Calculating the second-order effect and reinforcement of reinforced concrete box section columns has geometric nonlinearity and material nonlinearity. It requires integration and iterative solutions and is inconvenient in practical applications; moreover, China’s “Code for Design of Concrete Structures” (GB 50010-2010) uses the same formula as that for rectangular sections when calculating geometric nonlinearity. To find out a calculation method by hand that is specific to box-shaped sections and does not require iterative procedures, the theoretical derivation is adopted and divided into two gradations: (1) in terms of cross-section: using strain as the known variable to solve the internal force, thus solving the calculation problem of the bearing capacity of the cross-section; (2) in terms of members, the model column method can be used to solve the calculation problem of second-order effects of members. Finally, nomograms that can calculate the second-order effect and reinforcement of columns without iterative calculation are drawn, which contain five parameters, namely first-order bending moment, axial force, curvature, slenderness ratio, and the mechanical ratio of reinforcement. One of the nomograms corresponds to the cross-section resistance, and the other corresponds to the balance of internal resistance and external effect. Compared with the GB 50010-2010, the differences in the total bending moment and reinforcement ratio are within 10% and 20%, respectively. Compared with the numerical calculation results, the remaining examples are within 10% under normal load conditions.

Purpose To calculate the bearing capacity of annular reinforced concrete (RC) columns, if the second-order effects of members under bending and axial forces are further considered, both the nominal curvature method and the nominal stiffness method in EC2 require iterative calculations. To obtain a non-iterative calculation method. Design/methodology/approach The constitutive relationship of RC in EC2 is adopted, the known cross-sectional strain is used to determine the bearing capacity of the section, and the model column method is adopted to calculate the component’s second-order effect. The curvature distribution law of the equilibrium point of sectional resistance and external action is analysed, and the simplified formula for calculating the equilibrium curvature is proposed. Findings Based on the above work, a nomogram is drawn to determine the bearing capacity of columns. Finally, the nomogram and numerical calculation results are compared through specific examples. The results show that the nomogram is very close to the numerical calculation and always leans towards safety. It can serve as a supplement to the code and provide a method for the design and verification of annular columns. Originality/value A method for calculating the reinforcement of RC annular columns by hand.

PurposeThis paper aims to obtain a calculation method by hand without iteration.Design/methodology/approachThis paper adopts strains as known quantities to solve the internal forces and deformations of the section, simplifies the deflection curve of the column and obtains nomograms that can calculate the bearing capacity and reinforcement of circular reinforced concrete (RC) columns by hand.FindingsNomograms include five variables: mechanical reinforcement ratio, relative normal force, dimensionless bending moment, slenderness ratio and ultimate dimensionless curvature. Nomograms corresponding to all classes of concrete have been drawn, and their dimensionless form makes them widely applicable. The calculation results of nomograms are compared and analysed with numerical calculation results, and the difference is within 5%, meeting the engineering requirements.Originality/valueCalculating the bearing capacity of compression bending components requires considering second-order effects. Therefore, the calculation of the bearing capacity of circular RC columns requires iterative calculation, as it includes dual nonlinearity of material and geometry, and the two are coupled with each other. To calculate the bearing capacity of the section adopting ordinary concrete, it is necessary to solve the transcendental equation iteratively. For high-strength concrete, it can only be solved by numerical integration. A fast calculation method by hand is proposed in this paper.

Calculating the reinforcement of circular reinforced concrete (RC) columns involves not only the dual nonlinearity of the geometry and material but also the nonlinearity of the section width. Accurate solutions require iterative calculations. To develop the calculation method manually, the model column method was proposed to compute the second-order effect of the columns, and the strain method was used to calculate the ultimate strength of the sections analytically. The nomograms required to calculate the reinforcing steel content of the columns without iterations were obtained. The nomogram for calculating the section bearing capacity and reinforcing steel has three parameters (axial force, bending moment, and mechanical ratio of the reinforcing steel). Further, the nomogram for calculating the column bearing capacity and reinforcing steel has five parameters (axial force, bending moment, curvature, slenderness ratio, and mechanical ratio of the reinforcing steel), and the relationship between the five parameters can be expressed in a plan, which makes the application convenient. Finally, the calculation results of the nomograph were compared with those of the existing approximate calculation formulas and exact numerical methods, and the accuracy of the nomograms was verified.

为研究不同荷载形式和栓钉布置对简支组合梁的滑移和挠度的影响,采用ANSYS软件,建立有限元模型,分析栓钉均匀布置的有限元模拟结果与解析公式计算结果的吻合程度,并研究不同栓钉布置及施加不同荷载对简支组合梁滑移和挠度的影响.研究结果表明:当剪力图面积大小相同且施加荷载为对称集中荷载时,组合梁的滑移和挠度最大,跨中为集中荷载时的滑移和挠度最小.在多数荷载工况下,为保证组合梁整体栓钉个数不变,采用分段布置栓钉可以大幅度减小组合梁的最大滑移和跨中挠度.在对称集中荷载作用下,组合梁所产生的滑移和挠度最大.组合梁的ANSYS有限元模型的模拟结果与解析公式计算结果相比,模拟结果的精度更高,该研究可为类似工程计算提供借鉴.

针对规范计算长度系数法逐根构件求解无侧移框架整体稳定的不便,以及无法考虑同层柱之间的相互支援和层与层支援作用的不足,本文探寻了无侧移框架同层柱间支援以及层与层之间的支援规律,利用弹簧-摇摆柱模型采用结构转换的方法推导了无侧移框架柱临界刚度比系数;利用该系数通过分析无侧移框架特征结构单元确定结构层荷载因子,确定表征无侧移框架楼层刚度富余程度的层刚度富余系数和表征层间支援作用的层支援系数;基于轴力权重加权平均的方法推导了可直接计算无侧移框架整体稳定承载力的计算公式.该公式能够定量地计算无侧移框架楼层之间相互支援程度,避免了计算长度系数法可能因无法考虑2种支援作用造成的不合理设计,可供工程设计和理论计算使用.

Based on the stiffness activation of the compression column, the influence of the axial force area on the critical bearing capacity of double column pier with two-story is studied. Some rules are found and the corresponding calculation method of the horizontal critical bearing capacity of double column bridge with high piers is established, so that the solution of the critical force of column bridge with high piers is greatly simplified. This paper deduces the calculation formula of the horizontal critical force for double column bridge with high piers. These formulas can take into account the influence of the tie beams between the piers, which can make up for the deficiency of the standardized calculation length coefficient method and provide a fast calculation method and formula for bridge engineering design. Finally, three examples are selected for finite element calculation. The calculation results show that this method has good precision and accuracy, which can be suitable for arbitrary node load distribution and used for engineering design and theoretical calculation.

同时考虑剪切变形和二阶效应来解析计算杆件的临界力,是求解变系数临界微分方程的难题.本研究采用有限元法推导了变截面单元刚度矩阵.采用三次Hermite插值函数和三次拉格朗日插值函数来计算单元内的弯曲变形和惯性矩变化.采用线性插值函数来计算单元内的剪切变形和截面面积变化.利用最小势能原理对总势能进行变分,系统给出了计入弯曲变形、剪切变形以及轴力二阶效应的变截面构件单元刚度矩阵.最后,用自编的有限元程序对算例进行验证.研究结果表明:本算法的计算精度较高,还可分析二阶位移放大系数以及变截面门式刚架立柱之间的支援作用.

To calculate the reinforcement of a reinforced concrete column, the problems of the material nonlinearity and the geometric nonlinearity must be solved, which needs iterative solution process and is inconvenient for a practical application.Based on the constitutive relationship of concrete and steel bars, the precise cross-section internal force-curvature relationship is determined according to the section strain, and the deformation curve of the member is simplified as a quadratic parabola to calculate the external effect.According to the characteristics of the accurate section internal force-curvature curve and external action curve, and the “Code for Design of Concrete Structures”（GB50010-2010） and Eurocode 2,respectively, the ultimate curvature of the cross-section is simplified respectively, and finally the nomogram for calculating the second-order total bending moment and reinforcement of the member is drawn.The comparative analysis of specific calculation examples shows that the simplification of the Eurocode is more in line with the precise values and is more economical.

纤维增强复合材料对混凝土构件的受弯、受压及受剪的加固研究已经比较成熟,但针对纤维增强复合材料加固钢筋混凝土构件的扭转问题的研究还不多,目前规范中对于混凝土构件的抗扭加固也很少涉及.回顾和总结了纤维增强复合材料抗扭加固钢筋混凝土构件的研究现状,从粘贴形式和锚固方法两个方面归纳了抗扭加固方式;从原梁条件和加固参数两大项研究分析抗扭加固效果;探讨了纤维增强复合材料加固钢筋混凝土构件的抗扭机理和破坏模式并归纳总结了纤维增强复合材料加固钢筋混凝土受扭构件的承载力计算方法;分析总结了纤维增强复合材料加固钢筋混凝土受扭构件研究尚存的不足并对将来的发展趋势进行展望,为今后混凝土结构受扭加固项目提供方法借鉴,也为将来制定技术规范的修订提供研究资料和参考建议.

变截面构件在工程中应用较为广泛,但变形计算则较为复杂.本研究采用拉格朗日插值函数表示单元内的惯性矩和面积的变化,再分别用埃尔米特和拉格朗日插值函数计算单元内的弯曲变形和剪切变形,并根据势能驻值原理得到适用于多种变截面构件的变截面弯曲单元刚度矩阵,最后通过分析力的平衡条件和构件挠度的几何关系,得到考虑剪切变形的变截面弯曲单元刚度矩阵.采用自编的有限元程序与ANSYS分别对算例进行计算分析,讨论圆形构件和环形抵抗剪切变形的影响程度.研究结果表明:算例验证了单元刚度矩阵的正确性,对比发现由变截面构件组成的结构受力性能优于等截面构件组成的结构.

The calculation of ring-section reinforcement considering the second-order effect has triple nonlinearity, that is, the nonlinearity of material, geometry and section-width variation, it’s very difficult to calculate. In order to provide a fast calculation tool for the design work, a simplified model of the ultimate curvature of the ring-section column is proposed through calculation and analysis, then calculated the second-order eccentricity by the quadratic parabola hypothesis of the second-order deflection shape of the member, and finally the simplified n-mu second-order equilibrium equation has been obtained. The three-coordinate nomogram for calculation was drawn to further facilitate the design in the paper. The hand-calculated reinforcement of the ring-section column could be done only by making 4 auxiliary lines in the diagram, avoiding iterative solution of the transcendental equation. Because of the dimensionless derivation, this nomogram is multipurpose, it could solve the calculation problems of second-order reinforcement in the case of arbitrary section size and concrete grade of C15 ~ C50.

环形截面是工程结构中常见的截面形式,但混凝土环形截面配筋计算存在双重非线性(材料和截面宽度变化的非线性).《混凝土结构设计规范》中仅给出计算均匀配筋的超越方程组,需编程和迭代求解,不能手算,极为不便.另外,一些环形截面构件(如高桥墩、预制管桩等)长度长、截面尺寸大、钢筋用量大,若采用均匀配筋,中性轴附近钢筋应力小,经济性不好.若采用非对称配筋,将受力钢筋布置在远离中性轴的外围区域,可充分利用混凝土和钢筋强度,提高经济效益.为此,根据混凝土和钢筋的本构关系确定应变变化的范围和边界,从应变出发,利用解析方法由应变求解应力,进而计算内力,不需迭代,最终将计算结果绘制成便于手算配筋的诺谟图,计算快速方便.该方法适用于C50及以下强度混凝土和任意直径大小的环形截面.

Based on Rusch's creep constitutive relation, differential equations for the redistribution of shrinkage internal force and creep of the composite beam are derived and solved. The closed solution is cumbersome and is inconvenient to be applied practically. It is hard to solve the accurate solution for coupled differential equations. Therefore, a simplified approach is given. However, it ignores the influence of the redistribution of bending moment of the concrete slab on the axial strain and removes the coupling relationship of differential equations so that it makes the solution become convenient. The comparison of the results calculated by the two approaches shows that their calculated errors are small, within 3%, when the stiffness ratio of the concrete slab and the steel beam are less than 0.185. It also shows that the greater the stiffness of the steel beam, the greater the constraint on the creep of the concrete slab, so is the redistribution of internal force.

JTG 3362—2018《公路钢筋混凝土及预应力混凝土桥涵设计规范》计算考虑二阶效应的混凝土矩形墩柱截面承载力和配筋过程复杂且公式繁多,须先判断大小偏心再选择相应的计算公式,若采用等效矩形应力图简化计算又会带来一定的误差.针对这些问题,本文严格按照混凝土和钢筋的本构关系曲线计算其应力和内力,得到考虑二阶效应矩形桥墩对称配筋的无量纲诺模图,为工程设计提供一种简便实用的手算工具.同时,设计了钢筋混凝土偏心受压柱试验予以验证.结果表明:本文方法准确可靠,无需判断大小偏心,计算方便快捷,适用于对称配筋的任意截面尺寸和C50以下混凝土强度等级.

《混凝土结构设计规范》计算钢筋混凝土矩形截面承载力和配筋过程复杂且计算式繁多,采用等效矩形应力图简化会带来一定的误差,针对这些问题基于矩形截面应变变化规律推导了一种实用的计算方法.摒弃了等效应力图换算,通过分析极限承载力状态的应变变化区域,严格按混凝土和钢筋的本构关系的完整曲线进行推导,直接由混凝土和钢筋的应变求应力和内力,进而获得了精确的计算公式和图表,为工程设计提供一种简便实用的手算工具.计算偏心受力构件,无需判断大小偏心,计算十分方便和快捷,可适用于HRB500对称配筋的任意截面尺寸和C50以下混凝土强度等级.

圆形截面是工程中常使用的截面形式之一,但圆形截面的配筋计算较为困难,存在双重非线性(材料和截面宽度变化的非线性),《混凝土结构设计规范》给出了计算均匀配筋的超越方程组,且须迭代求解,无法手算.另外,一些圆形截面构件(如桥墩、桩基的预制桩和灌注桩等)的截面尺寸大,构件长,钢筋用量大,若采用均匀布置的配筋方式,中性轴附近的钢筋应力小,强度利用率低,经济性差.若采用非均匀配筋,在远离中性轴的外围区域布置受力钢筋,可大幅节省钢筋用量,且能充分利用钢筋及混凝土的强度.为此本文通过应变计算应力,再计算出内力的方法推导计算圆形截面配筋的公式,并将计算结果绘制成了能计算配筋的无量纲诺模图,由此可快速手算配筋,该图通用性强,可用于任意直径大小及C50以下的混凝土强度等级,是一能快速计算配筋的实用工具.

箱形和工字形截面是工程中常用的截面形式,但按《混凝土结构设计规范》计算此类截面的配筋公式繁多,还需事先判断,然后选择相应的计算公式,比如拉弯时,要判断拉力合力点是否在大小两侧钢筋之间,区分小偏拉或大偏拉;压弯时,要判断大小偏心,除此之外,还需判断中性轴是否在翼缘或在腹板内等.为了方便快速计算,本文不采用规范中的等效矩形应力换算,直接由混凝土和钢筋的应变求应力,进而计算内力.确定其可能的应变范围,由此应变可变成已知量,并将最终的计算结果绘制成了计算配筋的诺模图,该图为无量纲形式,可用于任意宽度和高度的截面尺寸和C50及以下混凝土强度等级.

《钢结构设计标准》给出了强支撑无侧移框架柱和无支撑自由侧移框架柱计算长度系数的计算表格,而对于介于这两者之间的弱支撑弹性侧移的框架柱,目前规范尚缺少相应的计算公式和表格.对此,本文基于弹簧摇摆柱模型建立了弱支撑弹性侧移框架柱的扩展结构,通过临界荷载因子实现了扩展结构的临界力与原结构的临界力之间的转换,将求解框架柱计算长度系数的复杂二阶问题转化为计算压杆抗侧刚度的简单一阶问题,获得了一种确定弱支撑受压柱计算长度系数的实用算法,并提供了相应的计算表格.本文还推导了可按照无侧移框架柱计算稳定性的侧移临界刚度,此刚度可作为计算框架柱二阶效应时选择按照P-Δ效应还是P-δ效应的判别标准.最后,选取了2个算例进行计算验证,计算结果表明:该方法具有很好的精度及准确性,可供工程设计使用.

This paper presents a new type of composite slim floor beam, determined by combining the results of an experimental study and theoretical analysis of the ultimate flexural strength of slim floor beams. The shear connectors play a significant role in the mechanical properties of this type of composite slim floor beam, because the precast concrete slab is laid on the bottom flange of the steel section and because the upper portion of the steel beam is encased in the cast-in-place concrete slab. To investigate the ultimate flexural strength, three specimens, which included headed studs, transverse steel bar shear connectors and no shear connectors, were tested. Additionally, a detailed numerical analysis was performed to verify the experimental results, which indicated that a higher-strength steel beam and thicker concrete slab can effectively enhance the stiffness and flexural capacity of the composite slim floor beam. Based on plastic mechanics and limit analysis theory, a calculation method was derived to estimate the ultimate flexural strength of a composite slim floor beam, and a comparison between the calculation and experimental results shows that the theoretical results exhibit good agreement with the experimental results, and the proposed analysis method can be used in future studies to gain a better understanding of the ultimate flexural strength of composite slim floor beams.