独立基础最小高度及合理台阶尺寸的计算确定

收稿日期:2005-01-07
作者简介:吴能森(1964-),男,福建福清人,副教授,博士,从事基础工程、路基工程及建筑结构研究。

文章编号:1007-6743(2005)02-0034-03
独立基础最小高度及合理台阶尺寸的计算确定
吴能森1,林 舟2
(1.福建农林大学交通学院,福州 350002;2.福建信息职业技术学院建筑工程系,福州 350003)
摘要:根据规范要求,推导了独立基础最小有效高度的计算公式,经系数化处理,形式十分简单,并将其中的尺寸影响系数制成表格,便于设计时快速查用。

经算例验证,本文的公式及表格用于确定基础最小高度及合理的台阶尺寸,方便、快速、有效。

关键词:独立基础;最小高度;合理尺寸
中图分类号:TU470 文献标识码:A 独立基础的设计首先是确定基础高度及阶梯尺寸,常规设计时采用试算法,即先按经验假定基础高度,得到基础的有效高度,然后进行基础混凝土的冲切承载力验算,直至抗冲切力稍大于冲切力为止。

要得到基础的最小高度及合理的台阶尺寸,往往需要多次的试算,尤其对初学者或缺乏经验者来说,试算法的工作量就更大。

由于冲切承载力的验算过程较烦琐,在工程设计时,设计者通常会假定偏大的基础高度,使验算通过即可,而不再进行优化试算求基础最小高度。

阶梯形独立基础台阶尺寸的确定更是如此。

基础高度及阶梯尺寸直接关系到基础的工程量,影响工程造价。

在沿海软土地区,通常浅基础以地表硬壳层为持力层,因此为满足软弱下卧层承载力要求和控制沉降,须最大限度地减小基础高度,做到/宽基浅埋0。

可见,寻求简单快速地确定基础最小高度及合理的台阶尺寸意义重大。

本文的工作旨在规范要求的基础上,求得形式简单且便于应用的计算公式及表格,使独立基础设计达到准确、快速、经济合理。

1规范要求
矩形独立基础在柱荷载作用下,如果基础高度或阶梯高度不足,一般先沿柱或台阶短边一侧发生冲切破坏,因此规范[1]要求
F 1[0.7B hp f 1b m h 0(1)式(1)右边部分为混凝土抗冲切力,左边部分为冲切力
F 1=p j A 1(2)式中B h p )受冲切承载力截面影响系数,当基础高
度h [800mm 时取1.0,当h \2000mm 时取0.9,其间按线性内插取用;f t )混凝土轴心抗拉强度设计值;b m )冲切破坏锥体上、下边长b t 、b b 的平均值;h 0)基础有效高度;A l )冲切力作用面积,见图1(b )及图1(c );p j )相应于荷载效应基本组合的地基净反力,中心受压时取平均值,偏心受压时取最大值p j ma x 。

2计算公式推导
当沿柱边冲切时,有b t =b c ,而且在大多数情况下,基础长宽比l/b 在2.0以内,冲切破坏锥体底边落在基础底面积之内,这时b b =b c +2h 0,如图1(b )所示。

于是
b m =(b t +b b )/2=b
c +h 0(3)
A 1=(l/2-a c /2-h 0)b-(b/2-b c /2-h 0)2
(4)
将式(3)、(4)代入(1)式得
p j [(l/2-a c /2-h 0)b-(b/2-b c /2-h 0)2][0.7B hp f t (b c +h 0)h 0(5)令 k =0.7B hp
f t /p j (6)则式(5)可整理为
h 2
0+b c h 0-G b 2c 4(k +1)\0(7)
G =(2n -1)X 2
-2(m -1)X -1(8)G 称为尺寸影响系数,式(8)中n =l/b;m =a c /b c ;X =b/b c 。

令 K =1+G /(k +1)(9) F =(K -1)/2(10)则由式(7)求得
h 0\F b c
(11)
第22卷 第2期 河 北 建 筑 科 技 学 院 学 报 Vol 122 No 122005年6月 Journal o f Hebei Institute of Archi tectural Science and Technolo gy Jun 12005
3计算公式应用
3.1确定基础高度
首先根据混凝土强度等级和地基净反力由式(6)求得k (偏安全地取B hp =1.0),根据
基底和柱截面尺寸由附表1直接查得或由式(8)求得G ,然后就可经式(9)、(10)、(11)的简单计算求得基础最小有效高度h 0,从而确定基础最小高度h(有垫层时h =h 0+45mm )。

3.2确定台阶尺寸
当600[h <900mm 时,阶梯形基础分二级;当h \900mm 时,阶梯形基础分三级。

以二级阶梯形基础为例,首先根据h 和每级高度300~500mm 的构造要求,确定第一级高度h 1(通常取h 1=h/2),从而确定h 01=h 1-45mm (有垫层时)。

将上述公式中的a c 、b c 换为a 1、b 1,见图1(c),保持k 、n 、m 不变(m 可根据情况自行调整),取X =2.0~2.5(三级基础取X =1.5~2.0),由n 、m 、X 查表1得G ,从而可由式(9)~(11)计算求得所需的最小有效台阶高度h 01mi n ,它只要不大于h 01即可。

通过调整X 取值,可使h 01min 尽可能接近h 01,进而根据X 、m 值得到合理的台阶尺寸a 1、b 1。

3.3算例
某单层工业厂房柱阶梯形独立基础,偏心受压,已知l @b =3.6m @3.0m ,a c @b c =600mm @400mm ,p j ma x =240kPa ,混凝土强度等级C 20,f t =1100kPa ,试确定该独立基础最小高度及合理的台阶尺寸。

1)基础高度确定:取B h p =1.0,由式(6)得k =0.7@1.0@1100/240=3.21;由n =l/b =3.6/3=1.2,m =a c /b c =600/400=1.5,X =b c /b =3000/400=7.5,查表1得G =70.25。

表1 尺寸影响系数G
n
m
1.01.01.11.21.11.11.21.31.21.31.41.51.31.31.41.51.41.31.41.51.51.31.41.5X =1.51.250.950.651.401.100.801.250.950.651.701.401.10
2.151.851.552.602.302.00X =1.61.561.240.921.751.431.111.621.300.982.141.821.502.652.332.01
3.162.842.52X =1.71.891.551.212.131.791.452.031.691.352.602.261.923.182.842.503.763.423.08X =1.82.241.881.522.532.191.852.462.101.743.102.742.383.753.393.03
4.404.043.68X =1.92.612.231.852.952.572.192.912.532.153.643.262.884.363.983.60
5.084.704.32X =2.03.002.602.203.403.002.603.403.002.604.203.803.405.004.604.205.805.405.00X =2.13.412.992.573.873.453.033.913.493.074.804.383.965.685.264.84
6.566.145.72X =2.23.843.402.964.373.933.494.464.023.585.424.984.546.395.955.51
7.366.926.48X =2.34.293.833.374.894.433.975.034.574.116.085.625.167.146.686.22
8.207.747.28X =2.44.764.283.805.434.954.475.625.144.666.786.305.827.937.456.97
9.088.608.12X =2.55.254.754.256.005.505.006.255.755.257.507.006.508.758.257.7510.009.509.00X =5.024.0023.0022.0028.0027.0026.0031.0030.0029.0036.0035.0034.0041.0040.0039.0046.0045.0044.00X =5.529.2528.1527.0534.2033.1032.0038.0536.9535.8544.1043.0041.9050.1549.0547.9556.2055.1054.00X =6.035.0033.8032.6041.0039.8038.6045.8044.6043.4053.0051.8050.6060.2059.0057.8067.4066.2065.00X =6.541.2539.9538.6548.4047.1045.8054.2552.9551.6562.7061.4060.1071.1569.8568.5579.6078.3077.00X =7.048.0046.6045.2056.4055.0053.6063.4062.0060.6073.2071.8070.4083.0081.6080.2092.8091.4090.00X =7.555.2553.7552.2565.0063.5062.0073.2571.7570.2584.5083.0081.5095.7594.2592.75107.0105.5104.0X =8.063.0061.4059.8074.2072.6071.0083.8082.2080.6096.6095.0093.40109.4107.8106.2122.2120.6119.0X =8.571.2569.5567.8584.0082.3080.6095.0593.3591.65109.5107.8106.1124.0122.3120.6138.4136.7135.0X =9.080.0078.2076.4094.4092.6090.80107.0105.2103.4123.2121.4119.6139.4137.6135.8155.6153.8152.0X =9.589.2587.3585.45105.4103.5101.6119.7117.8115.9137.7135.8133.9155.8153.9152.0173.8171.9170.0X =10.099.00
97.00
95.00
117.0
115.0
113.0
133.0
131.0
129.0
153.0
151.0
149.0
173.0
171.0
169.0
193.0
191.0
189.0
第2期
吴能森等:独立基础最小高度及合理台阶尺寸的计算确定*
35
续表1尺寸影响系数G(续)
n m
1.6
1.01.11.2
1.7
1.11.21.3
1.8
1.31.41.5
1.9
1.31.41.5
2.0
1.31.41.5
X=1.53.052.752.453.503.202.903.953.653.354.404.103.804.854.554.25 X=1.63.673.353.034.183.863.544.704.384.065.214.894.575.725.405.08 X=1.74.344.003.664.924.584.245.495.154.816.075.735.396.656.315.97 X=1.85.054.694.335.705.344.986.345.985.626.996.636.277.647.286.92 X=1.95.805.425.046.526.145.767.256.876.497.977.597.218.698.317.93 X=2.06.606.205.807.407.006.608.207.807.409.008.608.209.809.409.00 X=2.17.447.026.608.327.907.489.218.798.3710.099.679.2510.9710.5510.13 X=2.28.337.897.459.308.868.4210.269.829.3811.2310.7910.3512.2011.7611.32 X=2.39.268.808.4210.329.869.4011.3710.9110.4512.4311.9711.5113.4913.0312.57 X=2.410.239.759.2711.3810.9010.4212.5412.0611.5813.6913.2112.7314.8414.3613.88 X=2.511.2510.7510.2512.5012.0011.5013.7513.2512.7515.0014.5014.0016.2515.7515.25 X=5.051.0050.0049.0056.0055.0054.0061.0060.0059.0066.0065.0064.0071.0070.0069.00 X=5.562.2561.1560.0568.3067.2066.1074.3573.2572.1580.4079.3078.2086.4585.3584.25 X=6.074.6073.4072.2081.8080.6079.4089.0087.8086.6096.2095.0093.80103.4102.2101.0 X=6.588.0586.7585.4596.5095.2093.90105.0103.7102.4113.4112.1110.8121.9120.6119.3 X=7.0102.6101.299.80112.4111.0109.6122.2120.8119.4132.0130.6129.2141.8140.4139.0 X=7.5118.3116.8115.3129.5128.0126.5140.8139.3137.8152.0150.5149.0163.3161.8160.3 X=8.0135.0133.4131.8147.8146.2144.6160.6159.0157.4173.4171.8170.2186.2184.6183.0 X=8.5152.9151.2149.5167.3165.6163.9181.8180.1178.4196.2194.5192.8210.7209.0207.3 X=9.0171.8170.0168.2188.0186.2184.4204.2202.4200.6220.4218.6216.8236.6234.8233.0 X=9.5191.9190.0188.1209.9208.0206.1228.0226.1224.2246.0244.1242.2264.1262.2260.3 X=10.0213.0211.0209.0233.0231.0229.0253.0251.0249.0273.0271.0269.0293.0291.0289.0
由式(9)得K=1+70.25/(3.21+1)=4.21,由式(10)得N=(4.21-1)/2=1.61,再由式(11)得h0\1.61@400=644mm,则h\h0+45= 689mm,取h=700mm。

2)台阶尺寸确定:取h1=h/2=350mm,则h01=305mm;取X=2.5,则b1=b/X=1200mm。

由X=2.5、n=1.2、m=1.5查表1得G=5.25。

同上,求得K=1+5.25/(3.21+1)=1.5,N= (1.5-1)/2=0.25,则h01min=N b1=0.25@1200 =300mm,小于并接近于h01,合理。

故台阶尺寸宜取b1=1200mm,a1=mb1=1800mm。

4结语
本文的公式(11)及表1不仅能快速地求得柱下钢筋混凝土独立基础的最小有效高度及最小高度,而且能比较方便快速地确定阶梯形独立基础的合理台阶尺寸,与试算法相比,效率和准确性大大提高,很容易实现基础埋深和基础工程量最小的目的,从而达到降低基础工程造价、控制基础埋深与做到/宽基浅埋0等技术经济效果。

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The computation on minimal heights and step sizes of isolated foundation
W U Neng2sen1,LIN Zhou2
(1.College o f Traffic,Fujian Agriculture and Forestry University,Fuzho u350002,China;2.Department o f A rchitectural
Engineering,Fujian Vocati onal College o f Informati on and Technology,Fuzhou350003,China)
Abstract:Based on the demand in the norm,the expressions to computing minimal heights of the isolated foundation is deduced.B y means of technical disposal,its form is quite simple with a fe w coefficients in which the size coefficient is transformed a numeric table for quick design.It is validated by a engineering example that they are convenient, quick and available f or reasonable design.
Key words:isolated f oundation;minimum height of the bases;rational siz es
(责任编辑刘存英) 36河北建筑科技学院学报2005年。