土木工程毕业设计外文翻译

75 □ 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：

MD?wD?2/8?2.5?152/8

?70.13 ki pfeetThe applied live load moment is given by活载作用下的弯矩为：

MD?wD?2/8?2.7?152/8

?75.94 ki pfeetThe 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：

Mu?1.4MD?1.7ML

?1.4?70.31?1.7?75.95 ?227.53 ki pfeetThe 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：

2Mu?Ku(mabxw)d

?936?12?162/12,000

?239.62 ki pfeet? MuHence the section is adequate.从而这个弯矩是满足的。

76 □ Flexure of reinforced concrete beams钢筋混凝土梁的性能

The design moment factor is弯矩设计系数为

Ku?Mu/bWd2?227.53?12,000/(12?162)

?888.79 poun pdsesrq ua irnechKu/fC'?888.79/4000and 和

?0.2222From Table 3-2, the corresponding tension reinforced index is从表3-2可知，相应的张拉系数是

29 9 ? ? 0.The required tension reinforcement ratio is given by所需受拉钢筋的配筋率是：

? ??f'c/fy

?0.299?4000/60,000 ?0.020The required area of tension reinforcement is受拉钢筋的截面面积为

As ??bwd

?0.020?12?16?3.8 s3qua irnechesProvide 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：

77 □ Flexure of reinforced concrete beams钢筋混凝土梁的性能

cc ? 0 . 7 i5nch esThe effective depth provides is 有效高度为

d ?h-cc?db/2

?7?0.75?0.5/2 ?6 inchesThe 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： As ?0.2 s2qua irnech esThe tension reinforcement ratios provide is given by受拉钢筋的配筋率为：

? ?As/bwd

?0.22/(12?6)?0.00306??min?(?0.0018 from ACI Section 7.12.2)??max?(?0.0160 fro mAC SIecti1o0n. 3).3

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：

? ??fy/fc'

?0.00306?60,000/3000 ?0.0612From Table 3-2, the corresponding value of由表3-2可得，其相应的值为： Ku/fc'?0.0531

The allowable factored moment is given by允许弯矩设计值为：

Mu ?Kubwd2?0.0531?3000?12?62/12,000+ ?5.73 ki pfeet

The self weight of the slab is板的自重为：

WSD?7?12?0.15/144 ?0.087 k5i ppefro otThe total dead load is given by 恒载的总值为：

wD?wSD?wAD

?0.087?50.026 ?0.113 k5i ppefro ot78 □ Flexure of reinforced concrete beams钢筋混凝土梁的性能

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：

MD?wD?2/10

?0.1135?152/10 ?2.55 ki pfeetThe 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：

MuD?1.4?MD

?1.4?2.55 ?3.57 ki pfeetThe allowable factored live moment is given by 活载弯矩设计值为：

MuL?Mu?MuD

?5.73?3.57 ?2.16 ki pfeetThe 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;

ML?MuL/1.7

?2.16/1.7?1.27 ki pfeetThe 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：

wL?10ML/?2n

?10?1.27?1000/152 ?56.4 poun pdsefro otThe 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

79 □ Flexure of reinforced concrete beams钢筋混凝土梁的性能

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 Mr?Mu?Mmax? resid umaolme nThe required area of compression reinforcement is given by所需受压钢筋的截面面积为：

' As?Mr/?fs'(d-d')

Where 式中 fs'?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：

AT?Mr/?fs'(d-d')?Af/fy''ss

The total required area of tension reinforcement is受拉钢筋的总面积为：

As?Amax?AT?Amax?Mr/?fy(d-d')

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： a ?fyAmax/0.85fc'bw

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/?1

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： ?'??c(1?d'/c) Where 式中 ?c?0.003

The stress in the compression reinforcement is受压钢筋的应力强度为：

fs'??cEs(1?d'/c)

?0.003?29,000,000(1?d'/c)?87,00(01?d/c)?fy'

85 □ Flexure of reinforced concrete beams钢筋混凝土梁的性能

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：

?Mn??[cc(d?a/2)?Cs(d?d')]/12

?0.9[345.4(27?4.23/2)?215.8(27?2)]/12 ?103 k3ip fseet3.2.3 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： a?Asfy/0.85fc'b?1.18?d where ? may be determined from Table 3-2 using the calculated value of Mu/fc'bd2. 式中?是由表3-2利用Mu/fc'bd2.来确定的

The required reinforcement ratio, corresponding toMu, is given by在Mu作用下，其所需的配筋率为：

???fc'/fy

and the required area of tension reinforcement is 和所需的受拉钢筋的截面面积为： As??bd

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：，

?Mn?0.85?fc'bhf(d?hf/2)?0.765fbhf(d?hf/2)'c

and the corresponding area of tension reinforcement is和相应的受拉钢筋的截面面积为： As?0.85fc'bhf/fy

The conditions a ultimate load in a flanged member, when the depth of the equivalent rectangular stress block exceeds the flange thickness, are shown in Figure 3-7. The area of reinforcement required to balance the compressive force in the outstanding flanges is given by

当矩形截面受压区高度大于T型截面的翼缘厚度时，T型截面梁的最终荷载由图3-7所示。

86 □ Flexure of reinforced concrete beams钢筋混凝土梁的性能

为平衡翼缘超出的压力，其所需的钢筋截面面积为：

Asf?Cf/fy?0.85fc'hf(b?bw)/fy

The corresponding design moment strength of the outstanding flanges is超出翼缘部分的相应弯矩值为：

Mf??Asffy(d?hf/2)

The residual moment to be developed by the beam web is 由梁来承担的剩余弯矩为： Mf?Mu?Mf

The required reinforcement ratio to provide the residual moment is其所需的配筋率为： ?w?0.85fc'[1?(1?Kw0.383fc')0.5]/fy where 式中 Kw?Mr/bwd2

The corresponding reinforcement area required to developed the residual moment is 来抵抗剩余弯矩的相应的钢筋截面面积为： Asw?bwd?w

Figure 3-7 Flanged member with tension reinforcement

图3-7 在拉力作用下的T型截面梁

Alternatively, the value of ?wmay be determined from Table 3-2 using the calculated value of

Mr/fc'bwd2.The corresponding reinforcement area required to developed the residual moment is 其中?w是由表3-2利用式Mr/fc'bwd2来确定的，来抵抗剩余弯矩的相应的钢筋截面面积为： Asw??wbwdfc'/fy

The total reinforcement area required is 钢筋总面积为： As?Asf?Asw

The total reinforcement ratio is ??As/bd钢筋的总配筋率为： The maximum allowable reinforcement ratio is given by Section 10.3.3 as 由10.3.3小节可知，最大配筋率为：

' ?max?0.75bw(?b??f)/b

Where式中 ?f?Asf/bwd

87 □ Flexure of reinforced concrete beams钢筋混凝土梁的性能

and 和

0.75?b??max ?0.75?0.85?87,000?1fc'/fy(87,000?fy)

is the maximum allowable reinforcement ratio for a rectangular section which may be obtained from Table 3-3

.由表3-3可得，对矩形截面梁而言，配筋率已是最大值。

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