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基于分形理论无腹筋混凝土梁的受剪性能

于江 吕旭滨 秦拥军

于江, 吕旭滨, 秦拥军. 基于分形理论无腹筋混凝土梁的受剪性能[J]. 工程科学学报. doi: 10.13374/j.issn2095-9389.2020.03.19.003
引用本文: 于江, 吕旭滨, 秦拥军. 基于分形理论无腹筋混凝土梁的受剪性能[J]. 工程科学学报. doi: 10.13374/j.issn2095-9389.2020.03.19.003
YU Jiang, LÜ Xu-bin, QIN Yong-jun. Experimental study on concrete beams without web reinforcement based on fractal theory[J]. Chinese Journal of Engineering. doi: 10.13374/j.issn2095-9389.2020.03.19.003
Citation: YU Jiang, LÜ Xu-bin, QIN Yong-jun. Experimental study on concrete beams without web reinforcement based on fractal theory[J]. Chinese Journal of Engineering. doi: 10.13374/j.issn2095-9389.2020.03.19.003

基于分形理论无腹筋混凝土梁的受剪性能

doi: 10.13374/j.issn2095-9389.2020.03.19.003
基金项目: 国家自然科学基金资助项目(51668060)
详细信息
    通讯作者:

    E-mail:1332506524@qq.com

  • 中图分类号: TU375.1

Experimental study on concrete beams without web reinforcement based on fractal theory

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  • 摘要: 基于裂缝的发展及分布形态,探究无腹筋混凝土梁在不同剪跨比和纵筋配筋率作用下的剪切性能,采用剪跨比分别为1.5、2、2.5和纵筋配筋率分别为1.28%、1.62%、1.99%的9组无腹筋混凝土梁进行四点加载受剪试验,通过应用分形几何理论对试验梁表面的裂缝进行分析,使用盒计数法计算得到分级荷载及极限荷载作用下梁表面裂缝的分形维数,探讨了梁表面分形维数与极限荷载、分级荷载及跨中挠度之间的关系。结果表明:剪跨比与极限荷载及开裂荷载成反比,而纵筋配筋率与极限荷载成正比,但其对于开裂荷载的影响较小。无腹筋混凝土梁不论在分级加载作用下还是极限荷载作用下都具备明显的分形特征,在分级荷载作用下的分形维数在0.964~1.449,在极限荷载作用下的分形维数在1.33附近。分级荷载、跨中挠度与分形维数之间呈现较好的对数关系,分级荷载与分形维数的变化曲线受剪跨比及梁纵筋配筋率的影响具有一定的规律性,而跨中挠度受剪跨比的影响较小,在纵筋配筋率作用下,其曲线的曲率呈现出先增大后减小的趋势,但极限荷载与分形维数之间的关系具有一定的差异性,极限荷载会随着剪跨比的增大呈现出先增大后减小的趋势,随着纵筋配筋率的增大呈现出的差异性较大。

     

  • 图  1  无腹筋梁尺寸及配筋图(单位: mm)

    Figure  1.  Dimensions and reinforcement drawing of girder without rib (Unit: mm)

    图  2  加载装置布置图。(a)λ = 1.5;(b)λ = 2;(c)λ = 2.5;(d)现场布置图

    Figure  2.  Load device layout: (a) λ = 1.5; (b) λ = 2; (c) λ = 2.5; (d) site layout

    图  3  试验梁裂缝分布图。(a)WL-1;(b)WL-2;(c)WL-3;(d)WL-4;(e)WL-5;(f)WL-6;(g)WL-7;(h)WL-8;(i)WL-9

    Figure  3.  Crack distribution of test beam: (a) WL-1; (b) WL-2; (c) WL-3; (d) WL-4; (e) WL-5; (f) WL-6; (g) WL-7; (h) WL-8; (i) WL-9

    图  4  相同剪跨比、不同纵筋配筋率作用下的荷载与挠度间关系。(a) λ = 1.5;(b)λ = 2;(c)λ = 2.5

    Figure  4.  Relationship between load and deflection under the same shear-span ratio and different longitudinal reinforcement ratios: (a) λ = 1.5; (b) λ = 2; (c) λ = 2.5

    图  5  相同纵筋配筋率、不同剪跨比作用下荷载与挠度间的关系。(a)ρ = 1.28%;(b)ρ = 1.62%;(c)ρ = 1.99%

    Figure  5.  Relationship between load and deflection under the same longitudinal reinforcement ratio and different shear span ratios: (a) ρ = 1.28%; (b) ρ = 1.62%; (c) ρ = 1.99%

    图  6  开裂荷载与极限荷载对比图

    Figure  6.  Comparison of cracking load and ultimate load

    图  7  不同等级荷载下梁表面的lnN(L)–ln(1/L)图。(a)WL-1;(b)WL-2;(c)WL-3;(d)WL-4;(e)WL-5;(f)WL-6;(g)WL-7;(h)WL-8;(i)WL-9

    Figure  7.  lnN(L)–ln(1/L) diagram of beam surface under different grades of load: (a) WL-1; (b) WL-2; (c) WL-3; (d) WL-4; (e) WL-5; (f) WL-6; (g) WL-7; (h) WL-8; (i) WL-9

    图  8  极限荷载下梁表面的lnN(L)–ln(1/L)图

    Figure  8.  lnN(L)–ln(1/L) diagram of the beam surface under ultimate load

    图  9  极限荷载作用下梁的分形维数

    Figure  9.  Fractal dimension of the beam under ultimate load

    图  10  相同剪跨比、不同纵筋配筋率作用下的极限荷载与分形维数间的关系。(a)λ = 1.5;(b)λ = 2;(c)λ = 2.5

    Figure  10.  Relationship between ultimate load and fractal dimension under the same shear span ratio and different longitudinal reinforcement ratios: (a) λ = 1.5, (b) λ = 2, (c) λ = 2.5

    图  11  相同纵筋配筋率、不同剪跨比作用下的极限荷载与分形维数间的关系。(a)ρ = 1.28%;(b)ρ = 1.62%;(c)ρ = 1.99%

    Figure  11.  Relationship between ultimate load and fractal dimension under the same longitudinal reinforcement ratio and different shear span ratios: (a) ρ = 1.28%; (b) ρ = 1.62%; (c) ρ = 1.99%

    图  12  相同剪跨比、不同纵筋配筋率作用下的分级荷载与分形维数间关系。(a)λ = 1.5;(b)λ = 2;(c)λ = 2.5

    Figure  12.  Relationship between the graded load and the fractal dimension under the same shear span ratio and different longitudinal reinforcement ratios: (a) λ = 1.5; (b) λ = 2; (c) λ = 2.5

    图  13  相同纵筋配筋率、不同剪跨比作用下的分级荷载与分形维数间关系。(a)ρ = 1.28%;(b)ρ = 1.62%;(c)ρ = 1.99%

    Figure  13.  Relationship between the graded load and the fractal dimension under the same longitudinal reinforcement ratio and different shear span ratios: (a) ρ = 1.28%; (b) ρ = 1.62%; (c) ρ = 1.99%

    图  14  相同剪跨比、不同纵筋配筋率作用下的跨中挠度与分形维数间的关系。(a)λ = 1.5;(b)λ = 2;(c)λ = 2.5

    Figure  14.  Relationship between mid-span deflection and fractal dimension under the same shear-span ratio and different longitudinal reinforcement ratios: (a) λ = 1.5; (b) λ = 2; (c) λ = 2.5

    图  15  相同纵筋配筋率、不同剪跨比作用下的跨中挠度与分形维数间关系。(a)ρ = 1.28%;(b)ρ = 1.62%;(c)ρ = 1.99%

    Figure  15.  Relationship between mid-span deflection and fractal dimension under the same longitudinal reinforcement ratio and different shear-span ratios: (a) ρ = 1.28%; (b) ρ = 1.62%; (c) ρ = 1.99%

    表  1  水泥的化学成分(质量分数)

    Table  1.   Chemical composition of cement %

    SiO2Al2O3Fe2O3CaOMgOSO3K2ONa2OLi2O
    21.225.053.2660.240.972.670.500.73
    下载: 导出CSV

    表  2  粗骨料的实验性能

    Table  2.   Properties of coarse aggregate

    Micron content/%Water absorption rate/%Needle-like content/%Ruggedness/
    %
    Apparent density/(kg·m–3)
    0.30.5512640
    下载: 导出CSV

    表  3  试件参数信息

    Table  3.   Parameter information of test pieces

    NumberingSize/mmCompressive strength/MPaReinforcement diameter/mmLongitudinal strengthShear span ratioReinforcement ratio/%
    WL-11800×150×25041.03116HRB4001.51.28
    WL-21800×150×25044.10316HRB40021.28
    WL-31800×150×25042.77216HRB4002.51.28
    WL-41800×150×25038.46718HRB4001.51.62
    WL-51800×150×25037.00318HRB40021.62
    WL-61800×150×25036.83218HRB4002.51.62
    WL-71800×150×25038.60720HRB4001.51.99
    WL-81800×150×25038.47120HRB40021.99
    WL-91800×150×25046.21920HRB4002.51.99
    下载: 导出CSV

    表  4  不同荷载作用下梁表面分形维数

    Table  4.   Fractal dimension of beam surface under different loads

    Load/kNFractal dimension
    WL-1WL-2WL-3WL-4WL-5WL-6WL-7WL-8WL-9
    200.9640.951
    401.0181.0441.0400.9911.0421.0820.9911.0580.955
    601.0591.11.2751.0441.0751.2210.9991.0721.122
    801.0931.211.3361.1331.2151.3301.0541.1701.161
    1001.1641.321.2031.2831.4491.1571.2481.321
    1201.2671.2081.3401.1881.295
    1401.3041.2181.3571.1931.354
    1601.3021.2761.207
    1801.3351.3561.255
    1901.333
    下载: 导出CSV

    表  5  分级荷载与分形维数关系的km

    Table  5.   k, m values of the relationship between the graded load and the fractal dimension

    ParametersWL-1WL-2WL-3WL-4WL-5WL-6WL-7WL-8WL-9
    k0.1560.1490.1130.1500.1410.0820.1400.1200.148
    m8.984–6.256.258.827–1.48127.0378.6934.824–20.653
    R20.9260.8960.8920.9430.9420.8900.8980.9170.921
    下载: 导出CSV

    表  6  跨中挠度与分形维数关系的nv

    Table  6.   n, v values of the relationship between the mid-span deflection and the fractal dimension

    ParametersWL-1WL-2WL-3WL-4WL-5WL-6WL-7WL-8WL-9
    n0.1290.1080.1160.1230.0970.0560.1260.1020.093
    v83.04782.72773.28166.04968.4577551.30752.61348.898
    R20.9370.9390.9660.9500.9370.9220.9280.9040.966
    下载: 导出CSV
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  • 收稿日期:  2020-03-19
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