土的工程绪论土的工程 (100).pdf

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1、3.7.1 Additional stress beneath a strip foundation under vertical uniform loadStrip foundationIn theoryThe stress state in the interior of the ground is a plane problem.In engineeringApproximates to a strip foundation,its a planeproblem./l b l b/10Earth embankmentsStrip foundation under columnsStrip

2、 foundation under wallsStrip foundation base under vertical uniformly distributed loadCalculation of the additional stress due to a vertical uniform line load(Flamant solution)Take micro-load unitdF=pdyUsing Boussinesq solution of concentrate load:Integrating within the uniformline load areaRxzxyzRz

3、pypz23d20222022245/2z33RxyzRRFzpy z22d3d3 d222255z33dF=pdy(a)Additional stress due to a vertical uniform line load(b)土力学土力学Soil MechanicsSoil MechanicsProf.Prof.H.J.LiaoH.J.LiaoThe vertical uniformly distributed load intensity p0(KN/m2)acts thebase of the strip foundation with a width bTake a micro-

4、length d in the width direction,the uniform line load acting on the micro-width is dp=p0 d(a)(b)bdxzMxp0ozp0dMStrip foundation base under vertical uniformly distributed lod(c)土力学土力学Soil MechanicsSoil MechanicsProf.Prof.H.J.LiaoH.J.LiaoThe vertical additional stress at the point M with a vertical uni

5、form line load dpUsing Flamant solution of line load,Substituting formula(c)into formula(b)Integrating within the width range(-b/2,b/2)of the strip basezsThe coefficient of the vertical additional stress when the stripfoundation is subjected to a vertical uniform load,can be obtainedby looking up th

6、e corresponding table according to x/b，z/b.xzRdpzpz()2d2d02242z033xzpz dpbb()22222zz020s3(d)(e)土力学土力学Soil MechanicsSoil MechanicsProf.Prof.H.J.LiaoH.J.LiaobdxzMxp0ozp0d(c)Integrating within the width range(0,b)of the strip foundationbs(x/b,z/b)The coefficient of thevertical additional stress when th

7、e originof the coordinate is taken at the edge ofthe strip foundation.xzpzpb()d22202zb00s3(f)土力学土力学Soil MechanicsSoil MechanicsProf.Prof.H.J.LiaoH.J.LiaoThe vertical uniform load intensity p0acts on the base of thestrip foundation with a width of b.Please solve the verticaladditional stress at point

8、s M,M and N at the depth z=b underthe two edges and the center point of the foundation respectively.Coordinate origin is taken at the midpoint of the widthCoordinate originis taken at any sidePositionMNMPositionMNMx/b0.500.5x/b00.51z/b111z/b111sz0.410.550.41sb0.410.550.41Example土力学土力学Soil MechanicsSoil MechanicsProf.Prof.H.J.LiaoH.J.LiaoStatementStatement:Thanks for some pictures and materials fromthe Internet used in this courseware only for teaching.