The Calculation Form of Single Footing Spread Foundation（earthquake action is considered ）1 Spread Foundation1．1 Foundation number:　#8-31．2 Characteristic value of subgrade bearing capacity1．2．1 Calculation formula ：according to 《Code for Design of Building Foundation 》（GB 50007－2002)fa ＝ fak + ηb * γ * (b - 3) + ηd * γm * (d - 0.5) （formula 5.2.4） thereinto ：fak ＝85.00kPa ηb ＝0.00ηd ＝ 1.00Under foundation bottom γ ＝10.00kN/m Above foundation bottom γm ＝20.00kN/mb = 3.50m d = 2.00mWhen b ＜ 3m ， b ＝ 3m1XY1．2．2 Input the above data into（formula 5.2.4）：Design value of bearing capacity of FDN soils:fa ＝115.00kPa1．2．3When performing the seismic checking computations to the natively subgrade and foundation, the subgrade bearing capacity can be adjusted according to《Code for Seismic Design ofBuildings》（GB 50011－2001）（formula 4.2.3）:The enhance coefficient of seismic subgrade bearing capacity :ξa = 1.10faE ＝ ξa * fa＝126.50kPa1．3 Basic Information　1．3．1 Pier Height（X Direction）hc＝2000.00mmPier width（Y Direction）bc＝2500.00mm1．3．2The estimated foundation area A0=Fk/(fa-γm*ds)= 1.64m1．3．3Foundation width（X Direction) b＝3000.00mmFoundation Length（Y Direction) L＝6000.00mmFoundation Height H ＝500.00mm1．3．4 Ratio of foundation width to height:　RATIO： (b - hc) / 2 / H ＝ 1.00(L - bc) / 2 / H ＝ 3.501．3．5 Concrete strength degree C30 fc ＝14.33N/mmft ＝ 1.433N/mm 1．3．6 Design value of rebar strength fy = 300.00N/mm The distance from the resultant force point of rebar to the nearest concrete edge:as =85.00mm1．3．7 The colligate sub-coefficient of loading γz ＝ 1.25The sub-coefficient of permaeant loading γG ＝ 1.20The efficient height of foundation H0 = 415.00mm1．3．8 The area of foundation A ＝ L * b ＝18.00m1．3．9 The foundation self weight and the soil weight above foundation slabThe thickness of backfill soil from the bottom of foundation slab ds ＝3000.00mm The standard value of foundation and the soil weight Gk＝γm*A*ds=1080.00kNThe design value G ＝ γG * Gk ＝1296.00kNThe standard value of vertical additional loading on FDN base Fk' ＝50.00kN1．4 The internal force which as controlling force　***********************************************************************Nk ----------- The standard value of the pier axis force（kN）；　mkx'、mky' --- The standard value of the moment on top of foundation （kN·m）；　Vkx 、Vky ---- The standard value of the shearing force on top of foundation(or bottom of pier)（kN）；　Fk ----------- The standard value of the vertical force（kN）； Fk ＝ Nk + Fk'　mkx 、mky ---- The standard value of the moment at foundation base（kN·m）；　mkx ＝ mkx' + Vky * H、 mky ＝ mky' + Vkx * H　F 、mx 、my -- vertical force、moment design value（kN、kN·m）； S ＝ γz * Sk　************************************************************************1．4．1 Vkx ＝28.00Fk =90.00Vky ＝64.00mkx＝1204.16Nk = 40.00mky＝499.76mkx'＝1172.16 mky'＝485.76≤ 2.>2,The specification not definitude thecalculation of reinforcement bar1.4.2 Overturning check1.4.2.1 Calculation along X direction Safe factor of overturning Ko= 1.25Resistant overturning moment My=(Fk+Gk)*b/2=1755.00kN·mResistant overturning coefficient Kx=My/mky= 3.51 >1.25 OK1.4.2.2 Calculation along Y directionResistant overturning moment Mx=(Fk+Gk)*L/2=3510.00kN·mResistant overturning coefficient Ky=Mx/mkx= 2.91 >1.25 OK1.4.3 Sliding Check(The soil pressures side direction are not calculated)Friction factor at FDN base f=0.401.4.3.1 Calculation along X direction Safe factor of sliding Ks= 1.25Resistant sliding force Fx=(Fk+Gk)*f=468.00kNResistant sliding coeffient Kx=Fx/Vkx=16.71 >1.25 OK1.4.3.2 Calculation along Y directionResistant sliding force Fy=(Fk+Gk)*f=468.00kNResistant sliding coeffient Ky=Fy/Vky=7.31 >1.25 OK1．5 Case on axis loadpk ＝ (Fk + Gk) / A （Formula 5.2.2-1）　pk = 65.00kPa≤ fa，OK!*******************************************************************************1．6 Case on eccentricity load *pkmax ＝ (Fk + Gk) / A + mk / W(For e≤[e])（Formula 5.2.2-2） *Pkmax= 2/3*(Fk+Gk)/(b*ay)(For e>[e]) （Formula 5.2.2-4） *pkmin ＝ (Fk + Gk) / A - mk / W （Formula 5.2.2-3） ********************************************************************************Calculation along X directionEccentricity ex ＝ mky / (Fk + Gk) ＝0.427max=b/2-ex= 1.073m[ex]=b/6=0.500mex≤ [ex] .Section modulus of FDN Wx ＝ L *b *b / 6 ＝9.000m pkmaxX ＝120.53kPa ≤ 1.2*faE=151.8kPa ,OKpkminX ＝9.47kPa ≥ 0，OK!Calculation along Y directionEccentricity ey ＝ mkx / (Fk + Gk) ＝ 1.029may=L/2-ey= 1.971m[ey]=L/6= 1.000mey> [ey],The specification does notdefinitude the FDN rebar calculation method Section modulus of FDN Wy ＝ b *L *L / 6 ＝18.000m pkmaxY ＝131.93kPa ≤ 1.2*faE=151.8kPa ,OK!pkminY ＝-1.90kPa<0Pkmax ＝ Max{PkmaxX，PkmaxY} ＝131.93kPa1．7 Punching shear check　*********************************************************Fl ≤ 0.7 * βhp * ft * am * Ho （Formula 8.2.7-1）am ＝ (at + ab) / 2 （Formula 8.2.7-2）　Fl ＝ pj * Al （Formula 8.2.7-3）　*********************************************************1．7．1 The reaction from load at the FDN base pj　pmaxX ＝ γz * pkmaxX ＝150.7kPapmaxY ＝ γz * pkmaxY ＝164.9kPapjX ＝ pmaxX - G / A ＝78.66kPapjY ＝ pmaxY - G / A ＝92.91kPa1．7．2 Along X Direction（b Direction）　******************************************************************************************************If b ＞ hc + 2 * Ho、l ＞ bc + 2 * Ho And L - bc ≤ b - hc ： *Alx ＝ 0.5 * (l + bc + 2 * Ho) * (l - bc - 2 * Ho) / 2 *+ l * (b - hc - l + bc) / 2 * If b ＞ hc + 2 * Ho、l ＞ bc + 2 * Ho And L - bc ＞ b - hc ： *Alx ＝ 0.5 * (b - hc + 2 * bc + 2 * Ho) * [(b - hc) / 2 - Ho] ** If b ＞ hc + 2 * Ho、l ≤ bc + 2 * Ho ： *Alx ＝ l * (b / 2 - hc / 2 - Ho) * If b ≤ hc + 2 * Ho，the punching shear check does not required in X direction * ***************************************************************************************************** Punching shear load area Alx ＝0.290m ab ＝ Min{bc + 2 * Ho，l} ＝ 3.330mamx ＝ (bc + ab) / 2 ＝ 2.915mFlx ＝ pjX * Alx ＝22.8kNβhp = 1.000.7 * βhp * ft * amx * Ho ＝1213.48kN≥ Flx ，OK !1．7．3 Along Y Direction（L Direction）　***************************************************************************************************If L ＞ bc + 2 * Ho、b ＞ hc + 2 * Ho And b-hc ≤ L-bc ： *Aly ＝ 0.5 * (b + hc + 2 * Ho) * (b - hc - 2 * Ho) / 2 *+ b * (l - bc - b + hc) / 2 * If L ＞ bc + 2 * Ho、b ＞ hc + 2 * Ho And b-hc > L-bc ： *Aly ＝ 0.5 * (l - bc + 2 * hc + 2 * Ho) * [(l - bc) / 2 - Ho]　* If L ＞ bc + 2 * Ho、b ≤ hc + 2 * Ho ： *Aly ＝ b * (L / 2 - bc / 2 - Ho) * If L ≤ bc + 2 * Ho，the punching shear check does not required in Y direction * **************************************************************************************************Punching shear load area Aly ＝ 3.998m ab ＝ Min{hc + 2 * Ho，b} ＝ 2.830mamy ＝ (hc + ab) / 2 ＝ 2.415mFlx ＝ pjY * Aly ＝371.4kNβhp = 1.000.7 * βhp * ft * amy * Ho ＝1005.33kN≥ Fly ，OK !1．8 Moment Calculation　*********************************************************************************************1．8．1 Moment Calculation　*According to《Code for Design of Building Foundation》（GB 50007－2002）, use these formula below： MⅠ＝ a1 ^ 2 * [(2 * l + a') * (pmax + p - 2 * G / A) + (pmax - p) * l] / 12　（Formula 8.2.7-4）　*MⅡ＝ (l - a') ^ 2 * (2 * b + b') * (pmax + pmin - 2 * G / A) / 48　*（Formula 8.2.7-5）　**when the step width/height<2, eccentricity<=1/6**********************************************************************************************X Direction（b direction）around pier（circle Y axis）：　MⅠx ＝ (b - hc) ^ 2 * [(2 * l + bc) * (pmaxX + pX - 2 * G / A)　+ (pmaxX - p) * l] / 48　MⅡx ＝ (l - bc) ^ 2 * (2 * b + hc) * (pmaxX + pminX - 2 * G / A) / 48　pX＝pminX + (pmaxX - pminX) * (b + hc) / b / 2=127.5kPaMⅠx ＝43.43kN·m　MⅡx ＝37.77kN·m　Y Direction（l direction）around pier（circle X axis）：　MⅠy ＝ (l - bc) ^ 2 * [(2 * b + hc) * (pmaxY + pY - 2 * G / A)　+ (pmaxY - p) * b] / 48　MⅡy ＝ (b - hc) ^ 2 * (2 * l + bc) * (pmaxY + pminY - 2 * G / A) / 48　pY ＝ pminY + (pmaxY - pminY) * (l + bc) / l / 2 = 116.12kPaMⅠy ＝317.11kN·m　MⅡy ＝ 5.60kN·m　MⅠ＝ Max{MⅠx，MⅡy} ＝43.43kN·m　MⅡ＝ Max{MⅡx，MⅠy} ＝317.11kN·m　1．8．2 Reinforcement Design　The enhance coeffient of bearing capacity for seismic case γRE ＝0.75MⅠmax ＝43.43kN·m　MⅡmax ＝317.11kN·m　Approximately rebar calculation formula for FND whole section: As = γRE*M/0.9/fy/H0The minimum rabar ratio of FDN ρmin ＝ 0.15%No. ① rebar AsⅠ＝291mmMinimum rabar section area AsⅠmin ＝4500mm　Actual rebar Diameter D=16mmSpacing S=200mmD16 @ 200 As= 6233mm OKNo. ② rebar AsⅡ＝2123mmMinimum rebar section area AsⅠmin ＝2250mmActual rebar Diameter D=16mmSpacing S=200mmD16 @ 200 As= 3217mm OK。