土木工程毕业设计外文翻译.doc

12 Flexure of reinforced concrete beams钢筋混凝土梁的性能 Example 3-10 (Design of a reinforced concrete beam with tension reinforcement only)=A reinforced concrete beam , with an effective depth of 16 inches and a width of 12 inches ,is reinforced with Grade 60 bars and has a concrete cylinder strength of 4000 pounds per square inch. The beam carries a superimposed dead load ,including its self weight, of 2.5 kips per foot run and superimposed live load of 2.7 kips per foot run over on effective span of 15 feet .Determine the area of tension reinforcement required.例3-10 （在拉力作用下钢筋混凝土梁的设计）一个钢筋混凝土梁，其有效高度为16英寸，宽度为12英寸，钢筋的强度等级为60，混凝土的强度等级为4000磅每平方英寸，计算跨度为15英尺，该梁承受的恒载为2.5千磅每英尺，活载为2.7千磅每英尺，求受拉钢筋的截面面积。Solution 解： The applied dead load moment is given by恒载作用下的弯矩为： The applied live load moment is given by活载作用下的弯矩为： The factored moment at mid span is obtained from ACI Equation (9-1) as由ACI方程式得到的在跨中的弯矩为： The maximum allowable factored moment for a singly reinforced beam is obtained from Table 3.3 as由表3.3得出，单筋混凝土梁的最大允许弯矩为： Hence the section is adequate.从而这个弯矩是满足的。The design moment factor is弯矩设计系数为 and 和 From Table 3-2, the corresponding tension reinforced index is从表3-2可知，相应的张拉系数是 The required tension reinforcement ratio is given by所需受拉钢筋的配筋率是： The required area of tension reinforcement is受拉钢筋的截面面积为 Provide three No. 10 bars which, from Table 1-7, given an area of 3.81 square inches. =由表1-7查得3根10元钢筋的面积是3.81平方英寸。Examples 3-11 (Analysis of a reinforced concrete slab) =A one-way, reinforced concrete slab is continuous over four, equal, clear spans of 15 feet. The slab has an overall depth of 7 inches with concrete cylinder strength of 3000 pounds per square inch. The reinforcement at the top of the slab at the first interior support consists of No. 4,Grade 60,bars at 11 inches on center. In addition to its own weight, the slab carries a superimposed dead load of 26 pounds per square foot. Determine the maximum uniformly distributed superimposed live load which the slab can support.例 3-11（钢筋混凝土板的分析） 一个四边连续，相等的混凝土单向板，其净跨为15英尺，板的全高为7英寸，其混凝土强度等级为3000磅每平方英寸，板的上部配筋为间距11英寸4根强度等级60的钢筋，包括板的自重，板上的恒载为26磅每平方英尺。求板所能承受的最大均布活载。Solution 解:The minimum allowable concrete cover to the reinforcement in the slab, in accordance with ACI section 7.7.1, is根据ACI 7.7.1小节知，混凝土最小保护层厚度为： The effective depth provides is 有效高度为 The area of tension reinforcement in a 12 inches width of slab with No. 4 bars at 11inches on center is obtained form Table 1-8 as由表1-8可得，宽12英寸配置元4间距为11英寸的受拉钢筋截面面积为： The tension reinforcement ratios provide is given by受拉钢筋的配筋率为： Hence the reinforcement provide is satisfactory.因此配置的钢筋是满足要求的。The tension reinforcement index is 受拉钢筋系数为： From Table 3-2, the corresponding value of由表3-2可得，其相应的值为： The allowable factored moment is given by允许弯矩设计值为： +The self weight of the slab is板的自重为： The total dead load is given by 恒载的总值为： Using the approximate moment coefficient given in ACI Section 8.3.3, the negative moment produced by the dead load at the first interior support is 利用由ACI 8.3.3小节给出弯矩近似法，由恒载产生的负弯矩为： The factored dead load moment is obtained from ACI Section 9.2.1 as由ACI 9.2.1小节得到恒载弯矩设计值为： The allowable factored live moment is given by 活载弯矩设计值为： The allowable non-factored live load moment is obtained from ACI Section 9.2.1 as由ACI 9.2.1小节得到活载弯矩标准值为; The allowable non-factored live load is obtained from ACI Section 8.3.3 as由ACI 8.3.3 小节得到的活载标准值为： The slab can support a uniformly distributed live load of 56.4 pounds per square foot. =此板所能承受的均布活载为56.4磅每平方英尺。 Figure 3-6 Reinforced concrete beam with compression reinforcement 图3-6 在压力作用下的钢筋混凝土梁3.2.2 Rectangular beam with compression reinforcement 3.2.2在压力作用下的钢筋混凝土梁When the applied factored moment exceeds the maximum design strength of a singly reinforced member with the maximum allowable reinforcement ratio, compression reinforcement and additional tension reinforcement must be provide, as shown in Figure 3-6.The difference between the applied factored moment and the maximum design moment strength of a singly reinforced section is在最大配筋率下，当单筋混凝土梁的施加弯矩值大于最大弯矩设计值时，其受压钢筋和附加受拉钢筋由图3-6所示，单筋混凝土梁的施加弯矩值与最大弯矩设计值之差为 The required area of compression reinforcement is given by所需受压钢筋的截面面积为： Where 式中 stress in the compression reinforcement受压钢筋的应力强度The additional area of tension reinforcement required is所需附加受拉钢筋的截面面积为： The total required area of tension reinforcement is受拉钢筋的总面积为： The depth of the stress block is obtained by equating forces and is given by由水平方向的平衡方程可得，受压区的高度为： The neutral axis depth is given by ACI Section 10.2.7 as由ACI 10.2.7 给出的中性轴高度为： c=a/The strain in the compression reinforcement is obtained from the strain diagram in Figure 3-6 and is由图3-6应力图得到，受压钢筋的应变为： Where 式中 The stress in the compression reinforcement is受压钢筋的应力强度为： The required area of compression reinforcement is所需受压钢筋的截面面积为： The maximum allowable tension reinforcement ratio is given by ACI Section 10.3.3 as由ACI10.3.3给出的受拉钢筋的最大配筋率为： Where 式中 In order to analyze a given member with compression reinforcement, an initial estimate of the neutral axis depth is required. Assuming that the compressive strain in the concrete is 0.003 the stress in the compression and tension reinforcement may now be determined. The total compressive force in the conctere and the compression reinforcement is then compared with the tensile foce in the tension reinforcement. The initial estimate of the neutral axis depth is then adjusted until these two values are equal. The maximum nominal moment provide by the section is obtained by taking moments of the forces in the concrete and in compression reinforcement about the centroid of the tension reinforcement. 为分析受压钢筋的混凝土梁，其最终是确定中性轴的高度，假设混凝土在压力作用下的压应变为0.003，那么受拉钢筋就可以确定了，在钢筋混凝土中，其混凝土和受压钢筋所承受的总压力与受拉钢筋所承受的总拉力是相等的，因此中性轴高度也就可以确定了，最大的名义弯矩值是由混凝土和受压钢筋所承受的总压力对受拉钢筋的形心取距而得到的。Example 3-12 (Design of a rectangular beam with compression reinforcement) =A reinforced concrete beam is reinforced with Grade 60 bars and has a concrete cylinder strength of 3000 pounds per square inch. The beam carries a superimposed live load of four kip per foot run over an effective span of thirty feet. The beam has an overall depth of 30 inches, a width of 12 inches, an effective depth to the centriod of the tension reinforcement of 27 inches, and a depth to the centriod of the compression reinforcement of 3inches.Determine the areas of tension and compression steel required.例 3-12 （配置受压钢筋的矩形梁的设计）钢筋混凝土梁，其配置的钢筋等级强度为60，混凝土的强度等级为3000磅每平方英寸，计算跨度为30英尺，在梁上施加得活载为4千磅每英尺，梁的全截面高30英寸，宽12英寸，距受拉钢筋形心处的有效高度为27英寸，距受压钢筋形心的高度为3英寸，求受拉钢筋和受压钢筋的截面面积。Solution 解：The self weight of the beam is梁的自重为： The dead load moment is given by恒载作用下的弯矩为： The live load moment is given by活载作用下的弯矩为： The maximum allowable reinforcement ratio for a singly reinforced beam is obtained from Table 3-3 as由表3-2可得，单筋截面梁的最大配筋率为： The maximum reinforcement area for a singly reinforced beam is单筋截面混凝土梁的最大配筋面积为： The maximum allowable design moment factor for a singly reinforced beam is obtained from Table 3-3 as 由表3-3可得，单筋截面混凝土梁的最大允许弯矩设计值为： The maximum design moment of a singly reinforced section is单筋截面混凝土梁的最大设计弯矩为： The additional area of tension reinforcement required is所需附加的受拉钢筋的截面面积为： The total required area of tension reinforcement is given by所需受拉钢筋的总面积为： The depth of the stress block is obtained by equating horizontal forces and is由水平方向的平衡方程可得受压区的高度为： The neutral axis depth is given by ACI Section 10.2.7 as 由ACI 10.2.7小节给出的中性轴高度为： The stress in the compression reinforcement is受压钢筋的应力强度为： The required area of compression reinforcement is所需受压钢筋的截面面积为： The maximum allowable tension reinforcement area is given by ACI Section 10.3.3 as由ACI 10.3.3小节给出的受拉钢筋的最大截面面积为： Example 3-13 (Analysis of a rectangular beam with compression reinforcement) =A reinforced concrete beam is reinforced with Grade 60 bars and has a concrete cylinder strength of 4000 pounds per square inch. The beam has a width of 24 inches, an effective depth to the centriod of the tension reinforcement of 3 inches. The compression reinforcement consists of 4 No. 11 bars and the tension reinforcement consists of 6 No.11 bars. Determine the design moment strength of the section.例 3-13（配置受压钢筋的矩形截面梁的分析）钢筋混凝土梁，其配置的钢筋等级强度为60，混凝土的强度等级为4000磅每平方英寸，宽度为24英寸，距受拉钢筋的形心的距离为3英寸，配置的受压钢筋为4根元11，受拉钢筋为6根元11，求所能承受的最大弯矩设计值。Solution解：The area of tension reinforcement provide by 6 No.11bars is obtained from Table 1-7 as由表1-7可得，6根元11的受拉钢筋截面面积为： The tension reinforcement ratio provided is given by受拉钢筋的配筋率为： The area of compression reinforcement provide by 4 No. 11 bars is 4根元11的受压钢筋的截面面积为： The compression reinforcement ratio provided is given by受压钢筋的配筋率为： Assume that the depth of the neutral axis is 假设中性轴的高度为： The stress in the tension reinforcement is obtained from Figure 3-6 as由图3-6可得，受拉钢筋的应力强度为： The stress in the compression reinforcement in obtained from Figure 3-6 as由图3-6可得，受压钢筋的应力强度为： The maximum allowable tension reinforcement ratio is given by ACI Section 10.3.3 as由ACI 10.3.3 小节给出，受拉钢筋的最大配筋率为： The depth of the stress block is given by ACI Section 10.2.7.1由ACI 10.2.7.1给出，受压区高度为： The compression force in the compressive stress block is在受压区混凝土所承受的压力为： The compressive force in the compression reinforcement is在受压区钢筋所承受的压力为： The tension force in the tension reinforcement is受拉钢筋的拉力为： Hence 因此 and the initial estimate for the depth of the neutral axis is correct.最终所确定的中性轴的高度是正确的。The design moment strength of the section is obtained by taking moment about the centriod of the tension reinforcement and is given by这段的弯矩值是对受拉钢筋形心取距而得到的，其值为： 3.2.3 Flanged section with tension reinforcement only（仅配置受拉钢筋的T型截面梁）A flanged member, with a flange width b, may be designed as a rectangular beam when the depth of the equivalent stress block is less than the flange thickness. 当受压区高度小于翼缘的厚度时，翼缘宽度为b的T型截面梁的设计可当作矩形截面梁来设计。The depth of the stress block given by 受压区高度为： where may be determined from Table 3-2 using the calculated value of .式中是由表3-2利用.来确定的The required reinforcement ratio, corresponding to, is given by在作用下，其所需的配筋率为： and the required area of tension reinforcement is 和所需的受拉钢筋的截面面积为： When the depth of the equivalent stress block equals the flange thickness, the design moment strength of the section is given by 当受压区高度等于翼缘的厚度时，其弯矩设计值为：， and the corresponding area of tension reinforcement is和相应的受拉钢筋的截面面积为： The conditions a ultimate load in a flanged member, when the depth of the equivalent rectangular stress block exceeds the flange thick