計(jì)要求。以剪切起控制作用的剪切破壞及彎剪破壞具有明顯的脆性特征,設(shè)計(jì)中應(yīng)予以避免。大量震后調(diào)查發(fā)現(xiàn)[12],強(qiáng)烈地震作用下,鋼筋混凝土柱容易發(fā)生柱端剪切破壞,主要原因是箍筋配置不足,出現(xiàn)塑性鉸后柱端抗剪承載力難以抵抗水平剪力。除此之外,窗間墻的不合理設(shè)置及錯(cuò)層結(jié)構(gòu)均容易形成短柱結(jié)構(gòu)形式,同樣會(huì)造成其在地震作用下發(fā)生剪切破壞。實(shí)際上,隨著中國(guó)抗震規(guī)范不斷發(fā)展更新,抗震設(shè)計(jì)體系得到逐步完善,尤其是《建筑抗震設(shè)計(jì)規(guī)范》(GB 50011—2010)的頒布,增加了有關(guān)實(shí)現(xiàn)抗震性能設(shè)計(jì)目標(biāo)的參考方法,但現(xiàn)役的建筑及橋梁結(jié)構(gòu)中仍有不少是按舊規(guī)范設(shè)計(jì)的,其抗震性能評(píng)估亟待進(jìn)行。因此,有必要對(duì)不同破壞模式的鋼筋混凝土柱抗震性能進(jìn)行研究,為結(jié)構(gòu)抗震設(shè)計(jì)及評(píng)估提供依據(jù)。
軸向荷載和水平荷載共同作用下的鋼筋混凝土柱的荷載變形關(guān)系可在一定程度上反映其抗震性能,包括抗剪承載力的大小及變形能力的強(qiáng)弱等。在對(duì)鋼筋混凝土結(jié)構(gòu)進(jìn)行彈塑性時(shí)程分析時(shí),需要先建立其構(gòu)件恢復(fù)力模型,其主要由骨架曲線及滯回規(guī)則兩部分組成,前者一般可通過(guò)單調(diào)加載荷載變形曲線計(jì)算獲得。對(duì)于彎曲破壞模式下的鋼筋混凝土柱,其剪切作用不明顯,采用傳統(tǒng)截面纖維分析法就能獲得較好的分析結(jié)果,而對(duì)于彎剪破壞和剪切破壞構(gòu)件,簡(jiǎn)單地采用截面纖維分析法不能對(duì)剪切作用進(jìn)行分析,計(jì)算結(jié)果誤差較大。
針對(duì)考慮剪切作用影響的鋼筋混凝土柱荷載變形曲線計(jì)算方法,各國(guó)學(xué)者已經(jīng)進(jìn)行了為數(shù)不少的相關(guān)研究[38]。Mostafaei等[34]在經(jīng)典修正壓力場(chǎng)理論基礎(chǔ)上建立了壓彎剪相互作用下鋼筋混凝土柱荷載變形曲線計(jì)算方法,其中柱構(gòu)件剪切特性采用修正壓力場(chǎng)進(jìn)行描述,彎曲特性采用截面纖維分析法進(jìn)行描述,但計(jì)算過(guò)程較為復(fù)雜,涉及大量迭代分析過(guò)程;Setzler等[5]按照彎曲作用和剪切作用主導(dǎo)程度對(duì)鋼筋混凝土柱構(gòu)件受力情況進(jìn)行分類并計(jì)算,得到了相對(duì)簡(jiǎn)單的荷載變形計(jì)算方法,但對(duì)于彎剪相互作用并未進(jìn)行深入考慮;魏巍巍等[6]在經(jīng)典修正壓力場(chǎng)理論基礎(chǔ)上考慮了受壓區(qū)混凝土抗剪承載力,建立了荷載變形計(jì)算模型,計(jì)算過(guò)程較為復(fù)雜;張勤等[7]采用經(jīng)驗(yàn)修正方法對(duì)彎剪破壞鋼筋混凝土柱荷載變形進(jìn)行了研究,蔡茂等[8]利用多彈簧模型得到剪力剪切位移關(guān)系,建立了考慮剪切作用的柱荷載變形計(jì)算方法。上述方法均對(duì)剪切作用進(jìn)行了考慮,但其計(jì)算過(guò)程較為復(fù)雜,或?qū)澕粝嗷プ饔每紤]不足,為此本文建立一種更為簡(jiǎn)便的計(jì)算方法,即考慮彎剪相互作用對(duì)鋼筋混凝土柱荷載變形曲線進(jìn)行計(jì)算。
簡(jiǎn)化修正壓力場(chǎng)理論是在經(jīng)典修正壓力場(chǎng)理論基礎(chǔ)上發(fā)展得來(lái)的,由Collins等[9]于1996年首次提出,2006年Bentz等[10]對(duì)其進(jìn)行了修正,該方法簡(jiǎn)化了傳統(tǒng)修正壓力場(chǎng)理論計(jì)算流程,避免了復(fù)雜的迭代過(guò)程,便于工程應(yīng)用,加拿大、美國(guó)、歐洲相關(guān)規(guī)范中抗剪設(shè)計(jì)均以該方法為理論基礎(chǔ)[1114]。實(shí)際上,簡(jiǎn)化修正壓力場(chǎng)理論僅適用于混凝土開(kāi)裂區(qū)的抗剪強(qiáng)度計(jì)算,而忽略了混凝土受壓區(qū)的抗剪貢獻(xiàn),對(duì)于壓彎剪共同作用下的鋼筋混凝土柱,難以進(jìn)行荷載變形全過(guò)程分析。此外,在鋼筋混凝土柱受力過(guò)程中,核心混凝土膨脹對(duì)箍筋應(yīng)力影響較大,其部分應(yīng)力用于為核心混凝土提供約束作用,為此本文在對(duì)箍筋抗剪承載力貢獻(xiàn)計(jì)算中考慮了核心混凝土膨脹的影響,基于簡(jiǎn)化修正壓力場(chǎng)理論對(duì)受拉區(qū)抗剪承載力進(jìn)行了計(jì)算,同時(shí)考慮了受壓區(qū)混凝土抗剪貢獻(xiàn),結(jié)合截面纖維分析法獲得壓彎剪作用下的鋼筋混凝土柱荷載變形曲線,最后與所收集的試驗(yàn)結(jié)果進(jìn)行了對(duì)比。
1鋼筋混凝土柱抗剪分析
本文將建立適用于彎曲、彎剪及剪切破壞3種不同破壞模式的鋼筋混凝土柱荷載變形分析方法。上述鋼筋混凝土柱抗剪分析中箍筋應(yīng)力采用的是箍筋屈服強(qiáng)度,可以對(duì)箍筋屈服后的抗剪承載力進(jìn)行計(jì)算,但對(duì)于箍筋屈服之前或箍筋不屈服的情況難以進(jìn)行適當(dāng)?shù)姆治?。鑒于此,本文采用傳統(tǒng)截面纖維分析法對(duì)箍筋屈服之前及箍筋不屈服的情況進(jìn)行分析,此時(shí)將按照彎曲理論對(duì)鋼筋混凝土柱進(jìn)行計(jì)算分析,其截面劃分如圖2所示(圖2中,yi為第i個(gè)條帶中心距受壓邊緣距離),建立計(jì)算截面分析模型,得出彎矩曲率關(guān)系,并根據(jù)塑性鉸模型(圖3)計(jì)算荷載變形曲線。圖3中,為截面曲率,y為受拉縱筋屈服時(shí)截面曲率,lp為塑性鉸長(zhǎng)度。
2.5荷載變形分析步驟
根據(jù)本文已經(jīng)建立的鋼筋混凝土柱箍筋屈服后抗剪承載力計(jì)算方法及引入變形分量的傳統(tǒng)截面纖維分析法,可對(duì)鋼筋混凝土柱荷載變形曲線進(jìn)行全過(guò)程分析,具體計(jì)算步驟如下:
(1)給定截面初始曲率0,已知軸向荷載P,根據(jù)式(9),(10)迭代計(jì)算截面中間應(yīng)變?chǔ)?,由式(11)計(jì)算截面彎矩。
(2)逐步增大截面曲率,并建立截面彎矩曲率關(guān)系。
(3)按式(12),(26)計(jì)算得出彎曲分析條件下的水平荷載V′及側(cè)向變形Δ。
(4)按式(1)計(jì)算箍筋屈服后鋼筋混凝柱抗剪承載力V。
(5)對(duì)比V′和V,當(dāng)V′≥V時(shí),即認(rèn)為箍筋已經(jīng)屈服,按剪切作用控制,水平荷載取V,并根據(jù)V修正剪切變形Δv,進(jìn)而得到相應(yīng)側(cè)向變形Δ。
(6)由已經(jīng)計(jì)算得到的水平荷載和側(cè)向變形,建立鋼筋混凝土柱荷載變形關(guān)系。
3計(jì)算結(jié)果與試驗(yàn)結(jié)果對(duì)比
為驗(yàn)證本文建議計(jì)算方法的合理性,收集了15個(gè)鋼筋混凝土柱低周反復(fù)試驗(yàn)數(shù)據(jù)(表1),構(gòu)件破壞類型包括彎曲破壞、彎剪破壞及剪切破壞3種類型,柱剪跨比為1.5~4.0,軸壓比為0.07~0.62,配箍率為0.068%~1.13%,縱筋配筋率為1.51%~3.03%,混凝土抗壓強(qiáng)度為21.1~46.5 MPa。
圖8為按本文計(jì)算方法得到的單調(diào)荷載變形曲線與試驗(yàn)骨架曲線的對(duì)比結(jié)果,其中,圖8(a)~(d)為彎曲破壞,圖8(e)~(m)為彎剪破壞,圖8(n),(o)為剪切破壞。由圖8可知,忽略循環(huán)加載制度的影響,按本文計(jì)算方法能夠?qū)澢?、彎剪、剪切破壞?gòu)件的荷載變形曲線進(jìn)行較好預(yù)測(cè)。對(duì)于彎剪、剪切破壞情況,構(gòu)件在達(dá)到剪切破壞點(diǎn)后承載力開(kāi)始顯著下降,計(jì)算荷載變形曲線能夠?qū)ζ浼羟衅茐狞c(diǎn)進(jìn)行較為準(zhǔn)確的預(yù)測(cè),承載力下降段吻合較好,能夠得到各構(gòu)件的極限位移。對(duì)于彎曲破壞構(gòu)件,本文通過(guò)計(jì)算給出其水平承載力下降至0的曲線,通過(guò)對(duì)比發(fā)現(xiàn),能夠準(zhǔn)確計(jì)算其屈服位移、水平承載力及破壞點(diǎn)。
選取彎曲破壞構(gòu)件No.3、彎剪破壞構(gòu)件2CLH18、剪切破壞構(gòu)件3CMD12的箍筋應(yīng)力fsv進(jìn)行分析,結(jié)果如圖9所示。對(duì)于上述3種破壞模式,由核心混凝土膨脹引起的箍筋拉應(yīng)力均呈不斷增加趨勢(shì),用于箍筋抗剪的組成則隨之下降,需要說(shuō)明的是,圖9所示為箍筋屈服后應(yīng)力分析。此外,對(duì)于彎曲破壞構(gòu)件,其箍筋抗剪貢獻(xiàn)下降速度最慢,剪切破壞構(gòu)件最快,彎剪破壞構(gòu)件位于兩者之間。實(shí)際上,對(duì)于彎曲破壞構(gòu)件,由于剪切作用影響不大,其截面受力以受彎為主,因此箍筋抗剪貢獻(xiàn)隨位移增加下降趨勢(shì)不夠明顯。相比之下,彎剪、剪切破壞構(gòu)件主要以剪切作用控制其破壞,箍筋抗剪作用對(duì)構(gòu)件影響較大,因此其隨位移增長(zhǎng)下降趨勢(shì)較為明顯。4結(jié)語(yǔ)
(1)本文基于簡(jiǎn)化修正壓力場(chǎng)理論對(duì)壓彎鋼筋混凝土柱構(gòu)件進(jìn)行了抗剪分析,并進(jìn)一步考慮了核心混凝土膨脹對(duì)箍筋抗剪貢獻(xiàn)影響以及受壓混凝土的抗剪承載力貢獻(xiàn),結(jié)合傳統(tǒng)截面纖維分析法對(duì)鋼筋混凝土柱進(jìn)行了分析,最終得出能夠考慮剪切作用影響的鋼筋混凝土柱荷載變形曲線計(jì)算方法。
(2)通過(guò)與試驗(yàn)骨架曲線進(jìn)行對(duì)比可知,本文方法計(jì)算的鋼筋混凝土柱荷載變形曲線與試驗(yàn)曲線吻合較好,同時(shí)適用于彎曲、彎剪及剪切3種破壞類型的鋼筋混凝土柱分析。與以往方法相比,本文方法避免了復(fù)雜的迭代計(jì)算過(guò)程,且力學(xué)分析模型清晰,具備一定理論依據(jù),可用于鋼筋混凝土柱荷載變形性能分析。
參考文獻(xiàn):
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