框架结构设计例题第三部分.docx

1、框架结构设计例题第三部分7荷载作用效应组合7.1荷载作用效应姐合的原则按照教材所述的荷载作用效应组合原则，按承载力极限状态计算时，应当进行以下组合:(1) 无地震作用时取竖向恒载效应5G与竖向活载效应5Q的基本组合，并考虑弯矩调幅；组合工况 A: S=1.20Sa +1.40Sq 组合工况 B: S=1.35Sg +0.7X1.40Sq由于本例抗震设防烈度为7度(0.15g)，地震作用较大，同时水平风荷载较小。因此， 无地震作用时，未考虑竖向荷载效应与水平风荷载效应的基本组合。通过比较并根据实际经验可知，由于活荷载所占比例很小(约占总荷载的15%左右)， 对框架梁、柱，起控制作用的基本组合均为

2、组合工况B。(2) 有地震作用时取重力荷载代表值的荷载效应(Sg +0.5Sq)与水平地震作用效应SEh的地震组合：组合工况 C: S=1.20(Sg +0.5Sq)1.30Sek 组合工况 D: S=1.00(Sg +0.5Sq)1.30Sek7.2无地震作用时竖向荷载作用下的基本组合根据7.1节组合原则，竖向荷载作用下框架基本组合内力结果见表7.1表7.3。在表7.1中，应注意：(1) 表中Mg、Mq分别为竖向恒荷载、活荷载作用下各控制截面弯矩。(2) 弯矩组合工况为：M=1.35Mg+0.7X1.40MqX1.1;其中，系数1.1为考虑活荷载 最不利布置时，将满布活荷载时的弯矩放大10%

3、。(3) 调幅前的跨中弯矩辱=q2/8 +(M左+ M右)/2 (此处，M左、M右皆取负值)。(4) 考虑调幅15%后，梁端弯矩降低15%，相应的跨中弯矩M中按平衡条件求得。 其计算公式为：中=q2/8 + 0.85x(M左 + M右)/2 = M中- 0. 075(M左 + M右)(此处，M左、M右皆取负值)表7.1竖向荷载作用下的梁端及跨中弯矩基本组合层号内力及AB跨BC跨CD跨其组合MABzMAByMab中MBCzMBCyMbc中MCDzMCDyMcd中Mg-51.48-67.2347.69-21.50-21.50-7.88-67.23-51.4847.695Mq-4.32-4.912.

4、52-1.03-1.03-0.19-4.91-4.322.52组合弯矩-74.16-96.0567.09-30.14-30.14-10.85-96.05-74.1667.09调幅15%-63.04-81.6579.86-25.62-25.62-6.32-81.65-63.0479.86Mg-76.86-81.6147.96-14.96-14.96-3.94-81.61-76.8647.964Mq-15.78-18.4111.41-2.62-2.621.60-18.41-15.7811.41组合弯矩-120.77-130.0377.05-23.02-23.02-3.60-130.03-120.7

5、777.05调幅15%-102.66-110.5295.86-19.57-19.57-0.14-110.52-102.6695.86Mg-75.49-81.4948.70-15.09-15.09-4.07-81.49-75.4948.703Mq-16.36-18.6611.00-2.36-2.361.86-18.66-16.3611.00组合弯矩-119.55-130.1377.61-22.92-22.92-3.49-130.13-119.5577.61调幅15%-101.61-110.6196.34-19.48-19.48-0.05-110.61-101.6196.34Mg-75.86-81

6、.6248.46-14.96-14.96-3.94-81.62-75.8648.462Mq-16.46-18.6810.94-2.33-2.331.88-18.68-16.4610.94组合弯矩-120.15-130.3277.22-22.71-22.71-3.28-130.32-120.1577.22调幅15%-102.12-110.7796.00-19.30-19.300.12-110.77-102.1296.00Mg-70.27-79.3852.37-17.98-17.98-6.96-79.38-70.2752.371Mq-14.98-18.2211.91-3.01-3.011.21-1

7、8.22-14.9811.91组合弯矩-111.01-126.8183.54-27.52-27.52-8.10-126.81-111.0183.54调幅15%-94.36-107.79101.38-23.39-23.39-3.97-107.79-94.36101.38在表7.2中，应注意：(1) 表中心、Fq分别为竖向恒荷载、活荷载作用下各控制截面剪力。(2) 组合工况为：组合剪力 1: F=1.35Fg+0.7X1.40Fq 组合剪力2: F=1.20Fg+1.40Fq(3) 各跨跨中剪力均较小，对箍筋计算不起控制作用，故表中未给出。表7.2竖向荷载作用下的梁端剪力及跨中剪力基本组合层号内力

8、及AB跨BC跨CD跨其组合VABzVAByVBCzVBCyVCDzVCDyVG62.4967.2718.1618.1667.2762.495Vq4.234.411.131.134.414.23组合剪力180.9186.8923.3623.3686.8980.91组合剪力288.5195.1325.6225.6295.1388.51Vg76.3777.8114.6914.6977.8176.374VQ16.8817.685.635.6317.6816.88组合剪力1115.28118.1225.5125.51118.12115.28组合剪力2119.64122.3725.3525.35122.3

9、7119.64Vg76.1878.0014.6914.6978.0076.183VQ16.9317.635.635.6317.6316.93组合剪力1115.12118.2825.5125.51118.28115.12组合剪力2119.43122.5725.3525.35122.57119.43Vg76.2277.9614.6914.6977.9676.222Vq16.9417.625.635.6317.6216.94组合剪力1115.18118.2225.5125.51118.22115.18组合剪力2119.49122.5125.3525.35122.51119.49Vg75.7178.4

10、714.6914.6978.4775.711Vq16.7917.775.635.6317.7716.79组合剪力1114.35119.0425.5125.51119.04114.35组合剪力2118.66123.3525.3525.35123.35118.66表7.3各柱竖向荷载下的柱端内力基本组合柱号A柱B柱层号恒载效应活载效应组合效应恒载效应活载效应组合效应5柱顶弯矩M39.573.8357.17-26.57-2.42-38.24轴力#141.947.47198.94213.1815.21302.69柱底弯矩M50.527.9676.01-45.38-10.77-71.82轴力#179.4

11、67.47249.59250.7015.21353.35剪力V23.103.0234.15-18.45-3.38-28.224柱顶弯矩M26.347.8243.22-21.27-5.02-33.63轴力#388.4537.31560.97500.5983.65757.77柱底弯矩M27.809.1546.50-45.01-11.53-72.06轴力#425.9737.31611.62538.1183.65808.43剪力V13.884.3523.00-16.99-4.24-27.103柱顶弯矩M27.807.2144.59-21.40-4.76-33.55轴力#634.7767.20922.8

12、0788.20152.041213.06柱底弯矩M27.419.0545.86-44.88-11.50-71.85轴力#672.2967.20973.45825.72152.041263.71剪力V14.154.1723.19-16.99-4.17-27.032柱顶弯矩M28.567.4145.81-21.78-12.29-41.46轴力#881.1297.111284.681075.76220.411668.28柱底弯矩M53.7710.7383.11-48.42-12.29-77.41轴力#918.6497.111335.341113.28220.411718.94剪力V21.114.65

13、33.06-18.00-4.39-28.611柱顶弯矩M16.494.2526.43-12.98-2.92-20.38轴力#1126.97126.860.001363.84288.942124.35柱底弯矩M8.252.1213.22-6.49-1.46-10.19轴力#1179.34126.861716.431416.21288.942195.05剪力V4.581.187.34-3.61-0.81-5.66注：(1)组合工况为： 5=1.355g+0.7X1.405q(2) D柱、C柱组合后的各项内力数值分别与A柱、B柱相同，只是弯矩、剪力为反号7.3水平地震作用效应与竖向荷载作用效应的地震

14、组合7. 3. 1水平地震作用下的梁端及跨中内力的地震组合根据7.1节组合原则，框架梁的地震组合内力结果见表7.4及表7.5。在表7.4中，应注意：(1) 表中Mg、Mq、Me分别为竖向恒荷载、竖向活荷载、水平地震作用下各控制截面弯 矩标准值。(2) 组合时所用弯矩的正负，按照材料力学规定，以使梁下部受拉为正。(3) 组合1：重力荷载代表值作用下的支座弯矩Mi左、Mi右按M;=1.20Mg+0.6Mq计算， 然后在此基础上考虑调幅15%。(4) 组合2：支座最大负弯矩及跨中最大正弯矩组合，考虑抗震调整系数Yre，取 M2= Yre (M1+1.3Me)，并考虑左震、右震两种情况。组合时，先进行

15、支座弯矩组合，然后按 照公式进行胯间最大弯矩组合。1)当水平地震作用由左向右(称为“左震”)在重力荷载代表值q (己乘以重载分项系数1.2)、弯矩M1左、M1右以及地震弯矩Me左、 Me右作用下，计算出胯间最大弯矩距左端的距离：x = RA / q (7.3.1)其中 Ra = OK / 2 + (法 + 乂右#成 + M右)/ 入 (7.3.2)(注：式7.3.2与式7.3.3中的M1左、M1右、Me右为负值)。左震时，取x1=max (x， 0)胯间最大弯矩：2M间腿x = 7rIRAX qX1 / 2 + + M1右)(7.3.3)2)当水平地震作用由右向左(称为“右震”)x、Ra、M间

16、max仍如式(7.3.1)、(7.3.2)、(7.3.3)计算，只是Me左、Me右改变正负 号，并且取 x1=min (x，l)。(5) 组合3：支座最大正弯矩及跨中最大正弯矩组合。支座最大正弯矩取 M+=Yre(1.3Me-1.0Mg-0.5Mq )= Yre(1.3Me - M/1.2)胯间最大弯矩仍然按照式(7.3.1)、(7.3.2)、(7.3.3)计算，只是需将q、M1左、 M1右分别除以分项系数1.2,并区分左震、右震两种情况。表7.4水平地震作用下的梁端及跨中弯矩地震组合层号跨跨度lqgMi左-组合1Mi右-组合1Me左（左震）Me右（左震）M2-组合2（左震）M2组合2（右震）

17、M支左M支右RAxX1取值M胯间maxM支左M支右RAxX1取值M胯间maxAB跨6.6024.38-54.72-71.0881. 27-56.2438.20-108. 1450.882.092.0978.03-120. 281.52105.054.314. 3149.495BC跨3.0014.98-22.46-22.4660.01-60.0141.67-75.35-29.54-1.970.0041.67-75.3541.6774.474.973.0041.67CD跨6.6024.38-71.08-54.7256.24-81.271. 52-120.2855.842.292.2949.49-1

18、08. 1438.20110.014.514. 5178.03AB跨6.6031.17-86.45-92.64178. 21-131.97108.92-198.1540.841.311.31128.98-238.5959.20163.035.235.2381.154BC跨3.0014.00-16.60-16.60140.83-140.83124.86-149.76-101.05-7.220.00124.86-149. 76124.86143.0610.223.00124.86CD跨6.6031.17-92.64-86.45131.97-178.2159.20-238. 5942. 721.37

19、1.3781. 15-198. 15108.92164.915.295. 29128.98AB跨6.6031.17-85.34-92.64270.41-195.96199.65-260.549.910.320.32200.83-327.66121.58193.636.216. 21123.353BC跨3.0014.00-16.59-16.59209. 11-209. 11191.44-216.33-160.22-11.440.00191.44-216. 33191.44202.2414.443.00191.44跨6.6031.17-92.64-85.34195.96-270.41121.58-

20、327.6612.120.390.39123.35-260.54199.65195.846.286. 28200.83AB跨6.6031.17-85.77-92.78339.65-256.43266.83-319.60-15.60-0.500.00266.83-395.48180.43219.227.036.60180.432BC跨3.0014.00-16.45-16.45273.64-273.64254.46-279.13-216.15-15.430.00254.46-279. 13254.46258.1618.433.00254.46CD跨6.6031.17-92.78-85.77256.

21、43-339.65180.43-395.48-13.47-0.430.00180.43-319.60266.83221.347.106.60266.83AB跨6.6031.17-79.31-90.26405. 50-298.56335.88-358.79-37.46-1.200.00335.88-454.85223.40239.907.706.60223.401BC 跨3.0014.00-19.88-19.88318.61-318.61295.73-325.55-255.12-18. 220.00295.73-325. 55295.73297. 1321.223.00295.73CD跨6.60

22、31.17-90.26-79.31298. 56-405.50223.40-454.85-34. 15-1.100.00223.40-358.79335.88243.217.806.60335.88续表7.4层号跨M3-组合3（左雇）M3组合3（右雇）选中的地震组合弯矩最大值M支左M支右RAxX1取值M胯间maxM支左M支右RAxx1 取值M胯间maxM支左M支右M胯间max5AB跨45.04-99. 2537.891.871.8771.54-113.4410.4092.064.534. 5343.-120.28-108.1478.03BC跨44.47-72.55-33. 29-2.670.0

23、044. 47-72.5544.4770. 735.673.0044. 47-75.35-75.3544.47CD跨10.40-113. 4442.022.072.0743.-99.2545.0496. 194.734. 7371.54-108.14-120.2878.034AB跨119.72-186.5723.850.920.92127.94-227.7870.78146.045.625.6280.10-238.59-198.15128.98BC 跨126.94-147. 68-104. 55-8.960.00126.94-147.68126.94139. 5611.963.00126.94

24、-149.76-149.76126.94跨70.78-227. 7825.410.980.9880.10-186.57119.72147.615.685.68127.94-198.15-238.59128.983AB跨210.31-248.96-7.05-0.27-0.27211.03-316.99133. 16176.676.806.80133. 55-327.66-260.54211.03BC跨193.51-214.26-163. 73-14.030.00193. 51-214.26193.51198. 7417.033.00193. 51-216.33-216.33193.51CD跨13

25、3. 16-316.99-5.21-0.20-0.20133. 55-248.96210.31178. 516.876.87211.03-260.54-327.66211.032AB跨277.55-308.-32.57-1.25-1.25292.86-384. 76192.03202. 257.797.79205. 72-395.48-319.60292.86BC跨256.52-277.08-219.65-18.820.00256. 52-277.08256.52254. 6621.823.00256. 52-279.13-279.13256.52CD跨192.03-384.76-30.80-1.19-1.19