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16 shows the horizontal membrane stress and theplate-bending stress in the pile cap along the x-direction.This shows that a horizontal tensile stress occurs in thepile cap elements to the left of the pier, and a horizontalcompressive stress occurs to the right. From the resultfor the plate-bending stress in Fig. 16(b), it is found thatthe cap shows a slightly convex curvature on the outside of the piles and a concave curvature between the piles. Inthe pile cap elements on the right side of the pier, a sig-nificant bending stress is estimated, which is caused bythe combined effect of the external axial and lateralloads.4.4. Pile head reactionsThe axial and lateral loads and bending moments in theinpidual pile heads were estimated and compared withthose obtained from the displacement method. The resultsare shown in Fig. 17. From an equilibrium check, it wasfound that the present method satisfied the equilibriumcondition, although the distributed loads were somewhatdifferent from those obtained from the displacementmethod. Somewhat larger forces were distributed to theleading row (piles 2 and 4) and somewhat smaller axialforces to the trailing row (piles 1 and 3) in the presentmethod, as compared with the results obtained from thedisplacement method. It is likely that the compressive hor-izontal stress in the pile cap on the right side of the pierincreases the lateral forces in the leading row and the ten-sile horizontal stress decreases the lateral forces in the trail-ing row.The bending moments at the pile heads calculated by thepresent method were 152 kN m in the trailing row and264 kN m in the leading row. The values obtained by thedisplacement method were 23 kN m regardless of the pilelocation. Significantly larger bending moments are gener-ated at each pile head in the present method compared withthe results obtained by the displacement method. There-fore, it is concluded that the maximum load on the inpid-ual piles in a group is highly influenced by the flexibility ofthe pile cap.Note that in the present method, the bending moment atthe pile head in the leading row is opposite to that in thetrailing row. The reason for this is that as a combined axialand lateral load is acting on the center portion of the pilecap, the pile heads in the leading row tend to rotate in acounterclockwise direction and, simultaneously, the trail-ing row tends to rotate in a clockwise direction, as shownin Fig. 18.In the present method, large lateral forces (30 and34 kN) and bending moments (194 and 222 kN m) aredeveloped in the y–z plane, perpendicular to the loadingdirection, even though no lateral loads are applied in thisplane (Fig. 17). However, the lateral forces and bendingmoments in piles 1 and 3 and those in piles 2 4 are identicalin magnitude but opposite in direction, canceling all thelateral loads and moments in the y–z plane out, and there-fore have no effect on the overall equilibrium conditions ofthe pile cap.Deformedpile capClockwiserotationCounterclockwiserotationMomentMomentVHMomentFig. 18. Direction of bending moments at the pile head connected toflexible pile cap. in Fig. 13. The basic elastic modulus E0 is 2.5 · 107kN/m2.Fig. 20 shows well the significant effect of the elastic mod-ulus on the maximum load on the inpidual piles. In pres-ent method, a very large lateral load is distributed to theleading row when the elastic modulus of the pile cap islow, but when a very high elastic modulus (E/E0 =10) isused, identical lateral loads are generated in the two rows,and these loads are almost equal to the results from thestiffness method (Group 6.0). FBPier 3.0 predicts smallerlateral loads than both the present method and Group6.0, since the model of a pile in FBPier 3.0 is different fromthe model in the present method and in Group 6.0, as pre-viously described.As shown in Fig. 20(b), the bending moment in the lead-ing row has a large negative value ( 264 kN m), and thatin the trailing row has a large positive value (152 kN m),for E/E0 = 1 with the present method. The absolute magni-tudes of these two bending moments are larger than thatcalculated by the stiffness method (Group 6.0), which wasvery small, only 23 kN m. However, it should be noted thatthese bending moments at the pile head are significantlysmaller than the maximum bending moments developedat a depth of 3D (=4.5 m) depth in this piled pier, as shownin Fig. 19.