【正文】 m the cylinder tests of and the splitcylinder tensile strength (again on firstlift cylinders) of 660 psi () are also quite representative of prototype concrete.Reinforcing in the shell consisted of . () diameter steel wire placed in two directions along the ruling lines nominally in the middle surface of the shell. There were forty wires evenly spaced in each direction giving a nominal steel ratio based on a . (13mm) thick shell of percent. The wire spacing was in. (14 cm) at the throat and in. (22 cm) at the base. Thus the spacing was from 15 to 18 times the nominal shell thickness. This violates the maximum spacing of twice the shell thickness remended by ACIASCE Committee 334 (Ref. 7) and may have contributed to the mode of failure that was experienced. The top of the shell was thickened into a ring 2in. wide and lin. deep (50mm ? 25ram) reinforced with six wires as described in Refs. 2 and 3. The wire was annealed and then straightened. The average yield strength of tensile specimens was = ksi (564MP). The modulus of elasticity was Es = ? 106 psi (206 GP).Construction and Testing of ShellThe sequence for the model construction was as follows.(1) Assemble inner form and apply bondbreaking pound (grease).(2) Assemble reinforcing wires. These include those in a reinforced concrete beam at the top of the shell. The shell wires were threaded at the top and bottom and attached to the rings with nuts.(3) Assemble first lift of greased outer form. Place spacer pieces made of aluminum tubing (13ram) long at the four corners and interior locations to attempt to assure proper spacing between forms.(4) Fill lower lift with pumped concrete.(5) Repeat steps (3) and (4) for the other lifts.(6) After curing, remove all forms and install top plywood cover over the shell.Test ResultsShell GeometryMeasurements of deviation from the ideal geometry were taken at 132 locations. These consist of differences from the idealshell horizontal radius to the middle surface at the locations indicated in Figs, 2 and 3. It was found that the maximum deviation in the radius was about + 3 percent. These results are given in Ref. percent deviation in a vertical distance along a meridian expressed as a slope S is significant only in a local sense. In this regard, since the locations at which measurements were made were spaced 12in. (.3m) apart the slope was defined over three data points as (1)Where == the net radial deviation of the shell middle surface over a gage length H = 24 in.。= radial deviations at the ends of the gage length. While is the radial deviation at the center of the gage length H. The values of S obtained by applying (1) to the data for each vertical line are given in Ref. 8. The overall maximum values of S were percent.Shell ThicknessThickness measurements at 138 locations were made after the shell was tested to failure by drilling holes at the locations indicated in Figs. 2 and 3 including those adjacent to the strain gages. The thicknesses measured are displayed as contour lines in Fig. 5.Structural Response and FailureStrain vs. load curves for the last test of the shell prior to failure is presented in Figs. 68. In general the response is linear up to the maximum load of psi () with no indication of buckling. The failure load was ( kPa) for Test 1 and ( kPa) for Test shown on the plots are theoretical curves based on membrane theory and converted to strains by （2）where ，N are the membrane strain and membrane force in either the meridional or circumferential 0 directions respectively。 h is the measured shell thickness at the gage location。 and is Poisson39。s ratio. The membrane forces andwere determined from membrane theory. Additionally, the values of No were modified by considering the presence of measured geometry imperfections. Following Gupta and AIDabbah due to imperfections in conjunction with induced membrane forces, is (3) in which (4)for a circular shape of imperfection meridian or (5)In these r=horizontal radius of the shell For the shell geometry and measured imperfections the results obtained for the no from (4) and (5) are nearly the same. The value of puted from kPa (3) is added to that obtained from the membrane solution.Values of internal forces and moments calculated from experimental data at various gage locations and at the maximum load applied are given in Table 2. It is seen that fairly large moments exist at the ring/shell connections and the fixed base as would be expected. Unexpectedly, a large moment 4 ft below the throat was observed. This was undoubtedly due to the imperfections present. Also, the effect of imperfections is seen in the results for and at the throat at the different locations.In considering possible causes for these failures, the shell was again analyzed using the equations of modified for nonlinear materials2 these are （6）in which，The geometry buckling parameters are given by (7)in which are buckling coefficients. These are taken here to be =，=，=，=.From consideration of the membrane forces due to suction (including axial forces induced from the reaction of the top cover to the shell wall) the critical buckling pressure can be determined as (8a)When dominates, and (8b)When dominates. In the above are the .concrete uniaxial pressive strength and associated strain.The term is given by (9)Where and (10)N= (11)The term (12)and (13)While = that portion of the total reaction from the top cover carried into the shell wall. For the present case 3 = . The term is the value takes at a value of corresponding to the top of the shell.In the above is the instantaneous