1.1 Classification and Behavior of Structural Systems and Elements系统结构和元素的分

类和作用

1.2 Determinate and Indeterminate Structures 静定和超静定结构

1.3 Structural Dynamics 结构动力学

2.1 Materials for Concrete and Mix Proportion 砼材料及配比

2.2 Properties of Concrete 砼的性能

2.3 Steel Materials 钢材料

2.4 Structural Steel Shapes 型钢

Chapter 3. Structural Design concepts 结构设计

3.1 Load conditions and Load Paths 负载条件和加载路径

3.2 Limit State Design 极限状态设计

4.1 Flexural Behavior of Reinforced Concrete Beam

钢筋混凝土梁的弯曲性能

4.2 Shear and Diagonal Tension in Reinforced Concrete Beam

钢筋混凝土梁的剪切和斜拉

4.3 Bond , Anchorage, and Development Length

连接，锚固，基本锚固长度

1.1 . Classification and Behavior of Structural Systems and Elements

系统结构和元素的分类和作用

Common rigid elements include beams, columns or struts, arches, flat plates, singly curved plates, and shells having a variety of different curvatures. Flexible elements include cables (straight and draped) and membranes(planar, singly curved, and doubly curved). In addition, there are a number of other types of structures that are derived from these elements(e.g, frames, trsses, geodesic domes, nets, etc. )(figure 1.1)

常见的刚性元件包括梁，柱，支撑，圆拱，平板，单向板弯曲面，具有不同的曲率的翘体。柔性元素包括电缆（直披）和膜结构（平面，单向板弯曲面，双曲面）。此外也有一些来自这些元素（如框架，桁架，测量短程线，网格等）

Frames 框架

The frame has rigid joints that are made between vertical and horizontal members. This joint rigidity imparts (给予) a measure of stability against lateral forces. In a framed system both beams and columns are bent or bowed（弯如弓的）as a consequence of the action of the load on the structure.

框架的垂直和水平直接有刚性连接，这样的节点给予了一定程度上的稳定性抵抗侧向作用力。在一个框架的系统张，梁和柱的弯曲或弓形弯如弓的形状都是结构上负载的作用效果。 Trusses 桁架

Trusses are structural members made by assembling short, straight members into triangulated patterns. The resultant （组合的, 合成的）structure is rigid as a result of the exact （精确的) way

the individual line elements are positioned relative to one another. Some patterns (e.g. a pattern of squares rather than triangles) do not necessarily yield a structure that is rigid (unless joints are treated in the same way as in framed structures). A truss composed of discrete elements is bent in an overall way under the action of an applied transverse loading in much the same way that a beam is bent. Individual truss members, however, are not subject to bending but are only either compressed or pulled upon.

桁架结构构件是通过短直杆组装成三角形的图案。组合的结果的精确方式相对于彼此的位置的各行元素的结构是刚性的。不一定会产生某些刚性的模型（例如，一个模型的平方不一定是三角形图案）（除非在框架结构中相同的处理）。由分立元件组成的桁架在大致相同的方式，弯曲梁所施加的横向载荷的作用下，在一个整体方式的弯曲。个人桁架构件，不能弯曲只能压缩或拉后。

Arches拱门

An arch is a curved, line-forming structural member that spans between two points. The exact shape of the curve and the nature of the loading are critical determinants as to whether the resultant assembly is stable. When shapes are formed by simply stacking rigid block elements, the resultant structure is functional and stable only when the action of the load is to induce in-plane forces that cause the structure to compress uniformly. Structures of this type cannot carry loads that induce elongations or any pronounced type of bowing in the member (the blocks simply pull apart and failure occurs). The strength of a block structure is due exclusively to the positioning of individual elements, since blocks are typically either simply rested one on another or mortared together. The positioning is, in turn, dependent on the exact type of loading involved. The resultant structure is thus rigid only under very particular circumstances.

圆拱 一个拱形的弯曲线形成的结构部件，两点之间的跨越。曲线的精确性质和性质是所得到的组件是否是稳定的关键决定因素。当通过简单地堆叠刚性块体元件的形状形成的结构是功能性的和稳定的，又有当负载的作用是诱导面内的力量时才导致结构的均匀压缩。这种类型的结构不能进行负载诱导伸长或任何明显的拉伸（只需拉开块发生故障）。嵌段结构的强度是由于单个元素导致的，由于块通常是在躺在另一个上或砂浆砌在一起。只有在非常特殊的情况下，所得到的的结构才是刚性的。

The rigid arch is frequently used in modern building. It is curved similarly to block arches but is made of one continuous piece of deformed rigid material. If rigid arches are properly shaped, they can carry a load to supports while being subject only to axial compression, and no bending occurs. The rigid arch is better able to carry variations in the design loading than is its block counterpart made of individual pieces. Many types of rigid arches exist and are often characterized by their support conditions (fixed, two-hinged, three-hinged).

现代建筑中常用的刚性拱，同样是弯曲的阻止拱，但它是由一块连续变形的刚性材料制成的。如果制成刚性拱的形状，它们可以承受的负载支座仅受轴向压缩的同时并没有发生弯曲。刚性拱是能够更好地进行变化的块对应的单件制成的。存在许多类型的刚性拱的特点常常是它们的支持条件（固定，双绞链、三铰链）

Walls and Plates墙板

Walls and flat plates are rigid surface-forming structures. A load-bearing wall can typically carry both vertical loads and lateral loads (wind, earthquake) along its length. Resistance to out-of-plane forces in block walls is marginal. A flat plate is typically used horizontally and carries loads by bending to its supports. Plate structures are normally made of reinforced concrete or steel.

墙板 墙壁和平板表面形成的结构是刚性的。承重墙通常可以进行沿其长度的垂直荷载和侧向荷载（风。地震）。砌块墙的平面的抵抗力是微不足道的。通常用于平板进行水平和通过弯曲其支持负载。板结构通常是由钢筋混凝土或刚组成的。

Horizontal plates can also be made by assembling patterns of short, rigid line elements. Three-dimensional triangulation schemes are used to impart stiffness to the resultant assembly.

水平板也可以通过组装短，刚性线的模式。三维三角形测量设计是用来赋予所得到的组件的刚度的。

Long, narrow rigid plates can also be joined along their long edges and used to span horizontally in beam-like fashion. These structures, called folded plates, have the potential for spanning fairly large distances.

长，狭窄的刚性板也可以加入和使用到时尚的水平跨越梁中。这些结构，被称为折叠的板，有可能跨越相当大的距离。

Cylindrical Shells and Vaults 柱形壳和拱顶

Cylindrical barrel shells and vaults are examples of singly curved-plate structure. A barrel shell spans longitudinally such that the curve is perpendicular to the direction of the span. When fairly long, a barrel shell behaves much like a beam with a curved cross section. Barrel shells are invariably made of rigid materials (e.g., reinforced concrete or steel). A vault, by contrast, is a singly curved structure that spans transversely. A vault can be conceived of as basically a continuous arch.

柱形壳和拱顶 圆柱型的筒和拱顶都是单独的弧形板式结构的例子。一个镜筒外壳跨越纵向曲线垂直的方向的弧度。当足够长的时候，每筒外壳采用的弧形截面梁很像。筒，炮弹等都提出了硬质材料（如钢筋混凝土或钢）。相反的，储藏库是一个单独的弧形结构，横向跨越。储藏库可以设想基本是是一个连续的拱。

Spherical Shells and Domes球壳和圆顶

A wide variety of doubly curved surface structures are in use .These include structures that are portions of spheres and those that form warped surface (e.g , the hyperbolic paraboloid ). The number of shapes possible is actually boundless. Probably the most common doubly curved structures is the spherical shell. It is convenient to think of this structure as a rotated arch. This analogy, however, is actually misleading with respect to how the structure actually carries loads because of the fact that loadings include circumferential forces in spherical shells which do not exist in arches. Domed structures can be made of stacked blocks or a continuous rigid material (reinforced concrete). Shells and domes are very efficient structures capable of spanning large distances using a minimum of material.

球形壳 各种各样的双曲面结构都在使用中，这些包括球部和它所形成的扭曲的表面的结构（例如，双曲抛物线）。一些可能的形状实际上是无限的。也许最常见的双曲面结构是球壳。它认为这种结构的旋转拱很方便。但是，这个比喻实际上是误导了结构是如何进行负载的。因为，载荷包括切线力在球壳中不存在拱门。圆顶结构，可以由层叠块或连续的刚性材料（钢筋混凝土）组成。壳顶结构是非常有效的，它能够用最少的材料覆盖很大的距离。 Cables（索）

Cables are flexible structural elements. The shape they assume （take on ）under a loading depends on the nature and magnitude of the load. When a cable is simple pulled on at either end, it assumes a straight shape. This type of cable is often called a tie-rod.When a cable is used to span between two points and carry an external point load or series of point loads, it deforms into a shape made up of a series of straight-line segments. When a continuous load （distributed load,）

is carried, the cable deforms into a continuously curving shape. The self –weight of the cable itself produces such a catenary curve Suspension cables can be used to span extremely large distances 索 索是可弯曲的结构元件。它们呈现加载的形状取决于负载的性质和严重程度。当很简单地拉索的任一端时，它假定了直板造型。这种类型的索通常被称为转向横拉杆。当索用于跨越两个点之间并进行外部负载或一系列的点荷载，变形的形状由一系列的直线段。当进行连续负载（分布荷载），索变形成了连续弯曲的形状。索本身的自重产生这样的悬链线，吊索可用于跨越非常大的距离。

Membranes, Tents, and Nets 膜、 帐篷、网

A membrane is a thin, flexible sheet. A common tent is made of membranes surfaces. Both simple and complex forms can be created using membranes. For surfaces of double curvature, such as a spherical surface, however, the actual surface would have to be made as an assembly of much smaller segments, since most membranes are typically available only in flat sheets. A further implication of using a flexible membrane to create the surface is that it either has to be suspended with the convex side pointing downward or, if used with the convex side pointing upward, supplemented by some mechanism to its shape. Pneumatic, or air-inflated, structures. The shape of the membrane is maintained by the internal air pressure inside the structure. Another mechanism is to apply external jacking forces that stretch the membrane into the desired shape. Various stressed-skin structures are of this general type. The need to pretension the skin, however, imposes various limitations on the shape that can be formed. Spherical surfaces, for example, are very difficult to pretension by external jacking forces, while others, such as the hyperbolic paraboloid, can be handled with comparative ease.

膜、 帐篷、网 是一个薄的膜，柔性板，一个常见的帐篷是由膜表面构成的。既简单又复杂的形式可以创建使用膜。对于双曲率，如球面的表面。但是实际的表面将要作为一个组件的更小的段，因为大多数膜通常仅适用于平板。用一柔性膜片创建表面的再一个含义是，它要么必须暂停与凸侧朝向下方，或者，如果使用凸侧朝上，通过一些机制来补充其形状。充气式膜结构的膜形状是由内部的结构的内部气压。另一种机制是应用外部抬升力，拉伸膜成所需的形状。强调皮肤的各种结构的这种通用类型，然而，需要预拉伸皮肤施加各种条件的限制，可以形成的形状。球的表面，是非常困难的外部顶力，但是其他的，如双曲抛物面可以比较容易处理。

Nets are very analogous to membrane skins. By allowing the mesh opening to vary as needed, a wide variety of surface shapes can be formed. An advantage of using crossed cables is that the positioning of the cables mitigates fluttering due to wind suctions and pressures. In addition, tension forces are typically induced into the cables by jacking devices, so that the whole surface is turned into a type of stretched skin. This also gives the roof stability and resistance to flutter.

网是非常类似的膜皮，通过使网眼根据需要进行变化，各种各样的表面形状可以形成。使用交叉索的一个优点是，使索的定位减轻由于风的吸力和压力产生的飘动。此外，张力通常诱导索顶装置，使整个表面变成一种类型的伸展。这也给了顶板稳定性和抗颤性。

1.2 2.Basic Issues in the Analysis and Design of Structures

结构分析与设计中的基本问题

1 Fundamental Structural Phenomena1. 基本结构现象

Structure components could break apart or deform badly. The forces causing overturning or collapse come from the specific environmental (e.g., wind, earthquakes, occupancies )or from

the self-weight of the form itself. These same applied loadings produce internal force in a structure that stress the material used and may cause it to fail or deform. There are several fundamental ways in which failure can occur.

结构组件可以破坏或严重变形，由力的作用造成的倾覆或来自特定的环境（例如，风，地震，占用）再或者是本身的自重的形式。这些相同的应用负荷产生的内力在一个结构中使用的材料可能会导致其变形或失败。有几个基本的方法，其中可能会发生故障。

A first set of concerns deals with the overall stability of a work. As a whole unit, a structure might overturn, slide, or twist about its base, particularly when subjected to horizontally acting wind or earthquake forces. Sliding under its own weight. Overturning or twisting need not be caused only by horizontally acting forces. A work might simply be out of balance under its own self-weight and overturning. The use of wide, rigid foundations helps prevent overturning, as does the use of special foundation elements such as piles capable of carrying tension forces.

第一组关注处理工作的整体稳定性。作为一个整体单元，结构可能会倾覆，滑移，扭转。尤其是当风或地震的水平作用时，其自身重量下滑，翻倒或扭转不只是引起水平作用力。在自身的重量和倾覆的作用下，可能只是失去了平衡。使用宽，刚性的基础，有助于防止倾覆，不使用例如能够携带张力桩的特殊要数。

A second set of concerns deals with internal, or relational, stability. If the parts of a structure are not properly arranged in space or interconnected appropriately, an entire assembly(组装)can collapse internally. Collapses of this type invariably involve large relative movements within the structure itself. Assemblies may be internally stable under one loading condition and unstable under another. Horizontally acting wind or earthquake forces, in particular, cause collapses of this kind. There are several basic mechanisms-walls, frame action, cross bracing –for making an assembly internally stable.

第二组关于处理内部关系稳定。如果有部分的结构空间组合不合理，或真个组装不合理，可以适当地相互连接，内部折叠。这种类型导致的坍塌总是涉及大型结构本身的相对运动。组件可能是一个装载条件下内部稳定和不稳定的根据项。水平因素风或地震尤其会使其坍塌。有几个基本的机制墙壁，框架动作，交叉支撑组件的内部稳定。

A third set of concerns deals with the strength and stiffness of constituent elements.There are many structure issues that revolve around the strength of component parts of a structure. These failures, which may or may not lead to total collapse, may be caused by excessive tension, compression, bending, shear, torsional, bearing forces, or deformations that are developed internally in the structure as a consequence of the applied loadings. Associated with each force state are internal stresses that actually exist within the fabric of the material itself. By carefully designing components in response to the force state present, the actual stresses developed in the components can be controlled to safe levels.

第三组的关注处理的强度和刚度的结构元素。很多结构围绕一个结构组成部分的强度问题。这些故障可能会导致全面崩溃，可能是由于过度紧张，压缩，弯曲，剪切，扭转，轴承，或变形，在结构内部开发的应用负荷的后果。每个受力状态，实际上存在于物质材料本身的内应力。通过仔细地设计组件的受力状态，开发组件的实际应力可以被控制到安全水平。

2. Structural Stability结构稳定性

A Fundamental consideration in designing a structure is that of assuring its stability under any type of possible loading condition. All structures undergo some shape changes under load.In a stable structure deformations induced by the action of the load tend to restore the structure to its

original shape after the load has been removed. In an unstable structure, the deformations induced by a load are typically massive and often tend to continue increasing as long as the load is applied. An unstable structure does not generate internal forces that tend to restore the structure to its original configuration. Unstable structures quite often collapse completely and instantaneously as a load is applied to them. It is the fundamental responsibility of the structural designer to assure that a proposed structure does indeed form a stable configuration.

设计结构的最基本需要考虑的问题，是任何类型的可能负载的条件下确保其稳定性。所有的结构进行一些稳定结构的变形引起的负载的作用下的形状变化，趋向于回访到初始形状的结构已经被删除。在不稳定的结构中，由负载引起的变形通常是大规模的，并且常常施加载荷时，只要继续增加。一个不稳定的结构不会产生内部的力量，往往恢复到原来的配置结构。经常不稳定结构完全折叠和瞬间作为负载被施加到它们身上。它的基本结构设计师的责任，以确保建议的结构确实形成一个稳定的配置。

Stability is a crucial issue in the design of structures that are assemblies of discrete elements. For example, the post-and-beam structure illustrated in figure 1.2a is apparently stable. Any horizontal force, however, tends to cause deformations of the type indicated in figure 1.2b. clearly, the structure has no capacity to resist horizontal load, nor does it have any mechanism that tends to restore it to its initial shape after the horizontal load is removed. The large changes in angle that occur between members characterize an unstable structure that is beginning to collapse. This particular structure will collapse almost instantaneously under load. Consequently, this particular pattern of members is referred to as a collapse mechanism.

稳定是一个至关重要的问题，在设计分立元件的组件结构。例如，梁柱结构示意图1.2a所示显然是稳定的。然而，在任何水平方向的力往往会造成在图1.2b的不同变形。结构清楚，有没有能力抵抗水平荷载，也没有任何机制，倾向于恢复到其初始形状，水平荷载后删除。出现大的变化角度特征不稳定的结构开始崩溃。这种特殊的结构将在负载下瞬间崩溃。因此，这个特定的图案被称为“崩溃机制”

There are really only a few fundamental ways of converting a self-standing structure of the general type shown in figure 1.2a fron an unstable to a stable configuration. These are illustarated in figure 1.2d. the first is to add a diagonal member to the structure. The structure cannot now undergo the parallelogram indicated in figure 1,2b without a dramatic release in the length of the diagonal member (this would not occur if the diagonal were adequately sized to take the forces involved). Another method used to assure stability is through shear walls. These are rigid planar surface elements that inherently resist shape changes of the type illustrated. A reinforced concrete or masonry wall can be used as a shear wall. Either a full or a partial wall can be used (the required extent of a partial wall depends on the magnitudes of the forces involved). A final method used to achieve stability is through stopping the large angular changes between members that are associated with collapse by assuring that the nature of the nature of the connections between members is such that their angular relationship remains a constant value under any loading. This is done by making a rigid joint between members. This is a very common form of joint.

真的只有一项独立的通用型数字1.2a不稳定的一个稳定的配置结构转换的一些基本方法。这些在图1.2d上。成为第一个是增加一个对角构件的结构。结构现在不能接受对角线的长度（如果对角线有足够大的力量，这种情况不会发生）没有一个戏剧性的释放b图1,2所示的平行四边形。用来保证稳定性的另一种方法是通过剪力墙。这些平面的表面是刚性的元素本质上所示类型的抗蚀剂形状的变化。可用于钢筋混凝土或砖石墙作为剪力墙。完整或部分的壁可用于（部分壁所需的程度上依赖于所涉及的力的大小）。用于实现稳定的最后一

种方法是通过停止大角度变化，确保结构之间的连接的性质就是这样原理的性质，它们的角的关系仍然是一个恒定值。这是通过成员之间的刚性连接，是一个非常普遍的形式的联合。

There are, of course, variants on these basic methods of assuring stability. Still most structures composed of discrete elements rely on one or the other of these basic approaches for stability. More than one approach can be used in a structure (e.g. a structure having both rigid joints and a diagonal), but a measure of redundancy is obviously involved.

当然，在这些基本的方法保证稳定的变体。仍然由分立元件组成的结构依赖于一个或另一个稳定这两种基本方法。在一个结构中，可以使用一个以上的方法（例如，具有两个刚性接头和对角线结构），但显然这涉及一定程度的冗余。

静定和超静定结构

1.2Determinate and Indeterminate Structures静定与超静定结构

1.2.1 Statically Determinate Structures超静定结构

Structures are said to be statically determinate when the forces and reactions produced by a given loading can be calculated using only the equations of equilibrium. The simply supported beam shown in Figure 1.3 is statically determinate. We can solve for the three unknown reactions using the equations of equilibrium and then calculate the internal forces such as bending moment, shear force, and axial force at any given location along the length of the beam.

结构被称为静定时的力和反应的一个给定的荷载产生可以只使用平衡方程计算。简支梁在图1.3所示是静定。我们可以解决三未知的反应，利用平衡方程，然后计算等内力弯矩，剪切力，和在任何给定的位置沿梁的长度的轴向力。

1.2.3 Force Method 力法

The force method (also called the flexibility method) is used to calculate internal forces and reactions in statically indeterminate structures due to loads and imposed deformations. 力法（又称弹性法）是用来计算内力和反应静不定结构因荷载和施加变形。

在力法的步骤

The steps in the force method在力法的步骤

（1）Determine the degree of statical indeterminacy of the structure. Parameter n will be used to denote the degree of indeterminacy.

（1）确定静不定结构的程度。参数n可以用来表示不确定性的程度。

(2) Transform the structure into a statically determinate system by releasing a number of statical constraints equal to the degree of statical indeterminacy,n. This is accomplished by

releasing external support conditions

creating internal hinges.

The system thus formed is called the primary system. Number the released constraints from 1 to n.

（2）通过释放一些静态约束等于静不定度的结构转化为静定系统，这是通过

释放外部支持条件，创建内部铰链。由此形成的系统称为原发性系统。编号从1到N的释放的约束

（3）For a given released constraint j, introduce an unknown redundant force Xj corresponding to the type and direction of the released constraint.

（3）基本体系沿多余未知力方向的位移应与原结构位移相同

（4）Apply the given loading or imposed deformation to the primary system. Calculate displacements due to the given loading at each of the released constraints in the primary system. These displacements are called Δ1P , Δ2P , ΔnP .., .

（4）将给定的加载或主系统的附加变形。计算的位移由于在原系统在每个发布约束给定载荷。这些位移被称为Δ1P，2PΔ，ΔNP ..，

（5）For a given released constraint j, apply a unit load Xj =1 to the primary system. Calculate displacements due to Xj =1 at each of the released constraints in the primary system. These displacements are called

（5）对于一个给定的发布约束J，申请单位负载XJ = 1到主系统。计算的位移由于XJ = 1在每个释放的约束在主系统。这些位移被称为，，

(6)Solve for redundant forces X1 through Xn by imposing the compatibility conditions of the original structure.These conditions transform the primary system back to the original structure by finding the combination of redundant forces that make displacement at each of the released constraints equal to zero.The conditions are expressed mathematically as follow

This is a system of n linear equations in n unknows,The displacements arw all know.The unknow forces are Xj.It can thus be seen that the name of force method was given to this method because its primary computational task is to calculate unknown forces,i.e.,the redundant forces X1 through Xn.

（6）解决多余力X1到XN利用原结构的相容性条件。这些条件将原系统回到原来的结构的发现使位移在每个发布约束等于零冗余力量的结合。条件的数学表达如下

这是一个N未知数的线性方程系统，位移ARW都知道。未知的力量是XJ。由此可以看出，力方法的名称分配给该方法由于其计算的基本任务是计算未知的力量，即，多余的力X1到Xn。

(7)Calculate force S at a given location in the structure using the following combination

where quantities Xj have been calculated from the n by n system of equations given in Step6,S0 is the force due to the given load or imposed deformation in the primary system,and X0 is the force due to Xj applied to the primary system.Force S can be bending moment,shear,axial force,or reaction.

（7）计算力的结构中在某一位置使用下列组合

在大量XJ已经从n的n系统方程计算了六，S0力是由于负载或施加的变形的主要系统，和x0是力由于XJ施加到主系统。力的可弯曲，剪切，轴向力，或反应。

1.2.4The classical Displacement Method 经典的位移的方法

The force method is a method for calculating the response of statically indeterminate strures by which the unknows are force quantities(the redundant force X1,X2...,Xn)and the equations used to solve for the unknows are based on geometrical conditions (compatibility conditions at the location of each redundant force).It is possible to consider an analogous method for calculating the response of statically indeterminate structures in which the unknowns are displacement quantities and the equations use to solve for the unknowns are based on statical conditions (equilibrium conditions).

力法是一种计算响应静不定结构的未知力量（多余力的X1，X2……，xn）和方程来求解未知量是基于几何条件（在每一个多余的力的位置的相容性条件）。可以考虑类似的方法计算响应的静不定结构的未知位移量和方程求解的未知数是使用基于静态条件下（平衡条件）。 the method is referred to as the classical displacement method.It is helpful to outline the major elements of the method.It is assumed that the joints of the structure do not undergo translational displacement.

该方法被称为传统的位移法。它有助于轮廓的方法的主要元素。它是假定的结构节点不发生平动位移。

(1)For a given structure and loading,consider the joints to be fully fixed against rotation

（1）对于一个给定的结构和加载，考虑关节得到充分固定在旋转

(2)Calculate the moments in each member of the structure due to the given loads,assuming full fixity at joints.These moments are called fixed-end moments.

（2）计算结构的每一成员由于负载的时刻，假设固定节点。这些时刻被称为固定端弯矩。

(3)Calculate the moments iat the ends of each member due to unit displacements of the joints.

（3）计算时刻的IAT的每一个成员由于接头的两端单元位移。

（4）Express the total moment at each end of a given member as the sum of the fixed-end moments and the product of unknown joint displacements times the moments produced by unit joint displacements calculated in Step 3.

（4）表示的总的时刻在一给定成员每一端为固定端的时刻和未知节点位移时间单元节点位移在步骤3中计算产生的矩的乘积的总和。

(5) Generate an equation of moment equilibrium at each joint.

（5）产生在各关节的力矩平衡方程。

(6) Solve the system of equations for the unknown joint displacements.

（6）求解未知节点位移方程组。

(7) Calculate the member end moments using the expressions derived in Step 4 and the values of joint displacements calculated in Step 6.

（7）使用在步骤4中得到表达和节点位移在步骤6中计算值的构件端弯矩计算。

（8）Calculate all remaining forces in the structure (shear forces and axial forces).

（8）计算结构中的所有剩余的部队（剪力和轴力）。

Force method can solve all statically indeterminate structures. computational complexity prohibitive for structures with more than three unknown forces.

力的方法可以解决所有的静不定结构，计算的复杂性，高昂的结构与三多个未知的力量。

Classical displacement method allows a solution based on a member-by-member procedure, rather than one that requires consideration of the structure as a whole;

based on the pre-solution of standard cases of intermediate 媒介物 load and displacement reduce the number of unknowns in a given solution.

传统的位移法允许基于构件的构件程序的解决方案，而不是一个需要考虑的结构作为一个整体；基于中间媒介物载荷与位移的标准的情况下，预解在一个给定的溶液减少未知数的个数 。

1.2.5Moment Distribution Method 力矩分配法

The moment distribution method is used for statically indeterminate beams and frames by simple hand calculations. This is basically an iterative (迭代的) process. The procedure involves artificially restraining temporarily all the joints against rotation and writing down the fixed end moments for all the members. The joints are then released one by one in succession 连续. At each released joint the unbalanced moments are distributed to all the ends of the members meeting at that joint.

力矩分配法用于静不定梁和框架通过简单的手工计算。这基本上是一个迭代过程（迭代的）。该过程涉及人为地抑制暂时所有接头和旋转的固定端的时刻写下所有的成员。接头然后释放一个个相继连续。 在每个节点不平衡弯矩释放在联合分布于会员大会结束一切。

A certain fraction of these distributed moments are carried over to the far ends of members. The released joint is again restrained temporarily before proceeding to the next joint. The same set of operations are carried out at each joint till all the joints are completed. This completes one cycle of operations. The process is repeated a number of times or cycles till the values obtained are within the desired accuracy.

一定比例的这些分布的矩进行了构件的远端。释放接头又得到了暂时的抑制后再进行下一节。一组相同的操作在每个节点到所有节点进行完成。这就完成了一个周期的操作。这个过程是重复的次数或周期直到得到的值是在所需的精度。

Figure 1.5 indicates a basic problem of moment distribution.The question is,given a unit moment applied to jointA,what moments are produced in each of the members.One way to proceed is to solve the problem for a unit joint rotation andthen scale the resulting solution for a unit moment.For a unit rotation the moment in each member at joint A is just its stiffness kI=(4EI/L)i.The(1.2.3公式) which is called the joint stiffness.For anapplied unit moment this solution scales so that the moment in each meber at joint A is(1.2.4公式) this is called the distribution factor of member i at join A . That is member distribution factor=member stiffness/joint stiffness

图1.5显示的弯矩分布的一个基本问题。问题是，给定一个适用于节点及单元的时刻，什么时刻都在每一成员的产生。的方式来进行，以解决单位共同旋转而产生的解决方案规模单位的时刻的问题。对一个单位在每个旋转力矩会员在关节是其刚度ki＝（4ei／L）——（1.2.3公式），称为关节僵硬。因为从单元转动这个解决方案的尺度，每个成员在关节力矩（1.2.4公式）这就是所谓的分布因子的成员在加入我。这是成员的分配系数=构件刚度/关节僵硬

The problem inFigure 1.6 can be solved.First, the center joint is fixed (the rotation is set to zero ) which gives the so- called fixed-end moment solution for beam on the right and no response in the beam on the left.This solution is valid except that it requires an external moment to be applied to the center joint.the final solution is constructed by releasing or balancing the center joint which is equivalent to applying a clockwsie moment of wl2/12 to this joint.Using the idea of

distribution and carry over,the solution is completed in this figure.Note that the sign convention used implies that a counter-clocwise moment on the end of a member is positive.Care must then be exercised in drawing the final moment diagram which uses a different a different sign covention.

图1.6的问题是可以解决的。第一，中心节点是固定的（旋转设置为零），梁的右侧和左侧梁没有反应了，所谓的固定端弯矩的解决方案。该方案是有效的，它除了需要应用于中心joint.the最终解的外部力矩是通过释放或平衡中心联合相当于应用wl2 / 12 clockwsie时刻本联合建造。使用分布式的思想和携带，解决的办法是在图中完成。注意，使用的符号规定意味着在一个部件的端clocwise时刻计数器是积极的。然后，必须使用不同的符号绘制不同的最后一刻图执行公约。

1.3Structural Dynamics 结构动力学;

1.3.1Equations of Motion for Linear Single-Degree-of –Freedom 运动方程的线性单自由度

The essential physical properties of a linearly elastic structural system subjected to external dynamic loading are its mass,stiffness properties,and energy absorption capability or damping.The principle of dynamic analysis may be illustrated by cinsidering a simple single-storey structure as shown in Figure1.7.The structure is subjected to a time-varying force f(t).k is the spring cinstant that relates the lateral storey deflection x to the storey shear force,and he dash pot relates the damping force to the velocity by a damping coefficient c.If the mass,m,is assumed to concentrate at the beam,the structure becomes a single-degree-of -freedom (SDOF)system.The equation of motion of the system may be written as(1.3.1公式).

一个线性弹性结构体系进行了外部动力荷载的基本物理特性是它的质量，刚度，和能量吸收能力或阻尼。动态分析的原理，可以通过一个简单的单层结构，考虑在figure1.7.the结构显示了受到时变力F（t）。K是弹簧常数，涉及横向偏转X层的层高的剪切力，和他锅涉及阻尼力速度的阻尼系数C。如果质量，m，是假设集中在梁，结构成为一个单自由度（SDOF）系统的运动方程可系统。被写为（1.3.1公式）。

If a stucture is subjected to a sinusoidal motion such as a ground acceleration of xg=fsinwft,it will oscillate and after some time the motion of the structure will reach a steady state,For example,the equation of motion due to the ground acceleration(1.3.2公式)where 2sw=c/m and w2=k/m,w is the resonate natural frequency of the system.

如果一个结构进行正弦运动如XG = fsinwft地面加速度，它将振荡，经过一段时间的结构的运动会达到一个稳定的状态，例如，由于地面加速度的运动方程（1.3.2公式）在2SW = C / M和W2 = K /M，W是共振系统的自然频率。

The solution to the above equation consists of two parts,the general solution and the particular solution,If the system is damped,oscillation corresponding to the general solution will decay with time,After some time,the motion will reach a steady state and the system will vibrate at a constant amplitude and frequency.This motion,which is called forced vibration,is described by the particular solution expressed as(1.3.3公式).Substituting Equation (1.3.3)into Equation (1.3.2),the displacement amplitude can be shown to be (1.3.4公式).

上述方程的解由两部分组成，一般的解决方案和特定的解决方案，如果系统的阻尼，以一般的解决方案对应的振荡会随时间衰减，一段时间后，运动会达到一个稳定状态，系统将在一个恒定的振幅和振动频率。这种运动，这是所谓的强迫振动，被表示为特定的解决方案描述（1.3.3公式）。代入方程（1.3.3）为方程（1.3.2），位移幅值可以是（1.3.4公式）。

When the dynamic force is applied at a frequency much lower than the natural frequency of the system(wf/w<<1),the response is quasi-static.The response is proportional to the stiffness of the structure,and the displacement amplitude is close to the static deflection.

当动态力施加在频率比系统的自然频率低得多（工作流/ w＜＜1），反应quasi-static.the响应对结构的刚度成正比，与位移幅值接近静挠度。

When the force is applied at a frequency much higher than the natural frequency(wf/w)>>1),the response is proportional to the mass of the structure.

当力施加在频率比自然频率高得多（工作流/ W）> > 1），响应于结构的质量成正比。 When the force is applied at a frequency close to the natural frequency,the displacement amplitude increases significantly.The condition at which wf/w=1 is known as resonance.

当力被施加在一个频率接近的固有频率，位移幅值明显增加。在该条件下工作流/ W = 1被称为共振。

1.3.2 Equations of Motion for Linear Multiple-Degree-of-Freedom Systems对于线性多自由度系统的运动方程

In multiple degree systems,an independent differential equation of motion can be written for each degree of freedom.The nadal equations of a multiple degree system consisting of n degrees of freedom may be written as(1.3.5公式)where [m] is a symmetrical n*n matrix of mass,[c] is a symmetrical n*n matrix of damping coefficient,and {F(t)} is the force vector which is zero in the case of free vibration.

在多自由度系统，一个独立的运动微分方程可以为每个自由度写的。纳达尔方程的多自由度系统组成的n个自由度的可写为（1.3.5公式）在[ M ]是一个对称的n×n矩阵的质量，[C]是对称的N * n矩阵，阻尼系数，和{F（t）}力矢量是零的情况下自由振动。

Consider a system under free vibration without damping.The general solution of Equation(1.3.5) is assumed in the form of(1.3.6) where angular frequency w and phase angle o are common to all x' s.In this assumed solution,o and c1,c2,...,cn are the constants to be determined from the initial boundary conditions of the motion and w is a characteristic value (eigenvalue) of the system.

考虑下一个无阻尼系统的自由振动方程的一般解。（1.3.5）的形式是在假定（最佳），角频率和相位角O是所有X的。常见的这种假设解，O和C1，C2，……，CN是从运动和W初始边界条件确定的常数是一个特征值（特征值）的系统。

Substituting Equation (1.3.6) into Equation (1.3.5) yields (1.3.7公式) where [k] and [m] are the n*n matrices,w2 is scalar,and {c} is the amplitude vector.For nontrivial solutions, solution to Equation (1.3.7) requires the determinant of {[k]-w2[m]}*{c}={0}.The expansion of the determinant yields a polynomial of n degree as a function of w2,the n roots of which are the eigenvalues w1,w2,Wn.

（1.3.6）式代入公式（1.3.5）产量（1.3.7公式）其中[K]和[]是n * n的矩阵，W2是标量，{C }是振幅矢量。对于非平凡解，解决方程（1.3.7）要求的行列式{[K]-W2[M]} *{C}={0}。行列式的扩展产生一个n次多项式为W2的功能，其中N根的特征值W1，W2，Wn。 The resulting motion is a sum of n harmonic motions,each governed by the respective natural frequency w,written as (1.3.8公式).

由此产生的运动是一个总和的n次简谐运动，有各自的自然频率w，写成（1.3.8公式）。

2.1 Structural Material结构材料;

2.1.1 Materials for Concrete and Mix Proportions 混凝土材料及配比

Concrete is a mixture of aggregate，and often controlled amounts of entrained air,held together by a hardened paste made from cement and water.Although there are other kinds of cement，the word cement in common usage refers to as portland cement. A chemical reaction between the portland cement and water causes concrete to harden to a stone-like condition. This reaction is called hydration. Hydration gives off heat，known as the heat of hydration.Because hydration hardens concrete，freshly placed concrete submerged underwater will harden. When correctly proportioned，fresh concrete can be molded into nearly any size or shape. Upon hydration of the cement by- the water,concrete becomes stone-like in strength，durability, and hardness.

混凝土骨料的混合物，通常控制的夹带的空气的量，通过硬化浆体由水泥和水一起举行。虽然还有其他种类的水泥，在常见的词，指的是波特兰水泥的水泥。波特兰水泥和水之间的化学反应引起混凝土硬化的一块石头像条件。这个反应称为水化。水化发热，称为水化热。由于水化硬化混凝土，新浇混凝土水下会变硬。当比例正确，新鲜混凝土可以被塑造成几乎任何尺寸或形状。对水泥水化的水，石混凝土成为像强度，耐久性，和硬度。

Portland cement. 波特兰水泥。

Portland cement is the most commonly used modern

hydraulic cement. In this case，the word hydraulic is the cement's characteristic

of holding aggregate together by using water or other low-viscosity fluids.

Portland cement is a carefully proportioned and specially processed chemical

combination of lime，silica，iron oxide，and alumina.

波特兰水泥是最常用的现代液压水泥。在这种情况下,这个词是水泥的特点的液压聚集在

一起的控股通过使用水或其他低粘度液体。波特兰水泥是一种精心相称,专门加工化学结合石灰、硅、铁氧化物、氧化铝。

Water. 水。

Unless test or experience indicates that a particular water source is

satisfactory，water should be free from acids, alkalis，oils, and organic

impurities.

除非试验或经验表明一个特定的水源是令人满意的,水应该是免费的从酸、碱、油类、有机杂质。

Aggregate. 骨料。

Inert filler materials(usually sand and stone or gravel) make up between 60 and 80 percent of the volume of normal concrete. Aggregate is often washed when impurities are found that can retard cement hydration or deteriorate the concrete's quality. All aggregate is screened to ensure proper size gradation，because concrete differs from other cement-water-aggregate mixtures in the size of its Aggregate, 'the aggregate' s physical and chemical properies alse affect concrete properties aggregate size, shape, and grade influence the amount of water required. For example limestone aggregate requires more water than marble aggregate of similar size. Aggregate surface texture influences the hond between the aggregate and the cement paste. In properly mixed concrete ,the paste surrounds each aggregate particle and fills all spaces between the particles The elastic properties of the aggregate influence the elastic properties of the concrete and the paste’s resistance to shrinkage. Reactions between the cement paste and the aggregate can either improve or harm the bond between the two consequently，the concrete's quality

惰性填料材料(通常是沙子和石头或砾石)组成60 ~ 80%的普通混凝土的体积。聚合通常是当杂质洗发现可以延缓水泥水化或恶化

混凝土的质量。所有骨料是筛选以确保适当的大小分级,因为混凝土不同于其他水泥水骨料混合物在大小它的骨料,骨料的物理和化学性能也将影响具体的属性集料尺寸,形状,和年级影响数量的水要求。例如石灰石骨料要求更多的水比大理石骨料大小相近的。骨料表面纹理影响本田

在聚合和水泥膏。在正确地拌混凝土,围绕每个骨料颗粒和粘贴填充粒子之间的所有空间弹性性能的总体影响的弹性性能混凝土和膏的抗收缩。反应之间的水泥粘贴和骨料可以改善或伤害他们的关系

因此,混凝土的质量

Admixtures. 外加剂。

Admixtures are added to the concrete mixture to accelerate or retard the initial set， improve workability, reduce water requirements, increase strength，improve durability，decrease permeability, and impart other properties.They usually cause a chemical reaction within the concrete.Admixtures admixtures are normally classified into accelerating admixture，set-retarding admixtures ，air-entraining ,pigments，agents，plasticizers，fly ash，silica fume，color pigments, and miscellaneous materials. Many admixtures fall into more than one classification.

外加剂的加入加速或延缓的初始设置，混凝土拌合物改善和易性，减少水的要求，增加强度，提高耐久性，降低渗透率，并赋予其它特性。他们通常会产生化学反应，在混凝土外加剂。外加剂通常分为速凝剂，缓凝外加剂，引气，颜料，剂，增塑剂，粉煤灰，硅粉，色素，杂项材料。许多外加剂陷入一个以上的分类。

2.1.2 desirable concrete property理想的混凝土的性能

1. Plastic Concrete 塑性混凝土

Plastic Concrete is a concrete in a relatively fluid state that is readily molded by hand，like a lump of modeling clay. A plastic mix keeps all the grains of sand and the pieces of gravel or stone encased and held in place. The degree of plasticity influences the quality and character of the finished product.

塑性混凝土是混凝土在相对流体状态，易于成型用手，像一块橡皮泥。塑料混合使砂的谷物 和碎石或石包裹和地点举行的程度.可塑性影响质量和成品的品质。

The workability of a concrete mix gives a measure of the ease with which fresh concrete can be placed and compacted. The concrete should flow reading into the form and go around and

cover the reinforcement ,the mix should retain , its consistency and the aggregates should not segregate.A mix with hig workability is needed where sections are thin and/or reinforcement is complicated and congested.

混凝土混合物的加工性的容易性給出了一個衡量可以放置新鮮混凝土和壓實。混凝土流量讀數進入的形式和去走一走，覆蓋加固，組合應保留，它的一致性和總量不應segregate.A混合HIG加工性是必要的，其中部分是薄的和/或複雜的加固和擁擠。

The main factor affecting workability is the water content of the mix. Plasticizer will increase workability The size of aggregate, its grading and shape, the ratio of coarse to fine aggregate and the aggregate-to-cement ratio also affect workability to some degree.

影響加工性的主要因素是混合的水含量。增塑劑總大小將增加可操作性，其分級

形狀，粗到細集料和水泥的總比的比例也在一定程度上影響可操作性。

Hardened concrete is the end product of any concrete design.the essential

properties thati it must have are strength,durability ,and watertinghtness

硬化混凝土的任何具体的设计必不可少的最终产品，它必須是強度，耐用性和水密性 Strength. 强度。

the concrcte's ability io resist a load in compression, flexure or shear is a measure of its strength. Concrete strength is largely determined by the ratio of water to cement in the mixture and curing condition.

混凝土的抗压缩能力IO负载，弯曲或剪切是衡量其强度。混凝土的强度在很大程度上取决于水在混合水泥的配比和固化条件。

Durability. 耐久性。

Climate and weather affect durability . thus , the concrete's abilities to resist the effects of wind, frost ,snow,ice,abrasion,and the chemical reaction of soils or salts are a measure of its durability. as the water to cement ratio increases，durability decreases correspondingly

气候和天气影响耐久性。因此，本混凝土的抗风，霜，雪，冰，磨损的影响，和

土壤或盐的化学反应是衡量其耐久性。当水灰比的增大，耐久性降低相应

Durability should be a strong consideration for concrete structures expected to last longer than five years. Air-entrained concrete has improved freeze-that durability

耐久性应是一个重要的考虑混凝土结构的预期持续超过五年。加气混凝土提高了冻结耐久性 Watertightness. 水密性。

Tests show that the watertightness of a cement paste depends on the water to cement ratio and the extent of the chemical-reaction process between the cement and water. The watertightness of air-entrained concrete is superior to that of nonair-entrained concrete. 測試表明，水泥的防水貼取決於水與水泥之比和化學反應的程度之間的水泥和水的過程。空氣夾帶的水密性混凝土優越的夾帶nonair的混凝土。

The strength and deformation characteristics of concrete thus depend on the grade and type of cement，aggregates，admixtures，water to cement ratio, environmental conditions and curing. Plain concrete after preparation and placement needs curing to attain strength. The increase of strength with its age during curing is considered to be marginal after 28 days.

因此，混凝土的強度和變形特性取決於等級和種類的水泥，骨料，外加劑，水與水泥之比，環境條件和固化。普通混凝土製備後安置需要固化達到強度。強度的增加，其年齡 在固化過程中被認為是邊緣28天后。

Plain concrete is very good in compression but weak in tension. That is why steel is used as reinforcing material to make the composite sustainable in tension also.Plain concrete，thus when reinforced with steel bars in appropriate locations is known as reih forced concrete.

普通混凝土是很好的壓縮，但緊張弱。因此鋼被用作增強材料，以在拉伸的複合可持續也。普通混凝土，因此，當收服被迫與適當的鋼筋位置被稱為遏制強制式混凝土。

2.1.3 proportioning concrete mixtures配比混凝土混合物

the various components of a mix are proportioned so that the resulting concrete has adequate strength，proper workability for placing, and low cost. The third calls for use of the minimum amount of cement that will achieve adequate properties.

各个组成部分的混合比例是使所产生的混凝土具有足够的强度，适当可行放置，且成本低。使用的最小水泥用量，将获得足够的性能。

The two primary methods used to proportion a mix design are the trial-batch method and the

absolute-volume method. Proportions of ingredients for concrete should be selected to make the most economical use of available materials that will produce concrete of the required workability, durability, and strength basic relationships already established and the laboratory tests provide guidance for optimum combinations, Recommended and typical mixes of concrete for various types or classes of work will detcermine how to proprtion concrete mix, factors affecting this include: (l) water to cement ratio, (2) type andd size of aggregate (3) air or nonair-entrained concrete, and (4) slump of the mix.

比例混合设计使用的两种主要方法是审批方法和绝对体积法。混凝土的配料比例应选择使现有材料的最经济的使用将生产所需的加工性，耐久性混凝土，强度基本已经建立的关系与实验指导最佳组合，推荐和各种具体的典型的混合工作类型或类将detcermine如何比混凝土配合比，因素影响包括：（1）的水灰比，（2）骨料的类型和大小（3）或空气夹带和nonair混凝土，（4）混合料的坍落度。

The water to cement ratio is determined by the strength, durability,and

watertightness requirements of the hardened concrete. Strength, durability and watertightness are usually specified by the structural-design engineer, but a tentative mix proportion can be determined from knowledge of a prior job 。Always remember that a change in the water to cement ratio changes the characteristics of the hardened concrete. In addition to the water required for hydartion, water is needed for wetting the surface of the aggregate. As water is added, the plasticity and the fluidity of the mix increase (i. e. , its workability improves), but the strength decreases because of the larger volume of voids created by the free water.

水灰比的确定的强度，耐久性，和硬化的混凝土的水密性要求。强度，耐久性，水密性通常是由结构设计工程师指定，但初步配合比可以从现有的工作知识确定永远记住，在换水灰比的变化硬化的混凝土的特性。此外，所需的hydartion，水是需要的润湿表面的总和。由于水增加，塑性和混合增加流动性（即，其和易性提高），但强度下降，因为空隙体积较大所产生的游离水。

The better the gradation of the aggregate, i. e. the smaller of the volume of voids, the less cement paste is needed to fill these voids. Fine aggregates are used to fill the spaces between the coarse aggregate particles and to increase the workability of the mix. Aggregate that does not have a large grading gap nor an excess of any size gives a smooth grading curve produces the best mix.

骨料的级配越好，即体积更小空隙，减少水泥浆体需要填补这些空隙。细骨料的使用填充粗集料颗粒之间的空间和增加组合的加工性。总没有一个大的等级差距也不是超出尺寸提供一个平滑的级配曲线产生最好的组合。

The maximum size of coarse aggregate that produces concrete of maxi strength for a given cement content depends upon the aggregate source as well as the aggregate shape and grading; thus, in most cases, a decrease will take place in the overall cost. The larger the maximum size of the coarse aggregate, the less paste (Water, cement and usually entrained air) that is required for a given concrete quality. The maximum size of aggregate should not exceed one-fifth the minimum dimension of the member or three-fourths the space between reinforcing bars. For pavement or floor slabs, the maximum Size of aggregate should not exceed one-third the slab thickness

粗骨料产生的对于一个给定的水泥含量最大强度混凝土的最大大小取决于骨料来源以及骨料形状和分级；因此，在大多数情况下，减少将在总成本。较大的粗骨料的最大尺寸，不酱（水，水泥和通常夹带的空气），对于一个给定的混凝土质量要求。骨料的最大尺寸不超过五分之一的最小尺寸的成员或四分之三钢筋之间的空间。路面或水泥板，骨料的最大尺寸不应超过三分之一的板坯厚度

1.3 Structural Dynamics 结构动力学

Chapter 2. Structural Material 土木工程材料

2.1 Materials for Concrete and Mix Proportion 砼材料及配比

2.2 Properties of Concrete 砼的性能

2.2.1 compressive strength 抗压强度

1. cube compressive strength 立方体抗压强度

the cube compressive strength of the concrete,f,is given in terms of the characteristic compressive strength of 150mm size cubes tested at 28 days. Figure 2.1shows an idealized normal distribution of the values of compressive strength for a sizeable number of test cubes. （第一题答案大概在这）The horizontal axis represents the values of compressive strength. This is also termed as frequency. The average of the values of compressive strength(mean strength)is represented as f. the characteristic strength is defined as the strength of the concrete below which not more than 5% of the test results are expected to fall. The value of the normal distribution.第二题答案大概在这)

立方体抗压强度的混凝土，楼给出为150mm的尺寸在28天测试的多维数据集的特征抗压强度。图2.1显示了一个理想化的常态分布相当数量的立方体试块的抗压强度值。横轴表示抗压强度的值。这也被称为频率。抗压强度的值的平均值（平均强度）表示为f。特征强度被定义为混凝土的强度不超过5％的测试结果低于该预计将下降。常态分布的值。 Concrete is graded on the basis of its characteristic compressive strength and expressed in MPa. The grades are designated by one letter C and a number from 15 to 18 indicating the characteristic strength may be different in different countries.

混凝土的基础上，其特征抗压强度分级，以MPa表示。成绩指定一个字母“C”和一个数字从15到18，表明特征强度可能在不同的国家是不同的。

2. prismatic compressive strength棱柱抗压强度

the prismatic compressive strength of concrete is close to the axial compressive strength of concrete in column. Prismatic specimens with a height-to-width aspect ratio of 3 to 4 are adopted. 的棱柱形的混凝土的抗压强度是混凝土柱的轴心抗压强度。的高度与宽度的纵横比为3?4的棱柱形样品通过。

2.2.2 tensile strength 抗拉强度

the tensile strength of concrete can be expressed as follows;

混凝土的拉伸强度可以表示如下;

1 .axial tensile strength 轴向抗拉强度

it is measured by testing prismatic specimens under direct tension .there are considerable difficulties in determining the true tensile strength of concrete . minor misalignment and stress concentration in the graping devices are apt to mar the result.

它是测量，由测试棱柱标本的直接拉伸下，有相当大的困难，确定真正的混凝土抗拉强度。轻微的未对准和应力集中在graping装置容易擦伤的结果。

The following expression gives an extimation of axial tensile strength of concrete from its characteristic cube compressive strength.

下面的表达式给出其特征立方体抗压强度混凝土轴向拉伸强度的DOA估计。

2.splitting tensile strength劈裂抗拉强度

the result of split-cube test is a measure of the tensile strength of concrete ,a 150mm

concrete cube, the same as the one used for cube compressive test ,is inserted in a compression testing machine. Pads are inserted between the compression platens of the machine and the cube to equalize and distribute the pressure. It can be shown that in an elastic cube so loaded, a nearly uniform tensile stress of magnitude f=2p/ exists at the right angle to the plane of loading application, correspondingly, such cube, when tested, splits into two halves along that plane, at a stress f that can be computed from the equation f ,where P is the applied compressive load at failure,and a is the length of cube.（第四题答案大约这）

劈裂抗拉强度分割多维数据集测试的结果是一定程度的混凝土的拉伸强度，150毫米 混凝土立方体，立方体抗压强度试验使用了一个相同，被插入在压缩试验机。垫之间插入机器的压盘和多维数据集的压力平衡和分发。可以证明，在一个弹性的多维数据集以便加载，F =2π/在合适的角度的平面的加载应用程序存在，相应地，这样的多维数据集，在测试时，

被分为两半沿该平面几乎均匀的拉伸应力级，在应力f以从方程f，可以计算，其中P是破坏时所施加的压缩载荷，a为立方体的长度。

2.2.3the modulus of elasticity弹性模量

the modulus of elasticity is determined from a low cycle loading test of prismatic specimen. The loading is limited to a maximum value of 0.5f. the loading-unloading cycle is repeated 5 to 10 times.

弹性模量来确定从一个低的棱柱形试样的循环载荷试验。装载被限制到最大值为0.5F。装载 - 卸载循环反复进行5?10次。

The modulus of elasticity obtained from low cycle loading test is given by the following equation（第三题大概在这）

低循环载荷试验从得到的弹性模量是由下面的公式给出

2.2.4 shrinkage of concrete混凝土收缩

any workable concrete mix contains more water than is needed for hydration. If the concrete is exposed to air , the large part of this free water evaporates in time , the rate and completeness of drying depending on ambient temperature and humidity conditions. As the concrete dries, it shrinks in volume, probably due to the capillary tension that develops in the water remaining in the concrete. Conversely, if dry concrete is immersed in water, it expands, regaining much of the volume loss from prior shrinkage. Shrinkage, which continues at a decreasing rate for several months, depending on the configuration of the member, is a detrimental property of concrete in several respects. When not adequately controlled, it will cause unsightly and deleterious cracks, as in slabs, walls, etc. in structures that are statically indeterminate(and most concrete structures are), it can cause large and harmful stresses. In prestressed concrete it leads to partial loss of initial prestress. For these reasons, it is essential that shrinkage be minimized and controlled.

任何可行的混凝土配合比中含有较多的水比需要水化。如果混凝土暴露于空气中，这个自由水分蒸发时间的很大一部分，取决于环境温度和湿度条件下的干燥速率和完整性。作为具体的干燥，但在体积收缩，可能是由于在剩余的水在混凝土中的毛细管张力，开发。相反，如果在水浸泡干燥混凝土，膨胀，重新获得与前收缩的体积损失。收缩率，持续数个月的下降速度，根据配置的部件，是在以下几个方面的混凝土产生有害的属性。当没有足够的控制，它会造成难看的和有害的裂缝，如地砖，墙面，超静定结构中（和最混凝土结构）等，它可能会导致大的和有害的应力。预应力混凝土初始预应力部分损失。由于这些原因，至关重要的是，最小化和控制收缩。

1. effect of cement and water contents on shrinkage

水泥和水的含量对收缩率的影响

water content is probably the largest single factor influencing the shrinkage of paste and concrete. Typical shrinkage values for concrete specimens with a 5 to 1 aggregate-cement ratio are 0.04, 0.06, 0.075 and 0.085 percent for water-cement ratios of 0.4,0.5,0.6 and 0.7, respectively. One of the reason is that the density and composition of calcium silicate formed at different water-cement ratios may be slightly different. In general, a higher cement content increases the shrinkage of concrete; the relative shrinkages of neat paste, mortar and concrete may be of the order of about 5,2 and 1.

含水量可能是最大的单一因素影响浆和混凝土的收缩。 5合1水灰比混凝土试件典型的收缩值是0.04，0.06，0.075％和0.085％的水胶比为0.4,0.5,0.6和0.7，分别。的原因之一是，形成在不同的水与水泥比硅酸钙的密度和成分可能会略有不同。一般情况下，较高的水泥含量，增加混凝土的收缩，相对整齐的泥浆，砂浆和混凝土的收缩可能是5,2和1的顺序。

Fineness of cement seems to be a factor in shrinkage and particles coarse than No.200 sieve, which react with water very slowly, have a restraining effect similar to that of aggregate. Thus, high-early-strength cement, which is finely ground, shrinks about 10 percent more than normal cement. Low-heat and Portland-pozzolan cements shrink a further 20 and 35 percent, respectively. This is believed to be caused by larger quantities of calcium silicate, the shrinking component, present in them.

水泥细度，似乎是一个因素，在收缩率和粗颗粒比200号筛，与水发生反应很慢，有抑制效果，类似的集料。因此，高早强水泥，细磨，收缩约10％，比常规的水泥。低热量和波特

兰火山灰水泥进一步缩小20％和35％，分别。这被认为是由于较大数量的硅酸钙，收缩组件，呈现在其中。

2.type and gradation of aggregate集料的类型和层次

As stated previously ,the drying shrinkage of concrete is a fraction of that of neat cement because the aggregate particles not only dilute the paste but also reinforce it against contraction. It has been shown that when readily compressible aggregate is used, concrete will shink as much as neat cement, and that expanded shale leads to shrinkage one-third more than that of ordinary aggregate. Steel aggregate on the other hand,leads to shrinkage one-third less than that of ordinary concrete. In general terms the elastic properties of aggregate determine the degree of restraint offered. The size and grading of aggregate do not, by themselves, influence the magnitude of shrinkage, but an aggregate incorporating larger sizes permints the use of a mix with less cement and hence a lower shrinkage. Increasing the maximum aggregate size and thereby the aggregate content by 20 percent of the total volume of the concrete will ensure a substantial decrease in shrinkage.

如前所述，混凝土的干燥收缩的影响是纯水泥的一小部分，因为聚集体颗粒不仅稀糊，而且也加强反收缩。它已被证明，当可压缩合容易地被使用时，将热收缩不亚于纯水泥混凝土，膨胀页岩导致收缩率的三分之一超过普通骨料。钢合另一方面，导致收缩小于普通混凝土的三分之一。总体而言，集料的弹性性质决定提供的限制程度。集料的大小和分级本身，不这样做，影响收缩的幅度，但是汇聚将较大尺寸permints以较少的水泥，从而以较低的收缩率的混合使用。最大骨料粒径的总含量，从而增加混凝土的总体积的20％，以确保收缩率大幅下降。

3.effect of admixtures

as can be predicted for the effect of water-cement ratio on shrinkage, admixtures that increase the water requirement of concrete increase shringkage and those that decrease the water requirement decrease it. Calcium chloride in the amount ofen added as an accelerator—2 percent by weight of the amount of cement—may increase drying shrinkage by as much as 50 percent.（第五题）

可以预见的收缩，增加混凝土的收缩和减少需水量减少，从而增加了需水量的外加剂水灰比的效果。氯化钙的量奥芬水泥的用量（重量）作为促进剂的2％的增加，可能会增加干燥收缩率高达50％。

The over-all effect of the use of air-entrained concrete is not to increase shrinkage. Some admixtures, if used in somewhat larger than normal doses, do increase shrinkage greatly and care must be exercised in the proportioning.

过度所有加气混凝土的使用效果是在不增加收缩。一些外加剂，如果略大于正常剂量使用，不增加收缩大大，必须小心谨慎配比。

2.2.5 creep of concrete混凝土徐变

Creep is the slow deformation of a material over considerable length of time at constant stress or load. The nature of the creep process is shown schematically in figure 2.4. this particular concrete was loaded after 28 days with resulting instantaneous elastic strain. If the same stress is kept for a period of time, and additional strain due to creep effect can be recorded. If the sustained load is removed, the strain decreases immediately by an amount equal to the elastic strain at the given age; this is generally lower than the elastic strain on loading since the elastic modulus has increased in the intervening period. This instantaneous recovery is followed by a gradual decreased in the intervening period. This instantaneous recovery is followed by a gradual decrease in strain, called creep recovery. This recovery is not complete because creep is not simply a reversible phenomenon.

渐变是缓慢变形的材料在恒定应力或负载在相当长的时间。潜变过程中的性质，是示意性地示出在图2.4中。这个特殊的混凝土被加载后28天产生的瞬时弹性应变。如果在一段时间内保持相同的应力，并且可记录，可额外的压力，由于蠕变效应。如果持续负载被删除，应变减小立即金额相等于在给定的年龄弹性应变，这是普遍低于上加载的弹性应变的弹性模量，因为在此期间增加了。瞬时恢复之后的逐渐减少在此期间。瞬时恢复之后逐渐减少，应变，蠕变恢复。这种复苏是不完整的，因为蠕变不单纯是一个可逆的现象。

Creep does not include any immediate elastic strains caused by loading or any shrinkage or swelling caused by moisture changes. When a concrete structural element is dried under load, the creep that occurs is one to two times as large as it would be under constant moisture conditions. Adding normal drying shrinkage to this and considering the fact that creep can be several times as large as the elastic strain on loading, it may be seen that these factors can cause considerable deflection and that they are of great importance in structural mechanics.

潜变不包括通过加载或任何收缩或膨胀湿度变化引起的任何直接引起的弹性应变。当用在负载下的混凝土结构元件，发生蠕变的一到两倍大，因为它会在不变的湿度条件下。添加正常的干燥收缩于此，考虑潜变的事实，还可以数次上加载的弹性应变大时，可以看出，这些因素可能会导致相当大的挠度和结构力学中是非常重要的。

1. factors influencing creep影响潜变因素

concrete that exhibits high shrinkage generally also shows a high creep, but how the two phenomena are connected is still not understood. Evidence suggests that they are closely related. When hydrated cement is completely dried, little or no creep occurs; for a given concrete the lower the relative humidity, the higher the creep.

混凝土，具有较高的收缩率一般也显示出较高的蠕变，但如何连接这两种现象仍然没有完全理解。有证据表明，他们是密切相关的。当水合的水泥完全干燥，很少或没有发生蠕变，对于一个给定的混凝土的低的相对湿度下，较高的蠕变。

Strength of concrete has a considerable influence on creep and within a wide range creep is inversely proportional to the strength of concrete at the time of application of load. From this it follows that creep is closely related to the water-cement ratio. There is no doubt also that the modulus of elasticity of aggregate controls the amount of creep that can be realized and concretes made with different aggregates exhibit creep of varying magnitudes.

混凝土强度具有相当大的影响潜变和在宽范围内的潜变负载的应用时混凝土的强度成反比。从这一点如下，潜变是密切相关的水灰比。这是毫无疑问也集料的弹性模量控制的蠕变量，可实现混凝土采用不同的聚合表现出不同程度的潜变。

Experiments have shown that creep continues for a very long time; detectable changes have been found after as long as 30 years. The rate decreases continuously; however, it is generally assumed that creep tends to a limiting value. It has been estimated that 75 percent of 20-year creep occurs during the first year.(第六题)

实验已经表明，潜变持续很长的时间，只要30年后，已发现可检测的变化。率连续减小，但是，它一般假设，潜变趋向于限制值。据估计，75％，20年的潜变发生在第一年期间。

2. effects of creep潜变的影响

creep of plain concrete does not by itself affect strength, although under very high stresses creep hastens the approach of the limiting strain at which failure takes place. The influence of creep on the ultimate strength of a simply supported reinforced concrete beam subjected to a sustained load is insignificant, but deflection increases considerably and may in many cases be a critical consideration in design, another instance of the adverse effects of creep is its influence on the stability of the structure through increase in deformation and consequent transfer of load to other components. Thus, even when creep does not affect may be extremely serious as fat as the performance of the structure as a whole is concerned.

普通混凝土的潜变不影响本身的实力，虽然非常高应力下潜变加快极限应变的方法，在故障发生。潜变极限强度的钢筋混凝土简支梁受持续负载的影响是微不足道的，但偏转大大增加，并在许多情况下可能是一个关键的设计考虑，潜变的不利影响的另一个实例是它的影响力通过增加变形和由此产生的负载转移到其他组件的结构的稳定性。因此，即使当潜变不影响可能表现为脂肪的结构作为一个整体而言是极为严重的。

The loss of prestress due to creep is well known and accounted for the failure of all early attempts at prestressing. Only with the introduction of high tensile steel did prestressing become a successful operation. The effects of creep may thus be harmful. On the whole, however, creep unlike shrinkage is beneficial in relieving stress concentrations and has contributed to the success of concrete as a structural material.

由于蠕变预应力的损失是众所周知的，占所有早期的尝试中失败的预应力。只有引进高强度钢，预应力成为一个成功的操作。蠕变的影响，因此可能是有害的。但是，就整体而言，潜变不同收缩率，有利于缓解应力集中，作为结构材料和混凝土的成功作出了贡献。

Questions

1 define characteristic strength of concrete.

定义混凝土的强度特性。

2 how and when is the characteristic compressive strength f determined? 如何以及何时确定特征抗压强度确定的F？

3 how to determine the modulus of elasticity of concrete?

如何确定混凝土的弹性模量吗？

4 how to test the splitting strength of concrete?

4混凝土劈裂强度如何测试？

5 how to control shrinkage of concrete?

5如何控制混凝土收缩？

6 describe the property of concrete creep based on figure 2.4.

6描述混凝土的质量的徐变根据图2.4。

7 what are the factors influencing creep of concrete?

7哪些因素影响混凝土的徐变？（宽范围内的潜变负载，湿度等因素）

1) 内在因素 ── 混凝土组成成分

a) 水泥用量越多，徐变越大；b) 水灰比越大，徐变越大；c) 骨料越坚硬，徐变越小。

2) 环境因素 ── 养护时的温度、湿度

养护时温度高、湿度大，徐变越小。

3) 应力条件 ── 混凝土的应力大小

混凝土的应力越大，徐变也越大。

(5) 徐变对混凝土结构和构件的工作性能的影响

由于混凝土的徐变，会使构件的变形增加；

在预应力混凝土结构中会造成预应力损失。

2.3 Steel Materials 钢材料

2.3.1 steel properties 钢的性能

Structural steel is an important construction material. It possesses attributes such as strength, stiffness, toughness, and ductility that are very desirable in modern constructions.

Strength is measured in terms of the matrrial’s yield strength, f. the common steel strength grades used in constructions are Q235,Q345,Q390 and Q420. The stress-strain curve of steel Q235 from uniaxial coupon test is shown in figure 2.5. it is seen that the proportional limit stress (marked at point A) and the yield stress(marked at point B) are very close, and thus the small difference between the two stresses can be ignored. The stress-strain curve also shows a small plateau beyond the elastic limit and then an increase in strength due to strain hardening. At point E, necking occurs and the specimen fails rapidly to fracture.

结构钢是一种重要的建筑材料。它具有的属性，如强度，刚度，韧性和延展性，在现代建筑中是非常理想的。

强度测量的材料的屈服强度 。共同建设中使用的钢材强度等级Q235，Q345，Q390和Q420。 Q235钢的应力 - 应变曲线从单轴券试验如图2.5所示。可以看出，比例极限应力（在点A处标记）和屈服应力（标记为B点处）都非常接近，因此，两者之间的应力小的差别可以忽略不计。应力 - 应变曲线也示出的一个小高原超过弹性极限，则由于应变硬化的强度增加。在E点时，缩颈和标本未能迅速断裂。

The stress-strain curve of high strength steel materials is shown in figure 2.6. there is no clear yielding point in the curve, and the plastic flowing is almost invisible. The yield stress is determined by the 0.2% of offset strain method. In the coupon test, the specimen is fractured suddenly and there is no remarkable necking phenomenon.

高强度钢材料的应力 - 应变曲线，在图2.6中示出。有在曲线没有明显的屈服点，塑性

流动几乎是不可见的。由0.2％的偏移应变法确定的屈服应力。在试验，试样突然断裂，并没有显着的颈缩现象。

Stiffness is the ability of a material to resist deformation. It is measured as the slope of the materal’s stress-strain curve. Stiffness does not vary appreciable for different steel grades. Toughness is the ability of a material to absorb energy before failure. It is measured as the area under the material’s stress-strain curve.

刚度是一个材料抵抗变形的能力。这是测量的材料的应力 - 应变曲线的斜率。刚度不随可观的不同的钢种。韧性是在出现故障前的材料吸收能量的能力。这是测量材料的应力 - 应变曲线下的面积。

Ductility is the ability of a material to undergo large inelastic, or plastic, deformation before failure. It is measured in terms of percent elongation or percent reduction in area of the specimen tested in uniaxial tension. Ductility generally decreases with increasing steel strength. Ductility is a very important attribute of steel. The ability of structural steel to deform considerably before failure by fracture allows an indeterminate structure to undergo stress redistribution. Ductility also enhances the energy absorption characteristic of the structure, which is extremely important in seismic design.

延展性的能力构成重大故障前进行大无弹性，或塑料，变形。据测定，在％的伸长率或在单轴拉伸测试的试样面积减少百分之。延展性普遍提高钢的强度降低。钢的延性是一个很重要的属性。结构钢变形的能力大大骨折发生故障之前，允许一个不确定的结构进行应力重分布。延性也增强了的能量吸收特性的结构，这是极为重要的抗震设计。

2.3.2 types of steel钢的类型

Structural steels used for construction purpose are generally grouped into several major classifications.

用于建筑用途的结构钢一般分为几个主要的分类。

Carbon steels: in addition to iron, the main ingredients of this category of steels are carbon(maximum content=0.22%) and manganese, with a small amount of silicon and copper, the most commonly used structural carbon steel is Q235, which is extremely ductile and is suitable for both bolting and welding.

碳钢：除铁，这类钢的主要成分是碳（最大含量=0.22％）和锰，用少量的硅和铜，最常用的碳素结构钢Q235的是，这是非常延展性，适合螺栓和焊接。

High strength low alloy steels; these steels possess enhances strength as a result of the presence of one or more alloying agents such as chromium, copper, nickel, silicon, vanadium, and other in addition to the basic elements of iron, carbon, and manganese. Normally, the total quantity of all the alloying elements is bellow 5% of the total composition. These steels generally have higher corrosion-resistant capability than carbon steels. Q345,Q390 and Q420 are all high strength low alloy steels.

低合金高强度钢，这些钢具有增强强度剂，如铜，镍，铬，硅，钒，除了铁，碳的基本要素和其他一种或多种合金的存在下，作为结果，和锰。通常情况下，所有的合金元素的总数量，是波纹管的总组合物的5％。这些钢材通常具有较高的耐腐蚀能力比碳钢。 Q345，Q390和Q420低合金高强度钢。

Quenched and tempered alloy steels; the quantities of alloying elements used in these steels are in excess of those used in carbon and low alloy steels. In addition, they are heat treated by quenching and tempering to enhance their strengths. These steels do not exhibit well-defined yield points. These steels, despite their enhanced strength, have reduced ductility.

淬火和回火合金钢，用于这些钢的合金元素的数量超出那些用于碳钢和低合金钢。此外，他们通过淬火和回火的热处理，以提高他们的长处。这些钢没有表现出良好定义的屈服点。这些钢材，尽管他们增强实力，降低延展性。

2.3.3 design considerations 设计考虑

Special problems occur with steel work and good practice must be followed to ensure satisfactory performance in service.

特殊问题的发生，必须遵循与钢的工作和良好做法，以确保安全因素令人满意。

1. Fatigue 耐久

Fatigue failure can occur in members subjected to fluctuating loads such as crane girders or bridge structures. Failure occurs through initiation and propagation of a crack that starts at a fault

or structural discontinuity and the failure load may be well below its static value.

耐久失效可能发生波动负荷，如吊车梁桥结构构件。故障发生时通过一条缝，开始出现故障或结构不连续，破坏荷载可能会远远低于其静态价值的萌生和扩展。

Welded connections have the greatest effect on the fatigue strength of steel structures. Tests show that bull welds give the best performance in service while continuous fillet welds are much superior to intermittent fillet welds.

焊接连接有钢结构的疲劳强度的影响最大。测试结果表明，防撞焊缝给表现最好的服务，同时连续角焊缝远优于断续角焊缝。

The maximum stress level at the weld toe is known as the hot spot stress. The fatigue life of a welded structure can be predicted based on the hot spot stress range at the welded region. Alternatively, fracture mechanics approach can also be used to calculate the remaining life of welded structures with initial crack. Under cyclic service loading, crack always initiates at the areas of stress concentration.

被称为热点应力的最大应力水平上面的焊趾。焊接结构的耐久寿命可以预测基于热点应力在焊接区域的范围。另外，断裂力学的方法也可以被用于计算焊接结构的剩余寿命与初始裂纹。根据循环服务的负担，裂纹总是发起的应力集中区域。

2. brittle fracture脆性断裂

Structural steel is ductile at temperatures above 10 but it becomes more brittle as the temperature falls. And fracture can occur at low stresses below 0. The charpy impact test is used to determine the resistance of steel to brittle fracture. In this test, a small specimen is broken by a hammer and the energy or toughness to cause failure at a given test temperature is measured.

在10以上的温度下结构钢的韧性，但它变得更脆，随着温度的下降。骨折可以发生在低应力低于0。的夏比冲击试验是用来确定钢的耐脆性断裂。在该试验中，一个小的试样用锤打破的能量或韧性造成的故障在给定的试验温度的测量。

By careful selection of steel grade with adequate impact toughness and good detailing, the likelihood of brittle fracture can be reduced. Thin plates are more fracture resistance than thick ones. Abrupt changes of section and stress concentration should be avoided. Fillet welds should not be laid down across tension flanges and intermittent welding should not be used.

精心挑选的钢级有足够的冲击韧性和良好的细节，可以减少脆性断裂的可能性。薄板断裂性比厚的。应避免突然变化的部分和应力集中。角焊缝不应放下跨张力法兰和间断焊接不应使用。

3. Fire protection 消防

Steel structures without fire protection may suffer serious damage or even collapse in a fire catastrophe. This is because the mechanical properties of steel deteriorate by heat during fires, and the yield strength of conventional steel at 600 is less than 0.3 of the specified yield strength at room temperature. Fire protection can be provided by encasing the member in concrete, fire board or cementitious fiber materials. The main types of fire protection for columns and beams are shown in figure 2.7. more recently, intumescent paint is being used especially for exposed steelwork.

没有防火的钢结构在火灾灾难可能会严重受损甚至崩溃。这是因为钢的机械性能恶化，通过热在火灾过程中，与传统的钢的屈服强度在600指定的在室温下的屈服强度小于0.3。可以提供防火保护套部件，在混凝土中，防火板或水泥纤维材料。立柱和横梁的防火保护的主要类型，如图2.7所示。最近，正在使用的膨胀型涂料，尤其是对裸露的钢结构。

4. Corrosion protection 腐蚀防护

Atmospheric corrosion occurs when steel is exposed to a continuous supply of water and oxygen. The rate of corrosion can be reduced if metallic coating or painting is used. Other methods of corrosion protection are sherardizing, concrete encasement and cathodic protection. 发生的大气腐蚀钢暴露于水和氧的连续供应。可以减小腐蚀的速度，如果使用金属涂层或涂漆。渗锌防腐蚀保护的其他方法，具体的装箱和阴极保护。

Questions

1. how to describe the mechanical properties, l.e. , strength, stiffness, toughness and ductility, from a typical stress-strain curve of steel material measured from uniaxial coupon test?

怎么形容的力学性能，L.E. ，强度，刚度，韧性和延展性，从一个典型的钢材料应力 - 应变曲线从实验中测量的？

2. what are the general measures in practical engineering for fire protection and corrosion protection for steel members?

在实际工程中的钢构件防火和防腐蚀保护的一般措施是什么？

答案后两段

2.4 Structural Steel Shapes 型钢

Steel sections used for construction are available in a variety of shapes and sizes. In general, there are three procedures by which steel shapes can be formed: hot-rolled, cold-formed, and welded.

用于建筑型材可在各种形状和大小。一般来说，有钢材的形状也可以形成有三个程序：热轧，冷弯，焊接。

2.4.1 rolled and formed sections 推出，冷弯型钢

Rolled and formed sections are produced in steel mills from steel blooms, beam blanks or coils by passing them through a series of rollers. Rolled and formed sections have the following shapes, which are also shown in figure 2.8;

钢厂从钢华，梁坯或线圈通过他们通过一系列的辊轧制，冷弯型钢生产。轧制和形成部分具有以下的形状，这也示于图2.8;

I-section: these are very efficient sections for resisting bending moment about the major axis. I部分：这部分是非常有效的抵抗弯矩的长轴。

H-section: these are sections produced primarily to resist axial load with a high radius of gyration about the minor axis to prevent buckling in that plane.

H-部分：这部分主要生产具有高回转半径的短轴防止屈曲，平面抵抗轴向载荷。

Channels: these are used for beams, bracing members, truss members and in compound members.

通道：用于梁，支撑构件，桁架构件和复合成员。

Equal and unequal angles: these are used for bracing members, truss members, purlins and sheeting rails.

平等和不平等的角度：这些都是用于支撑构件，桁架，檩条和塑料布轨。

Structural tees: the sections are produced by cutting an H-section into two parts . tees are used for truss members,ties and light beams.

三通结构：部分是通过切割H型钢分为两部分。三通用于桁架构件，领带和光束。

Circular, square and rectangular hollow section. These are mostly produced from hot-rolled coils, and may be hot-finished or cold-formed. A welded mother tube is first formed and it is rolled to its final square or rectangular shape. In the hot process, the final shaping is done at the steel normalizing temperature whereas in the cold process, it is done at ambient room temperature. These sections make very efficient compression members, and are used in a wide range of applications as members in roof trusses, lattice girders, in building frames, for purlins, sheeting rails, etc.

圆形，方形和矩形空心部分。这些大多是从热轧带卷，并可能是热成品或冷弯。首先形成焊接母管被卷到其最终的正方形或长方形的形状。在热的过程中，最终成形而在寒冷的过程中在钢正火温度，在室温的温度下完成。在这些区域里进行非常高效的压缩部件，和用于在大范围内的应用程序的成员在屋架，格构梁，在建立帧，檩条，床单导轨等

2.4.2 compound sections 复合截面

Compound sections are formed by the following means(see Figure 2.9).

化合物部分是由下面的装置（参见图2.9）。

(1) Strengthening a rolled section such as an H-section beam by welding with cover plates, as shown in figure 2.9a.

（1）通过焊接盖板加强，如轧制的第一个H型截面梁，如图所示在图2.9A。

(2) Combining two members carry loads from separate directions.

（2）将两个成员进行负载从不同的方向。

(3) Connecting two members together to form a strong combined member.

（3）两名成员连接在一起，形成一个强大的组合成员。

Examples are the laced and battened members shown in figure 2.9c.

例如图2.9c中的缀条和缀条连接构件。

2.4.3 built-up sections内置的部分

Built-up sections are made by welding plates together to form I, H or box members which are termed plate girders, built-up columns, box girders or box columns,respectively, as shown in figure 2.10. these members are used where heavy loads have to be carried, or where long spans are required.

内置的部分是由板焊接在一起，形成I，H股或箱部件被称为板梁，内置列，箱形梁或箱型柱，分别为，如图2.10所示。使用这些成员必须进行重物，或长跨度的要求。

2.4.4 cold-rolled open sections冷轧的开口部分

Thin steel plates can be formed into a wide range of sections by cold rolling. The most important uses for cold-rolled open sections in steel structures are for purlins and sheeting rails. Three common sections—the zed,sigma and lipped channel—are shown in figure 2.11.

广泛的部分，可以形成薄钢板冷轧。钢结构冷轧开口部分的最重要的用途是用于檩条和压片轨。三种常见的部分的ZED，西格玛和唇通道，如图2.11所示。

Questions

Introduce different types of steel sections and their application briefly.

简要介绍不同类型的型钢及其应用

红色部分是答案，答案不全，考到自己再找找

Chapter 3. Structural Design concepts 结构设计

3.1 Load Conditions and Load Paths负载条件下和负载路径

3.1.1 Vertical Loads竖向荷载作用下

Gravity loads act in the same direction as gravity (i.e., downward or vertically) and Include dead, live, and snow loads.

重力荷载作用在同一方向的重力（即，向下或垂直），包括恒载,活荷载，和雪荷载. The tributary area is the area of the building construction that is supported by a structural element, including the dead load (i.e., weight of the construction) and any applied loads (i.e., live load). For example, the tributary gravity load on a floor joist would include the uniform floor load (dead and live) applied to the area of floor supported by the individual joist.

支流地区的建筑是由一个结构元件支撑的区域，其中包括恒荷载（即，建筑物的重量），任何施加的载荷（即，活载）. 例如，在地板托梁的支流重力荷载包括统一的楼面荷载（恒载和活）应用于个别龙骨支持地板面积。

Wind uplift forces are generated by negative (suction) pressures acting in an outward direction from the surface of the roof in response to the aerodynamics of wind flowing over and around the building. As with gravity loads, the influence of wind uplift pressures on a structure or assembly (i. e. ,roof) are analyzed by using the concept of tributary areas and uniformly distributed load. The major difference is that Wind pressures act perpendicular to the building surface (not in the direction of gravity) and that pressures vary according to the size of the tributary area and its location on the building, particularly proximity to changes in geometry (e.g., eaves, corners, and ridges).

风隆起的力量所产生的负作用（吸）从响应于风和周围的建筑屋顶的空气动力学表面向外的压力。 与重力荷载，风扬压力在一个结构或装配的影响（即，屋顶）是利用支流地区的概念分析和均布荷载。主要的区别是，风压作用垂直于建筑物表面（不在重力的方向）和压力根据支流区域的大小及其对建筑物的位置不同，特别是接近的几何形状的变化（例如，檐，角落，和脊）。

3.1.2 Lateral Loads横向荷载

The primary loads that produce lateral forces on buildings are attributable to forces associated with Wind, seismic ground motion, and soil. Wind and seismic lateral loads apply to the entire building. Lateral forces from wind are generated by positive wind pressures on the

windward face of the building and by negative pressures on the leeward face of the building, creating a combined push-and-pull effect, and resulting uplifting, racking or sliding of building. Seismic lateral forces are generated by a structure’s dynamic inertial response to cyclic ground movement. The magnitude of the seismic shear load depends on magnitude of the ground motion, the building’s mass, and dynamic structural response characteristics (i.e., dampening, ductility, natural period of vibration, etc.). For low-rise structures, a simplified seismic load analysis employs equivalent static forces based on fundamental Newtonian mechanics (F=ma) with somewhat subjective (i.e., experience-based) adjustments to account for inelastic, ductile response characteristics of various building systems. 产生的侧向力对建筑物是由于与风的力量的主要荷载，地震地面运动，和土壤。风和地震荷载适用于整个建筑。从风侧力是通过在建筑物的迎风面正风压和通过对建筑物的背风面产生的负压，创建一个组合的推拉效应，以及由此产生的抬升，货架或滑动的建筑。地震力是由结构的动力响应的地面运动产生的惯性循环。地震的震级剪切载荷取决于地面运动幅度，建筑物的质量，和结构动态响应特性（即，阻尼，延性，振动，等等。自然周期）。低层结构，一个简化的地震荷载的等效静力分析采用基于基本的牛顿力学（F = MA）与主观的（即，基于经验的）的调整，考虑到非弹性，各种建筑系统的韧性响应特性。

3.1.3 Load Path of a masonry structure某砖混结构的荷载路径

1. The Vertical Load Path竖向荷载路径

2. Lateral Load Path横向载荷路径

3.2 Limit State Design极限状态设计

Limit state design requires the structure to satisfy two principal criteria:结构的极限状态设计需要满足两个主要标准：

ultimate limit state承载能力极限状态

serviceability limit 正常使用极限状态

3.2.1 Ultimate Limit State

To satisfy the ultimate limit state , the structure must not collapse when subjected to the peak design load. A structure is deemed to satisfy the ultimate limit state criteria if all design values of load effect combination, such as the combination of bending, shear and tensile or compressive stresses, are below the design values of bearing capacity calculated for the section under consideration. The ultimate limit state criteria can also be set in terms of stress rather than load. Thus the structural element being analysed ( e. g. , a beam or a column or other load bearing element, such as walls) is shown to be safe if it satisfies the ultimate limit state criteria.

为满足承载能力极限状态，结构不崩溃时的峰值负载设计。结构被视为符合标准，如果极限状态荷载效应组合设计值，如弯曲的组合，剪切和拉伸或压缩应力，在承载力计算所考虑的截面的设计值。极限状态的标准，也可以设置在应力比负荷。这样的结构的元分析（例如，梁、柱等承重构件，如墙）被证明是安全的如果它满足极限状态的标准

3.2.2 Serviceability Limit State正常使用极限状态

To satisfy the serviceability limit state criteria, a structure must remain functional and must not cause occupant discomfortable under routine conditions. A structure is deemed to satisfy the serviceability limit state when the constituent elements do not deflect by more than certain limits laid down in the building codes, the floors fall within predetermined vibration criteria, and crack widths in concrete are kept below specified dimensions. A structure where the serviceability requirements are not met, e. g. , the beams deflect by more than the serviceability limit, will not necessarily fail structurally. The purpose of the serviceability limit requirements is to ensure that

people in the structure are not unnerved by large deflections of the floor, vibration caused by walking, sickened by excessive swaying of the building during high winds. And to keep beam deflections low enough to ensure that brittle finishes on the ceiling above do not crack.

为了满足正常使用极限状态的标准，结构必须保持功能，不能在常规条件下引起乘员不适。结构被视为满足正常使用极限状态时的构成要素不偏离超过一定范围内的建筑规范规定，地板落在预定的振动准则，并在混凝土裂缝宽度保持低于指定的尺寸。一个结构的适用性要求没有得到满足，例如，光束偏转超过极限，也不一定会失败的结构。的极限要求的目的是确保在结构的人不由地大挠度引起的不安，行走振动，通过在高风的建设过度摇摆生病。梁的挠度和保持足够低，以确保脆完成在天花板上面不裂。

3.2.3 Characteristic Loads 荷载标准值

Buildings will be subjected to loads from various sources. The principal ones can be classified as dead load, live load and wind load .In some cases structrres may be subjected to other loads, such as those due to earthquakes or pressures from retained material. The expected maximum magnitude of each is referred to as the characteristic load.

建筑将受到来自各种来源的负载。主要的因素可分为恒载，活载和风荷载。在某些情况下structrres可能会受到其他荷载，如地震或保留的材料的压力。每个预期的最大值，称为负载特性。

Dead loads are those due to the self weight of the structure and any permanent fittings and finishes; their magnitude can be estimated on the basis of material densities and component sizes. 静荷载是由于结构的自重和任何永久设备和完成；它们的大小可以是对材料的密度和大小的基础上估计。

Live loads are those associated with occupation and use of the building. Personnel, storage, furniture all constitute loads under this heading. The magnitude of such loads cannot be quantified with any precision and it is therefore necessary to make some allowance based upon the type of activity to be performed within the building. 活荷载是那些占用相关建设。人员，存储，家具都是负载在这个标题下。这样的负载的大小不能量化以任意精度，根据是建筑物内进行活动的类型进行补贴是必要的

The magnitude of wind loads is closely related to wind speed but also depends upon a number of factors associated with the shape and dimensions of the building and its local environment.The design wind speed represents the maximum likely speed at a particular geographical location and is based upon statistical data. This may be modified if ,for instance ,the building site is particularly sheltered, such as may be the case in a city centre, or exposed ,such as on the coast. The effect of this wind condition in terms of forces on the structure in related to the building geometry and is expressed as wind pressure coefficients for the walls and roof.

风荷载的幅度是密切相关的风的速度还取决于许多的建筑与当地环境的形状和尺寸的相关因素。设计风速的最大可能的速度在一个特定的地理位置和基于统计数据。这可能被修改，如果，例如，网站建设是特别保护，如在城市中心，是的情况下或暴露的，如在海岸。这风条件在结构上的力在建筑物的几何形状相关术语的作用，表示为墙体和屋面风压系数。

3.2.4 Partial Safety Factors部分安全因素

The characteristic\normal values of loads anr based on statistical data .It is assumed that in ninety-five percent cases the characteristic loads will not be exceeded during the life of the structures (Figure3.4). However, structures are also subjected to overloading . Hence , structures should be designed with loads obtained by multiplying the characteristic loads with suitable factors of safety depending on the nature of loads or their combinations, and the limit state being

considered. These factors of safety for loads are termed as partial safety factors for loads .Thus, the design loads are calculated as

特征正常负荷值在统计数据的基础上的。它是假定百分之九十五例特征载荷时不得超过结构的寿命（figure3.4）。然而，结构也进行超载。因此，结构设计应具有的特征荷载的安全取决于负载或它们的组合的本质因素相乘得出合适的负载，和极限状态考虑。这些安全系数荷载称为荷载分项系数。因此，设计荷载计算

Similarly, the characteristic strength of a material obtained from the statistical approach is the strength of that material below which not more than five percent of the test results are expected to fall(see Figure 3.4). However, such characteristic strengths may differ from sample to sample also .Accordingly, the design strength is calculated by dividing the characteristic strength by the partial safety factor for the material, where RM depends on the material and the limit state being considered.

同样，从统计方法获得的特性的材料的强度，材料在不超过百分之五的测试结果预计将下降的强度（见图3.4）。然而，这种特性的优势可能从不同的样品也。因此，设计强度除以特征强度的安全系数计算的材料，在RM取决于材料的极限状态考虑.

GB50010-2002 states that RM for concrete and steel reinforcement should be taken as 1.4 and

1.1 ,respectively. However,when assessing the deflection, the material properties such as compressive strength should be taken as those associated with the characteristic strength of the material .It is worth mentioning than that of concrete(1.4)because the sttel for reinforcement is produced in steel plants and commercially available in specific diameters with expected better quality control than that of concrete.

受美国RM混凝土和加强钢筋应取为1.4和1.1，分别。然而，在评估偏转，材料性能如抗压强度应作为这些材料的特性强度有关。值得一提的是，（1.4）由于混凝土加固sttel是钢铁厂生产和商业上可用的特定直径的预期比，控制混凝土的质量更好。

3.2.5 Limit State Design

The limit state design approach uses two factors --one applied to the load and one applied to the resistance or strength property --that permits a more consistent treatment of safety across a broader range of design conditions.

极限状态设计方法使用两个因素——一个适用于负载和一个应用于电阻或强度特性——允许在更广泛的设计条件，安全更一致的处理.

Figure 3.4 shows that, for a given hazard condition and given material, increasing the partial safety factor for load and\or decreasing the level of safety.Figure 3.4 depicts the variable nature of building loads and resistance and the safety margin relative to design loads and nominal resistance.

图3.4显示，对于一个给定的危险条件和给定的材料，增加荷载分项系数和\或降低安全水平。图3.4描述了建筑荷载和抗力变量的性质和安全边际相对设计载荷和额定电阻

For ultimate limit states, the resistances to bending moment ,shear force, axial thrust, torsional moment at every section shall not be less than their appropriate values at that section due to the most unfavourable combination of the design loads on the structure. That is

承载能力极限状态，弯矩，剪力的电阻，轴向推力，扭矩在每一段不应小于相应的值，部分由于对结构设计荷载最不利组合。这是

Design resistance<=Design load combination设计电阻＜＝设计荷载组合

Further, the structure or part of the structure should be assessed for rupture of one or more critical sections and buckling due to elastic or plastic instability considering the effects of sway or

overturning.

此外，该结构的结构或部分应评估一个或更多的关键部分，由于弹性或塑性屈曲考虑摇摆或倾覆失稳破裂的影响。

For serviceability limit states the standard combination, frequency combination and quasi-permanent combination of loads are adopted separately. The crack width and deformation caculated shall not exceed the corresponding limits of the provisions.

对于正常使用极限状态的标准组合，频组合和荷载准永久组合分别采用。裂缝宽度和变形计算应不超过相应的规定限值。

Chaper 4. Concrete Structure 钢筋混凝土结构

4.1. Flexural Behavior of Reinforce Concrete Beam

受弯构件正截面性能

4.1.1 Introduction 介绍

Plain concrete beam are ineffective as flexural members because the tensile strength in bending is a small fraction of the compressive strength. As a consequence, such beams fail on the tension side at low loads long before the strength of the concrete on the compression has been fully utilized. For this reason, steel reinforcing bars are placed on the tension side as close to the extreme tension fiber. In such a reinforced concrete beam, the tension caused by the bending moment is chiefly resisted by steel reinforcement, while concrete alone is usually capable of resisting the corresponding compression. Such joint action of the two materials is assured, if relative slip is prevented. This is achieved by using deformed bars with their high bond strength at the steel-concrete interface, and, if necessary, by special anchorage of the ends of the bars.

普通混凝土梁的受弯构件是无效的因为在弯曲抗拉强度为抗压强度的一小部分。作为一个结果，例如梁的失败在张力侧在低负荷长在压缩的混凝土的强度得到充分利用。为此，钢筋放置在张力侧接近极端紧张的纤维。在这样一个钢筋混凝土梁，由弯矩引起的拉力是由钢筋混凝土主要的抵制，而仅仅是通常能够抵御相应的压缩。这种联合行动的两种材料是保证，如果发生相对滑移。这是通过使用变形钢筋的粘结强度高的钢-混凝土界面，实现了和，如果需要，由特别锚固端的钢筋。

4.1.2Reinforced Concrete Behavior 钢筋混凝土的行为

1. Moderate reinforced Behavior 适筋

When the relatively moderate amount of reinforcement are employed, at some value of the load the steel will reach its yield point. At that stress( yield point), the reinforcement yields suddenly and stretches a large amount and the tension cracks in the concrete widen visibly and propagate upward, with simultaneous significant deflection of the beam. When this happens, the strain in the remaining compression zone of the concrete increases to such a degree that crushing of the concrete ensues at(跟着发生) a load only slightly larger than that which caused the steel to yield. Effectively, therefore, attainment of the yield point in the steel determinates the carrying capacity of moderately reinforced beam. Such yield failure is gradual and is preceded by visible sign of distress (恶化，损坏), such as the widening and lengthening of cracks and the marked increase in deflection.

当钢筋相对温和的量使用，在一些负载的钢产量将达到一点价值。在应力（屈服点），增强突然产生和延伸量大，在混凝土扩大明显，向上传播的张力裂缝，梁挠度的同时显著。当这种情况发生时，应在混凝土的增加的剩余压缩带到这种程度，破碎的混凝土是在负载仅稍大于所引起的钢产量。有效，因此，在钢的屈服点确定承载力达到适度的钢筋混凝土梁。这种屈服破坏是渐进的和前面的窘迫可见的标记，如延长裂缝和挠度明显增加，扩大。

2. Over-reinforced Behavior 超筋

On the other hand, if large amounts of reinforcement or normal amounts of steel of very high strength are employed, the compressive strength of the concrete may be exhausted before the steel starts yielding. Concrete fails by crushing when strains become so large that they disrupt the integrity[in5te^riti] 完整性 of the concrete. Compressive failure through crushing of the concrete is sudden, of an almost explosive nature, and occurs without warning. For this reason, it is good practice to dimension beams in such a manner that should they be overloaded, failure would be initiated by yielding of the steel rather than by crushing of the concrete.

另一方面，如果大量的加固或正常的高强度钢的大量采用，混凝土的抗压强度可排钢开始前屈服。混凝土的失败是由破碎时，菌株变得如此之大，他们破坏了混凝土的完整性。压缩破坏通过混凝土破碎是突然的，几乎是爆炸性的，并没有出现警告。出于这个原因，它是很好的做法尺寸梁以这样的方式，他们应该被重载，失败会发起的钢的屈服而不是由破碎的混凝土。

3. Lightly Reinforced Behavior 少筋

Another mode of failure may occur in very lightly reinforced beam.If the flexural strength of the cracked section is less than the moment that produced cracking of the previously uncracked section,the beam will fail immediately and without warning of distress upon 紧接着 formation of the first flexural crack.

在轻轻钢筋混凝土梁可能出现另一个失败模式。如果开裂截面的抗弯强度小于产生的先前未开裂截面开裂弯矩，梁将不能立即、无痛苦的在第一弯曲裂纹的形成的警告

4.1.3 Design of Reinforced Concrete Beam钢筋混凝土梁的设计

1. Strength Design of Rectangular beam with tension reinforcement only单筋矩形梁的强度设计 The basic assumptions made in flexural design are:

在抗弯设计的基本假设

(1) Sections perpendicular to the axis of bending that are plane before bending remain plane after bending.

This assumption ensures that the cross-section of the member does not warp [wC:p]使翘曲due to the loads applied. It further means that the strain at any point on the cross-section is directly proportional to its distance from the neutral axis.

垂直于平面弯曲，弯曲前保持平面的轴段弯曲后。

这种假设使得对构件截面不翘曲由于施加的载荷。它还意味着在截面上任意点的应变是成正比的中性轴的距离

(2) A perfect bond exists between the reinforcement and the concrete such that the strain in the reinforcement is equal to the strain in the concrete at the same level.

钢筋的应变和相同位置处混凝土的应变相同----假定混凝土与钢筋之间粘结可靠

(3) Concrete is assumed to fail when the compressive strain reaches 0.0033.

This is a clearly defined limiting strain of concrete in bending compression beyond which the concrete will be taken as reaching the state of collapse. It is very clear that the specified limiting strain of 0.0033 does not depend on the strength of concrete.

混凝土被假定为失败时的压应变达到0.0033。

这是一个明确的极限应变的混凝土在弯曲压缩以后，混凝土作为达到崩溃的状态。很显然，所规定的极限应变0.0033，并不取决于混凝土的强度。

(4) The acceptable stress-strain curve of concrete is assumed to be parabolic抛物线的，像抛物线的混凝土受压时的应力-应变关系

(5) The tensile strength of concrete is ignored. 混凝土的抗拉强度被忽略。

Concrete has some tensile strength (very small but not zero). Yet, this tensile strength is ignored and the steel reinforcement is assumed to resist the tensile stress.

混凝土具有一定的抗拉强度（很小但不为零）。然而，这是被忽略的抗拉强度和钢筋的抗拉应力的假设，认为拉区混凝土开裂并退出工作

However, the tensile strength of concrete is taken into account to check the deflection and crack widths in the limit state of serviceability.

然而，混凝土的抗拉强度是考虑到检查挠度和裂缝宽度在正常使用极限状态。

(6) The design stresses of the reinforcement are derived from the representative stress-strain curves

设计应力的钢筋是来自代表的应力-应变曲线

钢筋的应力-应变关系

The maximum strain in the tension reinforcement in the section at failure is 0.01.

This assumption ensures ductile failure in which the tensile reinforcement undergoes a certain degree of inelastic deformation before concrete fails in compression.

During the loading to failure of a reinforced concrete beam, the strain distribution over the depth of the beam is assumed to be linear. The stress distribution in the concrete above neutral axis is essentially parabolic in shape.

最大应变在受拉钢筋的截面在0.01失败。

这个假设保证延性破坏，受拉钢筋的非弹性变形进行一定程度的混凝土在压缩之前失败。 在加载的钢筋混凝土梁的破坏，在梁的应变分布的深度被假定为线性。在以上的中性轴的形状的混凝土应力分布是抛物线。

An Equivalent rectangular stress distribution(压区混凝土等效矩形应力图形)has been proposed by design code which simplifies calculations with little loss in accuracy. It is assumed that at failure the tension reinforcement has yielded and that the maximum compressive strain is 0.0033. The intensity of the equivalent uniform compressive stress and its depth are easily calculated from the two conditions that (1) the total compression force C, and (2) its location, i.e., distance from the top fiber, must be the same in the equivalent rectangular as in the idealized stress distribution. 等效矩形应力分布已被设计代码，简化了计算精度的损失不大了。它是假定在失败的受拉钢筋的产生，最大压应变为0.0033。的等效均匀压应力的强度和深度是很容易计算的两个条件：

（1）总的压缩力，和（2）的位置，即，从顶部的光纤距离，必须是相同的等效矩形在理想化的应力分布。

The equivalent rectangular stress distribution can be used for deriving the ultimate strength design equations of beams. The basic design equations for the moment capacity of a singly reinforced rectangular beam can be established by considering the equilibrium of forces and moments

等效矩形应力分布可用于导出梁的极限强度设计方程。对于一个单独的钢筋混凝土矩形梁的弯矩承载力设计的基本方程可根据力平衡和力矩平衡建立

For beams reinforced with moderate amount of steel ss=fy

对加固梁的适量钢SS＝FY

2. Balanced Strain Condition 平衡应变条件

Whether or not the steel has yielded at failure can be determined by comparing the actual relative concrete compression zone depth, with the balanced relative concrete compression zone depth, representing the relative at the same load that causes steel to yield. A balanced relative concrete compression zone depth producing a balanced strain condition can be established on the

condition that, at balanced failure,the steel strain in exactly equal to the yield strain when the strain in the concrete simultaneously reaches the crushing strain of

是否钢筋屈服破坏可以通过比较实际相对混凝土受压区高度，确定，与平衡相对混凝土受压区高度，使钢产量表示在相同的负载相对。一个平衡的相对混凝土受压区高度产生一个平衡的应变条件下可以建立的条件下，在平衡的破坏，钢应变相等的屈服应变时的混凝土应变同时达到破碎应变

It can be seen that the relative concrete compression zone depth is only related to the material properties. Then from the equilbrium requirment thatC=T from which the balanced reinforcement ratio can be derived

To ensure an moderate-reinforced beam with ductile and yielding of the tension reinforcement, Design code GB50010-2002 limits the amount of reinforcement or relative concrete compression zone depth in order to prevent nonductile behavior:

To ensure against sudden failure due to lack of adequate reinforcement,a lower limit can be established for the reinforcement ratio by equating the cracking moment computed from the corresponding plain concrete beam to the strength of the cracked section. The minimum allowable reinforcement ratio given by GB50010-2002 is

可以看出，相对混凝土受压区高度对材料性能的关系。然后从平衡要求＿＝T，从中可以推导出的平衡配筋率

为了确保一个温和的钢筋受拉钢筋的韧性和屈服梁，设计规范GB50010-2002界限相对受压区高度钢筋或混凝土量以防止延性行为：

为了确保对由于缺乏适当的加固突发故障，下限可以建立等同的开裂弯矩计算出相应的素混凝土梁的开裂截面强度配筋率。允许的最小配筋率高是由

4.1.4 Rectangular Beams with Tension and Compression Reinforcement 双筋矩形截面受弯构件

If a beam cross section is limited because of architecture or other consideration so that the concrete can not develop the compression force required to resist the given bending moment ;截面的弯矩较大，高度不能无限制地增加beam cross section is alternately subjected to positive and negative moment截面承受正、负变化的弯矩reinforcement shall be added both in beam.There are situations in which compreesion reinforcement in used for reasons other than strength.It has been found that the inclusion of some in some cases,bars will be placed in the compression zone as stirrup-support bars continuous throughout the beam span.

如果一个梁横截面是因为建筑或其他考虑，使混凝土的发展不能要求抵制了弯矩的压缩力有限；梁截面的交替进行正、负弯矩钢筋应加在梁。在有些情况下，压缩加固用于其他比强度的原因。人们已经发现，在某些情况下，一些夹杂物，钢筋也会被放置在压缩区配箍支撑杆连续贯穿梁的跨度。

4.1.5 T beams

With the exception of precast system, reinforced concrete floor, roofs, decks, etc., are almost always monolithic.

Figure 4.7 shows a reinforced concrete floor system.The section 1-1 at mid span is subjected to a positive moment.A part of the slab will act with the upper part of the beam to resist longitudinal compression.The resulting beam crosssection is T-shaped rather than rectangular.The slab forms the beam flange,while the part of the beam projecting below the slab forms the web. The section 2-2 at the support is subjected to a negative moment, the slab being under tension and ignored, and the beam width is that of the web.

与预制系统异常，钢筋混凝土楼板，屋顶，甲板，等，几乎都是单片。

图4.7显示了一个钢筋混凝土楼盖体系。第1-1跨中承受正弯矩。该板的一部分将与梁上部抗纵向压缩。由此产生的光束截面为T形而非矩形板形式。梁翼缘，而光束投射在下面板坯的部分形成网络。第2-2支撑承受负弯矩，板坯在张力和忽视，和波束宽度的网页。

1. Effective Flange Width 有效翼缘宽度

As Figure 4.8 indicates, the compressive stresses, in a T-section, are at a maximum value at points adjacent to the beam and decrease approximately in a parabolic form to zero at a distance from the face of the beam. Stresses also vary vertically from a maximum at the top fibers of the flange to a minimum at the lower fibers of the flange.

As a means of simplification, rather than varying with distance from the web, an effective flange width of uniform stress may be assumed.The effective width depend primarily on the beam span and on the relative thickness of the slab.

如图4.8所示，压应力，在一个T形截面，在相邻的束点最大值约在一个抛物线形式为零，从梁面距离的减小。应力也不同垂直于带翼缘的顶部纤维最高到最低限度，在带翼缘的下纤维。

为简化的一种手段，而不是从Web的距离不同，受力均匀的有效翼缘宽度可以假定。有效宽度主要取决于梁的跨度和板上的相对厚度

2. Strength Analysis 承载力分析

The neutral axis of a T beam maybe either in the flange (Type I T section) or in the web (Type II T section), depending upon the proportion of the cross section, the amount of tensile steel, and the strength of material. If the calculated depth to the neutral axis is less than or equal to the slab thickness, the beam can be analyzed as if it were a rectangular beam of width equal to the effective flange width, as shown in Figure 4.8. When the neutral axis is in the web, as in Figure 4.9, a T beam analysis is required as follows.

As a computational devices, it is convenient to divide the total reinforcement into two parts. The first part As1 represents the steel area which, when stressed to fy, is required to balance the longitudinal compressive force in the rectangular portion of the beam. The remaining part As2, at a stress fy, is balanced by the longitudinal force in the overhanging portion of the flange that are stressed uniformly at

the中性轴T梁也许either in the带翼缘的（I型T段金in the Web）（II型T段），这取决于upon the比例of the截面，the amount of拉伸钢铁，and the strength of material。如果计算to the中性轴深度小于或等于to the板厚度，分析了梁can be as if it were a矩形梁宽度equal to the of有效带翼缘的宽度，as shown in图4.8。当中性轴is in the Web，as in图，分析了T梁is required如下。

有计算设备，它是方便to divide the总增强into two股份。第一部分AS1代表the钢铁area which，when stressed to FY，is required to平衡纵向力系数in the矩形部分of the梁。the remaining方面AS2，at a力FY，是平衡by the纵向力in the overhanging部分of the带翼缘的that are stressed一致。

4.1.6 Constructional Details of Beams截面尺寸和配筋构造

1.Concrete Protection for Reinforcement混凝土保护层厚度

To provide the steel with adequate concrete protection against fire and corrosion, a certain minimum thickness of concrete cover outside of the outermost surface of steel must be maintained .The thickness required will vary,depending on the type of member and condition of exposure. For cast-in-place concrete, concrete protection at surface not exposed directly to the

ground or weather should not be less than 15 mm for slabs and walls, and 25 mm for beams and columns. If the concrete surface is to be exposed to the weather or in contact with the ground, a protecting covering of at least 20 mm is required for slabs and walls, and 30 mm for beams and columns

提供足够的钢混凝土防火保护和腐蚀，混凝土保护层的钢的外表面在特定的最小厚度必须保持。厚度的要求会有所不同，这取决于暴露的成员和条件类型。现浇混凝土，表面不直接接触地面或天气混凝土保护不应小于15毫米和25毫米的楼板和墙壁，梁、柱。如果混凝土表面被暴露在恶劣天气或与地面接触，保护覆盖至少20毫米的砖和墙的要求，和30毫米的梁、柱

一类环境中梁、板的混凝土保护层厚度一般取为：混凝土强度等级≤C20时，梁30mm，板20mm；混凝土强度等级≥C25时，梁25mm，板15mm

2. Concrete Proportions 混凝土配比。

Reinforced concrete beam may be wide and shallow, or relative narrow and deep. Consideration of maximum material economy often leads to proportions with beam depth h in the range from about 2 to 3.5 ( or 2.5 to 4 for T beam) times the width b.

钢筋混凝土梁可以宽浅，或相对窄而深。最大实体经济的考虑，通常会导致束深度H在约2至3.5的范围内的比例（或2.5至4倍的宽度B T梁）

梁适宜的截面高宽比h/b，矩形截面为2～3.5，T形截面为2.5～4。

To simplify construction and thereby to reduce cost, the beam depth h is always rounded upward to the next higher 50mm when h is less than or equal to 800mm, and to the next higher 100mm when h is greater than 800mm.

为了简化施工，从而降低成本，梁高度H总是向上舍入到下一个更高的50mm当H小于或等于800mm，和下一个更高的100mm当H是大于800mm。

梁的截面高度h一般可取250、300…800、900、1000㎜等，h≤800mm时以50mm为模数，h＞800mm时以100mm为模数；

The beam width b (or web width for T beam) should be 100, 120, 150, 180, 200, 220, 250mm, and should be rounded upward to the next higher 50mm when b is greater than 250mm.

矩形梁的截面宽度和T形截面的肋宽b宜采用100、120、150、180、200、220、250mm，大于250mm时以50mm为模数。

3. Selection of Bars and Bar Spacing

Common reinforcement bar sizes ranges from 12mm to 25mm.

梁纵向受力钢筋的常用直径d=12~25mm。

It is necessary to maintain a certain minimum distance between adjacent bars to ensure proper placement of concrete.The minimun spacing of tension reinforcement must be adequate to allow full consolidation of the concrete around the bars.The minimum clear horizontal spacing between parallel tension bars in a layer shall not be less than 25mm or 1 bar diameter. The clear distance between adjacent compression bars shall not be less than 30mm or 1.5 bar diameter. Whichever is larger.

When parallel reinforcement is placed in two or more layers, design code requires that longitudinal bars shall have a clear vertical spacing not less than 25mm or 1.5 bar diameter, and the bars in the upper layer should be placed directly above those in the bottom layer.

Bar diameter shall not be less than 10mm when the beam depth is greater than or equal to 300mm, or 8mm when the beam depth is less than 300mm.

要保持相邻杆之间一定的最小距离，保证混凝土的妥善安置。受拉钢筋的最小间距必须足以

让周围的钢筋混凝土全部合并。的最小水平间距平行拉伸杆之间有一层不应小于25mm或1杆直径。相邻的压杆之间的净距应不小于30mm或1.5杆直径。以较大者为准。

当平行加固是放置在两个或更多层，设计规范要求，纵向钢筋应有明确的垂直间距不小于25mm或1.5杆的直径，并在上层的钢筋应直接放置高于底层。

钢筋直径不应小于10mm时的梁深度大于或等于300mm，或8mm时的梁深度小于300mm。 直径：当h＜300mm时，d≥8mm；当h≥300mm时，d≥10mm。

At least 2 bars should span the full length of the beam when the beam width is greater than or equal to 100mm, or at least 1 bar when the beam width is less than 100mm.

至少有2条要跨越整个梁的长度时的光束宽度大于或等于100mm，或至少1条当光束宽度小于100mm。

梁中受拉钢筋的根数不应少于2根

If the web depth of the beam is large, greater than 450mm., additional reinforcement should be placed at the side faces to control cracking. The amount of skin reinforcement to add need not less than 0.1% of the web cross-section area and the spacing of the skin reinforcement need not exceed 200mm

如果梁的腹板深度大，大于450mm。，附加钢筋应放在侧面的裂缝控制。额部皮肤加固加不少于0.1%的Web横截面积和皮肤的钢筋间距不超过200

Questiuons

1. Name three different types of reinforced concrete beams and their specific applications.

2. State and explain the significance of the six assumptions of the design of flexural members employing ultimate limit state.

3.

4.

5.

6. Describe the moderate-reinforced behavior of flexural members. Describe th over-reinforced behavior of flexural members. Describe the lightly reinforced behavior of flexural members. What is balanced strain condition?

7. How would you design a beam with moderate-reinforced behavior?

8. Why do we consider most of the beams as T or L-beams between the supports and rectangular beams over the support of continuous span?

9. Define the‖effective width‖of flanged beams

10. How woule you design a Type 2 Tbeam with moderate-reinforced behavior?

1。三种不同类型的钢筋混凝土梁及其具体应用。

2。说明对受弯构件采用极限状态设计的六个假设的意义。

3。描述了温和的钢筋受弯构件的行为。

4。在加固受弯构件的行为描述了。

5描述的行为。钢筋受弯构件。

6株。平衡的条件是什么？

7。你会如何与温和的增强行为的梁的设计？

8。为什么我们认为大多数的梁或l-beams支矩形梁之间在连续跨的支持？

9。―带翼缘的梁的―有效宽度定义

10。如何将你设计一个2型T梁中钢筋的行为吗？

4.2 Shear and Diagonal Tension in Reinforced Concrete Beam

Shear failure of reinforced concrete, more properly called diagonal failure, is more dangerous than flexural failure because of its catastrophic 灾难性的nature. If a beam without properly designed

shear reinforcement is overloaded to failue,shear collapse is likely to occur suddenly, with no advance warning of distress. This is in strong contrast with the nature of flexural failure. For moderate reinforced beam, flexural failure is initiated by gradual yielding of the tension steel, accompanied by obvious cracking of the concrete and large deflection, giving ample warning and providing the opportunity to take corrective measures. Because of these differences in behavior, reinforced concrete beams are generally provided with special shear reinforcement to ensure the flexural failure would occur before shear failure if the member should be severely overloaded. 钢筋混凝土的剪切破坏，更恰当地称为对角线的失败，比受弯破坏更危险，因为其灾难性的灾难性的性质。如果没有适当的设计抗剪加固梁的剪切破坏是超载，崩溃可能会突然发生，没有危机预警。这与弯曲破坏性强的对比。温和的钢筋混凝土梁，受弯破坏是由张力钢逐渐屈服开始，伴随着明显的混凝土和大变形开裂，给予足够的警告和提供的机会，采取纠正措施。由于这些不同的行为，钢筋混凝土梁的抗剪钢筋一般都设有特殊保证弯曲破坏之前会出现剪切破坏，如果成员应该严重超载。

4.2.1 Formation of Diagonal Cracks due to Shear

由于剪切斜裂缝的形成

In the case of simply supported beam subjected to two-points loading, the moment and shear distribution is such that the moment is constant in the mid span and in two side spans, shear force is constant. These two side spans are called ―shear span―剪跨. For the elastic beam, the flexure stress , shear stress , and the principal tensile stress are determined according to the beam theory. Since concrete material is weak in tension, the magnitude and direction of principal tensile stresses are important. At the location of zero shear stress, i.e., the extreme tension fiber, the principal tensile stress takes the horizontal direction. At the point of zero normal stress, i.e., the neutral axis, the principal tensile stress is equal to shear stress, and its direction is 45 degrees with respect to the member axis

As the principal tensile stress increases and exceeds the tensile strength of concrete,crack occurs in the direction perpendicular to the direction of principal tensile stress.

在的情况下的简支梁进行两点加载梁，弯矩和剪力分布是这样的，在中跨和边跨在两个时刻是恒定的，剪切力是恒定的。这两个被称为―剪边跨跨度‖剪跨。的弹性梁，弯曲应力，剪切应力，和主拉应力是根据梁理论确定。由于混凝土材料在张力较弱，主拉应力的大小和方向是很重要的。在位置零剪切应力，即，极端紧张的纤维，主拉应力以水平方向。在零的正应力的点，即，中性轴，主拉应力等于剪切应力，其方向是45度的相对于轴的成员 作为主拉应力增加，超过了混凝土的抗拉强度，裂纹发生在垂直于主拉应力方向。

4.2.2 Reinforced Concrete without Shear Reinforcement无腹筋梁的斜截面受剪性能

For a reinforced concrete without shear reinforcement, flexural crack is firstly formed in regions of large moments, and its direction is parallel to the member axis. The flexural tension strength can be furnished by the tension steel after the formation of tension cracks in the concrete. The longitudinal tension reinforcement has been so calculated and placed that it is chiefly effective in resisting longitudinal tension near the tension face. It does not reinforce the tensionally weak concrete against the diagonal tension stresses that occur elsewhere, caused by shear alone or by the combined effect of shear and flexure. Eventually, these stresses attain magnitudes sufficient to open additional tension cracks in a direction perpendicular to the local tension stress. They are known as diagonal cracks, in distinction to the vertical flexural cracks. Diagonal cracks occur in regions in which the shear forces are high.

Three types of failure modes have been observed in the many tests of reinforced beams without

shear reinforcement. The mode of failure is influenced by the shear span to effective depth ratio 对钢筋混凝土无腹筋，弯曲裂纹首先在较大弯矩的区域形成，其方向平行于构件轴线。弯曲抗拉强度可由受拉钢筋在混凝土中的拉裂缝形成后。纵向受拉钢筋已计算和放置，它主要是在抗纵向张力附近的张力面有效。它不加强张弱混凝土斜拉应力，在其他地方发生，引起的剪切单独或联合作用的剪切和弯曲。最终，这些应力达到程度足以在垂直于局部拉应力方向打开附加张力裂纹。他们被称为斜裂缝，以区别于竖向弯曲裂缝。斜裂缝出现的区域中的剪切力高。

三种类型的失效模式已经在许多试验观察钢筋梁的抗剪加固。故障模式的影响的剪跨比 剪跨比是影响无腹筋梁破坏形态的最主要参数

Where a is the distance between the support and the nearest concentrated load.

(1) Diagonal tension failure. The diagonal crack, once formed, spread either immediately or at only slightly higher load, traversing the entire beam from the tension reinforcement to the compression face, splitting it into two and failing the beam. This process is sudden and without warning and occurs chiefly in the beams with shear span to effective depth ratio of about 3 or more.

其中一个是支持和最近的集中荷载之间的距离。

（1）斜拉破坏。斜裂缝，一旦形成，传播或者立即或仅略高负荷，遍历整个梁的张力钢筋受压面，分裂成两个和失败的光束。这个过程是突然，没有警告，主要发生在梁的剪跨约3或更多的有效深度比。

(2) Shear compression failure . The diagonal crack, once formed, spreads toward and partially into the compression zone but stops penetrating to the compression face.In this case no sudden collapse occurs,and the failure load may be significantly higher than that at which the diagonal cracks first formed. The stress state becomes like a compression arch formed by diagonal cracks.In this case the beam fails when this arch crushes under diagonal compression.This behavior is chiefly observed in the beams with shear span to effective depth ratio ranging from 1 to 3.

（2）剪压破坏。斜裂缝，一旦形成，洒向部分为压缩区而停止穿透受压面。在这种情况下，没有突然发生坍塌，和故障负载可能会显着高于在斜裂缝形成。应力状态变得像一个压缩拱斜裂缝的形成。在这种情况下，梁失败时，这个拱压碎在对角的压缩。这种行为主要是观察在梁的剪跨比范围从1到3。

(3) Diagonal compression failure. For the case of so called deep beam, i.e., the shear span to effective depth ratio is very small (a/h0 < 1.0), the shear resisting mechanism is formed as a compression strut joining the loading and support points.

Since all of these failures are preceded by diagonal cracking of web concrete,so they are called as‖shear failure‖.

Figure4.14 shows portion of a beam in which a diagonal tension crack has formed.Considering the part of the beam to the left of the crack, shown in solild line, there is an external upward shear force Vext acting on this portion.

Once a crack is formed, no tension force perpendicular to the crack can be transmitted across it. However, as long as the crack is narrow, it can still transmit force in its own plane through interlocking of the surface roughness. Aggregate interlock forces amounts to one-third and more of the shear force 骨料咬和作用The other internal forces are those in the uncracked portion of the concrete,Vcz,and those across the longitudinal steel, acting as a dowel ,Vd.

（3）斜压破坏。对于所谓的深梁，即，剪跨比很小（A / H0≤1），抗剪机理是由压杆连接的

负载和支撑点。

由于所有这些失败之前，通过对角Web混凝土开裂，因此他们被称为―剪切‖。

figure4.14显示一梁，斜拉裂缝形成的部分。考虑梁的局部裂纹的离开，在solild线所示，外部有一个向上的剪切力作用在这部分外接电源。

一旦形成裂纹，无张力垂直于裂纹可以被传输过它。然而，只要破解是狭隘的，它仍然可以通过表面粗糙度联锁发送在其自身平面内的力。骨料咬合力相当于剪切力骨料咬和作用其他内力的三分之一和更多的是那些在混凝土未开裂部分，VCZ，和那些在纵向钢，作为一个定位销，VD。

4.2.3 Reinforced Concrete with Web Reinforcement

Economy of design demands that a flexural member be capable of developing its full moment capacity rather than having its strength limited by premature shear failure. This is also desirable because structures, if overloaded, should not fail in a sudden and explosive manner,but should show adequate ductility and warning of impending distress.The latter is typical of flexural failure caused by the yielding of the longitudinal bars ,which is preceded by gradual excessively large deflections and noticeable widening of cracks. Therefore, special shear reinforcement, known as web reinforcement, is used to increase this strength.

4.2.3钢筋混凝土有腹筋

经济的设计要求的受弯构件能够发展其全部时刻的能力，而不是其强度受到过早剪切破坏。这是因为结构是可取的，如果超载，不应该在一个突然的爆炸性的方式失败，但应该表现出足够的延性和即将到来的危机预警。后者是典型的由纵向钢筋屈服所引起的弯曲破坏，这是之前逐渐过大挠度和裂缝明显加宽。因此，特殊的抗剪钢筋，称为钢筋网，用来增加强度。

1. Types of Web Reinforcement

Typically, web reinforcement is provided in the form of vertical stirrups, spaced at varying intervals along the axis of the beam depending on the requirements , as shown in Figure

4.15.Multiple-leg stirrups such as shown in Figure 4.15d are sometimes necessary. Relatively small sized(一定大小的) bars are used, generally 6 to 12 mm in diameters. Stirrups are formed to fit around the main longitudinal bars at the bottom and hooked or bent around longitudinal bars at the top of the member to improve anchorage and provide support during construction.

1箍筋类型。

通常情况下，钢筋网是垂直箍筋的形式提供的，在不同的时间间隔取决于要求沿梁轴，如图

4.15.multiple-leg箍筋如图所示4.15d有时是必要的。相对小的尺寸（一定大小的）条，一般6至12毫米的直径。形成箍筋适合在主筋的底部和钩状的或弯曲的纵筋在构件上提高锚固施工期间提供支持。

Alternatively, shear reinforcement maybe provided by bending up a part of the longitudinal steel where it is no longer needed to resist flexural tension,as suggested by Figure 4.15e. In continuous beams, these bent-up bars may also provide all or part of the necessary reinforcement for negative moments. The requirements for longitudinal flexural reinforcement often conflict with those for diagonal tension, and because the saving in steel resulting from use of the capacity of bent bars as shear resistance is small, most designers prefer to include vertical stirrups to provide for all the shear reinforcement, counting on the bent part of the longitudinal bars, if bent bars are used, only to increase the overall safety against diagonal tension failure.

另外，剪切弯曲的钢筋，它不再需要抗弯曲力的一部分也许提供加固，图4.15e建议。在连续梁，这些弯筋也可以提供所需的全部或部分负弯矩钢筋。纵向钢筋的要求经常发生冲突，与那些对角紧张，因为节约钢中使用弯曲的杆力产生的剪切阻力小，大多数设计者喜欢包括

垂直箍筋提供所有的抗剪钢筋，指望的纵向钢筋的弯曲，如果弯曲棒用，只能增加对斜拉破坏整体的安全。

2. Behavior of Web Reinforced Concrete Beams有腹筋梁受剪性能

Web reinforcement (抗剪钢筋) has no noticeable effect prior to the formation of diagonal cracks. In fact, measurements show that the web steel is practically free of stress prior to crack formation. 斜裂缝出现后，拉应力由箍筋承担After diagonal cracks have been developed, web reinforcement augments(增加) the shear resistance of a beam in four separate ways:

钢筋网的斜裂缝形成之前有没有明显的影响。事实上，测量结果表明，腹板钢几乎是免费的应力在裂纹的形成。后斜裂缝已被开发，腹筋梁的抗剪承载力增大了四种不同方式：

(1) Part of the shear force is resisted by the bars that traverse a particular crack.

(2) The presence of these same bars restricts the growth of diagonal cracks and reduces their penetration into the compression zone. This leaves more uncracked concrete available at the head of the crack for resisting the combined action of shear and compression. 增加了剪压区的面积

(3) The stirrups also counteract the widening of the cracks, so that the two crack faces stay in close contact. This makes for a significant and reliable interlock force.箍筋控制了斜裂缝的开展

(4) The stirrups ie the longitudinal reinforcement into the main bulk (主要部分)of the concrete 吊住纵筋provides restraint against the splitting of concrete along the longitudinal reinforcement 延缓了撕裂裂缝的开展 increases the share of the shear force resisted by dowel action. 增强了纵筋销栓作用

（1）的剪切力的部分是由钢筋，遍历一个特定的裂纹的抵抗。

（2）这些钢筋的存在限制了斜裂缝的增长和降低渗透压区。这使得更多的未开裂的混凝土裂缝的头可抗联合作用下的剪切和压缩。（3）箍筋也抵消了裂纹的扩展，使两个裂纹面保持密切联系。这使得一个显着的和可靠的联锁力。（4）箍筋即纵筋在混凝土主体提供了约束对混凝土断裂沿纵向钢筋增加的剪切力通过销栓作用拒绝分享。

From this it is clear that failure will be imminent when the stirrups start yielding. This not only exhausts their own resistance but also permits a wider crack opening with consequent reduction of the beneficial restraining effects,point(2)to point(4),above. The observed failure modes in reinforced beams with shear reinforcement are similar to that in beams without shear reinforcement. The modes of failure are influenced by

这一点是明确的，破坏即将开始时箍筋屈服。这不仅耗尽了自己的抵抗也允许更宽的裂缝开口与有益的抑制作用随之减少，点对点（2）（4），上述。观察到的故障模式在钢筋梁的抗剪钢筋是类似于梁的抗剪加固。失效模式的影响

shear span to effective depth ratio剪跨比stirrup ratio配箍率

配箍率ρsv

式中 Asv- the cross section area of the stirrup 配置在同一截面内箍筋各肢的全部截面面 积：Asv ＝nAsv1，

n- the number of stirrup legs箍筋肢数，

Asv1 -the area of one stirrup leg 单肢箍筋的截面面积；

b -beam width，矩形截面的宽度，T形、I形截面的腹板宽度；

s - stirrup spacing箍筋间距。

3. Shear Capacity of Reinforced Concrete

Since web reinforcement is ineffective(无效的 ) in the uncracked beam, the magnitude of the shear force or stress that causes cracking to occur is the same as that in a beam without web reinforcement. Most frequently, web reinforcement consists of vertical stirrups. The forces acting

on the portion of such a beam between the crack and the nearby support are shown in Figure 4.16.

They are the same as those of Figure 4.except that each stirrup traversing the crack exerts a force on the given portion of the beam. Here Asv is the cross-section area of the stirrup(in the case of the U-shaped stirrup of Figure 4.15b it is twice the area of one bar)and f is the tensile stress in the stirrup.

钢筋混凝土受剪承载力

由于钢筋网是无效的（无效的）在无裂纹梁，剪切力的大小，或应力开裂原因的发生是在一个无腹筋梁相同。最常见的，包括垂直箍筋的钢筋网。作用于裂纹和附近的支持之间的这种梁部分的力量，如图4.16所示。他们是那些人物4.except每个箍筋穿越裂缝对梁的给定部分施加一个力相同。这里本是箍筋截面面积（在U型箍筋图4.15b它两次一杆的地区为例）和F在箍的拉伸应力。

Equilibrium in the vertical direction requires

Where Vsv=mAsvFyv is the vertical force in the stirrups ,Asv=nAsv1,and m being the number of stirrups traversing the crack. If p the horizontal projection of the crack, p is conservatively equal to the effective depth of the beam ,implying a crack somewhat flatters than 45°.

The sum of the first three internal shear components in Equation(4.2.3)is the shear strength contribution of the concrete (including the contribution from the uncracked concrete, aggregate interlock and dowel action)to the total shear resistance, and is denoted Vc.Thus, the shear capacity of reinforced concrete beam with stirrups is

在垂直方向上的均衡要求

在VSV = masvfyv在箍筋的垂直力，ASV = nasv1，与M箍筋穿越裂缝的数量。如果P裂纹的水平投影，P保守等于梁的有效深度，这意味着有些奉承比45°裂纹。

的第一个三内部剪切分量方程的总和（4.2.3）是混凝土抗剪强度的贡献（包括从未开裂的混凝土，骨料和销栓作用的贡献）的总的剪切阻力，并表示VC。因此，箍筋的钢筋混凝土梁的抗剪能力是

For common members with rectangular, T- or I- section subject to shear and flexure 矩形、T形及I形截面一般受弯构件

For isolated beam subjected to concentrated loads λ── shear span to effective depth ratio， λ is not to be taken greater than 3 or less than 1.5. 计算截面的剪跨比。当λ＜1.5时，取 λ=1.5；当 λ＞3 时，取λ= 3。

In practice, shear design is carried out at only one or two critical locations. The critical locations need be taken at the face of the support, at the section where web width changes, where tension reinforcement bends up,or where stirrup spacing varies.

在实践中，抗剪设计是在只有一个或两个关键位置进行。需要采取的关键位置在支撑面，处网页宽度的变化，在受拉钢筋的弯曲，或在箍筋间距的变化

3. Limitation on Cross-Section Dimension截面限制条件

When beam is heavily reinforced with shear stirrups, failure is due to local crushing of concrete in the compression strut prior to yielding of the shear reinforcement. To prevent the brittle diagonal compression failure, the cross-section dimension of reinforced concrete beam subjected to shear and moment is limited

linear interpolation method shall be adopted when 4.0＜ hw/h0 ＜6.0 βc——─ strength reduction factor for high strength concrete.

当梁的钢筋剪切箍筋，失败的原因是局部破碎的混凝土压杆的抗剪钢筋屈服前。为防止脆性斜压破坏，截面尺寸的钢筋混凝土梁的剪力和弯矩是有限的

线性插值法时应采用4＜HW / H0＜6βC——─高强混凝土强度折减系数。

5. Minimum Web Reinforcement

When stirrups in a beam are not adequate to constrain cracks, diagonal tension failure occurs on the formation of first diagonal tension cracking and stirrups yield.

当配箍率小于一定值时，斜裂缝出现后，箍筋因不能承担斜裂缝截面混凝土退出工作释放出来的拉应力，而很快达到极限抗拉强度并破坏，其受剪承载力与无腹筋梁基本相同。

A minimum stirrup ratio should apply in the beam where

为防止这种少筋破坏，《规范》规定当V>0.7ftbh0时，配箍率应满足

6.Detailing of Transverse Reinforcement

Stirrups are unable to resist shear unless they are crossed by an inclined crack. It is possible for a 45 degree crack to cross the web without intersecting a stirrup if the stirrup spacing exceeds beam depth. To ensure that a diagonal tension crack will be crossed by at least one strirrup and to reduce diagonal tension crack widths when

Maximum spacing and minimum diameter of stirrups are limited.

If the shear force is no greater than Vc, then theoretically no web reinforcement is required.Even in such a case , to ensure that the sudden failure doesn’t occur on the formation of a diagonal tension crack caused by an unexpected overload, GB 50010-2002 specifies that the required maximum spacing and the minimum diameter of stirrups when

详细的横向钢筋。

箍筋无法抵抗剪切除非他们由一个斜裂缝相交。对于一个45度的裂纹不相交的箍筋箍筋间距超过如果梁深度交叉网络是可能的。为确保斜拉裂缝将由至少一个strirrup交叉和降低斜拉裂缝宽度时

箍筋最大间距和最小直径是有限的。

如果剪切力不大于VC，那么还需要理论上的无腹筋。即使在这样的情况下，确保不发生突发性故障的意外过载引起的斜拉裂缝的产生，GB 50010-2002指定所需的最大间距和箍筋最小直径时

Questions

1. Name and explain the three different failure modes of reinforced concrete beams without shear reinforcement under the combined effects of bending moment and shear force.

2. What are the main factors influencing the failure modes of reinforced concrete beams with or without shear reinforcement under the combined effects of bending moment and shear force?

3. Why would web reinforcement augment the shear resistance of a beam?

4. How do you determine the critical sections for shear in a beam?

5. How do we determine the minimum shear reinforcement in rectangular beams?Why do we provide the minimum shear reinforcement?

6. How would you prevent the brittle diagonal compression failure of reinforced concrete?

1。名称和解释三个不同破坏模式的钢筋混凝土梁的抗剪加固弯矩联合作用下的剪切力。

2。影响破坏模式的钢筋混凝土梁或没有剪加固弯矩联合作用下的剪切力的主要因素是什么？

3。为什么腹筋梁的抗剪承载力提高了？

4。你怎么确定在梁剪切临界截面？

5。我们如何确定矩形梁的最小抗剪加固？为什么我们提供最小抗剪加固？

6。你会如何防止钢筋混凝土斜压破坏的脆性？

4.3 Bond , Anchorage, and Development Length

4.3.1 Fundamentals of flexural bond

If the reinforced concrete beam of Figure4.17a was constructed using round reinforcing bars , and , furthermore, if those bars were greased or lubricated before the concrete were cast, the beam would be only little stronger than if it were built of plain concrete without reinforcement. If a load were applied, as shown in Figure4.17b, the bars would tend to maintain their original length as the beam deflects, the bars would slip longitudinally with respect to the adjacent concrete, it is essential that bond forces be developed on the inter face between concrete and steel, such as to prevent significant slip from occurring at that interface.

4.3.1 基本面弯曲粘结

如果钢筋混凝土梁的构造Figure4.17a使用圆钢筋,此外,如果这些钢筋被抓或润滑在混凝土是铸,梁会只有小比如果它被建造的素混凝土没有钢筋。如果一个负载应用,见Figure4.17b,钢筋将会倾向于保持其原始长度的梁偏转,钢筋将会滑纵向对相邻的混凝土,它是必要的,是发达的粘结部队国米之间面临混凝土和钢,如防止重大滑移的发生在那个界面。

Figure4.17c shows the bond forces that act on the concrete at the interface as a result of bending, while Figure 4.17d shows the equal and opposite bond forces acting on the reinforcement. It is through the action of these interface bond forces that the slip indicated in Figure4.17b is prevented.

Figure4.17c显示了粘结的力量作用于混凝土在接口由于弯曲,而图4.17 d显示了大小相等、方向相反的粘结力的强化。正是通过这些接口的作用,指出粘结部队在Figure4.17b是防止滑倒。 Some years ago, when plain bars without surface deformations sere used, initial bond strength was provided only by the relatively weak chemical adhesion and mechanical friction between steel and concrete, Once adhesion and static friction were overcome at larger loads, small amount of slip led to interlocking of the natural roughness of the bar with the concrete. However, the natural bond strength is so low that in beams reinforced with plain bars , the bond between steel and concrete was frequently broken. Such a beam will collapse as the bar is pulled through the concrete. To prevent this, and anchorage was provided, chiefly in the form of books. If the anchorage is adequate, such a beam will not collapse, even if the bond is broken over the entire length between anchorages. This is so because the member acts as a tied arch, as shown in Figure4.18, with the uncracked concrete shown shaded representing the arch and the anchored bars preventing the tied rod. In this case, over the length in which the bond is broken, bond forces are zero. This means that over the entire unbonded length the force in the steel is constant and equal to T=M_/z. As a consequence, the total steel elongation in such a beam is larger that is beams in which bond is preserved, resulting in larger deflection and greater crack widths.

几年前,当普通钢筋没有表面变形使用,最初的粘结强度干枯了仅由相对较弱的化学附着力和机械摩擦钢铁和混凝土之间,一旦粘附和静态摩擦是克服在大负载、少量的滑动导致联锁的自然粗糙度与混凝土的钢筋。然而,自然粘结强度太低,在梁钢筋与普通钢筋,钢筋和混凝土之间的关系经常被打破。这种光束将会崩溃钢筋拉通过混凝土。为防止这种情况,和锚固提供,主要是在形式的书籍。如果锚地是足够的,这种光束不会崩溃,即使粘结是破碎的整个长度锚地之间。这是因为成员充当一个绑拱,见图4 18,无裂缝的混凝土显示阴影代表拱和锚定钢筋防止绑杆。在本例中,长度,粘结被打破,粘结力量是零。这意味着在整个无粘结长度的力在钢是恒定的,等于T = M_ / z。因此,在这样一个总钢伸长梁大这是梁,粘结是保存,导致更大的挠度和裂缝宽度更大。

To improve this situation, deformed bars are now universally used. With such bars, the

shoulders of the projecting ribs bear on the surrounding concrete and result in greatly increased strength, It is then possible in most cases to dispense with special anchorage devices such as hooks. In addition, crack widths as well as deflections are reduced.

为了改善这种情况,变形钢筋现在普遍使用的。这样的钢筋,肩膀上的投射肋骨熊周围的混凝土和导致大大增加强度,然后就可以在大多数情况下,免除特殊锚固装置如钩。另外,裂缝宽度和挠度减少。

4.3.2 Bond strength and development length 粘结强度和基本锚固长度

For Reinforce bars in tension, two types of bond failure have been observed. The first is direct pullout of the bats, which occurs when ample confinement is provided by the surrounding concrete cover thickness and bar spacing. The second type of failure is splitting of the concrete along the bar when cover confinement or bar spacing is insufficient to resist the lateral concrete tension resulting from the wedging effect of the bar deformations. Present-day design methods require both possible failure modes be accounted for.

为加强钢筋在紧张,两种类型的粘结失败曾被观察到。第一个是直接撤离的蝙蝠,它出现在充足的限制是由周围的混凝土保护层厚度和钢筋间距。第二种类型的失败是分裂的混凝土在钢筋当盖监禁或钢筋间距是不足以抵抗侧混凝土张力产生的楔入效应钢筋的变形。现在的设计方法既需要可能的失效模式是占了。

1. Bond strength 粘结力

If the bar is sufficiently confined by a mass of surrounding concrete, then, as the tensile force on the bar is increased adhesive bond and friction are overcome4, the concrete eventually crushes locally ahead of the ribs immediately adjacent to the bar interface, as shown in Figure4.19, and bar pullout results. The surrounding concrete remains intact. For modern deformed bars, adhesion and friction are much less important than the mechanical interlock of the deformations with surrounding concrete.

1 负载强度

如果钢筋充分限制大量的周围的混凝土,然后,随着拉伸力在钢筋上增加粘结和摩擦是overcome4,混凝土最终粉碎前的本地立即毗邻钢筋肋骨界面,见图4 19,钢筋撤军的结果。周围的混凝土仍然完好无损。现代预应力钢筋、粘附和摩擦是更重要的比机械联锁与周围混凝土的变形。

Bond failure resulting form splitting of the concrete is more common in beams than direct pullout. Such splitting comes mainly form wedging action when the ribs of the deformed bars bear against the concrete. It may occur either in a vertical plane as in Figure4.20a or horizontally in the plane of the bars as in Figure4.20b. The horizontal type of splitting frequently begins ar a diagonal crack. The dowel action increase the tendency toward splitting. This indicates that shear and bond failure are often intricately interrelated.

When pullout resistance is overcome or when splitting has a spread all the way to the end of an unanchored bar, complete failure occurs. Sliding of the stell relative to the concrete leads to immediate collapse of the beam.

粘结失败导致分裂的形式在梁混凝土更为普遍比直接撤离。这样的分割主要是形成楔入作用当肋骨的变形钢筋与混凝土承担。这可能发生在一个垂直平面要么在Figure4.20a或横向平面的钢筋在Figure4.20b。水平类型的分裂频繁一斜裂缝开始基于―增大化现实‖技术。这个销行

动增加分裂倾向。这表明剪切和粘结失败往往是唇齿相依的。

当拔阻力是克服或当分裂有一路铺到最后一个非固定杆,发生完全故障。滑动的钢相对于混凝土导致立即崩溃的梁。

2.development length 锚固长度

The development length is defined as that length of embedment necessary to develop the full tensile strength of the bar, controlled by either pullout or splitting. When reference to Figure4.21, the moment, and therefore the steel stress, is maximum at point a (neglecting the weight of the beam) and zero at the supports. If the bar stress is a, at a, then the total tension force A,a must be transferred form the bar to the concrete in the distance l by bond forces. To fully develop the strength of the bar, A,f, the distance l must be ar least equal to the development length of the bar, established by pull-out tests. In the beam of Figure4.21, if the actual length c is equal to or greater than the development length l, no premature bond failure will occur. That is , the beam will fail in bending or shear rather than by bond failure. This will be so even if in the vicinity of cracks local slop may have occurred over small region along the beam.

It is seen that the requirement for safety against bond failure is this; the length of the bar, from any point of given steel stress (a, or at most f,) to its nearby free end must be at least equal to its development length. However, if the actual available, length is inadequate for full development, special anchorage, such as by hooks, must be provided.

锚固长度定义为长度埋置必要开发完整的抗拉强度,钢筋的控制通过撤军或分裂。当参考图4 21,此刻,因此钢应力最大点,是一个(忽略梁的重量)和零在支持。如果杆应力是一个,在一个,然后总张力,必须转移到具体的形式钢筋在距离l通过粘结部队。充分发挥实力的钢筋,一个f、l的距离必须ar至少等于发展条的长度,建立了拉拔力测试。在梁的图4 21,如果实际长度c等于或大于长度,不过早发展粘结将发生故障。那是,梁会失败在弯曲或剪切而不是粘结失败。这将是如此,即使在裂缝附近的当地污水可能发生在小区域沿梁。

它被认为对安全性的需求,这是对粘结失败;条的长度,从任何角度给出钢应力(或最多f),其附近的自由端必须至少等于其锚固长度。然而,如果实际可用的,长度是不足以充分发展、特殊锚固,如通过钩子,必须提供。

3.Factors influencing development length锚固长度的影响因素

Experimental research has identified the factors that influence development length, and analysis of the test data has resulted in the experimental equations used in present design practice. The most basic factors include concrete tensile strength, cover thickness, spacing of the reinforcing bars, and the presence of transverse steel reinforcement.

实验研究已经确定了影响因素,锚固长度,并分析测试数据导致实验方程用于现有设计实践。最基本的因素包括混凝土抗拉强度、保护层厚度、钢筋的间距,存在横向钢筋。

The tensile strength of the concrete is important because the most common type of bond failure in beams is the type of splitting shown in Figure4.20. The development length si inverse proportional to the axial tensile strength of concrete, f, but is mot inverse proportional to the cube compressive strength of concrete, f.

混凝土的抗拉强度是很重要的,因为最常见的类型的粘结失败在梁是类型的分裂图4 20所示。锚固长度成正比的si逆轴向拉伸强度的混凝土,f,但出去逆成正比的立方体抗压强度的混凝土,f。

Cover thickness also influences splitting clearly, if the horizontal or vertical cover is increase, more concrete is available to resist the tension resulting from the wedging effect of the deformed bars, resistance to splitting is improved, and development length is less.

覆盖层厚度也影响分割清楚,如果水平或垂直覆盖增加,更多的混凝土可以抵制张力产生的楔入效应的变形钢筋、抗分裂是改善和锚固长度是更少。

Similarly, Figure4.20b illustrate that is the bar spacing is increased( e.g if only two instead of three bars are used), more concrete per bar would be available to resist horizontal splitting. In beams, bars are typically spaced about one or two bar diameters apart. On the other hand, for slabs, footings, and certain typs of members, bar spacings are typically much greater, and the required development length is reduced.

同样,Figure4.20b说明是钢筋间距增加(e。如果只有两个相反的g使用三块),更具体的每条可以抵抗水平分割。在梁、钢筋通常间隔约一或两条直径分开。另一方面,对于板,立足点,和特定的形式,钢筋的成员,间距通常更大,所需长度减少发展。

Transverse reinforcement improves the resistance of tensile bars to both vertical failure or horizontal splitting failure because the tension force in the transverse steel tends to prevent opening of the actual or potential crack.

横向加固提高抗拉伸钢筋两个垂直或水平分割失败失败因为张力的横向钢倾向于防止开放的实际或潜在的裂纹。

Based on the result of a statist real analysis of pull-out data, with appropriate simplifications, the length l, needed to develop stress f, in a reinforcing bar may be expressed as

基于一个真实的结果分析出的数据的中央集权,适当简化,长度,需要开发压力,f钢筋可以被表示为

4.3.3 anchorage of tension bars by hooks 锚固拉力杆挂钩

1.standard dimensions 标准尺寸

In the event that the desired tensile stress in a bar cannot be developed by bond alone, it is necessary to provide special anchorage at the end of the bar, usually by means of a 90°or a 180°hook. The dimensions and the bend radii for such hooks have been standardized in code as follows:

所需的拉伸力是不能被单独开发的，通常必须通过一个90度或180度的钩的装置，在最后提供特殊的锚固，例如像钩子的尺寸和弯曲半径已经有了标准化的代码，如下所示：

(1). A 180 degrees bend plus an extension of at least 3 bar diameters at the free end of the bar 弯曲180度在自由端处至少延长3倍的直径

(2). A 90 degrees bend plus an extension of at least 15 bar diameters at the free end of the bar 弯曲90度在自由端处至少延长15倍的直径

(3). For stirrup and tie anchorage, a 135 bend plus an extension of at least 5 bar diameters, but not less than 50mm, or a 90 degrees bend plus an extension of at least 10 bar diameters at the free end of the bar，as shown in Figure 4.23.

对于钢筋和锚固钢筋而言，135弯曲加上至少5倍直径的延伸，但不小于50mm，或90度弯曲加上钢筋直径至少10倍的自由端延伸。如图4.23

2. Mechanical Anchorage机械锚固

For some special cases, e.g. at the ends of main flexural reinforcement in deep beams, there is no room for hooks or the confinement steel, and special mechanical anchorage devices must be used. They may consist of welded short transverse bar, welded plate, or T-headed bar.

对于某些特殊情况下，例如主要在抗弯钢筋的底端，有钩或没有空间限制的钢，必须使用特殊的机械锚固装置，包括了短钢筋焊接，焊接平板，短钢焊在T头

4.3.4 钢筋的连接 Bar Splices

In general, reinforcing bars are stocked by suppliers in lengths of 9 or 12 meters for bars. For this reason, and because it is often more convenient to work with shorter bar lengths, it is frequently necessary to splice bars in the field. Splices in the reinforcement at points of maximum stress should be avoided, and when splices are used they should be staggered, although neight condition is practical, for example, in compression splices in column.

一般情况下，钢筋库存的供应商只供应9米或12米。由于它对于更短的杠长度来说更方便，所以它经常被用作焊接棒。为避免接片的最大受力点的加强，用于拼接时，尽管长度够长，它们也应该错开。例如在列中的压缩熔接。

There are three choices for joining bars together (1) mechanical splices, (2) welded splices, and (3)lap splices.

有三种连接方式：（1）机械连接（2）焊接连接（3）搭接连接

The mechanical and welded splices must be tested to show the development in tension or compression of at least 125% of the specified yield strength of the bar. Welded splices must conform to structural welding code for reinforcing steel. Since splices introduce weak links into the structure, they should be located as much as possible away from points of maximum force and critical locations.

机器和焊接连接必须经过测试，强度至少为125%的拉伸或压缩。焊接连接必须符合钢筋结构焊接规范。由于接头被引入到结构中的薄弱环节，他们应该被放在尽可能远离力量最大处和关键的位置。

Splices for bars smaller than 16mm in diameter are usually made simply by lapping the bars a sufficient distance to transfer stress by bonding from one bar to the other. The lapped bars are usually placed in contact and tightly wired so that they stay in position as the concrete is placed. Design code prohibits the use of lapped splices for main reinforcement in axially loaded tension members and tension members with small eccentricity, tension bars that are greater than 28mm in diameter, or compression bars that are greater than 32mm in diameter.

小于16mm的采用搭接，通过钢筋与混凝土之间的粘结强度来传递钢筋的内力。 轴心受拉及小偏心受拉构件的纵向受力钢筋不得采用绑扎搭接接头；直径大于28mm的受拉钢筋及直径大于32mm的受压钢筋不宜绑扎搭接接头。

Generally, bars in tension need to be lapped over a distance of at least 1.2 times the develop length, and in no case be less than 300mm. the lap splice length in compression shall not be less than 70% of that in tension, not be less than 200mm. if any of the load combinations is expected to introduce tension in the column reinforcement, column bars should be lapped as tension splices.

一般来说，对答接头是锚固长的1.2倍且不能小于300mm,受压是受拉的70%且不小于200mm.如果任何荷载组合能够出台张柱力加固，柱杆张力按受拉处理。

No more than half of the total reinforcement be spliced within the required lap length. This may be achieved by staggering alternate bar splices at least a lap length. Ties should be provided through the tension lap splice length with a maximum spacing of 5 times the minimum diameter of lapped bars or 100mm, whichever is less. The spacing of ties provided through the compression lap splice length shall not exceed 10 times the minimum diameter of lapped bars, nor be greater than 200mm. The diameter of ties shall not be less than 1/4 of the maximum diameter of lapped bars.

不超过一半的总加固拼接内的搭接长度，这可能是实现备用杆接头错开至一个搭接长度。当钢筋受拉时，箍筋间距s不应大于搭接钢筋较小直径的5倍，且不应大于100mm；

当钢筋受压时，箍筋间距s不应大于搭接钢筋较小直径的10倍，且不应大于200mm。在纵向受力钢筋搭接长度范围内应配置箍筋，其直径不应小于搭接钢筋较大直径的0.25倍。

Questions

1. explain the importance of the bond and why it is essential to provide berween steel and

concrete in beam.

解释粘结的重要性以及为什么它是钢和混泥土的必要物质

2. what is development length? What are the factors that influence the development length? 什么是基本锚固长度，影响锚固长度的因素是什么？

3. how would you determine the development lengths of bars?

如何确定钢筋的锚固长度

4. how would you splice reinforcing bars?

怎么拼接钢筋