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1、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 sup

2、erimposed 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 (在拉力作用下鋼筋混凝土梁的設(shè)計)一個鋼筋混凝土梁,其有效高度為16英寸,寬度為12英寸,鋼筋的強度等級為60,混凝土的強度等級為4000磅每平方英寸,計算跨度為

3、15英尺,該梁承受的恒載為2.5千磅每英尺,活載為2.7千磅每英尺,求受拉鋼筋的截面面積。Solution 解: The applied dead load moment is given by恒載作用下的彎矩為: The applied live load moment is given by活載作用下的彎矩為: 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彎矩為: The maximum allowable factored moment for a singly r

4、einforced beam is obtained from Table 3.3 as由表3.3得出,單筋混凝土梁的最大允許彎矩為: Hence the section is adequate.從而這個彎矩是滿足的。The design moment factor is彎矩設(shè)計系數(shù)為 and 和 From Table 3-2, the corresponding tension reinforced index is從表3-2可知,相應(yīng)的張拉系數(shù)是 The required tension reinforcement ratio is given by所需受拉鋼筋的配筋率是: The req

5、uired area of tension reinforcement is受拉鋼筋的截面面積為 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元鋼筋的面積是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 o

6、f 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 superi

7、mposed dead load of 26 pounds per square foot. Determine the maximum uniformly distributed superimposed live load which the slab can support.例 3-11(鋼筋混凝土板的分析) 一個四邊連續(xù),相等的混凝土單向板,其凈跨為15英尺,板的全高為7英寸,其混凝土強度等級為3000磅每平方英寸,板的上部配筋為間距11英寸4根強度等級60的鋼筋,包括板的自重,板上的恒載為26磅每平方英尺。求板所能承受的最大均布活載。Solution 解:The minimum al

8、lowable concrete cover to the reinforcement in the slab, The effective depth provides is 有效高度為 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,寬12英寸配置元4間距為11英寸的受拉鋼筋截面面積為: The tension reinforcement ratios provid

9、e is given by受拉鋼筋的配筋率為: Hence the reinforcement provide is satisfactory.因此配置的鋼筋是滿足要求的。The tension reinforcement index is 受拉鋼筋系數(shù)為: From Table 3-2, the corresponding value of由表3-2可得,其相應(yīng)的值為: The allowable factored moment is given by允許彎矩設(shè)計值為: +The self weight of the slab is板的自重為: The total dead load is

10、given by 恒載的總值為: Using the approximate momentat the first interior support is The factored dead load moment is obtained The allowable factored live moment is given by 活載彎矩設(shè)計值為: The allowable non-factored live load moment is obtained The allowable non-factored live load is obtained The slab can suppo

11、rt a uniformly distributed live load of 56.4 pounds per square foot. =此板所能承受的均布活載為56.4磅每平方英尺。 Figure 3-6 Reinforced concrete beam with compression reinforcement 圖3-6 在壓力作用下的鋼筋混凝土梁compressionWhen the applied factored moment exceeds the maximum design strength of a singly reinforced member with the ma

12、ximum 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,當(dāng)單筋混凝土梁的施加彎矩值大于最大彎矩設(shè)計值時,其受壓鋼筋

13、和附加受拉鋼筋由圖3-6所示,單筋混凝土梁的施加彎矩值與最大彎矩設(shè)計值之差為 The required area of compression reinforcement is given by所需受壓鋼筋的截面面積為: Where 式中 stress in the compression reinforcement受壓鋼筋的應(yīng)力強度The additional area of tension reinforcement required is所需附加受拉鋼筋的截面面積為: The total required area of tension reinforcement is受拉鋼筋的總面積為

14、: 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,受壓區(qū)的高度為: c=a/The strain in the compression reinforcement is obtained from the strain diagram in Figure 3-6 and is由圖3-6應(yīng)力圖得到,受壓鋼筋的應(yīng)變?yōu)椋?Where 式中 The stress in the compression reinforcement is受壓鋼筋的應(yīng)力強度為: The requ

15、ired area of compression reinforcement is所需受壓鋼筋的截面面積為: The maximum allowable tension reinforcement 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

16、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 tw

17、o 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. 為分析受壓鋼筋的混凝土梁,其最終是確定中性軸的高度,假設(shè)混凝土在壓力作用下的壓應(yīng)變?yōu)?.003,那么受拉鋼筋就可以確定了,在鋼筋混凝土中,其混凝土和受壓鋼筋所承受的總壓力與受拉

18、鋼筋所承受的總拉力是相等的,因此中性軸高度也就可以確定了,最大的名義彎矩值是由混凝土和受壓鋼筋所承受的總壓力對受拉鋼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 superim

19、posed 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.Dete

20、rmine the areas of tension and compression steel required.例 3-12 (配置受壓鋼筋的矩形梁的設(shè)計)鋼筋混凝土梁,其配置的鋼筋等級強度為60,混凝土的強度等級為3000磅每平方英寸,計算跨度為30英尺,在梁上施加得活載為4千磅每英尺,梁的全截面高30英寸,寬12英寸,距受拉鋼筋形心處的有效高度為27英寸,距受壓鋼筋形心的高度為3英寸,求受拉鋼筋和受壓鋼筋的截面面積。Solution 解:The self weight of the beam is梁的自重為: The dead load moment is given by恒載作用下的

21、彎矩為: The live load moment is given by活載作用下的彎矩為: The maximum allowable reinforcement ratio for a singly reinforced beam is obtained from Table 3-3 as由表3-2可得,單筋截面梁的最大配筋率為: The maximum reinforcement area for a singly reinforced beam is單筋截面混凝土梁的最大配筋面積為: The maximum allowable design moment factor for a s

22、ingly reinforced beam is obtained from Table 3-3 as 由表3-3可得,單筋截面混凝土梁的最大允許彎矩設(shè)計值為: The maximum design moment of a singly reinforced section is單筋截面混凝土梁的最大設(shè)計彎矩為: The additional area of tension reinforcement required is所需附加的受拉鋼筋的截面面積為: The total required area of tension reinforcement is given by所需受拉鋼筋的總面

23、積為: 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壓區(qū)的高度為: The stress in the compression reinforcement is受壓鋼筋的應(yīng)力強度為: The required area of compression reinforcement is所需受壓鋼筋的截面面積為: Example 3-13 (Analysis of a rectangular beam with compression reinforcement)

24、 =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 a

25、nd the tension reinforcement consists of 6 No.11 bars. Determine the design moment strength of the section.例 3-13(配置受壓鋼筋的矩形截面梁的分析)鋼筋混凝土梁,其配置的鋼筋等級強度為60,混凝土的強度等級為4000磅每平方英寸,寬度為24英寸,距受拉鋼筋的形心的距離為3英寸,配置的受壓鋼筋為4根元11,受拉鋼筋為6根元11,求所能承受的最大彎矩設(shè)計值。Solution解:The area of tension reinforcement provide by 6 No.11bars

26、 is obtained from Table 1-7 as由表1-7可得,6根元11的受拉鋼筋截面面積為: The tension reinforcement ratio provided is given by受拉鋼筋的配筋率為: The area of compression reinforcement provide by 4 No. 11 bars is 4根元11的受壓鋼筋的截面面積為: The compression reinforcement ratio provided is given by受壓鋼筋的配筋率為: Assume that the depth of the ne

27、utral axis is 假設(shè)中性軸的高度為: The stress in the tension reinforcement is obtained from Figure 3-6 as由圖3-6可得,受拉鋼筋的應(yīng)力強度為: The stress in the compression reinforcement in obtained from Figure 3-6 as由圖3-6可得,受壓鋼筋的應(yīng)力強度為: The compression force in the compressive stress block is在受壓區(qū)混凝土所承受的壓力為: The compressive for

28、ce in the compression reinforcement is在受壓區(qū)鋼筋所承受的壓力為: The tension force in the tension reinforcement is受拉鋼筋的拉力為: Hence 因此 and the initial estimate for the depth of the neutral axis is correct.最終所確定的中性軸的高度是正確的。The design moment strength of the section is obtained by taking moment about the centriod of

29、 the tension reinforcement and is given by這段的彎矩值是對受拉鋼筋形心取距而得到的,其值為: 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. 當(dāng)受壓區(qū)高度小于翼緣的厚度時,翼緣寬度為b的T型截面梁的設(shè)計可當(dāng)作矩形截面梁來設(shè)計。The depth of the stress block

30、given by 受壓區(qū)高度為: where may be determined from Table 3-2 using the calculated value of .式中是由表3-2利用.來確定的The required reinforcement ratio, corresponding to, is given by在作用下,其所需的配筋率為: and the required area of tension reinforcement is 和所需的受拉鋼筋的截面面積為: When the depth of the equivalent stress block equals t

31、he flange thickness, the design moment strength of the section is given by 當(dāng)受壓區(qū)高度等于翼緣的厚度時,其彎矩設(shè)計值為:, and the corresponding area of tension reinforcement is和相應(yīng)的受拉鋼筋的截面面積為: 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 Figur

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