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1、梁弯矩配筋的简化计算方法民用建筑所王晓星1. 前言随着计算机的发展，大型结构的计算越来越程序化，简便化，但 机算结果的正确性和适用性的判定仍然需要手算来完成，。我们一些 结构设计师尤其是新参加工作的设计师在结构计算中也过分依赖于 计算机，手算能力比较薄弱，特别是在现场服务中对结构问题的处理 时，往往时间紧，又要保证结构的安全和经济，加强自己的手算能力 和经验的积累对每个结构设计师都是必不可缺的。本文提出了混凝土 结构设计中最常用的梁弯矩配筋的简化计算方法，愿与大家共同商 讨。2. 简化计算方法梁弯矩配筋可先计算出矩形梁的截面系数A，按此系数查得配筋 系数的第一行，第二行对应的就是配筋系数值，H
2、RB335配筋系数表见 附表1，HRB400配筋系数表见附表2。配筋系数表有如下的特点： 截面系数浮动范围非常大，而配筋系数却很小，多数只是0.001位的 变化，而且各混凝土强度等级的截面系数范围均同。所以如果我们能式中：M为梁的弯矩设计值(kNm)B为梁的宽度(m)h0为梁的有效高度(m)As为配筋面积(cm2)公式中括号内为单位不参预计算，对于T形梁和板只需取前几个 系数即可。配筋系数表第二行的第一个数为最小配筋率，最后一行为 受压区高度为0.55h0。当精度要求不高时，对于T形梁和板采用I级 筋时可直接取配筋系数为0.050; II级筋可取配筋系数为0.035。精确 计算的公式在此不再细
3、述，可参见混凝土结构教科书或钢筋混凝土结 构计算手册。3. 计算示例1：某梁所承受弯矩设计值为145kN m，取梁高为500，梁宽为250,混 凝土强度等级C30;HRB335钢筋;试计算配筋.C30 混凝土； HRB335截面系数A650100020003000400050005500配筋系数0.03410.0350.0360.0380.0400.0430.045简化计算:受压区高度X = h0 -:h2 - 2 X 一M=99mm :o a 1 x f x b相对受压区高度6= Xh = 99460 = 0.214堂，=0.550 ,0纵向受拉钢筋 Ay = a 1x f xbxxf =
4、1177mm22:某板跨中弯矩设计值为6.5 kN m/m，板厚取为100，混凝土强度等级C25; HRB335钢筋;试计算配筋.简化计算：Ay = -65 x 0.035 = 2.84cm 2 = 284mm 2 0.08精确计算（取1m宽为单元）：受压区高度x = h0 -h2 一 2x = 6mm:0a 1 x f x b相对受压区高度 6 = Xh = 680 = 0.074 = 0.550 /0纵向受拉钢筋 Ay = a 1x f xbxx：f = 281mm24. 总结 由上述两例对比可知，计算误差均在允许范围内即小于5%。梁的弯矩配筋在结构设计中是最常用又重要的一部分，我们只要掌
5、握简 化计算方法就可以得到事半功倍的效果。附表1C20HRB335 f =300 yA581871131717142068238426672919314533463526368738201Y sfy0.03440.0350.0360.0370.0380.0390.0400.0410.0420.0430.0440.0450.046P (%)0.200.3050.4740.6340.7860.9301.0671.1971.3211.4391.5521.6591.752C25HRB335 f =300 yA58510791632212525642956330636183897414843714571
6、47401Y sfy0.03420.0350.0360.0370.0380.0390.0400.0410.0420.0430.0440.0450.046P (%)0.200.3780.5880.7860.9741.1531.3221.4831.6371.7831.9232.0572.178C30HRB335 f =300 yA6301297196225533081355239724348468449845253549257001Y sfy0.03410.0350.0360.0370.0380.0390.0400.0410.0420.0430.0440.0450.046P (%)0.2150.4
7、540.7060.9451.1701.3851.5891.7831.9672.1432.3112.4722.62C35HRB335 f =300 yA6901515239129813598414846395078547058206134641466601Y f0.03410.0350.0360.0370.0380.0390.0400.0410.0420.0430.0440.0450.046P (%)0.2350.5300.8251.1031.3671.6181.8562.0812.2972.5032.6992.8863.062续附表1C40HRB335 f =300 yA75317322620
8、34104115474353065807625566577015733676101y sfy0.0340.0350.0360.0370.0380.0390.0400.0410.0420.0430.0440.0450.046p（%）0.2560.6060.9431.2621.5641.8502.1222.3812.6282.8633.0873.3013.497C45HRB335 f =300 yA7941913289437684546524158616415691173547750810484501y sfy0.0340.0350.0360.0370.0380.0390.0400.0410.04
9、20.0430.0440.0450.046p (%)0.270.6701.0421.3941.7272.0442.3442.6302.9033.1623.4103.6473.884C50HRB335 f =300 yA8362095316941254977573764177024756680518485887292101y sfy0.0340.0350.0360.0370.0380.0390.0400.0410.0420.0430.0440.0450.046p（%）0.2840.7331.1411.5261.8912.2382.5672.8803.1783.4623.7333.9934.234
10、C60HRB335 f =300 yA90224943772491059256830763983619007958510101105101y sfy0.03390.0350.0360.0370.0380.0390.0400.0410.0420.0430.0440.0452p (%)0.3060.8731.3581.8172.2512.6643.0563.4283.7834.1214.4444.753附表2C25HRB400f =360 yA6989611632221727263170355838984194445445811y fs y0.02860.0290.0300.0310.0320.0
11、330.0340.0350.0360.0370.038p (%)0.20.2790.4900.6870.8721.0461.2101.3641.5101.6481.719C30HRB400f =360 yA70211541962266432763810427646845040535254801y sfy0.02850.0290.0300.0310.0320.0330.0340.0350.0360.0370.038p (%)0.2000.3350.5880.8261.0481.2571.4541.6391.8141.9802.053C35HRB400f =360 yA70413482291311
12、138254449499454705886625064141y fs y0.02840.0290.0300.0310.0320.0330.0340.0350.0360.0370.038p (%)0.2000.3910.6870.9641.2241.4681.6981.9142.1192.3122.405C40HRB400f =360 yA75515422620355843755088571162566732714873301y fs y0.02840.0290.0300.0310.0320.0330.0340.0350.0360.0370.038p (%)0.2140.4470.7861.1031.401.6791.9422.1902.4242.6452.748续附表2C45HRB400f =360 yA79417032894393048335621630969117436789781041y fs y0.02830.0290.0300.0310.0320.0330.0340.0350.0360.0370.038p (%)
