Theory of Flexural Shear, Bending and Torsion for a Thin-Walled Beam of Open Section

Aspects of the general Vlasov theory are examined separately as applied to a thin-walled channel section cantilever beam under free-end end loading. In particular, the flexural bending and shear that arise under transverse shear and axial torsional loading are each considered theoretically. These analyses involve the location of the shear centre at which transverse shear forces when applied do not produce torsion. This centre, when taken to be coincident with the centre of twist implies an equivalent reciprocal behaviour. That is, an axial torsion applied concentric with the shear centre will twist but not bend the beam. The respective bending and shear stress conversions are derived for each action applied to three aluminium alloy extruded channel sections mounted as cantilevers with a horizontal principal axis of symmetry. Bending and shear are considered more generally for other thin-walled sections when the transverse loading axes at the shear centre are not parallel to the section = s centroidal axes of principal second moments of area. The fixing at one end of the cantilever modifies the St Venant free angular twist and the free warping displacement. It is shown from the Wagner-Kappus torsion theory how the end constrained warping generates an axial stress distribution that varies with the length and across the cross-section for an axial torsion applied to the shear centre. It should be mentioned here for wider applications and validation of the Vlasov theory that attendant papers are to consider in detail bending and torsional loadings applied to other axes through each of the centroid and the web centre. Therein, both bending and twisting arise from transverse shear and axial torsion applied to each position being displaced from the shear centre. Here, the influence of the axis position upon the net axial and shear stress distributions is to be established. That is, the net axial stress from axial torsional loading is identified with the sum of axial stress due to bending and axial stress arising from constrained warping displacements at the fixing. The net shear stress distribution overlays the distributions from axial torsion and that from flexural shear under transverse loading. Both arise when transverse forces are displaced from the shear centre.

Experimental investigation of p-section concrete beams under contact explosion and close-in explosion conditions

This paper presents the results of an experimental investigation on explosive breaching of p-section concrete beams. Twenty three p-section concrete beams with a 100 cm length were tested. TNT charges were placed at three positions: contact detonation in the center, contact detonation above the web and close-in detonation in the center. The external and internal breach parameters of the panels were evaluated by measuring the diameter of the ejection crater, spalling crater and breach hole created by the charge detonation. The experimental results were compared to predict values obtained by the analytical models proposed by McVay, Morishita and Remennikov. A modified breach with crater limit line and breach without crater limit line were put forward based on the experimental results. The maximum cross-sectional destruction area ratio(MCDAR) values were used to evaluate the damage degree. The maximum value of MCDAR reached 0.331 corresponding to the C5 experimental condition, of which explosion occurred above the web.

Equivalent bending stiffness of simply supported preflex beam bridge with variable cross-section

In order to understand mechanical characters and find out a calculating method for preflex beams used in particular bridge engineering projects, two types of simply supported preflex beams with variable cross-section, preflex beam with alterative web depth and preflex beam with alterative steel flange thickness, are discussed on how to achieve the equivalent moment of inertia and Young’s modulus. Additionally, methods of calculating the equivalent bending stiffness and post-cracking deflection are proposed. Results of the experiments on 6 beams agree well with the theoretical analysis, which proves the correctness of the proposed formulas.

Mechanism of improving ductility of high strength concrete T-section beam confined by CFRP sheet subjected to flexural loading

For the purpose of inventing a new seismic retrofitting method for the reinforced high strength concrete (HSC) T-section beam using carbon fiber reinforced polymer (CFRP) sheet, three series, a total of twelve T-section beams with nine specimens confined by CFRP sheet in the plastic zone and three control beams were conducted up to failure under four-point bending test. The effectiveness of confining CFRP sheet on improving the flexural ductility of unstrengthened T-section beams was studied. The parameters such as the width and the thickness of CFRP sheet and the type of T-section were analyzed. The experimental results show that ductility and rotation capacity of plastic hinge can be improved by the confinement of CFRP sheet, and the ductility indices increase with the increment of width and thickness of CFRP sheet. A plastic rotation model considering the width of CFRP sheet and the effect of flange of T-section beam is proposed on the basis of the model of BAKER, and the test results show a good agreement with the perdicted results. The relevant construction suggestions for seismic retrofitting design of beam-slabs system in cast-in-place framework structure are presented.

SHEAR STRESS ANALYSIS OF TIMOSHENKO'S BEAM WITH MULTIPLY CONNECTED CROSS SECTION

In this paper, a finite element method is developed to numericallyevaluate the shear coefficient of Timoshenko's beam with multiplyconnected cross section. With focus on analyzing shear stressesdistributed at the neutral axis of the beam, an improved definitionof the shear coeffi- cient is presented. Based on this definition, aGalerkin-type finite element formulation is proposed to analyze theshear stresses and shear deflections. Numerical solutions of theexamples for some typical cross-sections are compared with thetheoretical results. The shear coefficient of tower sections of theTsing Ma Bridge is calculated by use of the proposed approach, sothat the finite element modeling of The bridge can be developed withthe accurate values of the sectional properties.

THE GENERAL SOLUTION FOR DYNAMIC RESPONSE OF NONHOMOGENEOUS BEAM WITH VARIABLECROSSSECTION

In this paper by means of the exact analytic method [1], the general solution fordynamic response of nonhomogeneous beam with variable cross section is obtained un-der arbitrary resonant load and boundary conditions. The problem is reduced to solvea non-positive differential equation. Generally, it is not solved by variational method.By the present method, the general solution for this problem may be written as an ana-lytic form. Hence, it is convenient for structure optimizing problem. In this paper, itsconvergence is proved. Numerical examples are given at the end of the paper. which in-dicates satisfactory results can be obtained.

EXACT SOLUTION FOR FINITE DEFORMATION PROBLEMS OF CANTILEVER BEAM WITH VARIABLE SECTION UNDER THE ACTION OF ARBITRARY TRANSVERSE LOADS

This paper deals with finite deformation problems of cantilever beam with variable sec- tion under the action of arbitrary transverse loads.By the use of a method of variable replacement, the nonlinear differential equation with varied coefficient for the problem can be transformed into an equation with variable separable.The exact solution can be obtained by the integration method. Some examples are given in the paper,and the results of these examples show that this exact solution includes the existing solutions in references as special cases.

Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting

A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule （GDQR） method. The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation. Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS, and good agreement is found. The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam. It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam, i.e., generating more voltage outputs over a wide frequency range, absorbing vibration, and being less weight.

Springback of I-Section Beam after Pure Bending with von Mises Criteria

The objective of the present paper is to introduce a theoretical analysis of bending I-sections after pure bending. The springback values are determined to provide a quantitative method for predicting the springback using von Mises criteria. The analytical methods for the I-section are given for two cases according to the positions of the yield point along the height of the beam. The controlling parameters on the springback of I-sections are studied. The results obtained are quite successful for the prediction of springback for bending I-sections.

The Efficiency of Reduced Beam Section Connections for Reducing Residual Drifts in Moment Resisting Frames

In most framed structures anticipated deformations in accordance with current codes fall into acceptable limit states, whereas they go through substantial residual deformations in the aftermath of severe ground motions. These structures seem unsafe to occupants since static imminent instability in the immediate post-earthquake may be occurred. Moreover, rehabilitation costs of extensive residual deformations are not usually reasonable. Apparently, there is a lack of detailed knowledge related to reducing residual drift techniques when code-based seismic design is considered. In this paper, reduced beam section connections as a positive approach are taken action to mitigate the huge amount of residual drifts which are greatly amplified by P-Δ effects. To demonstrate the efficacy of RBS, a sixteen-story moment resisting frame is analyzed based on a suite of 8 single-component near field records which have been scaled according to the code provisions. The results are then processed to assess the effects of RBS detailing on drift profile, maximum drift, and residual drift. Besides, a special emphasis is given to estimate overall trend towards drift accumulation in each story in the presence of RBS assembly. A main conclusion is that using this connection predominantly alleviates the adverse effects of P-Δ on amplifying residual drifts.

ON THE LIMIT CASE OF THE STEP-REDUCTION METHOD FOR CALCULATING NON-UNIFORM BEAM WITH VARIOUS SECTIONS

In this paper, the step reduction method is discussed, which was advanced by Prof. Yeh Kai-yuan for calculating a non-uniform beam with various sections. The following result is proved. The approximate solution by this method approaches the true solution if the number of the steps approaches the infinity. However, the measure of the error between the limit solution and the ture solution is not in the pure mathematics sense but in the mechanics sense.

Optimization of Sectional Dimensions of I-Section Flange Beams and Recommendations for IS 808: 1989

This study covers optimization of I-sectional flange beams. Scope of this study is limited to medium weight flange beams of Table 1 of IS 808:1983 but it can be further extended for the other sections of this code. Best possible geometric shape of the cross-section is found for maximum performance of the beam with minimum material consumption. All possible loading conditions are considered in the study for which a beam in flexure undergoes in its life. ANSYS software program is used for the analysis and optimizing the sections. It is found that sections MB 125, MB 300 and MB 400 of Table 1 of IS 808 are not the optimum sections but other alternative of these cross-sections is available which within the same material consumption performs better than these sections of IS code.

工艺孔对大截面部分包覆钢-混凝土组合梁受弯性能影响的试验研究

为了研究工艺孔对大截面部分包覆钢-混凝土组合梁(大截面PEC梁)受弯性能的影响,对5根不同构造的大截面PEC梁进行了静力试验,研究了两点加载下主次梁腹板开洞方式对大截面PEC梁试件受弯性能、延性、破坏模式等的影响规律。结果表明:静力荷载作用下,各个试件均表现出良好的延性,腹部开孔对试件承载力和截面刚度有一定的削弱作用。型钢主钢件的应变与混凝土的应变沿截面高度方向均大致呈线性变化,符合平截面假定。按《部分包覆钢-混凝土组合结构技术规程》(T/CECS 719—2020)计算得到的开工艺孔的大截面PEC梁抗弯承载力与试验值误差较小,受尺寸效应影响不大,所采用计算公式安全可靠。

类氦C离子诱发不同金属厚靶原子的K-X射线

利用中国原子能科学研究院HI-13MV串列加速器上提供的动能为15—55 MeV的类氦C离子分别轰击Fe,Ni,Nb和Mo金属厚靶,采用HpGe探测器测量了K-X射线,获得了相应的K-X射线的发射截面.本文中由于各个靶原子外壳层电离度的不同,类氦C离子与Fe,Ni靶原子相互作用发射的K_(β)与K_(α)X射线的分支强度比随入射离子动能增加而减小,而Nb,Mo靶原子发射的K-X射线分支强度比变化不明显.利用厚靶截面公式计算了靶原子K-X射线的发射截面,并与不同的理论模型及质子的结果进行了对比.结果表明随类氦C离子动能的增大,Fe,Ni靶原子发射的K_(β)与K_(α)X射线的总产生截面与考虑多电离的两体碰撞近似修正模型最为符合Nb,Mo靶原子发射的K_(β)与K_(α)X射线的总产生截面与平面波恩近似模型的理论值最为接近.质子与单核子C离子能量相同时,质子比类氦C离子激发不同靶的K-X射线产生截面约小3个数量级.

工字形钢梁-矩形钢管柱单向螺栓节点抗弯承载力理论计算方法

针对工字形纯钢梁和钢-混凝土组合梁分别与矩形钢管柱和矩形钢管混凝土柱采用单向螺栓(也称单边拧紧螺栓)连接形成的4种节点形式,对其在弯矩作用下的受力机理及破坏模式进行分析,讨论导致节点失效的因素。总结节点在弯矩作用下的9种失效模式,包括:单向螺栓拉断、端板受弯屈服、矩形钢管柱壁翼板受拉屈服、矩形钢管柱壁翼板受压屈服、矩形钢管柱壁腹板受压屈曲、混凝土楼板局部压溃、钢筋屈服、矩形钢管柱内混凝土局部压溃、矩形钢管柱壁腹板受压屈服,进而基于破坏模式给出节点各组件承载力的计算公式。对4种节点在不同破坏模式下的正弯矩承载力和负弯矩承载力进行分析,给出节点承载力计算公式。将节点抗弯承载力的理论计算结果与试验结果进行对比,验证理论计算方法的可靠性。

幂函数形式连续变截面梁振动的弯曲固有频率分析

为给变截面变幅杆弯曲振动提供设计依据,该文使用微分方程解析法求解变截面梁固有频率。首先,建立变截面梁模型,其中截面面积和惯性矩均按幂次函数变化。得到变截面梁自由振动时挠度的解析表达式,并获得不同边界条件下梁弯曲振动的固有频率方程。其中惯性矩所对应幂指数与截面面积的幂指数的差值为4时,可得自振频率方程的精确形式;而幂指数差值不等于4时,给出近似解法。其次,对4种具体的变截面梁求解不同边界下的自振频率,并与瑞利-里兹法所得的自振频率解比较。验证精确解法结果的正确性,并发现近似解法结果的相对偏差在5%以内。该解析方法较瑞利-里兹法具有能快速求解的特点,且易于分析截面参数对梁固有频率的影响。由算例可得,边界和其他参数不变时,梁的同阶次无量纲自振频率随着幂次指数的增加而增加。几何参数中仅截面形状参数改变时,随着形状参数的增加,梁的同阶次无量纲自振频率随之减小,但固定-自由梁的第1阶自振频率除外。

型钢混凝土T形梁纯扭及弯扭性能试验研究

为研究型钢混凝土T形梁在纯扭和弯扭作用下的受力性能,以翼缘宽度、型钢含钢率、配箍率、翼缘纵筋直径及弯扭比为变化参数,设计并完成12根型钢混凝土T形梁的纯扭、弯扭静载试验。观察了试件的破坏过程,获取了试件的扭矩-扭率全过程曲线、开裂扭矩和极限扭矩等特征参数,深入分析了纯扭、弯扭作用下不同变化参数对型钢混凝土T形梁抗扭性能的影响规律,揭示了其抗扭破坏机理。结果表明:T形截面梁和矩形截面梁的破坏形态基本一致,其中钢筋混凝土梁呈现为脆性破坏,型钢混凝土梁呈现为延性破坏;T形试件翼缘、型钢和混凝土之间存在相互约束作用,翼缘和型钢大幅增强了试件的抗扭强度和延性;试件翼缘的最优高宽比为2.33;随着型钢含钢率的增大,试件的抗扭强度和延性呈增大趋势,平均提升幅度分别为30.99%、101.14%;试件的极限扭矩随着弯扭比的增大而增大,平均提高了7.86%。最后,提出了型钢混凝土T形梁的开裂扭矩和极限扭矩计算方法,所得计算结果与试验结果吻合良好。

基于视觉检测的智能桥梁检查车设计与分析

针对公路变截面梁的特点,提出了一种基于视觉检测的智能检查车。该智能检查车由车体平台和视觉检测平台组成,既能无人智能快速检测,又能人工定点维修,有效地提高了桥梁养护效率及检查工作的安全性。介绍了车体平台的具体结构设计和视觉检测平台的具体组成,并对智能检测和人工检查做了对比试验分析,结果表明智能检测比人工检查具有更好的病害检测完整性和更高的检测效率。

考虑衬砌截面协调变形约束的既有隧道受盾构下穿施工影响的Fourier能量变分解

目前关于新建盾构开挖诱发既有地铁隧道变形的理论研究,大多将既有隧道简化为不含接头的Euler-Bernoulli梁,而忽视了衬砌截面的剪切变形与管片接头的局部刚度削弱。此外,既有地基模型理论较少考虑衬砌管片与接触土体的协调变形约束。首先,采用Loganathan-Polous公式计算盾构开挖诱发的土体自由位移场,并将既有隧道视为考虑剪切变形的Timoshenko梁,基于沿轴线变化的抗弯与剪切刚度函数来描述管片接头的局部削弱作用;然后,结合能量变分原理与连续弹性体Mindlin解,建立考虑衬砌截面协同变形约束的隧道位移控制方程,将盾构开挖诱发的附加荷载施加于既有隧道,并使用Fourier级数方法求解既有隧道纵向变形;最后,将Fourier能量变分解与3组工程实测数据进行对比验证,取得了较好的一致性。此外,考虑隧道抗弯刚度、剪切刚度、接头刚度削弱作用、土体参数与隧道空间位置等因素的共同影响,使用抗弯系数、剪切系数及接头系数进行敏感性分析。结果表明,考虑截面变形协调约束的理论解更为符合实际,不考虑变形协调约束所得隧道位移结果偏大;衬砌接头局部刚度的削弱作用将造成隧道弯矩沿轴线在接头处发生明显锯齿状突变;抗弯系数与剪切系数的增长均导致隧道结构所受弯矩降低;剪切系数由低到高的增长将导致隧道变形模式发生“弯曲控制-弯剪混合-剪切控制”三阶段变化;隧道变形模式进入“剪切控制”阶段的过程中,抗弯刚度的变化对隧道内力影响逐渐降低;接头系数的增长将造成隧道所受弯矩降低,但隧道抗弯刚度较大时其影响逐渐减弱。