我们可以通过对方程d2v / dx2 = M / EI的积分来确定弹性曲线的方程。该方程的求解需要两个连续的积分，以获得弹性曲线的挠度v。对每次积分，有必要引入积分常数，求出该常数以获得一个特定问题的唯一解。应该了解到双重积分法只适合于弹性变位，因而梁的转角是非常小的。而且，该法只考虑了由于弯曲引起的挠度。
          

UNIT 7
           Concrete and reinforced concrete are used as building materials in every country. In many, including the United States and Canada, reinforced concrete is a dominant（主要的） structural material in engineered construction（建造的建筑物）. The universal（通用的）nature of reinforced concrete construction stems from（归因于）the wide availability of reinforcing bars（钢筋）and the constituents（组成部分）of concrete, gravel,sand, and cement, the relatively simple skills required in concrete construction（施工）, and the economy（经济性）of reinforced concrete compared to other form of construction. Concrete and reinforced concrete are used in bridges, buildings of all sorts（各种各样）, underground structures, water tanks, television towers, offshore oil exploration and production structures（近海石油开采和生产结构）, dams, and even in ships.
            混凝土与钢筋混凝土作为建筑材料在每个国家被使用着。在很多国家，包括美国和加拿大，钢筋混凝土是建造的建筑物中主要的结构材料。钢筋混凝土建筑物通用的特性归因于能大量得到钢筋和混凝土的组分（即碎石、砂和水泥），混凝土施工需要相对简单的技术，以及与其他形式的建筑相比钢筋混凝土的经济性。混凝土与钢筋混凝土用于桥梁、各种房屋、地下结构、水箱、电视塔、近海石油开采和生产结构、大坝甚至船舶。
Mechanics of Reinforced Concrete
钢筋混凝土的力学
         
 Concrete is strong in compression but weak in tension. As a result, cracks develop（形成）whenever（每当）loads, or restrained shrinkage（收缩限制）or temperature changes, give rise to（导致）tensile stresses in excess of（超过）the tensile strength of the concrete. In the plain concrete（素混凝土）beam, the moments due to applied loads are resisted by an internal tension-compression couple（拉压力偶）involving tension in the concrete. Such a beam fails very suddenly and completely when the first crack forms. In a reinforced concrete beam, steel bars（钢筋）are embedded in the concrete in such a way that the tension forces needed for moment equilibrium after the concrete cracks can be developed in the bars.
            混凝土受压强、受拉弱。因此，每当受荷、收缩受阻或温度变化引起的拉应力超过混凝土的抗拉强度时，便会发生开裂。在素混凝土梁中，因外力引起的力矩由内部的拉-压形成的力偶来抵抗，此力偶中包含了混凝土的拉力。当第一条裂缝形成时，此梁会突然、完全地失效。在钢筋混凝土梁中，钢筋埋置在混凝土内的方式应能使混凝土开裂后在钢筋中产生平衡力矩所需的拉力。

           The construction（施工）of a reinforced concrete member involves building a form or mold（模具）in the shape of the member being built. The form must be strong enough to support the weight and hydrostatic pressure（静水压力）of the wet concrete, and any forces applied to it by workers, concrete buggies（料车）, wind, and so on. The reinforcement（钢筋）is placed in this form and held in place（固定就位）during the concreting（用混凝土浇筑）operation. After the concrete has hardened, the forms are removed（拆除）.

            钢筋混凝土构件的施工包括以在建构件的形状搭建模板或模具。模板必须足够强劲以支承湿混凝土的重量和静水压力，以及任何由工人、混凝土料车、风等施加给它的力。钢筋置于模板中，并在混凝土浇筑过程中固定就位。当混凝土硬化后便拆除模板。
Factors Affecting Choice of Concrete For a Structure
影响一个结构选择混凝土的因素
            The choice of whether a structure should be built of concrete, steel, masonry, or timber（木材）depends on the availability（可得性）of materials and on a number of（许多）value decisions（价值判断）.

            一个结构选择由混凝土、钢材、砌体还是木材建造取决于材料的可得性和许多价值判断。
    Economy    Frequently, the foremost（最重要的）consideration is the overall cost（总费用）of the structure. This is, of course, a function of the costs（费用函数）of the materials and the labor necessary to erect them. Frequently, however, the overall cost is affected as much or more by the overall construction time（总的建造时间）since the contractor and owner must allocate（分配）money（资金）to carry out the construction and will not receive a return on this investment （收回投资）until the building is ready for occupancy（居住）. As a result, financial savings（财务的节约）due to rapid construction may more than offset（足以抵消）increased material costs. Any measures designer can take to standardize the design and forming（加工）will generally pay off（使人得益）in reduced overall costs.