矩形水池计算
============================================================================ 设计资料：
池顶活荷P1=1.5(KN/m^2) 覆土厚度ht=320(mm) 池内水位Hw=3500(mm) 容许承载力R=120(KN/m^2) 水池长度H=14700(mm) 水池宽度B=11000(mm) 池壁高度h0=3500(mm) 底板外伸C1=600(mm) 底板厚度h1=300(mm) 顶板厚度h2=180(mm) 垫层厚度h3= 100 (mm) 池壁厚度h4=300(mm) 地基承载力设计值R=120(KPa)
支柱数n1=6 支柱截面尺寸a1 = 350(mm)
地下水位高于底板Hd=1900(mm) 抗浮安全系数Kf = 1.10
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一.地基承载力验算
( 1 )底板面积AR1 = (H + 2 * h4 + 2 * C1) * (B + 2 * h4 + 2 * C1)
= ( 14.7 + 2 * 0.3 + 2 * 0.6 ) * ( 11 + 2 * 0.3 + 2 * 0.6 )
=211.2(m^2)
( 2 )顶板面积AR2 = (H + 2 * h4) * (B + 2 * h4)
= ( 14.7 + 2 * 0.3 ) * ( 11 + 2 * 0.3 )
=177.4(m^2)
( 3 )支柱重量Fk1 = 25 * a1 * a1 * H0 * n1
= 25 * 0.35 * 0.35 * 3.5 * 6
=64.31(KN)
( 4 )池顶荷载Pg = P1 + ht * 18
= 1.5 + 0.32 * 18
=7.26 (KN/m^2)
( 5 )池壁重量CB = 25 * (H + 2 * h4 + B) * 2 * H0 * h4
= 25 * ( 14.7 + 2 * 0.3 + 11 )* 2 * 3.5 * 0.3
=1380.(KN)
( 6 )底板重量DB1 = 25 * AR1 * h1
= 25 * 211.2 * 0.3
=1584 (KN)
( 7 )顶板重量DB2 = 25 * AR2 * h2
= 25 *177.4 * 0.18
=798.3(KN)
( 8 )水池全重G = CB + DB1 + DB2 + Fk1
=1380.+1584 +798.3 +64.31
=3826.6(KN)
( 9 )单位面积水重Pwg = (H * B * Hw * 10) / AR1
= ( 14.7 * 11 * 3.5 * 10) / 211.2
=26.79(KN/m^2)
( 10 )单位面积垫层重Pd = 23 * h3
= 23 * 0.1
=1.08(KN/m^2)
( 11 )地基反力R0 = Pg + G / AR1 + Pwg + Pd
=7.26 + 3826.6 / 211.2 + 26.79 + 1.08
= 53 (KN/m^2)
R0 = 53 (KN/m^2) < R = 120(KN /m^2) 地基承载力满足要求!
二.水池整体抗浮验算
底板外伸部分回填土重Fkt=[(H + 2 * h4 + 2 * C1) + (B + 2 * h4)] * 2 * C1 * H0 * 16
=[( 14.7 + 2 * 0.3 + 2 * 0.6 ) + ( 11 + 2 * 0.3 )]* 2 * 0.6 * 3.5 * 16
=1888.(KN)
抗浮全重Fk = G + ht * AR2 * 16+ Fkt (抗浮时覆土容重取16KN/m^3)
= 3826.6+ 0.32 *177.4 * 16 +1888.
= 6543 (KN)
总浮力Fw = AR2 * (Hd + h1) * 10
= 177.4 * ( 1.9 + 0.3 ) * 10
= 3903 (KN)
Fk= 6543 (KN) > Kf * Fw= 4293.3 (KN) 整体抗浮验算满足要求!
三.水池局部抗浮验算
单位面积抗浮力G1=[(16 * ht + 25 * h1 + 25 * h2) * AR2 + Fk1] / AR2
=[(16 * 0.32 +25 * 0.3 +25 * 0.18 ) * 177.4 + 64.31] /177.4
= 17 (KN/m^2)
局部浮力Fw1 = 10 * ( Hd + h1 )
= 10 * ( 1.9 + 0.3 )
= 22 (KN/m^2)
G1= 17 (KN/m^2) < Fw1= 22 (KN/m^2) ****局部抗浮能力不足****!
四.荷载计算
（1）池内水压Pw= rw * H0 = 10 * 3.5 = 35 (KN/m^2)
（2）池外土压Pt：
池壁顶端Pt2 = [Pg + rt * (ht + h2)] * [Tan(45-φ/2) ^ 2]
= [7.26 + 18 * ( 0.32 + 0.18 )] * [Tan(45-30/2) ^ 2]
= 5.41(KN/m^2)
池壁底端Pt1 = [Pg + rt * (ht + h2 + H0 - Hd) + rt * Hd] * [Tan(45-φ/2) ^ 2] + 10 * Hd = [7.26 + 18 *( 0.32 + 0.18 + 3.5 - 1.9 )+10 * 1.9 ] * [Tan(45-30/2)^2] + 10 * 1.9
= 40.35(KN/m^2)
池底荷载qD = Pg + (Fk1 + CB) / AR2
= 7.26 +(64.31+1380.) / 177.4
= 14.09(KN/m^2)
五.内力计算
(H边)池壁内力计算
H / H0 =14700 /3500=4.2
由于 H / H0 > 2
故按竖向单向板（挡土墙）计算池壁内力
1.池外（土、水）压力作用下池壁内力
Pt0 = Pt1 - Pt2=40.35 -5.41= 34.94 (KN/m^2)
U = Pt2 / Pt1=5.41 /40.35=0.1
V = (9 * U ^ 2 + 7 * U + 4) / 20) ^ 0.5=(9 * 0.1^ 2 + 7 *0.1+ 4) / 20) ^ 0.5=0.4 QA = [(11 * Pt2 + 4 * Pt1) * H0] / 40=[11 * 5.41 + 4 * 40.35) * 3.5 ] / 40=19.
Y0 = (V - U) * H0 / (1 - U)=(0.4-0.1) * 3500 / (1 -0.1)=1.1
最大弯矩Mn1 = QA * Y0 - [Pt2 * (Y0 ^ 2)] / 2 - [(Pt0 * (Y0 ^ 3)] / (6 * H)
= 19. * 1.1 - [5.41* (1.1 ^ 2)] / 2 - [ 34.94 * (1.1 ^ 3)] / (6 * 14.7 ) = 17.0(KN-m)
底端弯矩Mn2 = -(7 * Pt2 + 8 * Pt1) * H0^2 / 120
= -(7 *5.41 + 8 * 40.35) * 3.5 ^2 / 120
= -36.(KN-m)
角隅最大弯矩Mj1 = -0.076 * Pt1 * H0 ^ 2
= -0.076 *40.35 * 3.5 ^ 2
= -5.0(KN-m)
2.池内水压力作用下池壁内力
最大弯矩Mw1 = 0.0298 * Pw * H0 ^ 2
= 0.0298 * 35 * 3.5 ^ 2
= 12.7(KN-m)
最大弯矩位置，距底端 0.553 * H0 = 1.9355 (m)
底端弯矩Mw2 = -(Pw * H0 ^ 2) / 15
= -( 35 * 3.5 ^ 2) / 15
= -28.(KN-m)
角隅最大弯矩Mj2 = -0.035 * Pw * H0 ^ 2
= -0.035 * 35 * 3.5 ^ 2
= -15.(KN-m)
