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热轧钢板校平机设计含3张CAD图,热轧,钢板,校平机,设计,CAD
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附录一：破损钢板在热矫直过程中的原理摘要：成型结构钢中最具代表性的一个基本组成就是钢板。桥梁结构的损坏主要表现在这些基础钢板以及它们的一些强的和/或者比较弱的轴的弯曲。这篇文章的目的就是描述钢板热矫直的基于 实验和分析的研究以及提出与钢板应用有关的一些工程学标准。我们组织一项实验计划来研究钢板在热矫直中的反应并且分析一些重要的影响该反应的参数。实验中我们将各种钢板加热至 300 度以上。发现影响矫直的一些基本的因素有 V 字形热度的角度、加热过程中钢的温度和外部施加的力。加热后的塑性变形直接与这些参数成比例。为了帮助工程师们去预测热矫直中钢板的反应，我们得到一个简单的数学公式。这个公式反映了每 V 字形热度的平均塑性变形与 V 字形角、加热温度、外界施加的力、热膨胀系数和屈服应力的关系。这个公式能够很好地和实验数据吻合，而且是第一个包含有加热温度及外部力的大小的简单公式。这一分析方法也会逐渐地扩展到以下几个方面：轧制成型、轴向加载的物质和简单或复合的珩架结构。绪论成型结构钢中最具代表性的一个基本组成就是钢板。桥梁结构的损坏主要表现在这些基础钢板以及它们的一些强的和/或者比较弱的轴的弯曲。这篇文章的目的就是描述钢板热矫直的基于实验和 分析的研究以及提出与钢板应用有关的一些工程学标准。这一工作形成了轧制成型中热矫直扩展的基础。几个关于钢板的 V 字形热度的研究已经实施。V 字形热度指的是钢板的强轴的矫直倾向的加热曲线，我们将在以下的部分当中进行详细的描述。这些研究已经尝试着去分析影响 V 字形热度的参数并且演变出一个基于该数据的初步模型。Nicholls 和Weeerth（1972）描述了一个顶角在 2460并且有一个 6增量、大小为 211 的 V 字形热度作用于一个 10mm 厚的 A36 钢板上所产生的弯曲度。这个 V 字形的深度也分为满深度、四分之三深度和二分之一深度不等。除了得出 V 字形角和它的深度越大产生的弯曲越大这个结果外，他没有做其他的有关这些参数的影响的估算。Roeder(1986)也做了一个关于未损坏的 V 字形热度钢板的研究。他采用了一些精密的检测设备，如热电偶、接触式高温计和应变仪。另外还有常规的工具，如游标卡尺和钢板标尺。由于这是第一次的尝试着去从实验和分析的角度来量化钢板在热矫直过程中的很大范围的一些参数，所以这项工作是很有意义的。这些参数主要是 V 字形几何学、样本几何学、加热温度、速度、钢种、控制力、最初的残余应力和淬火。Roeder 的关于这些参数结论是基于 60 度左右的温度得到的。结果这只有很少数的反复的热度利用了同一参数。虽然从这个数据中我们可以得到它们的变化趋势，但是由于数据太少，限制了对结果的量化价值。尽管这样，他的研究却给我们提供了这里所提到的很多实验工作的最初的基础。Roeder 的大部分结论是：l 一个实用的和安全的加热上限是 650（1200）l 当加热温度保持在大约 720（1330）这个相变温度以下时，材料性能上的变化很小l 由 V 字形热度所产生的塑性变形是直接和 V 字形角和加热温度成正比的l 由 V 字形热度所产生的塑性变形是直接和在加热过程中的 V 角的开口端集中的控制力成正比的l 淬火是很有效的并且可能增加 V 字形热度的变形，但是加热温度必须在相变温度以下【尽管一些试验员认为只有在加热温度低于 700或者 370才能进行淬火】l 塑性变形主要产生在 V 字形热度区域以内l 塑性变形对钢板的几何形状很敏感的。但是多数的敏感度都可以归结于加热速度和加热流 程上的不同这篇文章里的研究可以扩展至 Roder 的工作并且包含足够的用来定量这些和一些其它的结论的反复的数据。关于热矫直的文献最近几十年就有了，1989 年前就在一些文章中出现了有关它的评论。但是， 整个过程的工程学量化已经缺少了。极少数技术人员目前还是用一些基于他们多年的经验的方法来指导他们进行维修。对于缺少这些经验的工程人员来说，他们就需要一套解析程序来决定他们怎么在一项特殊修理中将热矫直过程做好。由于经济上的原因，这些解析工具必须相当的快速、便于使用，并且能够适应不同的 V 字形几何、加热温度范围、外加负载和支持抑制。目前，存在着两个极端：（1）一些极度简单的模型（Holt 1965，1971；Moberg 1979），这些模型并不能计算出温度范围或者内在、外在的控制力对系统的影响；(2)全面的计算机模型（Chin 1962；Burbank 1968；Weerth 1971；Horton 1973；Roder 1985，1986，1987），这些模型是基于弹塑性有限元素或者有限条压力分析和一个相似的热量分析的。但是前者太简单以至于不能够精确估算过程中的表现；后者需要一个相当长的计算机计算过程，这样也不是实用的办公设计工具。结果，我们还是需要一个分析模型， 这种模型不仅实用，而且能够提供全面的有关所有重要的精确的预先表现的结论。一个没有包含在比较简单的公式中的重要的考虑就是外在、内在的控制力的影响。外在力是用 来产生弯曲活动从而将工件拉直。在加热过程中能够在 V 角的开口端产生压缩的外在力可以增加限制从而增加每一热度所产生的变形。被 Holt 和 Moberg 引用的领域中的应用涉及到控制力的使用。因为在大多数情况中，材料的单独的抑制将会比完美的紧闭少，这似乎说明在被修理的结构上的实际的与预料的活动之间的相互关系，就像 Holt 和 Moberg 所提到的那样，最初是外在力的影响的结果。一个改善了的模型应该百含有内在、外在力的影响。这篇文章的目的就是量化影响钢板热矫直的参数，并且设计一个简单有效的程序来预测热矫直 过程中变形了的钢板的反应。我们所选的方法必须首先就能够分析热矫直过程中可以产生重大影响 的所有参数。这个阶段的完成就需要我们对早先的研究所获得的试验数据进行研究，并且进行一项 更进一步的试验过程，从中获得另外的数据。当我们将这两者的数据结合起来后，一个用来预测钢 板的反应的分析程序就产生了。实验计划结果的评估V 角研究者认为其中一个影响钢板塑性变形的最基本的参数就是 V 角（Holt 1971； Roder 11986； Avent 1989）。数据显示出了塑性变形和 V 角之间的近乎线性的关系。正是因为这个，大多数的数据必须和 V 角一起作为纵坐标，而塑性变形Wp 作为横坐标。这样第一个最小二次方曲线就出现了。随后的图形就说明了这些变量之间的一致的比例关系。V 角深度以前的研究者（Holt 1971； Roder 1985）已经得出这样的结论：塑性变形和深度比 Rd 是成比例的，这个深度比就是指的 V 角深度 dv 与钢板宽度 W 的比。对 Roder 在 6507（12007）6807（61507）范围内的测试数据的再次研究对于 V 角深度的影响无关紧要。由于数据稀少，不论是深度比是 0.75 还是 0.67，都不会导致一贯发生的塑性变形。为了进一步评估这一现象，我们又组织了一连串的实验，深度比分别为 0.5、0.75 和 1，V 角从 207 变到 607。对于其中每一个情况，我们都用了至少 3 中温度作用于最初平直的钢板上，并且将结果求平均值。结果显示在图 2 中，对三种深度比、三种 V 角和 2 个增加了的比率进行了对比。增量比率反映了控制力常常在 V 字形热度区域产生一个大小相当于钢板最大弯曲功率 25%或者50%的瞬间力。就像在图 2 中看到的那样，深度比 75%和 100%轨迹相近。实际上，75%的深度比在 6 中情况之中的一个情况中导致较大一些的塑性变形。当和其它的两个相比较时，50%的深度比产生了 一个不稳定的行为。在 6 个当中的 3 中情况中，50%的深度比产生了较小的塑性变形。在另外的 3 中情况中，塑性变形是很相似的。为了进一步分析这种行为，我们将一些钢板毁坏并且再将它们矫直。毁坏程度是很大的，以至于我们要在大多数的钢板上都要施加至少 20 的热度。因此，更多的令人满意、意义重大的平均塑性变形就从这次测试中得到了。结果显示在图 3 中，对应一种增量比 0.5 和两个 V 角深度比 0.75、1.0。再次说明塑性变形的样式和 V 角深度比没有一个直接的关系。因此，尽管直觉告诉我们，增加 V 角深度比可以增加塑性变形，但是对于这一结论却没有实验证据。我们可以得到如下结论，0.751.0 之间的 V 角深度比对塑性变形的影响是很小的。但是，0.5 的 V 角深度比可能会减小塑性变形。钢板厚度和宽度研究者一般认为钢板的厚度对塑性变形的影响是可以忽略的。唯一的数据说明钢板厚度必须足够小以便于热量能够平衡地渗透钢板。实际的厚度一般在 1925mm（34-1 in.）之间。厚一点的钢板可以两边都进行加热以保证热量在厚度方向上的均衡渗透，或者将钢板稍微倾斜也可以实现。图 4 表示了不同厚度的钢板的测试结果。每一个长条代表了作用于单独一个钢板的至少 3 个热度的平均值。这个测试中没有应用控制力。结果说明可能发生在大多数热度情况下的钢板的变化。但是，对于三种不同的 V 角，并没有钢板厚度上的明显的模式。结果的随意性说明塑性变形不是钢板厚度影响的结果。我们在前面拥有较少参数的测试中也发现了相似的倾向（Roder 1985）。除了钢板的厚度，钢板的三种宽度也进行了研究，示于图 5 中。塑性变形是三种热度情况下的变形的平均值。我们留心了一个作用在 102mm（4-in.）的钢板上的罕见的极低的平均值。但是，却没有发现介于 203mm(8-in)和 302mm(12-in)宽度之间钢板中的区别。这些测试的结果表明钢板宽度和塑性变形之间并没有一个清楚的关系。Roder(1985)所做的测试同样说明了一个相似的倾向。总起来说，钢板厚度和宽度对塑性变形的影响是很小的。测试结果确确实实说明了热矫直过程 中的钢板反应的变化情况。这里所说的波动对变化特征的影响比钢板几何形状对它的影响要显著。 从而，钢板几何形状是作为影响塑性变形行为的辅助因素来看待的。温度热矫直中一个最重要的也是很难去控制的参数就是被加热材料厚度方向上的温度。影响温度的因素有火焰口的大小、火焰的强烈程度、加热速度和钢板的厚度。在这个实验中，Roder(1985)让富有经验的操作者加热，并且对其热度进行了仔细的测量。他发现这些操作者，在通过颜色来辨别温度时，通常判断误差大约为 567(1007)，而且在很多情况下都有 1117(2007)那么大。从而， 在温度控制中有相当可观的变化，即使这是很有经验的人做的。为了进一步清楚的定义 Roder 实验中数据所显示的变形行为，我们在钢板上作用了很多的加热温度来进行研究，从 3707到 8157，并且有一个 567的增量。结果显示在图 6 中，这里每一个数据点代表了三种热度循环，并且这些点由一条直线连接起来以便于辨认。这里一个很清楚并且有规则的随着温度的增加塑性变形也增加的曲线关系就有了。曲线之所以 那么有规律，是因为这些温度的调节是由一个技师来完成的，并且增量的调节也是步调一致的。大多数研究者认为对于除了淬火和调质处理了的高强度钢以外的所有的钢板的最大的加热温度是 6507。对于碳钢，更高的温度会导致更大的变形；但是，平面以外的扭曲有可能发生，而且表面损坏如蚀斑在 7607-8707时会产生。同时，温度超过 7007可能导致分子组成的变化进而可能导致冷却时材料性能上的变化。在这点上的极限安全温度是 6507。对于淬火、调质处理的钢，热矫直过程可以进行，但是对于A514 和A709(等级在100 和100W)温度必须控制在5937，对于A709(等级为 70W)温度为 5667，以保证调质温度不会超过所需的温度并且不会影响材料的性能。允许的能被热矫直的淬火、调质钢和 Shanafelt 和 Horn（1984）所建议的正好相反；但是，文章中并没有提及反作用。为了控制加热温度，对于不同厚度的钢板，我们要采取不同的加热速度和火焰口的大小、类型。 但是只要温度很快达到合适的水平，收缩影响还是相似的。这个结论已经被两个实验证明了，在这两个实验中，我们选择了不同的钢板，也用了不同强烈程度的火焰。其一，我们用了低强度的火焰缓慢地增加到 6507，另一个中，火焰强度很大同时快速地增大到最高温度。两种情况下地变形很相似。控制力控制力这个术语既可以是外在的力，也可以是内在的力。这些力如果能被合理的利用，可以促 进矫直过程。但是，不能被合理地理解，控制力会扰乱甚至是阻碍矫直过程。热矫直地基本理论就 是产生塑性变形导致厚度方向上的扩充，然后就是冷却阶段的纵向弹性收缩。尽管操作者已经意识到在矫直过程中的控制力的重要性，但是很少有研究者去量化它的影响。我们组织了一连串的测试用来估计这个参数。实验当中，我们在一块钢板上作用了一个控制力，最后这个控制力在强轴方向上产生了一个倾向于减小 V 角的瞬间力。这个瞬间力是没有量纲的，它只是在 V 角处产生了这个瞬间力的比率 M j M p 。这个测试包含有从 0 到 50%变化的控制比，其中有四个不同的 V 角而且 V 角延伸至要么四分之三钢板厚度要么整个钢板厚度。结果显示在图 7 和 8 中。从这个数据中我们得出如下的结论：塑性变形的变化和控制比的变化成比例的，合适的外在负载会很大程度上促进热矫直过程。Roder(1985) 也研究了不同的控制力的影响，也发现了相似的表现。但是数据点的数量很有限。图 7 和 8 中显示的结果是基于无形变的钢板在不同的数据点上进行了三到四次的加热得出的。任何一个确定的参数的总的数据点大约都是 6 或者更少。尽管这数据说明了基本参数所所引起的变化倾向，但是数据太少以致于不能够包含令人满意的价值。为了弥补这个缺陷，我们做了另外一组 实验，这实验是用了最初是被损坏了的同样 6mm 厚的钢板，然后进行加热一直到矫直完成。这两个钢板被加热至热度为 20 到 100。表格一中给出了这个实验中各个参数和塑性变形的概要情况。加热温度是 6507。其中的一些结果被划分在图 9 中用以说明控制力的影响。平均是三种情况下的平均数。平均数的 95%的置信区间也示于图 9 中，它提供了热矫直中典型的分散的测验数据。我们再一次发现塑性变形和控制力时成比例的。我们没有发现其中一个很有趣的现象，那就是最初的几次加热导致了相当大的塑性变形，特别 是第一次加热。这些最初的加热过后，塑性变形就一致变得比较小，并且后来的加热中再也没有显 示出什么有意义的变化。这种现象要归因于在损坏过程中产生的最初的残余应力。这个结果的含义 就是理论公式应该建立在有相当多的实验数据的基础上，而不是只有几个数据。这里所提到的所有 的数据中，序列中所有热度的平均值都应用到了。就像预料中的那样，当 3 个或多个热度的平均值作用于平直钢板上，10 个或者更多的热度的平均值作用于损坏了的钢板上时候，二者每一热度所发生的变化是很相似的。第二种类型的有可能施加到钢板的外部控制力就是轴向控制力。同样也进行了一连串的测试， 这个测试是对于每一 V 角我们都在钢板上施加了轴向的迭加负载。这个负载产生了一个 138MP 的轴向应力或者说是相当于公称屈服应力 56%的实际应力。这些结果表示在图 8 中，以便于和弯曲控制力产生的结果相比较。应用轴向载荷并不是一个很有效增加塑性变形的方法。为了概括这个实验研究的结果，已经发现的由 V 角产生的对塑性变形有很重要的影响的参数主要有：(1)V 角；(2)钢板温度；(3)外在的控制力。V 角深度在通常范围内，也就是钢板宽度的四分之三或者更大，看起来对变形影响很小。同样地，只要是需要的加热模式和温度能够达到，钢板的 尺寸对变形的影响也很小。概要和结论由于钢板是任何轧制或者建筑的基本的元素，所以理解钢板在热矫直过程中的反应是最基本的。 一些热矫直的实验过程都已经备份了文件，这些实验是对 70 的钢板样品采用近乎 600 的加热循环来进行的。我们对很多因素进行了估计以便于了解它们对塑性变形的影响，这些塑性变形是钢板上每一 V 字形热度产生的。另外，我们也建立了一个数学模型用来预测塑性变形的大小。在研究的实际范围内，热矫直过程中对塑性变形有着最重要的影响的一个因素就是 V 字形热度的角度、V 角区域的最高温度和外部力。已经证实了塑性变形和 V 角、温度、外部力是有着直接的比例关系的，尽管数据上有一点波动。另一方面，和钢板宽度有关的 V 角的深度对于 钢板宽度 75%的 V 角深度并没有什么重大意义。只要是热供应过程中热量能够很好的渗透钢板，钢板厚度也可视为无关紧要。为了帮助工程师来预测钢板在热矫直过程中的反应，我们建立了一个简单的数需公式。 这个公式表示的是每一的热度上的平均塑性变形与 V 角、钢板温度、外部力的大小、热膨胀系数和屈服应力之间的关系。公式和实验数据吻合的很好，并且是第一个包含有钢板加热温度、外部力的大小的简单计算公式。这种分析方法将会扩展至很大，从而包含有轧制成型行为，轴向加载物质和简单的和复杂的桁架。河海大学文天学院本科毕业设计（论文）附录二：HEAT STRAIGHTENING DAMAGED STEEL PLATE ELEMENTSBy R. Richard Avent，1 David J. Mukai，2 Paul F. Robinson，3 and RandyJ. Boudreaux4ABSTRACT: The fundamental element of any structural steel shape is the flat plate.Damage to bridge structures consists of these plate elements， in combination， bent about their strong and/or weak axes. The purpose of this paper is to describe experimental and analytical research on heat straightening as applied to plates and to present related engineering criteria for itsuse. An experimental program was conducted to evaluate the response of plates to heat straightening and to identify important parameters influencing behavior. Over 300 heats were applied to a variety of plates. The primary factors influencing straightening were the angle of the vee heat， steel temperature during heating， and external restraining forces. The plastic rotation after heating was directly proportional to these parameters. To aid engineers in predicting platemovements during heat straightening， a simple mathematical formula was developed. This equation relates the average plastic rotation per vee heat to vee angle， steel temperature， magnitude of restraining force， coefficient of thermal expansion， and yield stress. The formula compares well to the experimental data and is the first simple formula available that includes theparameters of heating temperature and magnitude of restraining force. The form of this analytical approach also will lend itself toward extensions， including the behavior of rolled shapes， axially loaded members， and composite and noncomposite girders.INTRODUCTIONThe fundamental element of any structural steel shape is the flat plate. Damage to bridge structures consists of these plate elements， in combination， bent about their strong and/or weak axes. The purpose of this paper is to describe experimental and analytical research on heatstraightening as applied to plates and to present related engineering design criteria for its use. This work forms the basis for extensions to heat straightening of rolled shapes.Several detailed studies have been conducted for vee heats applied to plates. The vee heat is the59usual heating pattern for straightening plates bent about their strong axis and is explained in detail in a later section. These studies have attempted to identify parameters that influence vee heats and to develop predictive models based on this data. Nicholls and Weerth (1972) described the bends produced by 211 vee heats whose apex angle varied from 247 to 607 in 67 increments applied to10- mm (3/8-in.) thick A36 steel plate. The vee depth was also varied over full depth， three-fourth depth， and onehalf depth. No attempt was made to evaluate the effect of these parameters other than the general result that the greater the vee angle and depth， the greater the bend produced.Roeder (1986) also conducted a study on undamaged vee heated plates. He employed sophisticated monitoring equipment such as thermocouples， contact pyrometers， and strain gauges， as well as more conventional tools such as vernier caliper and a steel ruler. His work is particularly significant as the first attempt to both experimentally and analytically quantify heatstraightening behavior for plates over a wide range of parameters. The parameters includedvee geometry， specimen geometry， heating temperature and rate， steel grade， restraining force， initial residual stresses， and quenching. Roeders conclusions were based on approximately 60 heats over a wide range of parameters. As a result there were relatively fewre-petitive heats using identical parameters. Although trends could be drawn from this data， its sparseness limited the quantitative value of the results. However， his research provided the initial basis for much of the experimental work reported here. Roeders most significant conclusionswere A practical and safe upper heating treatment limit is 6507C (1，2007F). Changes in material properties are small when the heating temperature remains below the phase transition temperature of approximately 7207C (1，3307F). The rotation produced by a vee heat is directly proportional to vee angle and heatingtemperature. The rotation produced by a vee heat is directly proportional to restraining forces that produce compression in the open end of the vee during heating. Quenching is effective and may increase vee heat rotations， but heating temperaturesshould be kept below the phase transition temperature although some practitioners recommend quenching only if the steel temperature is below 7007F or (3707C). Plastic strain occurs primarily within the vee heat region. Plastic strain is somewhat sensitive to geometry of the plate. However， much of this sensitivity can be attributed to differences in rate of heating and heat flow. The research described in this paper extends Roeders work and includes enough repetitive data points to quantify theseand other conclusions.Literature on heat straightening has been available for many years as reviewed in astate-of-the-art paper by Avent (1989). However， engineering quantification of the process has been lacking. The handful of practitioners currently using the method rely extensively on their many years of experience to guide them through a repair. An engineer lacking this wealth of experience needs a set of analytical procedures to determine how best to apply theheat-straightening process to a particular repair. These analytical tools， for reasons of economy， should be relatively fast， easy to apply， and allow for such considerations as different vee geometries， temperature ranges， external loadings， and support restraints. At present， two extremes exist: (1) Overly simplistic models (Holt 1965， 1971； Moberg 1979) that cannot take into account the effect of either temperature variations or internal and external restraint； and (2) comprehensive computer models (For Chin 1962； Burbank 1968； Weerth 1971； Horton 1973； Roeder 1985， 1986， 1987) based on elastic-plastic finite-element or finite-strip stress analysis combined with a similar thermal analysis. Whereas the former is too simplistic to accuratelypredict behavior， the latter requires such lengthy computational effort as to not be practical for design office use. As a result， there is a need for an analytical model that offers both practicality and comprehensive inclusion of all important variables to accurately predict behavior.An important consideration not included in the more simple formulations is the influence of external and internal restraining forces. External forces typically are applied to produce bending moments tending to straighten the member. The external forces， producing compression on theopen end of the vee during heating， will increase the available confinement and， therefore，increase the rotation produced per heat. The field applications cited by both Holt and Moberg involved the use of restraining forces. Because in most cases the material restraint alone will be less than perfect confinement， it seems likely that any correlation between the predicted andactual movement in the structures being repaired， as noted by both Holt and Moberg， isprimarily due to the influence of the external forces. An improved analytical model should include the effects of both internal and external restraints.The purpose of this paper is to quantify the parameters influencing the heat straightening of plate elements and to develop simple yet efficient procedures for predicting the response of deformed steel plates during the heat-straightening process. The approach chosen was to first identify all parameters that have an important influence on the heat-straightening process. This phase was accomplished by studying the experimental data available from previous research as well as by conducting an extensive experimental program to provide additional data. After synthesizing this experimental data， an analytical procedure for predicting member response wasdeveloped.EVALUATION OF RESULTS OF EXPERIMENTAL PROGRAMVee AngleResearchers agree that one of the most fundamental parameters influencing the plastic rotation of a plate is the vee angle (Holt 1971； Roeder 1986； Avent 1989). The data shows a fairly linear relationship between plastic rotation and vee angle. For this reason， most data will be plotted with the vee angle as the ordinate and plastic rotation wpas the abscissa. A first-orderleast-squares curve fit will sometimes be shown. Plots in succeeding sections show a consistent proportional relationship between these variables.Depth of VeePast researchers (Holt 1971； Roeder 1985) have concluded that the plastic rotation is proportional to the depth ratio Rd， which is the ratio of vee depth dvto plate width W. A review of Roeders test data in the range of 6507C (6807) 1，2007F (61507) is inconclusive as to vee depth effect. Recognizing that the data was sparse， neither the depth ratio of 0.75 nor 0.67 produced plastic rotations that were consistently hiearchial. To further evaluate this behavior， a series of tests was conducted for depth ratios of 0.5， 0.75， and 1.0 and vee angles ranging from 207 to 607. At least three heats were conducted on initially straight plates for each case and theresults averaged. The results are shown in Fig. 2 for a combination of three depth ratios， three vee angles， and two jacking ratios.The jacking ratios reflect that a jacking force was used to create a moment at the vee heat zone equal to either 25 or 50% of the ultimate bending capacity of the plate. As can be seen from Fig. 2， the depth ratios of 75 and 100% track each other well. In fact the 75% depth ratio resulted in slightly larger plastic rotations in all but one of the six cases. The 50% depth ratio resulted in an erratic behavior when compared to the other two. In three of the six cases the 50% depth ratio produced much smaller plastic rotations. In the other three cases， the plastic rotations were similar.To further verify this behavior， a series of plates was damaged and straightened. The degree of damage was large enough that at least 20 heats were required for most of these plates. Therefore， more statistically significant average plastic rotations were obtained from these tests. Results are compared in Fig. 3 for a jacking ratio of 0.5 and two vee depth ratios， 0.75 and 1.0. Again the pattern of plastic rotations does not have a direct correlation to the vee depth ratios.Therefore， although it would seem intuitive that increasing the vee depth would increase the plastic rotation， there is no experimental justification for such a general statement. It can be concluded that the variation of vee depth ratios between 0.75 and 1.0 has little influence on plastic rotation. However， a vee depth ratio of 50% may reduce the plastic rotations.Plate Thickness and WidthResearchers have generally considered plate thickness to have a negligible effect on plastic rotation. The only reservation has been expressed that the plate should be thin enough to allow a relatively uniform penetration of the heat through the thickness. The practical limiting value is on the order of 1925 mm (3/41 in.). Thicker plates can be heated on both sides simultaneously to ensure a uniform distribution through the thicknesses， or a rosebud tip can be used. The results from tests involving different plate thicknesses are shown in Fig. 4.Each bar represents the average of at least three heats on a single plate. No jacking forces were used in these tests. The results illustrate the level of variability that may occur among groups of heats. However， there is no discernable pattern among the plate thicknesses for the three different vee angles used. The randomness of these results indicates that plastic rotation is not a function of plate thickness. A similar trend was found in earlier tests with fewer variables (Roeder 1985).In addition to thickness， three plate widths were studied， as shown in Fig. 5.The plastic rotations are the average of three heats. An unusually low average was observed for the 102-mm (4-in.) width. However， little difference was found between the 203-mm (8-in.) and 302-mm (12-in.) widths. The results of these tests show no clear relationship between plastic rotation and plate width. Tests by Roeder (1985) also indicated a similar trend.In summary， the parameters of plate thickness and width show little definitive influence on plastic rotations. The test results do illustrate the variability of response typically found in heat straightening. It is probable that the fluctuations shown here reflect this variability characteristic rather than effects of plate geometry. Thus， plate geometry is considered to be a minor factor influencing plastic rotation behavior.TemperatureOne of the most important and yet difficult to control parameters of heat straightening is the through-thickness temperature of the heated metal. Factors affecting the temperature include size of the torch orifice，intensity of the flame，speed of torch movement，and thickness of the plate. In his experiments Roeder (1985) made careful temperature measurements of the heats produced by knowledgeable practitioners. He found that these individuals， when judging temperature bycolor， commonly misjudged by 567C (1007F) and， in some cases， as much as 1117C (2007F).Thus， there are considerable variations in temperature control， even with knowledgeable users.To more clearly define the behavior suggested by a limited number of data points in Roeders study， a series of heats were applied to plates in which the heating temperature was varied from 3707 to 8157C (7007 to 1，5007F) in increments of 567C (1007F). The results are shown in Fig. 6， where each data point represents three heat cycles， and the points are connected by lines for clarity in identification.A clear and regular progression of increased plastic rotation with increasing temperature is shown. Part of the reason for the regularity of the curve fits is that the same technician conducted all heats and varied the temperature in consistent step increments.The maximum temperature recommended by most researchers (Holt 1971； Shanafelt and Horn 1984； Roeder 1986) is 6507C (1，2007F) for all but the quenched and tempered high strength steels. For carbon steels， higher temperatures may result in greater rotation； however，out-of-plane distortion becomes likely and surface damage such as pitting will occur at 76078707C (1，40071，6007F). Also， temperatures in excess of around 7007C (1，3007F) may cause molecular composition changes that could result in changes in material properties after cooling. The limiting temperature of 6507C (1，2007F) allows for a safety factor in this regard.For the quenched and tempered steels， the heat-straightening process can be used， but thetemperature should be limited to 5937C (1，1007F) for A514 and A709 (grades 100 and 100W) and 5667C (1，0507F) for A709 (grade 70W) to ensure that the tempering temperature is not exceeded and that the properties are not adversely affected. Permitting quenched and tempered steels to be heat straightened is contrary to the recommendations of Shanafelt and Horn (1984)； however， no adverse effects have been noted in the literature (Avent 1989).To control the temperature， the speed of the torch movement and the size and type of orificemust be adjusted for different thicknesses of material. However， as long as the temperature quickly reaches the appropriate level， the contraction effect will be similar. This conclusion was verified by two test series on plates in which the intensity of the torch was varied. In one set， a low intensity torch moved slowly to achieve a 6507C (1，2007F) temperature， and in the other ahigh intensity torch was moved more quickly while again attaining the same maximum temperature. The rotations in both cases were similar.Restraining ForcesThe term restraining forces can refer to either externally applied forces or internal redundancy. These forces， when properly utilized， can expedite the straightening process. However， if improperly understood， restraining forces can hinder or even prevent straightening. The basic mechanism of heat straightening is to create plastic flow， causing expansion through the thickness (upsetting) during the heating phase， followed by elastic longitudinal contraction during the cooling phase.Although practitioners have long recognized the importance of applying jacking forces during the heat-straightening process， little research has been conducted to quantify its effect. A series of tests designed to evaluate this parameter involved applying a jacking force to a plate such that a moment is created about the strong axis in a direction tending to close the vee. This moment (at ambient temperature) is nondimensionalized for comparison purposes by forming a ratio of the moment at the vee due to the jacking force Mj to the plastic moment Mp of the cross section， that is Mj /Mp. This term is referred to as the jacking ratio. The tests included jacking ratios ranging from zero to 50% with four different vee angles and the vees extending over either three-fourth depth or the full depth of the plate. The results are shown in Figs. 7 and 8.It can be concluded from this data that the variation of plastic rotation is generally proportional to the jacking ratio， and the proper use of external loads greatly expedites the heat straightening process. Roeder (1985) also studied the effect of the jacking ratio variation and found a similar pattern of behavior. However， the number of data points was limited.The results shown in Figs. 7 and 8 are based on undeformed plates that were heated either three or four times with each data point representing the average. The total number of data points for any fixed set of parameters was typically six or less. Although such data illustrate the trendsassociated with variations of basic parameters， the data set is too small to obtain statistically meaningful average values. To fill this void， a test series was conducted on similar size 6-mm(1/4-in.) thick plates that were initially damaged and then heated until straightened. Ten damaged plates were straightened with the number of heats required per plate ranging from 20 to 100. A summary of the test parameters and resulting plastic rotations is given in Table 1.The heating temperature was 6507C (1，2007F). Some of the results are also plotted in Fig. 9， illustrating the jacking ratio effect. The mean values are plotted for three cases.The range corresponding to the 95% confidence interval for the mean is also shown， providing a measure of the scatter of the test data that is typical of heat straightening. Again， the plastic rotation is found to be proportional to the jacking ratio.An interesting phenomena that had not been noted in previous research was the relatively high (statistically significant) plastic rotations resulting after the first few heats， particularly the first. After these first few heats， the plastic rotations were consistently lower and showed no significant statistical variation with respect to heat number in the later heats. A similar， but muchless pronounced trend was noted on the undamaged plates. This behavior is attributed to the initial residual stresses induced during the damage process. The implications of this result is that theoretical formulations should be evaluated on experimental data with a large number of data points rather than on tests involving only a few heats. In all data presented here， the average ofall heats in a sequence was used. As expected， the movement per heat of initially straight platesand damaged plates were similar when 3 or more heats were averaged for straight plates and 10 or more averaged for damaged plates.A second type of constraint that may exert external forces on a member is axial restraint. A series of tests were conducted using a superimposed axial load on plates for various vee angles. The load created a 138-MPa (20-ksi) axial stress or an actual stress to nominal yield stress ratio of 56%. These results are shown in Fig. 8 in comparison to the results for flexural jacking ratios. The use of an axial-load jacking force is not an effective means for increasing plastic rotations.To summarize the results of the experimental study， the parameters that were found to havean important influence on the plastic rotations produced by vee heats are (1) vee angle； (2) steel temperature； and (3) external restraining force. The depth of the vee appears to have a smalleffect in the usual range of three-quarters of the plate width or greater. Likewise， the plate dimensions are of minor significance as long as the desired heating patterns and temperature can be attained.SUMMARY AND CONCLUSIONSBecause the plate is the basic element of any rolled or built up shape， understanding its response to heat straightening is fundamental. The experimental behavior of heat-straightened plates has been documented with nearly 600 heating cycles on some 70 plate specimens. Anumber of factors were evaluated to assess their effect on the plastic rotation produced by a vee heat on a plate bent about its strong axis. In addition， a mathematical model was developed to predict these rotations.Within the practical ranges studied， the most important parameters affecting plastic rotations during heat straightening are angle of the vee heat， maximum temperature of the vee zone during heating， and restraining forces on the plate. Plastic rotations were verified to be directly proportional to vee an
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