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.

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.

Production of p-rich nuclei with Z = 20-25 based on radioactive ion beams

Within the framework of isospin-dependent Boltzmann-Langevin model,the production cross sections of proton-rich nuclei with Z=20-25 are investigated.According to the reaction results for different isospin of projectiles^(48)Ni,^(49)Ni,and^(50)Ni,proton-rich fragments tend to be more easily produced in reactions with the protonrich projectile^(48)Ni.The production cross sections of the unknown nuclei in the vicinity of the projectile are sensitive to incident energy.It is observed that incident energy of 345 MeV/u is appropriate for producing proton-rich nuclei with Z=20-25.In projectile fragmentation reactions based on the radioactive ion beam of48Ni at 345MeV/u,several unknown proton-rich nuclei near the proton drip line are generated in the simulations.All these new nuclei are near-projectile elements near Z=28.The production cross sections of the new nuclei^(34)Ca,37,38Sc,^(38)Ti,^(40,41,42)V,^(40,41)Cr,and^(42,43,44,45)Mn are in the range of 10-2-102mb.Hence,projectile fragmentation of radioactive ion beams of Ni is a potential method for generating new proton-rich nuclei with Z=20-25.

Crack elongation and its width of large depth reinforced concrete beams

In order to meet the requirement of structural inspection,the crack spacing and crack width at various heights in the tensile zone of six large depth reinforced concrete beams were measured under several loading levels of serviceability state.The effects of the depth of normal section beams on the crack spacing and crack width were analyzed,and the modified model is proposed for calculating the average crack spacing by thinking about the depth of normal section,the reinforcement arrangement and the effective reinforcement ratio.The relationships of crack widths at any position in the tensile zone and at the reinforcement level on the side surface of beam were studied.By theoretical and statistical analysis,a method is proposed to calculate the ratios of crack widths between any position and the reinforcement level on the side surface of large depth reinforced concrete beams.

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.

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.

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.

A new finite element of spatial thin-walled beams

Based on the theories of Timoshenko＇s beams and Vlasov＇s thin-walled members, a new spatial thin-walled beam element with an interior node is developed. By independently interpolating bending angles and warp, factors such as transverse shear deformation, torsional shear deformation and their Coupling, coupling of flexure and torsion, and second shear stress are considered. According to the generalized variational theory of Hellinger-Reissner, the element stiffness matrix is derived. Examples show that the developed model is accurate and can be applied in the finite element analysis of thinwalled structures.

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.

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.

High Resolution Crossed Molecular Beams Study of the H+HD→H2+D Reaction

The H+H2 reaction is the simplest chemical reaction system and has long been the prototype model in the study of reaction dynamics. Here we report a high resolution experimental investigation of the state-to-state reaction dynamics in the H+HD→H2+D reaction by using the crossed molecular beams method and velocity map ion imaging technique at the collision energy of 1.17 eV. D atom products in this reaction were probed by the near threshold 1+1'(vacuum ultraviolet+ultraviolet) laser ionization scheme. The ion image with both high angular and energy resolution were acquired. State-to-state differential cross sections was accurately derived. Fast forward scattering oscillations, relating with interference effects in the scattering process, were clearly observed for H2 products at H2(v'=0,j'=1) and H2(v'=0,j'=3) rovibrational levels. This study further demonstrates the importance of measuring high-resolution differential cross sections in the study of state-to-state reaction dynamics in the gas phase.

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.

Analysis of Shear Failure in Reinforced Concrete Beams without Stirrups

This paper deals with flexural concrete members reinforced longitudinally but without transverse reinforcement. The conducted experimental investigations have shown that beams without web reinforcement may fail without attaining their full flexural capacity and then shear governs their failure. In the paper, there are presented recent results of the author＇s own experiments, which aimed at disclosing some aspects of the propagation of cracks in longitudinally reinforced concrete beams without stirrups. The experimental program has been designed especially to investigate the influence of the shear span-to-depth ratio on diagonal crack propagation and load carrying capacity of tested beams.

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.

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。

粘铝合金板加固RC梁抗弯性能试验及正截面承载力

为了探讨铝合金板厚度与端部U形铝合金箍板构造对RC梁破坏机理及抗弯性能的影响,对16根铝合金板加固RC梁进行了4点弯曲静力加载试验。在试验梁底铝合金板的表面以及试验梁跨中截面的顶面、侧面粘贴应变片,在试验梁底跨中、梁顶两端支座布置百分表。为了推导铝合金板加固RC梁的正截面承载力计算式,基于试验得到的破坏机理,通过引入6个基本假定,分析了5种不同破坏模式的相对受压区高度。建立了各破坏模式下铝合金板加固RC梁的正截面承载力计算式,并将其与引入文献中的试验结果进行了对比分析。结果表明:试件破坏形态包括适筋破坏、端部铝合金板与结构胶剥离、端部铝合金板与梁剥离及中部铝合金板剥离4种情况;当端部设置U形铝合金箍板时,可有效抑制端部铝合金板发生剥离,使钢筋与铝合金板的材料性能得到充分发挥,试件承载力与延性明显提升;当铝合金板厚度分别为2~6 mm时,试件承载力随铝合金板厚度的增加而提高;端部设置U形铝合金箍板可有效防止端部铝合金板发生剥离,但试件仍可能会出现中部铝合金板剥离现象;当试件出现适筋破坏特征时,试件抗弯承载力的计算值与试验值比值均在1以下。本研究所提计算式具有明显的规律性和适用性,可为工程实际设计提供参考。

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.

杭州电竞中心结构设计重难点概述

杭州电竞中心内圈主体结构采用钢框架-支撑结构,外圈采用“大倾角梭形斜柱+多段钢折梁框架”,是集承重与抗侧力于一体的结构体系,屋盖采用车辐式索承网格自平衡结构形式。详细介绍了地下结构、中央场馆结构的设计要点,门厅处利用建筑造型空间设计为多段钢折梁与跨层桁架相结合的结构形式;室内二层至三层楼面设计一浮空弧形人行桥,截面形式为薄壁钢箱梁,桥宽2.2m,跨度57m,采用“上挂下支”的稳定结构形式。对整体结构进行了静力弹性、动力弹塑性、振动台试验、典型节点有限元、整体稳定以及局部稳定等系列分析与试验。结果表明:结构在静力荷载和地震作用下强度和刚度均满足规范要求;典型节点极限承载力为荷载设计值的4.17倍;结构整体稳定性安全系数为3.79;斜柱局部稳定安全系数为2.52。合理的设计保证了结构的安全、经济和实用性。

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。