ML20052G313

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Relative Soil Impedances Beneath Electrical Penetration Wings for Midland Auxiliary Bldg
ML20052G313
Person / Time
Site: Midland
Issue date: 03/31/1982
From: Kennedy R, Kincaid R, Wesley D
STRUCTURAL MECHANICS ASSOCIATES
To:
Shared Package
ML20052G308 List:
References
SMA-13701.05R, SMA-13701.05R00, SMA-13701.05R001, SMA-13701.05R1, NUDOCS 8205180243
Download: ML20052G313 (61)
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{{#Wiki_filter:. SMA 13701.05R001 l RELATIVE S0IL IMPEDANCES BENEATH ELECTRICAL PENETRATION WINGS FOR THE MIDLAND AUXILIARY BUILDING by R. P. KENNEDY R. H.'KINCAID D. A. WESLEY R. D. THRASHER prepamd for: CONSUMERS POWER COMPANY JACKSON, MICHIGAN March, 1982 82 0 5180 PCS

t 1. PURPOSE OF STUDY The auxiliary building at the Midland Nuclear Generating Station is a reinforced concrete structure consisting of;the main auxiliary building, the control tower, and the east and west electrical penetration wing areas. A schematic representation of this complex structure is presented in Figure 1-1. In order to assess the dynamic loadings on this structure due to earthquake ground motion, a lumped-mass, three-dimensional model (shown in Figure 1-2) has been developed for the auxiliary building complex (Reference 1). This model incorporates all important mass and stiffness characteristics of the structure and preserves the overall physical geometry of the builoing. Basically, the model consists of two main sticks representing the main auxiliary building and control tower with the remaining six sticks, in conjunction with a series of plate elements, modeling the east and west electrical penetration wing areas. The stiffness elements representing story stiffnesses account for the actual distributed shear, flexural, and axial stiffnesses of the seismic-resistant structural elements. Stiffness elements acting as rigid links model the horizontal diaphragms. These elements also link together horizontally and vertically all lumped masses in the model. The plate elenents in the electrical penetration wing areas model the vertical south wall of this structure. Stiffness elements and lumped masses are used to model intermediate cross walls in the wing area. Soil-structure interaction for this structure has been developed using elastic half-space, frequency-dependent impedance functions. The global soil impedances have been based on the full auxiliary building foundation geometry. Examination of Figure 1-3 show this building has a very complex foundation shape. Because this structure has a thick base mat with many large interior shear walls stiffening the foundation, it was judged that assuming the total structure base mat acts rigidly was an acceptable procedure for developing global soil comoliances for the struc ture. However, because the electrical penetration wings are long 1-1

and narrow (Figures 1-1 to 1-3), there was concern that for North-South (N-5) excitation there might be some slight flexibility of the electrical penetration wing foundation relative to the main auxiliary / control tower foundation. Though this flexibility would not substantially affect the global soil impedances calculated by elastic half-space theory, flexing of the wings relative to the main auxiliary building and control tower might substantially influence in-structure floor response spectra calculated out in the wings. Therefore, in order to accurately define loadings and floor spectra in the wings, it may be necessary to correctiv distribute the portion of overall soil spring stiffness that supports the wing area to the nodal points in the mathematical model representing the wing foundation rather then lump all the soil stiffness at a single location beneath the auxiliary building foundation. Because of these concerns (Reference 2), a parametric study was conducted in order to determine the effect on spectra of the distribution of the soil impedance beneath the electrical penetration wings. Three cases were analyzed. The first case studied, defined as the global stiffness case, assumed that the soil compliance functions were developed using the overall structure foundation geometry and were located at the base mat centroid as shown in Figure 1-3. No soil springs were located beneath the wing areas for this case. In the second case, defined as the lower bound relative wing stiffness case, a crocedure was develooed that calculated the lowest reasonable relative stiffnesses for the springs i beneath the wing areas. Soil springs were then distributed beneath the wing areas and under the main auxiliary building / control tower foundation as shown schematically in Figure 1-4 Equilibrium of the overall model was considered in order to ensure this case had the same global soil characteristics as defined by case one above. The final case, defined as the upper bound relative wing stiffness case, used a procedure that calculated the highest reasonable relative stiffness for soil springs under the wings. As in case two, the soll stiffnesses beneath the auxiliary building / control tower foundation were adjusted to maintain the same global model characteristics defined by case one above. Using these models, comparisons of in-structure floor response spectra, peak 1-2 l l

acceleration, and peak displacements for each of the three models were made in order to d termine the importance of modeling the soil beneath the wings. Section 2 of this report presents the methodology used to develop the soil stiffnesses for each of these three cases. Comparisons of in-structure ficor response spectra, peak displacements, and accelerations j at typical lo, cations in the building for each of the three cases studied, are presented l in Section 3. Section 4 summarizes all important results and presents conclusions regardir.g sensitivity of the seismic response and the necessity of correctly modeling the soil beneath the wings. i 'f O i D t 1-3

ELECTRICAL PENETRATION AREA CONTROL TOWER FUEL STORAGE - EL 704'-0" EAST I M AIN -

  • O',

i 7 WING N l EL 696'-0" N I l l fgP'* I .i s_- J' L 614'-0" E 7l -MAIN BUILDING l \\ -WESTMAIN WING EL 634'-0" h EL 568'-0" i j I FIGURE l-1: SCHEMATIC REPRESENTATION OF THE HIDLAND AUXILIARY i

l + unr .u. O== aaa==* A l AUIlllART BulLDING SEl5MIC I G EL ~ 21 " O.!." :.'.'"... ..o. .h . l. c l aa.::a " J' *

  • g,g;;g

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-4 .n................,,.......: a e 1, -. ikT N iN3 ? % _.k;MMN ~ f4 ggN -pf V N$ _f . n. n j M g --.m..-. ; L ,o,;,-, f-Ksc,,;%---/,*d Af ~ a gi; ;;m ,.,,, A= y . y 1 1 A A Af p,J.. a i59 o /...,.... f -- A A ,,c . Je A i ^ f _A g4 o s y .g.,,2 g } g 2....... , pA /. A g y O/..,N ...N,.,g, u ,,............... e......... ....,A[,g]g f h1 T* 2 ss y. u, a y 0b fE A A a A ...%.. YA Yk Y h '~ A d.'. [- o A 1/ A/ A a a A A. A.. A A ..........3..<. A /A /4 A. -A NkN N A 265205 2'0 a 132 211 21i. ,,..g3 9 ,,.. U17 220 l'6 a 223 225 f/2 ~ C l l ME".!.B u -.. FIGURE l-2: MATilEMATICAL MODEL OF AUXILIARY BUILDING ~.. ".a.'.T.'.: " 8 1 3 i I 5 14 4 I s i a 4

l AUXILIARY BUILDING SCHEMATIC PLAN 8 8 8 a A 8 t (0,0) ~ .Y N A MAIN AUXILikRY BUILDING f Location of Global Soil Impedances for Global Stiffness Case, (Coordinates of Node 239 are: m a, 220' X = 82.64 ', Y =-2.31 ', Z = 565 ') 4l REACTOR BLDG REACTOR BLDG UNIT.1 UNIT 2 control Tower kEntrapped7 Jr K / ELECTRICAL ELECTRICAL PENETRATION ' PENETRATION AREA (WEST) AREA (EAST) 140' X 140' FIGURE l-3: SCHEMATIC REPRESENTATION OF AUXILIARY BUILDING FOUNDATION

~ ~ AUXILIARY BUILDING ~ . (With Conceptual Seismic Model) / / CONTROL- / AUXILIARY [y a TOWER y-BUILDING AUXILIARY = -o BUILDING I A ELECTRICAL / s e * O PENETRATION / [J ~ g AREA ( ) we-O E ( / // [h 4f / (ROTATIONAL SPRINGS NOT o itg ::p, SHOWN FOR CLARITY) '?.f.1-Q 4 bi:';c L / UNDERPINNING FIGURE l-4: SCliEMATIC REPRESENTATION OF AUXILIARY BdILDING MATilEMATICAL MODEL Sil0 WING PLACE S0Il SPRINGS BENEATil Tile PENETRATION WINGS

2. ANALYTICAL APPROACH 2.1 DEVEL0ftfNT OF GLOBAL SOIL IMPEDANCE Soil ' impedances under the' auxiliary buiTding were develoned based on frequency-dependent, elastic half-space equations, as shown in Table 2-1, with soil springs modeling the real part of the soil compliances and viscous dashpots modeling the imaginary part. These equations are based on relationships presented in Reference 3. The use of an elastic half-space, fonnulation required the development of an effective soil shear modulus for the half-space, Geff, to use in determining the soil impedances. Because the soil profile beneath the auxiliary building is comprised of differing soil layers of varying stiffness and shear wave velocities, a layered site analysis using the Program CLASSI (Reference 4) was conducted to determine best estimate soil effective elastic half-space shear moduli. Siace this procedure will be discussed in detail in a later SMA. report on the Seismic Margin Evaluation for the Midland Plant, it will not be presented herein. CLASSI layered site analyses demonstrated that effective shear moduli of 7,100 ksf for the two horizontal translation and torsional dof and 8,600 ksf for the rocking and vertical dof adequately represented the site characteristics for the best estimate soil case. The projected foundation geometry for the auxiliary building at elevation 562 feet is shown in Figure 1-3. Within the area shown as the control tower foundation, there is a large mass of entraoped soil. In developing the effective rectangular foundation properties for the auxiliary building complex, this soil was considered to act as cart of the foundation for horizontal translation and torsional dof. For rocking and vertical translation, the foundation geometrv was considered to consist of the base mat and spread footings only with no consideration given to the entrapped soil. The centroidal location for placement of the soil springs' and dashpots were calculated based on the actual foundation geometry for all degrees-of-freedom (dof). This location is 2-1 .es + y + -, - -y +-am- -***-r T --T

shown in Figure 1-3 for the global stiffness case and corresponds to node point 239 in the mathematical model shown in Figure 1-2, The frequency-dependent, elastic half-space equations cresented in Table 2-1 were used to define global soll impedances. The frequency-dependent coefficients in these formulations were developed based on References 5, 6 and 7. A Poisson's ratio of y = 0.42 and unit weight of a = 135, pcf for the soil was used in all cases. Using this data in conjunction with the effective soil moduli and equivalent rectangles based on actual foundation geometry discussed above, non-embedded soil springs and dashpots were developed for the structure. These soil impedances are presented in Table 2-2. When determining the dashoots values shown in Table 2-2, soil radiation damping was limited to 75% of theoretical elastic half space damping for horizontal translation and 4 torsional dof and to 50% of theoretical elastic half space damoing for rocking dof. These conservative limitations on soil geometric damoing were based on comparisons of soil radiation damping determined from the Ct.ASSI layered site analysis to soil radiation damping based on elastic half-space theory. The auxiliary building is embedded in the surrounding soil approximately 60 feet on all sides. The stiffening effects of the side soil were considered using a frequency-dependent embedment approach presented in Reference 1. Table 2-2 presents the calculated embednent f actors as a multiplier to be applied to the non-embedded, elastic half-space spring stiffnesses and dashpots. Table 2-2 also presents the l final global embedded spring stiffnesses and dashpots for the auxiliary building complex. Note in this table that the embedded dashpcts have been adjusted to account for 5 percent soil hysteretic damping. The i global soil springs and dashpot values are applied at the centroidal location shown in Figure 1-3 in the auxiliary building mathematical model. The spring and dashpot values presented in Table 2-2 are the basis for the global stiffness case. lp ~ 2-2 m r-v' e

2.2 LO'4R BOUND RELATIVE WING STIFFNESS CASE Figure 2-1 presents a plan view of the auxiliary building foundation geometry used to develop the lower bound relative wing stiffness case. This procedure assumes that for the translation dof beneath the wing area, the proportion of the overall global stiffness to be applied beneath the wing is given by: A Kw (X,Y,Z) = 'G(X,Y,Z) (2-1) AT wh'ere: K (X,Y,Z) = The global translational (X,Y, or Z direction) g soil spring stiffness as determined in Section 2.1 above. AT Total foundation plan area including the wings. = Ag Foundation plan area of a single wing. = This procedure assumes the maximum possible interaction between the wing foundation and the main auxiliary building / control tower foundation. This assumption overemphasizes the interaction effect on the wing stiffnesses since the soil beneath the outer extremities of the wings should not be influenced much by soil stresses beneath the main auxiliary building. The wings actually would he more indeoendent of the main auxiliary building foundation than this procedure assumes with a larger portion of the overall soil stiffness occurring beneath them. l Consequently, this procedure results in a lower-bound estimate of the relative wing stiffnesses. 2-3

o For rocking of the structure in the North-South (N-S) direction (about the Y axis), the rocking stiffness beneath the wing area, K. (N-5), g is determined in the following manner. First, the embedded elastic half space rocking stiffness, K* (N-5), and vertical stiffness, ((Z), are calculated for the wing area alone. These stiffnesses are developed assuming that the wing area, A, (see Figure 2-1) acts w independently from the rest of the auxiliary building foundation. The rocking stiffness K* (N-S) and vertical stiffness K (Z) of the wing are g determined based on the area and shape of the wing using the elastic half space stiffnesses presented in Table 2-1, G3ff as previously defined in Section 2.1, and the embedment f actors from Table 2-2. The rocking stiffnes (N-5) is then factored down proportional to the ratio in order to determine the actual rocking stiffness ((N-5) beneath*the wing area for the lower bound relative wing stiffness case. Note that_ the term ((Z) is defined by Equation 2-1 above and represents the lower bound relative wing stiffness in the vertical directi on. This factoring process assumes that the rotational soil stiffness, beneath the wing area is proportional to the vertical soil stiffness determined by tributary area considerations and again overemphasizes interaction effects between the main auxiliary building and the wing areas. This relationship for the wing rocking spring stiffness, K, (N-S) may be expressed as follows: K (Z) g K (N-S) =

7) K (N-S)',

(2-2) Details of these calculations for translational and rocking stiffnesses are presented jn Appendix A. Rocking stiffnesses in the East-West (E-W) and local torsional stiffnesses under the wings were not developed since the wing foundation is extremely stiff for these dof and local response of the wings is not expected to be significantly influenced by modeling soil springs beneath the wings for these di rections. 2-4

Once lower bound relative wing stiffnesses were determined for ) each of the wing areas shown in Figure 2-1, nodal springs were developed for application beneath the wings in the three-dimensional mathematical model of the auxiliary building shown in Figure 1-2. Thase nodal springs were determined from the overall wing translational and rocking stiffnesses defined by Equations 2-1 and 2-2 above, based on the contributary area of each nodal point beneath the wings. The nadal trans-lational springs developed for the electrical penetration wings are applied at node points 217, 220,168, 223, 226, and 272 for the east wing and at nodes 269, 205, 208,112, 211, and 214 beneath the west wing. The remaining soil stiffness is applied at node 239. However, in order to maintain the same global model characteristics defined by the global stiffness case discussed in Section 2.1, it was necessary to recalculate the magnitude and centroidal location of the soil springs, dashpots, and base mat masses defined beneath the auxiliary building / control tower portion of the model. In order to maintain the same center of rotation as defined by the global stiffness case, equilibrium considerations show that the centroidal location of node 239 must shif t to the new coordinates shown in Figure 2-1. Comparison of Figure 2-1 to Figure 1-3 shows that node 239 has shifted approximately 9.9 feet to the north of the location defined in the global stiffness case. Details of these calculations are given in Appendix A. Table 2-3 presents the lower bound relative wing stiffnesses used with the auxiliary building model. 2.3 Upoer Bound Relative Wing Stiffness Case The intent of this bounding procedure was to define the maximum possible relative soll spring stiffness beneath the wing areas. Maximum relative soil spring stiffnesses beneath the wing area are calculated whenever the minimum possible interaction effects between the main auxiliary / control tower and the wing areas occur. A simple procedure based on elastic half space theory was used to develoo upper bound relative soil spring stiffness for this case. Figure 2-2 presents a plan view of the auxiliary building foundation geometry used to develop the upper bound relative wing stiffness case. A composite foundation for the electrical penetration 2-5

/ wings and control tower was considered to be defined by the area enclosed by the dashed line in this figure. This idealized foundation includes the area of the east and west electrical penetration wing foundations and a foundation strip running the length of the control tower foundation equal in width to the electrical penetration wing foundations. Tnis composite foundation represents a realistic bound on the minimun portion of the overall auxiliary building / control tower foundation which would be expected to interact with the wing areas. This composite foundation was used to develop relative soil stiffnesses beneath the wing areas. In reality there would be more interaction between the rest of the auxiliary building foundation and the wing areas than this composite footing assumes and the relative soil stiffnesses beneath this composite footing wuld be smaller in magnitude than those determined using this procedure. Relative stiffnesses beneath the wing areas were then calculated based on the preceding formulation for the upper bound relative wing stiffness case. This may be expressed as: b K (X,Y,Z, (N-5))= E (,Y,Z,9(N-S)) (2-3) w A c c where: K (X,Y,Z, (N-S))= The translational (X,Y,X) or rotational w (,p(N-5)) relative soil spring stiffness based on the area of one wing. l K(X,Y,Z,(N-S))= The translational (X,Y,Z) or rotational (,(N-5)) c soil spring stiffness based on the geometry of the composite wing area, A, effective c soil shear modulus, Geff, and embedded elastic half space theory. 2-6

E o z Ac Foundation plan area of composite wing as = shown in shown in Figure 2-2. A Foundation plan area of a single wing. = g Once upper bound relative wing stiffnesses were determined for each of the wing areas shown in Figure 2-2, nodal springs were again developed for application beneath the wings in the three-dimensional mathematical model of the auxiliary building shown in Figure 1-2. These nadal springs were determined from the overall wing translational and rocking stiffnesses defined by Equation 2-3 above using the procedure discussed in Section 2.2. Table 2-3 presents a tabulation of the nodal stiffnesses developed for this case. The stiffnesses beneath the wing areas are approximately a factor of 3 and 5 higher (translational and rocking dof, respectively) than those presented for the lower bound relative wing stiffness case. The stiffness and location of the soil springs heneath the main auxiliary building / control tower was again adjusted for this case in order to maintain the sane overall soil stiffness as defined by 4 the global stiffness case. Figure 2-2 shows the location of node 239 for this case. Because of the relatively large, vertical wing stiffnesses, this nodal location has now shif ted about 38.7 feet north of the original location as defined by the global stiffness case (Figure 1-3) in order to 1 maintain the correct center of rotation. Details for these calculations may be found in Appendix A. i 2-7 e ,c-r -

TABLE 2-1 FRE00EtlCY DEPErl0ENT ELASTIC HALF SPACE IMPEDANCE Equivalent Equivalent Motion Soring Constant Damoing Coefficient Horizontal k =k 2(1+v)G8 /BL c =c k (static)R/p/G ' x j x x jx Rocking k,=k21 p BL c=ck.3(static)R/p/G 4 2 Vertical k,=k3 fy 8 y5L~ c =c k (static)R/p/G j 7 7 3z 3 Torsion k =k 16GR 73 C 'C N (static)R/p/G ' t 4 t 4t in which: Poisson's ratio of foundation medium, v = G shear modulus of foundation medium, = R radius of the circular base mat, = p density of foundation medium, = B width of the base mat in the plane of = horizontal excitation; length of the base mat perpendicular to the L = plane of horizontal excitation; k),k ' 3,k, 2 4 frequency dependent coefficients modifying the = c,c,c c static stiffness or damping z2 3 4 3 '. S l t (; H 3-d 3y { - i.o a - 4 g ..a =, 93 1 _____7_.-~__.. i - o.s { As o' ,,,, ~ o o.: o.2 o.4 o.s i.o a 4 e s.o S/L Constants p, p3 and s for x g Rectangular Bases

TABLE 2-2 GLOBAL SOIL STIFFNESS A'0 OAMDING C0]L$_TANTS FOR THE AUXILI ARY BUI1DJllG__C.0fP_LfJ A) SPRING CONSTANTS Non Embedded Embedment Embedded Motion Soil Stiffness Factor-Soil Stiffness Translational 6k 6k North-South 3.21 10 /ft 1.11 3.56 10 /ft 6k 6k East-West 3.36 10 /ft 1.10 3.70 10 7ft 6k 6k Vertical 3.64 10 /ft 1.09 3.97 10 /ft Rotational 10k-ft 10k-ft North-South 3.73 10 / rad 1.24 4.63 10 / rad 10k-ft 10k-ft Eas t-West 2.85 10 / rad 1.22 3.48 10 / rad 10k-ft 10k-ft Torsional 3.48 10 / rad 1.21 4.21 10 / rad B) RADIATION DAMPING COEFFICIENTS Motion Non Embedded Embedment Embedded Damping Coefficient Factor Damping Coefficient Translational North-South 1.12 105k-sec/ft 1.25 1.60 105k-sec/ft East-West 1.19 105k-sec/ ft 1.24 1.69 105k-sec/ f t Vertical 2.54 105k-sec/ f t 1.11 2.97 105k-sec/ft Rotational 8 8 North-South 4.53 10 k-ft-sec 1.44 9.07 10 k-ft-sec 8 8 Eas t-Wes t 2.03 10 k-ft-sec 1.46 5.01 10 k-ft-sec 8 8 Torsional 3.79 10 k-ft-sec 1.49 8.03 10 k-ft-sec

  • Includes 5% Soil Hysteretic Damping 2-9

TABLE 2-3 N00AL SPRfMG STfFFNESS FOR LOWER AND UPPER BOUND RELATIVE WING STIFFNESS CASES Node Lower Bound Relative Upper Bound Relative Number Direction Motion Wing Stiffness Case Wing Stiffness Case 4 I N-S Translation 4.17'10f 1.4110l E-W Translation 4.33 10 1.25 10 214,217 5.0010f 5 Vertical Translation 1.53 10 N-S Rocking 1.02 10 5.06 10 4.4910f 5 N-S Translation 1.52 10 E-W Translation 4.67 10 1.35 10 4 5 211,220 Vertical Translation 5.39 10 1.65 10 7 7 N-S Rocking 1.10 10 5.46 10 1.1810f 4.0010f N-S Translation E-W Translation 1.23 10 3.56 10 4 4 112,168 Vertical Translation 1.42 10 4.35 10 6 7 N-S Rocking 2.90 10 1.44 10 2.5010f 8.4710l N-S Translation E-W Trans1ation 2.60 10 7.53*10 4 4 208,223 Vertical Translation 3.01 10 9.20 10 6 7 N-S Rocking 6.13 10 3.04 10 2.1810l. 6.5710l N-S Translation 7.38 10 E-W Translation 2.27 104 4 205,226 Vertical Translation 2.62 10 8.02 10 6 7 N-S Rocking 5.35 10 2.65 10 5.4010)3 N-S Translation 1.8210l E-W Translation 5.61 10 1.62 10 269,272 Vertical Translation 6.48 10 1.9840 6 6 N-S Rocking 1.32 10 6.56 10 6 N-S Translation 3.26 10 2.54 10 6 E-W Translation 3.38 106 2.79 10 239 6 Vertical Translation 3.61 10 2.86 10 10 10 N-S Rocking 3.23 10 2.62 10 10 10 E-W Rocking 4.23 10 3.05 10 10 10 Torsion Rocking 3.68 10 2.39 10 NOTE: 1. Units on translational springs are kip /ft 2. Units on rotational springs are kip-ft/ rad 2-10

AUXILIARY BUILDING ~ SCHEMATIC PLAN 4.55 l e -i- (0, 0)

  • Y N

~ A MAIN AUXILikRY BUILDING,__ Location of soil Impedance Beneath Main Auxiliary Building / Control Toteer - (Coordinates of Node 239 are: X = 71.70', Y = 2.52 ', 2 = 564.25 ' ) "1 220' ~ l HEACTOR BLDG REACTOR BLDG uni r.1 UNIT 2 i~ c _ _,_ _, _ _ _ _. Entrapped "OK A Soil A g-- E--------", ELECTRICAL ELECTRICAL PENETRATION PENETRATION AREA (WEST) AREA (EAST) 140' 140' X FIGURE 2-1. SCllEMATIC REPRESENTATION OF AUXILIARY BUILDING FOUNDATION USED TO DEVELOP LOWER B0UND RELATIVE WING STIFFNESS CASE

AUXILIARY BUILDING SCHEMATIC PLAN 8 8 8 e a A 8 t (0,0) "Y N ~ A MAIN AUXILikRY BUILDING - Location of Soil Impedance Bencath Main Auxiliary Building / Control Tower - 'Y (Coordinates of Node 239 are: X = 42.96', Y =-3.19', Z = 562.09') 2 220' l REACTOR BLDG REACTOR BLDG UNIT.1 UNIT 2 / Areaofawin9,( 8 / Composite Win, Control Tower, r Footinl'=C K ELECTRICAL ELECTRICAL PENETRATION PENETRATION AREA (WEST) AREA (EAST) 140' Y 140' X FIGURE 2-2. SCHEMATIC REPRESENTATION OF AUXILIARY BUILDING FOUNDATION USED TO DEVELOP UPPER B0UND RELATIVE WING STIFFNESS CASE

l l l l 3. SEISMIC RESPONSE RESULTS l l 3.1 APPROACH In-structure (or floor) response spectra were develooed for each of the three soil cases studied. In-structure response spectra wre selected as the primary basis for comparison of the effects due to wing soil stiffness modelling assumptions since differences in the response spectra are more pronounced than in-structure accelerations or loads. However, peak accelerations and relative displacements were also chec' ed at selected locations. Because of the flexibility of the electrical penetration wings under N-S excitation, this direction of excitation and corresponding structural response represented the greatest potential for significant differences in floor response spectea between the different cases. In order to develop the floor response spectra, modal characteristics of the structure were required. Table 3-1 presents the fundamental frequencies for the X, Y, and Z directions for each of the three soil cases. Only minor shif ts irr frequency are evident. This demonstrates that placement of soil stiffness beneath wings does not significantly affect the global characteristics of the model and imolies that the base mat of the structure is essentially translating and rotating as a rigid body in all cases. In-structure response spectra were developed using modal superposition time history analysis on Computer Program MODSAP (Reference 8). Composite modal damping values associated with each mode were developed based on the Tsai Method (Reference 9) using Program S0ILST (Reference 10). A subsequent report by SMA will describe the develoament of the composite modal damoing values and therefore the damping values used and their basis will not be presented here. An artificial earthquake time history scaled to a neak accelera-tion of approximately 0.13g which essentially enveloped the ground response spectra for the original ground surf ace (Reference 11) was used 3-1

in all cases to excite the structure. A comparison of the time history response spectra with the design ground response saectra is shown in Figure 3-1 for 5% and 20% of critical damping. Typical locations in the structure were chosen for development of floor response spectra, peak relative displacsnents, and peak absolute accelerations. The locations studied were (see Figure 1-2): 1. Control Tower - Elevation 614 f t - Node 55 2. Control Tower - Elevation 659 ft - Node 44 3. Main Auxiliary Building - Elevation 614 f t - Node 28 4. Main Auxiliary Building - Elevation 628'5 f t - Node 24 5. Main Auxiliary Building - Elevrion 659 f t - Node 10 6. East Penetration Wing - Elevation 642.6 f t - Node 159 7. East Penetration Wing - Elevation 674.5 f t - Node 156 3.2 COMPARISCN OF IN-STRUCTURE RESPONSE SPECTRA Figures 3-2 to 3-8 show a comparison of 2 percent critical damping in-structure floor response spectra developed for the locations presented in the previous section for each of the three cases studied. These spectra were developed for N-S structural response under N-S ground mo ti on. The spectra are nearly identical in each case. However, the following trends may be noted from these spectra. First, in' the region of the fundamental N-S frequency of 2.7 hertz, the lower bound relative wing stiffness case and global stiffness case predict sligh'tly higher spectral accelerations than the upper cound relative wing stiffness case. In the higher frequency regions of the spectra (4 to 10 hertz) range, results show that for all three cases approximately the same spectral response is ootained throughout this frequency region with the exception of node 156 (Figure 3-8). For node 156, the lower bound relative wing stiffness case and global stiffness case credict higher responses than the upper bound relative wing stiffness case. The soectra at a given elevation all return to approximately the same ZPA for each of the three cases studied. 3-2 i

Table 3-2 presents a comparison of peak relative disolacements and peak absolute accelerations for these sane locations for the soil cases studied. Results are almost identical for all cases studied at a specific elevation.' The lower bound relative wing stiffness and global stiffness cases agree within 5% of each other at all locations and tend to have slightly higher responses than does the upper bound relative stiffness case (on the average about 5% higher for' acceleration and 2% higher for displacement). ? Maximum differences in structural response would be expected to occur under N-S excitation because this direction represents the greatest potential flexiblity of electrical penetration wings. Other directions would be expected to'show lesser differences. Because of the excellent comparisons shown for in-structure response spectra, ceak relative displacenents, and peak absolute accelerations for the three cases studied under N-S excitation, it was determined that additional work considering response in other directions was not required. 3-3 t l l l i-I

TABLE 3-1 FUNDAMENTAL STRUCTURE FREQUENCIES FOR CASES STUDIED Mode Direction Global Stiffness Lower Bound Relative Upper Bound Relative Case Wing Stiffness Case Wing Stiffness Case 4 1 East-West 2.60 2.63 2.59 2 North-Sou th 2.69 2.70 2.67 5 Vertical 3.67 3.71 3.72 s e 3-4

TA8LE 3-2 COMPARISON OF PEAK RELATIVE DISPLACEMENTS AND PEAK ABSOLUTE ACCELERATION FOR CASES STUDIED Peak Relative Displacements Peak Absolute Accelerations LOCATION (inches) (G' S) Lower Bound Upper Bound Lower Bound Upper Bound Global Relative Wing Relative Wing Global Relative Wing Relative Wing Eleva Stiffness Sti f fness Sti ffness Sti f fness Sti ffness Sti f fness Node tion Building Case Case Case Case Case Case 55 614' Control Tower 0.160 0.159 0.159 0.142 0.145 0.139 44 659 Control Tower. 0.219 0.220 0.218 0.165 0.167 0.156 }[ 28 614 Main Aux. 0.165 0.165 0.165 0.145 0.148 0.143 24 628.5 Main Aux. 0.181 0.180 0.180 0.150 0.151 0.145 10 659 Main Aux. 0.212 0.213 0.211 0.163 0.162 0.160 159 642.6 East Wing 0.249 0.234 0.230 0.181 0.175 0.166 156 674.5 East Wing 0.300 0.298 0.294 0.246 0.259 0.243

b ..l ...I 7 m-c- ~ DRMPlNC 0.05 m- ~' 0.20 m-Artificial Time flistory M - m-o Design Response Spectra N-m n z y oro e-2 cr m-ee-Ltj m- -.J m-

  1. ~

w a. y n-w~- p 37 ao a1 y) o)- m *: T w. o *~ ~ o w-o y m-tn Q_ m- 'a 10-' i 5 0 $ 5 i O 5 h 0* i li 0 $ 5 i E 5 '10' E 3 0 $ 5 i 5 5 '10' i FREQUENCY (HERT2) FIGURE 3-1: COMPARISON OF 5 AND 20 PERCENT CRITICAL DAMPING RESPONSE SPECTRA GENERATED FROM ARTIFICIAL TIME IIISTORY AND DESIGN TARGET RESPONSE SPFCTRA

8 10 2, 3, 4, 5, 6, 7, 8, 9, /0' 2, 3, 4, 5, 6, 7, 8, 9, lh DAMPING 0.020 E E Global Stiffness Case ~a Lower Bound Relative Wing o Stiffness Case o e m z-O N Upper Bound Relative Wing 2 Stiffness Case e-- 2 C \\ 58 i 8 dd- -d u u \\ Uk. \\ _k ao e if.. a a O \\ V m oo C8 od-g -d a r e - - ~ -..,. to m '8 8 1 0 5 5 i 5 0 '10' E 5 0 E } E O 'lif 10 FREQUENCY (HERTZ) FIGURE 3-2. NORTH-SOUTH CONTROL TOWER RESPONSE DUE TO NORTH-SOUTH GROUND MOTION, ELEVATION 614 Ft.. N0DAL POINT 55

i 8 10 2 3 4 5 6 7 8 9 /0' 2 3 4 5 6 7 8 9 1 21'- OAMPING 0.020 om om ~ Global Stiffness Case 0 Lower Bound Relative Wing o m St'iffness Case z-O~ Upper Bound Relative Wing ~l p Stiffness Case lO\\. 1 (C o wm a r o J. I-wo i -f u C o c \\/ C w w8 't m a r._ o ao _J Q (n tu EE o Oo. m a ..j' O g w ( r - u, 'S oo i i s i s i a i s a i i a a a i 10 2 3 4 5 6 7 8 9 $ 0' 2 3 4 5 6 7 69 lh' FREQUENCY (HERTZ) FIGURE 3-3. NORTH-SOUTH CONTROL TOWER RESPONSE OUE TO NORTH-SOUTH GROUND MOTION, ELEVATION 659 ft., NODAL POINT 44

2 10 2 3 4 5 6 7 8 9 l10' 2 3 4 5 6 i i l@ 7 8 9 i i i i i DAMPING 0.020 oo oo ~ Global Stiffness Case h -Lower Bound Relative Wing g Stiffness Case g ~ $d-j-[V Upper Bound Relative Wing -d i Stiffness Case e 1, 1 C i o I_ o 1 _9 \\ wo o U 4 u .s w a i 'N w? /' Y S F-t s\\ ~o Do' i __j s a 1 t (n V - s cu ES S od- -d o ( ..y_._..___ w u, iO A 4 5 5i56110' i 5 4 6 )$6 iTf FREQUENCY (HERTZ) FIGilRE 3-4. NORTH-SOUTH MAIN AUXILIARY BUILDING RESPONSE DUE TO NORTil-SOUTil GROUND MOTION, ELEVATION 614 Ft., N0DAL POINT 28

2 10 2 3 4 5 6 7 8 9 ) 0' 2 3 4 5 6 7 8 9 18 ~ DAMPING 0.020 0 o o Global Stiffness Case ~ Lower Bound Relative Wing o Stiffness Case [$ Upper Bound Relative Wing 8 z-1 Stiffness Case o e o i o ~ i i E 1 }) o U O o I.- L3 A wo 3 .o u 4 o C w b WS I N, ? n.. \\ s 20 gi ..o __lo i v, \\ m n C2 2 ca~ -d a < -e v w u,ag oo 5 10 E 5 0 5 5 i 5 $ '10' 5 5 0 5 i50 lif FREQUENCY (HERTZ) FIGURE 3-5. NORTH-SOUTH MAIN AUXILIARY BUILDING RESPONSE DUE TO NORTH-SOUTH GROUND MOTION, ELEVATION 628.5 Ft., N0DAL POINT.24

8,10 2, 3, 4, 5, 6, 7, 8, 9, ,1 0' 2, 3, 4, 5, 6, 7, 8, - 9, ,l@# ORMPING 0.020 o tn ~ sn ~ Global Stiffness Case L3

Lower Bound Relative Wing Stiffness Case

~ om o Z-Upper Bound Relative Wing N o~ Stiffness Case w C I? o W '. I! \\ O O J. 6 m W I w U i. 1 O t C

  • [

5 4 W8 \\ 8 s._ Do [ O ow g) .#k go o co-A( -o o a-3 ( --- e1- - e____ u, a_ g o l10 E 5 0 5 i $ $ 5 0' 5 3 0 i 50 1%' FREQUENCY (HERTZ) I IG'IRF 3-6. NORTH-500Til MAIN AUXILIARY BUILDING RESPONSE DUE TO NORTH-SOUTH GROUND MOTION, ELEVATION 659 Ft., N0DAL S0 INT 10

8 10 2, 3, 4, 5, 6, 7, 8, 9, t 2, 3, 4, 5, 6, 7, 8, 9, 18l' 10' ~ DRMPING 0.020 o* o ~ nn Global Stiffness Case Lower Bound Relative Wing La o Stiffness Case '~ ru a Z-Upper Bound Relative Wing o~ Stiffness Case ~ ~ f/S w

o \\

a \\ C o t w m t 8 J-t wo \\ o u \\g m o oi C % I wg ~k l-- ao o a t O D L .g\\ co go s. m o m Oh' o ,~.........,'":

==** _t =A' W ' = u w _ w w.x z u,. u, CL o O oo 5 10 5 5 0 E i $ $ '10' E 5 0 $ Si50 th' FREQUENCY (HERTZ) FIGURE 3-7. NORTH-SOUTH EAST ELECTRICAL PENETRATION WING RESP 0f,$E DUE TO NORTH-SOUTH GROUND M ELEVATION 642.6 Ft., N0DAL POINT 159

S 10' 2 3 4 5 6 7 8 9.1 0' 2 3 4 5 6 7 8 9 IT i i r ORMPING 0.020 ow a w 4 Global Stiffness Case f.i ' 1 9 I Lower Bound Relative Wing T O Stiffness Case 'u i o 7 ~ i g Upper Bound Relative Wing <v O- $ t Stiffness Case ~ ~ b g C Ctus d!! O J-LdO si-9 .A o { ! n /:s m o t L u .1 m a

i Id o

e- .{ O Do .i:: -g Jo IM J .i (f)

  • i m

\\ CO b.g O <n od-g - * ~.... -. ~ ~d m O ( td '8 o 9 5'g i j i 4 5 i 5 0 '10' E 0 $ $i$0 ITf o FREQUENCY (HERTZ) FIGURE 3-8. NORTil-SOUTH EAST ELECTRICAL PENETRATION WING RESPONSE DUE TO NORTH-SOUTH GROUND MOTION, ELEVATION 674.50 Ft., N0DAL POINT 156

4.

SUMMARY

AND CONCLUSIONS A parametric study has been conducted to evaluate the imoortance of developing discrete soil springs for use beneath the electrical pene-tration wings of the Midland Auxiliary Building mathematical model. Three cases were studied. The first case corresponded to a global stiffness case where soil impedances were developed based on the global foundation geometry of the auxiliary building complex and were attached to the mathematical model at, a single location (i.e. zero relative stiffness was placed under each wing).* The second case was defined as a lower bound relative wing stiffness case. This crocedure minimized the relative soil stiffness beneath the wings and represe..:ts a realistic lower bound on the relative soil stiffnesses which are beneath the electrical penetration wings. Discrete soil springs were modeled under both the wings areas and main auxiliary / control tower for this case. The final case studied was defined as an upper bound relative wing stiffness case. The intent of this case was to maximize the relative soil stiffness under the wings and be an upper bound on the relative soil stiffnesses beneath the wing areas. Care was taken when develooing cases two and three to maintain the same global stiffness and center of rotati.on as defined by the global stiffness case. Response of the structure under N-S excitation was developed for each of the three cases. Results were obtained for this direction only since it represents the greatest flexibility in the electrical penetration wings and the maximum differences in response for the different cases would be expected for ground motion in this dire: tion. In-structure floor response spectra, peak relative displacements, and peak absolute accelerations were developed for typical locations in the structure. Results showed that for all the locations studied, the floor resoonse spectra, accelerations, and displacements were virtually identical. These results indicate that the base mat of the structure is translatinq and rotating as a rigid body. Therefore, it does not make much difference 4-1

how the soil is modeled in the analysis, so long as it is dcne consist-ently. The lower bound relative wing stiffness and global stiffness cases predict slightly more conservative spectral acceleratinns, zero-period accelerations, and displacements than the upper bound relative wing stiffness case. Therefore, it is reconnended that the lower bound wing stiffness case be used for development of inertial loadings for determining monent and shear distributions in the struc ture. Either the lower bound relative stiffness or the global stiffness case should be used to determine in-structure floor response spec bra. 4-2

REFERENCES 1. Bechtel submittal to VC, " Auxiliary Building Seismic Model Revision 3 for Midland Plant Units 1 and 2 Consumers Power Company", September 28, 1981. 2. Kennedy, R. P., " Seismic Testimony for Midland Hearing", Nuclear Regulatory Commission, Docket F;,. 50-329 OL and OM, 50-330 OL and OM, Consumers Power Company, Midlir d Plant Units 1 and 2, December 14, 1981. 3. Richard, F. E., Hall, J. R. and R. A. Woods, Vibrations of Soils and Foundations, Prentice-Hall, Inc., New Jersey,1970. 4. Wong, H. L. and J. E. Luco, " Soil-Structure Interaction: A Linear Continuum Mechanics Approach (CLASSI), Report, CE, Department of Civil Engineering, University of Southern California, Los Angeles, California, 1980. 5. Veletsos. A. S., and Y. T. Wei " Lateral and Rocking Vibration of Footings", Journal of the Soil Mechanics and Foundations Division, Proceedings of ASCE, SM9, September,1971, pp.1227-1248. 6. Kausel, E., and R. Ushijima, " Vertical and Torsional Stiffness of Cylindrical Footings", Massachusetts Institute of Technology, Research Report R79-6, February,1979. 7. Luco, J. E., and R. A. Westmann, " Dynamic Response of Circular Footings", Journal of the Engineering Mechanics Division, Proceedings of ASCE, EMS, October,1971, pp.1381-1395. 8. Johnson, J. J., "M00 SAP-A Modified Version of the Structural Analysis Program SAP IV for the Static and Dynamic Response of Linear and Localized Nonlinear Structures", GA-A14006, UC-77, June,1976. 9. Tsai, N. C., " Modal Damping for Soil.-Structure Interaction", Journal of Engineering Mechanics Division, ASCE, Vol.100, No. EM2, pp. 323-341, April, 1974. 10. Johnson, J. J., Letter to Dr. Thiru Thiruvengadam, Consumers Power Company,1945 West Parnall Road, Jackson, Michigan, " Final Spectral Acceleration Values, Original Ground Surface and Top of Fill Site Specific Spectra Midland Site", January 27, 1982.

11. Levine, E.

N., Letter to Dr. Thiru Thiruvengadam, Consumers Power Company, 1945 West Parnall Road, Jackson, Michigan, " Final Spectral Acceleration Values, Original Ground Surface and Top of Fill Site Specific Spectra Midland Site", January 27, 1982. R-1

APPENDIX A BACKUP CALCULATIONS FOR DEVELOPMENT OF LOWER AND UPPER BOUND RELATIVE WING STIFFNESS CASES O e l /

I . g-STRUCTURAL Pare M CF J:b N2 DAT Ill41 4 av

  • 't^

mECHAnlCS couwents - ASSOCIATES CHKO.aY D" DATE EliI"- Wm a c. ie. c.... l .as /f ./ Shu, A,r - r f th:a .?> t'$ > cv:- y GIc.vidien

c. i

&Jis.l C e;I S ; r ;c n ir iI:e in /%/:n k, BUa. /%/- O, yen and lowe.r beved spirg diba:ec: : der le dechkal cle:irec/ine.4r Ic sud.de +he. eHed 'i , enti.},.Jics, wings o.r e -li n i,> f d l b e e ci,+)e. reepcint ei Me llel.,. H,e :r av.x, ,udel. TAe. fc,Ilewing a,jpca d ive: czn:ers's hue-6Nt l '"~' g Levn h on Mis d%::. N A, tu ~ %..l \\ Leson llevi.) 6 fep:: I-G.k.:!<le o lcLtI cy,:,.g : M h es:es % M e. o.v.e, bl4 + dee+rlefp.,,e bJ;<C: winn eaeo.: anthu.)%dhr. s s 2.. frof et flen ll.c U$f,asse: 5cc E '>>> N-$, t etEle, l Frs.:,Lll-n under fle. clectria: ;.

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u.,1 iu,, u.

., a ik., i< <, f 9:t i.,,,.y,/<,i.e< : .,.. -[! ' _ ~ l l i,..; L a n a M;s assvaph;n io./ya< !<<<. -r //;..on je,,-ll>/a 3, a w>n e s oc r :e nt.tI c,. s u, ,0 in t e c ' o,1 3, Eqnore

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i 7 MLE STRUCTURAL PACE _.f.O CF J:;b N:

  • e# h, OAT 1 Iid C 7

^ mECHAnlCS t sy couwenis J w r r'- l -. ~ /- ASSOC.IATES 5, -(/ d/h v.. CN K O. S Y """ DATE LlI l% wm . c.u c.... Kg(!:, vere.~<r.l) ~ ,' '., (le... r..r,)) E' ..') ( Eu..'. h. 'i..,., .<,' Wed. tie, b y) l' is... Rp (!cwea u i L - K j ;;*.. t, k,,. ^>lp ,k.,( e <c ,yjg..g p,,. v hce.: x), x! nee. +h etadic. LJi q.u. -uu,;. n a,,a.,,,.. ,p e,.= c y .%, ek+,ic.d ec..4A:ev....;,.,, dd,y,,c,ii,, y ~ % mf d +h etre. dure. Ki neme hevrf) -ddi,wd by 2. aLue G 1

s tlTLE - % A STRUCTURAL ' ACE '~ '- C F J; b N :- yg D A i n 1 f!'11

  • 2 cauunnis Loeve r 4 n/
  • Y mECHRnlCS CHKD.SY
  • OATE Al ! ITI-Abb,0Cl,ATES g, gg,,

Glok) Bed Es!,%de Ede)ltl Qr&.s: p revis ></y./t..! - l('f.n. s.s r - y an.)sts Ia te t<:".l

i. 4 t: u mp s' n

}L*Y,4's IXese sy:r u r: n.r e. fe u/lce. shEre ixe ad wh a s. &1.k fwnlsAbi,. &~ p. 28 3 chi s+;ffo n:es.ne - / X Npj.s'3.56 /C 'VFf Y l<g-to = 3,90 10 0 M/H 5 Nye,. l = 3.9'l e /0 /// y akv/ }' h',y 4 ~1.;c "#l,r.-6 mfion B = 2f..I ' L

  • D.3 '

$ 'Or 4') /i,, 4. 0,1+ f. 4 ) l'o r 2 -LJ flo f,'e n 2. ,l

  • loo $

bgn % 2,2X f9 k&.pec.: i b n,,1 A ' 'k+;.s =,$ ii+ B *L k a. z ( A w,,,, u,,n . ~ r I.

pf_y, m

c,, ,,p ;_.,_ ;_ y,,y _ 2.04- -le l e r...r.J te r-n. g.g - .,,g 2, zz y,,,,.._ e,4 gl.ki_ plc l.<,, t, * 'U" I I Xp lin..e < -i., ) ) 20 4.,y, (l,..,, L -.1, -l) 1 kz = 0. u ; k+= o,91. fr.m t:. I '7

2Acr Jab He TrTLE N Q STRUCTURAL Pace.: A/M oATE / seriS1 fi1ECHAnlCS ecuuexTs dev>'-"- M ,y ASSOCIATES ,< j,,. /' l ~r. M DATE 'III E W" ^ * * " ' * * ' ' ' 2 CHKD.ty ~ Lhe;4 i , e<oh., ic, Ax. 6% ,,,, /ex ~ A f H.e+h e. 1 ; m es,n helew shew: +he Aux. e!),. c.,,,p e x l L4., +Ae enadr~t k,ier, hd lie -, / consis !s sin a ux. a rc) rec:l c leetriy.l.Ler.*trdis wk.,:. L feondtkn of H a cedul kir. :2, il: wi+h a. !ary. anau of enhupped 4cwe.c ah.sid:ive)er...:11.;, N m. In deve!c ;be. q!cla! :o;! d;ff,ase coi! wn ne c e ne a.le ulD<,5,l biehn}/eaer.,,'$ cad,hn fhe. coil im,l soil was cer.sideced F:e: :;e cm.e. G.e. .e a ein d y '> h'e,, this nihajpe tor t,eei ur l.tI rrarslak,, dd a.rd i:rsler.,t.1: fer-ree.kt : 1 The uv<h. i +he. fs<: REM o uus aswm/ 6.<:ove. i>> d ><rAN/y hf ack uerh'eo.1 %alakian 1Ii Lily 4ifheed eenircidfleeJ.ans eF Me c.,i). As a. eentenvene.e. 6t- +L1: q wet e. elfad for rafi. ldren / +orsion lor ard vekir: /ve ldof. r-Asse f sen r tre. fet reviceu. were-dev* lefed ttvict:sly

p. O r'O 42. buf are 4.55 6.6 8.7 8

a ,~ (0, 0) .y N A i MAIN AUXILIARY BUILDING location of Global Soil Impedance: y for Global Stiffness Case, (Coordinates of Node 239 are: X = 82.64 ', Y =-2.31 ', Z = 565 ') 220' 4l REACTOR BLDG REACTOR BLDG UNIT.1 UNIT 2 Centrol Tower H (( Entrapped 7 / h[ l J g ELECTRICAL ELECTRICAL PENETRATION ' PENETRATION I AREA (WEST) AREA (EAST) \\

= l 140' x 140' ,r

f Pace 52 6c7 J;b No g g A STRUCTURAL M DATE /I?fl97 MECHANICS cowuENTs 0" A m I-r 8Y " ASSOCIATES CHKO. SY % *- DATE bl l I D wm , c, u,, e,,,, gp s t,J, C e.nfroils \\ L=uE; r.s Fer 6Ichs.l 6hifr at C.are b e.!'i <,a + Uu5'E.ti De 5 u c,l. G,. 4 i l p, g2 I a 11.'1 l p/ Elult:al Paa.M:c,, p /0.c f, i g,. }~ '? T , au / cabeid of an 'd'I D. J2,Jc,J /%,n A,x/6,, A./ 7~,, 4 v s %.n I col. A - A Ebb 24, L cs.r 1 6, s* ' d 7 Sek,hs /Uakl ku,. , ran. ry A = 1M +o + +647+2.624N)=3cs'icU.* </ > n 131 3!2'7'/21} 5 A2 7C' (1) N312- ) 1 = ygy,4 ff, E 20C?n - 2. S 4 [ 2 r1 ri a d - 2.31 0. Y* sog70 O f bf f$$m $ SY$ fL*N Cf.Z* 6lc. ter b x. bI s

b Tiits - STRUCTURAL. PAcr N F Jcb Nc-a C SMN cats /1%IF1 MECHANICS sy co u shis ASSOCIATES 2 CHKD. sY 9 DATs ",lIl#E W-a c o m. c.,.. Cedre.'}&l Lech,,1 t-r G!:l.,j Cllr7.. du \\ beia. ii.,, :la h r. + 7), ei. i., i EnT Col G.(, Ai:e.}ra!.*en 2,a /L, ~ IIC.8' r./ r.LJi.,al /!a:n A.x/&,,duI L + 4+ $l r -1.1! A6rie- %&L /hior, b = 30 /2l 2.{f391) = 32,105~ N# ,p. 20/11 (l11. 4 ) +

2. (/ 1,0 (x2.7,7)

X / 11C,8 1 .i 14 c,7 1 o 1: t ( - 2. :.r ] - ~ y= j.,..... - - . ;.,,c ALJu pessfa/ o. love are fro-p. o h n si .:fE Gic irr hs. ti!4 lhier Bate. E!e:af: ne ~1 fn. E.Ua. li,, da Elu t.

a dr J,-,,

!. %. t =:: Elev, c73 thin tw/Gr}ielTer.o s Ele v, AC ' L;iler.:r e.t in e!ed.r,

.=

i+.

PACEDl-!GF Jsb N -- STRUCTURAL TiTi.E $MN DATE i I t'l c 1 - MECHAnlCS couutnis CY' """"""" A SSOCI AT E S SI ' I E U W-a c.ne. c.... CHM O. B Y _ D DATE .n.,./ .0., e, G t t tz,hEen oE (e s' h $mp *.t sy t. {fyya_f[ {$6,;t. hy l s.t e. developed Soc- +ke lewe r le. ;,/ t <pper Soil Z,rp+;edariesTM uts s,salue. pts.a.., du,& Levnd w;.s iirm

u. ice, spr;r,e GoaH,. ILe. wiro -rem. in <r}e r /o mode./ L :sil,',%e, eeny.<eis e,,1 wiM H,e. o.a.':+.hree: cue, V n in r k o n.,

m a.d,21 & He. tron;,.A.,,J eas.. u't i le c J ::,, & s h ~ +o nueu ar/ s s. toil impehr.tes beneshk H. nin o. val,a y /h,Jr,I kwet,mk, o f L l w ild &> in ade r +o maink;,, l).c w,e. everdn}el chmkradea ourd k fkylela.I diffness esu. This peeedce whhb were. for inaink'ninA lhe. :sme. ab'Nrese r 6cdet ei teda.}&s, s's Je F.n ~ z d;~<Lic~lmodel on & vu+ ;ase. El &n a ep cd f,- J th e-lowet havi,2 wiy sh'Neees & se.

g STRUCTURAL #AfEUb CF Jab N2-TITLE SM DarE I I:o t h mECHAnlCS COMMENTS O '>I sv d ^^ """"""* A S S OCI A T ES AI* ') llels 224 lCeYOn DATE bIIl % MM s c a ns. c ea e. CMKD.EY c.n b. _ __... _) p__ __ a _g A. \\ l l. c L-g cucLr)h he .k'*., ef hC W6 E4 hrI O.L C.I ClO $ an Vq $ugose e. ta n e. e Wl ces.r citoM;ce. e ca. . '\\ 8. l USk., M X, Ks-kg i - Rg! i z a .%. n 2-6 2 c 7o~ Io erh. Me do'sLee. c, 3 ;v e. mode.l 8 a. on,+ displacemeadf' downward.a.n d. . sum momends a.bo u t M e. C.R. a, X c =%, b 3x c = Eh U T. 2 'o~ c.a.)c.ola.5e. +h 1. coeree.h memenb Hg

h..c ch 1 f

m u s 4 h,_ fo J 60 42. I. Gi, e >,:e hl A s. nif ecfa.fic,, Ital e.a.lee,!s f: h t i di, a,,. r,.,. - .t. c, E. Pl.a = M e,' 9 c 1 a 7. Giui> in edr l 8 a r.,s i f r e l ~ .-,1 ) :e h: e. E,- e ti o, s u e.i. h x+ ap.ilib ch i..

.. - U <,,,.. ; 1 i. n,.,,

+ (.c s).%; c +.g, n.-0 e For meM d /b =/4 e i k, =. L..a, l l

9-STRUCTURAL PACE 12 6._CF J::b N3 TITI E' S,M DATE /12/161 mECHAnlCS COWWENTS 'n

  • Sac av

""""" ASSOCI ATES M/t-e/5 "*'d DATE Sl ' l'*L W-a c.ne. c.,.. CHMD.sY (ek h h o .'4,] b

  • Ag :- Kg
  • #';g

+ K o, = Ke g ^, - i b* ~ s cmch of au s m a n,A ne Using ,a,S7,S*2-

3. C6 ' ID ' ~ Yz9o(3.56 lo0 = 3.2.6 10
  1. lff H-s k'x

= u3 2-b) K.I,t.31 = 3,70 *loNI - $2ie )" 3.38 10L K,p4 7o

  • 3. 6)
  • I O Yf4' Ucr$

l< = 39'7*lo'{l 3 csn. iveo wj,we .u,2,.,,.,,,. ,y,je u.7 7%e proceduce. shoa, en p, s.2a,s z.s 3 ves

a. dele siske i

e answer schen enly J. dia:eru' sis.t.re conssWere cr' ln /cea}&s.J4 e lecals'rio eb lAs new sprko cenhvicl. Neweest, xAen $re e dinasiki:9. r - c. :eiArxs N ibm ed.4'<i,x., er/ey n i/A n,hea n rs< <a c : <r M.: Mra

2. 9 w. -2,1.,,i en c cobti,i a n 1 <>.vi s'e<l. A be.1l fij-e:er/nde.ui/I Le.

~ dde.1n,,i.eJ,n/ w A li,.cl:e,, by so k g a.A e.a e,. (:e u. u,...< i::.a. i:. /ame n. n? un si.., ijt rewH:j;,c he-Y + 2 d r:c ficn :. L tac r dirccfibn +h'e.):'iheteres he l<aen % e.xrel,ed<: -L!nis al tr om 9 1a + U 1y d ;re J.hne i: 4). e !s,,ee.l. i .i

< e.vid,.,/.- a scesideaI wUA r
ek&s in.Je //-i In ?).;;. lit-4 u
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k iAc br dis ect>v :. i. i u- ?' wrlie.!* r

l
i. ML,. ineM.

10 STRUCTURAL PAraOIdcr JbN: Tivi.s av E b DATE 12ll A 2 mECHAnlCS couwenis ' ne ~4

  • 'r

"""""" ASSOCIRTES D DATE SII lO W" a cene. ca.e. ~,, f"' 4f CHKD. SY f.oeper Sco,~d. b)l, a ffif+r.es: G:c ~ & Go rd;<.s.fe. 573 'Wh ~56r h m,,6, r 3, }.v,wu "' 1:1 fM=0 y 2' Mx - %, @ = 0 g g,ut _ 8_[c,20lo< 2M r, - X 2.1b*/04-. '~ /2?4 'E,= 0,94' helce elte. C&C ' f $ =0 -K% (a )

2.
  • KY

=0 ~ 8 Rya, f(c.1110) 4 119 E l h 3.39 so' ~ ~ ~ ym E = 0 74,' he.lew e.le v. C & C ' z Us e. t = 0,9C' Lclcw eled. CM*' '{ (cord lr.ahe. vi 'bM hT ,xA K,* n O S' A-c.- ~,4 Kx,, = xxw, b0e01 ^~u Y s xy ,r ffNr--0 1 FI* : C X*z g Y + ( 85.ar - Si,45) R%,ue Ane I Mo h'ag,. Nx2 p ~ 4.2c (o.I!lo') Y 3.16 i 1/4x = C X Y +- M,l t h,, I 1 - M.et. %,,=- r P. n C 4.42

7. s.,,,,

4h n, o : iI

  • ~ ~ ~

= .:, H. t r ' s N 47 /

rL1' Ust.

/, Co ) l 'Y = o t" Ct';i s' ').

l I/ i TITLE PACE D F.CF J:b N2 g f STRUCTURAL p' 'g oATE I17Il#1 mECHAnlCS c o u u E N T s C er-A,. ::r AS,SOCl,ATES caxo.sy E* oATa sit 18t m X Ge r J:,,i < 3L21.U2.15 sna 44* bb p ItS*.8-;;':t } k l 1 9 2.o r } %, h N f#g y m rr nr S ti.j = o A', 91. 65 - /4 X.Y 1/4 =o ><yg (43 es) - Rf139 X=o 2 3 "YL x 44'"% X,= x.,. ' ' r d.u 2.11 91.orte.tn. icy y,g',u)- - - - - ,s X, _- 1,3 s.1, X 1= ~.el X, = 8. e l ' x,. 9,9 +' Bistences < rs in kt A'erk o f curre,,7 lee. dan use. x2.= 7 9+ H sinca we na a,,,Js,,,p,4,% is, Mis diraha. C ort e.sk-ho fa.Nen a.) Spia n O Otse. locbiem Uni l & fd ico af aid. ocle z29 loc.dlon sLeub Ue. 1. Ayly men ud we. wanh ?o de.ser ine N-s Ases. De.i.,, e. 11 eJXa.s (1c,z,' ~ mereesk a.h L.R. )vc h eti}la 3 okal ref. dl fret::a l 2. y2 /b = /b + Ykw [sc. n' + Sq.319 f-R :. s (c.n7 1 is -Ax g 1. t,(g [83 i-X [c,h Gl 1 Sc hlin a fc t-Ka -xt 2 2. -- h'ing (o,23 f X g, ~k Nr., LBrill F 8'I. Al N C 9y ' - VyW R * - Rl;.n [r,hL l' is'c 3,46 /(" -f[ifUi.,'C.2f:, /O - 3.61- )O [ 11) . 3 2.lo ' t ? ) * - 3. 38 N"[r.76 )' .3,,1,0 *in ' lts.d Xa = u l

I2

  • TITLE M/

STRUCTUR9l. PACEf.Li.CF Jsb No ' AMM DATE I12.cl':1 mECHAnlCS couuExis 'mnt ' r ~c s i sY CNMD.SY ** DATE SIII31- " ASSOCIATES ^Ot e br W6 a c... c.,.. 2. An!y i'n:r r M;, 4.~!) i...h. e inu+, a.d e + lh ; ni k: Solv e. fer X gyy z a,g'9 [7f.65 + 6,g E7,94 lice /44q 'E I/%y F X a 2 yy t *., At.% u ( o.74- )2 F %w e, t Y#ry * %gq - 2 Kpyr;, ' 39.LC *R,w - 9.WK,,, K,, - c. / +

  • 9, 3 2

6 g

Kpg, 4s a so - 1.(26.7z 10') ~ 49.CC *( o.3s.10') -1,9+*(3. L1.to')

= - & + (c.10 10 ' ) - 0. 7+. (3. 241c') M vyy = 4.za./o'# @ f 3 Al v,,il r.U ;... A cli,.c.le py am Ic edic,, l.J verf alvn 2. fieg = /Apu +.' <Xw C8c.3s*tm.6S*]t-X,,u1(c.)' n o ,s t-Ry,j E9 3.of_' *.' Kym CB,bt.' ' 'G3 M 4 Hp - 43.0 3

  • R ;... -

8,g i ' M,,,, '- c.2o k, = g g,_ y -Estst~FF1,st*].v,,, l<pg +.11

  • lo'* - 13.0r * (o,3 2 106) ~ 8 6 t '* [3.36.Ir ) - O

= A ^ LAT.M*tM4S*!(0.3D.lD'){k) Mjn =

3. 6 8
  • lo '"

f/ra.,'

13 mte STRUsTURAL PACE #1 CF J:b No-S/M D A ra / Il4 1 M MECHArilCS couwenTs ^ av ASSOC,.IATES CHKD.SY D DATE blIlTL - W-a c.o c.... lowe.r bour.Y b.l trtis cs baff2 CA 87 !) d.ff. $rCA. FA.flo f, AJ-s, y = E-u, 2 = %,d j fy = red [s kl 2-tJ A. f d x: dt1A Qe,} k 1 "h h al '#gc3f" IC ^U* A"" N4

Alci,

/ 'd '* sitc,de 4-d' (I+Y (f} ') Gii X 395 31905 1.17 Io44 Y 3f3f 3;t.9c5 4.33 10 0 1 2111 2 395 3c576 S.co 10 1 L I.0% 10 4/5 31165 4 49 to + Y +/C 319tf 4.6'1=lof~ ~ ) ?.20 2 4/5 30590 529 IO h'

l. IO 'IO X

/cq,5 % 24c5~ (,) 8 Ic f Il 2 Y /Clif 3290C l, % 3 10 Y l l0f E /C15 .30570 1.4 2 'Jo Y ey jgg 4, L90 to X ,231,f .31*e5 2.fo /04 4 166 y 131,f 31efer '.60 10 3,13) ? 2 21. 5 3CC1b 3.Ol*IO + y~ G /3 'l0 x 2c/.9 321c5 2./ 8 'to 4 0 'e Y 2.? /,7 321c5 2 27 lo + 2,153 226 E-2 c t. ') 20:1r

2. l:> 2 10$

535 10' x 49.9 s246: C40 Ic 3 ^ 2 l j'73 Y 19.9 J1?cf 3,4 f lo j 2.72 2 GT1 2c!T L.+& le' 4 /.31. /c ' 7 N-s x 2c:.- J::ct 3.16 Ic 5 5 E+ Y snr5 3.38 10,

    • et E

L'176 L.f."* 3n C?' 3.bl * (O " lQ 23#f 6 .3.20*/0 /o .d,.!/;: L0 g , 4,13.tn *0 ' f lAn l 3. 6 8 h '* l l l

I4-itTLE U A STRUCTURAL PAGE OF _ J b Nr-Ib< DATE / IM14 mECHAnlCS couwENTs 'fyer 6 m / ,3 Y """""" A S S O C, I A T E S $N/ fr.y - CHKD.SY E'd DATE M II C-wm a e, n. c.,.. uw ber) 6';fl<n. - r,.- TAe Aux. ald.

n y/a,,

esiew /ceI<: .y, os, we i. fe lle~s. g ts Ax c<,. /,,) %s, e - - - - -. _ _..; ~ trd 4,.ah,L M:,11 l d t > I' io 7' 'I i/ A L,/h ,re:dl/e.a,krachsien wl,'e], coul ccx.ur' nku c.cosi rio The.,nina,>,rs ,, h +)e. eladete<l puehd,:,, way so/ de Ax. All b aL iy dow)ii y 'y aoo e. I av// e.i.:ide.a eiyle. /cigtnv41;,,,as.ck!9 l de tai ve. el He lu o cle d ria ) y a c h d :,, w i,p u i., sh9 y,...,;.m a-di,./ </. i,zl,h tvi}/4 h /d! e,Ll,,u,}/*,xchd,%, wimg\\ d ' e,zL chftms. / +ecu EL u a.ux /co,dra/ h-e, wou. /.'l L ue Jh, &-il A e o s i,, Howeve q oue ce,xa,,;Lg,,,y caki <%f ,, <,,,,p. y,'.,a g l,,,_ .g,, .us s.r-e 1:.u.o,in. g w b ee 7.s l w / b ',, l-r '/ n i /,1l, ?::,,; e The a.e k s.1 w i m 4,<cv-f luks a: ir'%,..:: K M a'P.C ' c' V ,;,;.s-M - ^ l l-s-d ,,e X Y /- 1 l 4 p, c'e,J,e I I v e. M, g- '

, t.... :,.

5~,: i. -,, er !).,., t-,.,,,/.,l,>i,,,.J:. J. l<. e,>,/,.r M e : h e e /rre.,,,./ i.er I:,, i a As. vil i ~ 1:1 > le. < / /<r,,, }< / / s L. sed d %,,, na.,m. edes.i c..<<,~</ L :. sir.,I I,c,,r. % h-wir ee cat-a.

u,n s

!! !?c h,A.-t'! b.2 L ' /. p hs$' T)er l ln ti at i Er *

  • hr' hlr e

c

/5' TITLE STRUCTURAL PA:s cF J:b No AN/4 DAre /11510 2 mECHA0lCS ceuwenTs Me*+ B. / l sv """"""'" ASSOCI A TES D DATE alIl % wm a c.ne. c.... f W//r. u CHMD.BY ih., h+ < d u < lei e r Ih, :, in,- c Asw s..iN i - ~ ukich an,/ > un :. a. wei,lY.., d di wa,:: ud +M I ~ ~ i

0. 6f va+ eco!eI d he wir. : i <U,id.

Y e h. w iny, on e. A = 12 92. Ff* r = 92 iire it + r, - n ze + W;fipn x ,f/ h =- :/, p I=;Lbh3 A =- b h

k. s.J X h = l'*,

'{W = 89.6 f+ h = $ $ = /s.C ' /#2(71 sc4 7 '*' Z s I TY-b ' /312. # f3. 3 s i s for a.f.ev/ '/ [2 / /a 9 2. A4, / ho />A M *m, kc. 5 ber c.Y4cb son 3 u$4 l1 *s1.4 o / b or 4t-bs S3.3 ' hr~ bo hh dircchobis, / $Y/-A.IiEe hj lC/1 s: s,, A ConYI iswer g, ban t t u,'m L n -1 1 J 'l Ar = 213.L l24,1) 2c.i = :sns-W l s'3. 3 ' 1l-i 10 '1' .l; C3. 3 ' 3 E -b) % k p, U n /k / [ta u 4 /4 a. [= d,h =8.18 /3x ^e f.I+ /3 m 2,7a ,/. 9 g N-S 7h a /dL,. f.sc. M. [

  • ETA = 0 I11

/3 'le. I,2 7 Ap t 0,38 f.9 x Ha.)Fspue. Esuo.+iens (&quare.y beparda,,+ I4 = k, z ow) G A (X' ase p. a e - ci,bd,,,,) n,A, K=k g?u/!,(37 Oce j,17 - k,, k, k., 2 y g t. If = kz 7"D 2.li'L y 9 List.

rrei,

,J. : ^ 6 Co ' ri /m.% F m i,. L %,. %,',, J '=n--;~ p e p,,., .*!,,),,

/6 TITt.E Pace M CF J:b N g STRUCTURAL AMR DATs ! I?!! O-mECHAnt<S couweNTsMc e A~~ / sv CHKO.EY D" DATA 3I ! l D """""" ASSOCI ATES WN fdbW-- a c.ne. c.... N s' h n e s s c. ". her es e lt l,.lli, p bM2bx

  • FN Fe, y e9 e, = ubebed fuhrs (c,.

F F g ~ [C7C Xwinq MM.3 + Elale ' l Atis Bld "[j3973, p,v a D.@ ? wing SC?C g 1342 /k'Fe 3 Ewiny Cryr k 5~U N Os96)(lfC,4 !2.]('1 I 00)(I,l+) yhSqg'(j, o) Y4 M v a,, = 4.53 1c'K/H Al-S k, ={'$,'s')(o,q a l),4 i) (2 )(ri foc)(g, y,) jgg,g (1,, y ) x u.;,. = s.o g.io ' %. 5 '~M \\ I3A1%kO*b8I-cA1.)h.'70hg75ff,09) W' N ;3 577 y s 53 -to ' Mh+ k's,;, = ppdJ %;q= (c.7d(c.a s )[,$4365,\\ ) Yz,3,4,)f'i,3) (@,) ~ = /.83.to o " * /ca,l. 3

n. y ~<g f y,+3 cmtm.a..

,.,y_ sy,, _...,,., y m Wil4 '$r't l1 e'::e.- b cz;g/rj{ /s,. st,a, l l

l'/ mLa PArt 64AoF J:b N DAT ! 1 I41 ' > ' "~ g STRUCTURAL ' A MA' MECHANICS couwaxTs h r 6d ry """""" A S.S O C..I A T E S Ir // f-// o,,c CHKD.By D DATE hI1I " wm c... c.... &pt t~ 0 cur $5hr.e'.td' S./AA Lealb)f,w To %. I % e s+ B e.e.hI a gyg g Nede. Area b)h Ars Ed,'mdi 3 4: (fD * (H)' Soil X l.+l !cf Lif y 38f /392 1.25 10 E SE f I s 1,53.jc 1 Q C b(, 10 X I,51lo T 1ll Y f / S* /392 f 3S-10 ' '/ f E 1,l.f /c 220 fyy 5 % 'lO y X +,0 0

  • 1b *

//1 '/ /09.f /39 1 J. f4.jo + l i 4.3 5 */C ,gg by I,44'lO 4 X 8.47.I0 3,131 Ac6 y 23/, Y /29 1 7,53 lo i 2 9,2 0 '10 2 3 ',' fy, 3.04 10 A

7. 3 6 *!W 1,jC3 2C5 Y
I.d i311 c,.S7 it
  • g 8.0% =10$

i dy;. 7..bS*l5 X l.M

  • c '

2b1 / 44,] . 31.*. l.62 st A I t 1.9 6 IC, gz 4,y 4.56 */O' li L x

2. S+. 'O '

~ 5-:0 Y 2,79 /o' f s ' 2. a. ios , sa p, cr +c a m

fn
2. 4 2 * /a,,

Oy) 3.C!'10'O I,) 2.39

  • IC

) f To' Co IcvIAhr nr.lc ,!.Z'? A, '! ? s itNNt.'cIitY: Cw1

  • l

.s l [ htcre a ltbl ttn ld kd! 'l Nuffe!'sts i I

/8 TITLs STRUCTURAL Ns ff CF JbN av A N /< D4Ts 1 1211 4 i.'lECHAnlCS couwenTs Gre*IA mr CHKD.RY h DATE bliI R W ASSOCIATES

  1. [h-a-a c m. c....

GrruElen ef G !ehs{ $ ist fr.

..t! })?)t. ; 17

- (fper Lea,:) C,ge ?. cl / A'- 6 Kx = 1.56 iC ~ ~ 2 [C.o 9 /C ~ ]

  • 2. 54'It' ' # /t

/ n9 .E-l) My = 3.70 * /C ' ~ l ( M 3'lO O = L 71 */O # #dt Ilerk R s.121 = h.9 '?

  • 10' ~ 2.([. 53 * /0 0 = L b 6 /O tY.

Co.levlaken c F Aleu, Cur);,de: Eer A'e</e. 227 !Jse proadw e sw os p, rt 2 - cz F, Se.e p. a & feo in;&l cocedim las% 2- %d;,dc.

    • _~ 8 4.

J% , _%~ %.12. e f (0.90 b , N/.02 loN ,1. 2.,9 2.s+ to A i i i 2, - 3 21 h= z.6o use %. 2 9I Dibnus a.r e in number o f f+. Le.le u, eledien :/ y cm,./:,.., '.. 4.so Ru 4, t 2,%,,," Y, = P, ,(2. =

  • ~x:y

<an, y = 4.2o (0, 9 0 y1 - 4.62(o,ca) i 2.r+

2. sc.

Y,= c.26' Y= o,29 the.h.a=0.'cW 2 U,aaau : :n numbe r of fea.f. u.i J J G,re,: indh ch f ront.jojiena.l <f:rs,:4 : X.% rd;roic 94.ts.% 43.05..Ayo l 2. %zy = = ,.4 2 ~s 1 -( 1 .9 3.cr(0,'l e A x4 - '1 9. W (1,Il h

2. 6(,

1 79 X, "- 3 0, 2 2. E h. )(2 =' 3 b a 06 fY l 0' Li:Ta r.L.e s atL

n numbtr c.* t~

E u b^ / 'r '! $. 'If f.!!,[ 'Of fl ' e is," t' .. C f. " r.A y; /: 2S~. !. C ' $ Nee. we t,' 2 wcthY d PC EYht l/1 U$ e. c' 1

'MLE li ~ W ' 1 STRUCTURAL 'AC" A C' J5b N s a~ ,sY

r. H X.

04Tu 11211 A - mECHRolCS cowueNTs %-d e UJ,.. I """""""" A S S OC,. I A T E S (f'.'t ff r., CF ). S Y M" DATE M iI 4 vm . c on c.,.. Ec +a 5: > : 0-. : f N-1Ax,'1) A g,, '.n...-?.gj$)UCI1'EM.Al ~.Q,,, Y. 2 - e' x,w - x,nq l i Xp,., = 3. 48 -10 Ik)fl.1 I 10 0 {85,I1 '+ A7.tl 0 - 2,E6 Jo^ks ) - 6t(c.io6 /O ) - (2.71./09(2.,44Y b 10 K fi xeyg " 2.62./0 / rad 2abn Sion a.beul' Y [abouI E-id Ans) $jyy~ kg - 2Ks - M.(J *iq Xf x -8*x - iz,' If, s u M,, = +.63 to ' ~ 2. (1,RYio ) - 11.t,C%.//*.o')-(3 8.uk2.8 b.to') 3 f G+ (1,0%'lo ') 3.2 I* ( 2.5410) K,, =

3. o C 10 '0 lral.

Ao fa.fici, ski- ? k,*.y -(t)R O s.2 b es.ts*l IG = kg, y,- 93.br*K ~ ri Yu n ny xn Y,'.<xn, Xig- +. 21 ic -l9s.osho.9cs.io') -(.so,22)*(a.'11.: ~ L. - k (i.o2 : ')[25,3s*+ m.bsf - cc.24)'t.z.:1.io) sy = 2.21. io 'o k- %1

20 I TITLE CF Jcb N:r-PA::E oATa l 1711 4 _ g STRUCTURAL A#M MECHANICS couunnis c',/m44 J aY """""" ASSOCI ATES blIIN wm a c.iie. c.... //$4 # G e 2,S r CHKD.BY *;"" DATE Skla i a;(ir m c,s e G,h M (H) fledt 'f is si. 41 -2.s exce' l owe r-Bow,) b),',s !d, L ec C,a froan p.c2. 2,,s".1 P & :. hub 0.9[' desan y g, Ye t d' )kn jQ ,jf, a t' ,cN fI:. c. 21 ' !.zle.<f ' n ode. x shifk

4. 9 4 ',%lh Nede.

X Y 2 /6 'l/>'70 -If 1 S f,2 5-UAce r beonel Lu$hs di r'ti>.r.u $se o' rem f. CT ? t b,'[f,s 2.9l ' dewn l I' ' [' A *- l C I'YI' * '" *

  • th,)- (,l y :),,yh o, y '

node IB lcwl,'en e r. M, i Arer'.lh j ? m.. ;u /Jeds. X f ?- t /8 +2.% -3,/1 E4.2. "T l

LI ' TITLE STRUCTURAL PAC 8 # cr Jcb Ne men cATaIl't@ ~ MECHAnlCS ,sv couwenTs 2 CHKO.sY D DATE "II I5 W" ASSOCIATES a casie. c.'s. [.elu $ * $ / a.V 4 A t e /l I m.# ! i 'l'52.14 5 A %I.08 ' A i , -F-2.2, yg yn' I s, i I C y N sd 4 i Ate + h s le Il Jia d /L Vaus ei- %.elb,/i,udkn- ~ L ~ heir Ceirn,ed All soll impa..hecas luim'ed <t.+ lh e. base. m4anircal,~n +f e. A-Aox, 6L/. malAe.,,,J <.J o,. lel 3 Loe.<d,'en ci hus,8%Icenbre) Leg ::s,1 :;ro.I. e <.:,ohe.n (ou,,.c foun) 3 re.ld a uc. wina sprik.s+if fs. esses see used N s . f k if /Cenitel,.:w o,l,mpa,h,.m.vhe, qper leunf ( Lewy;en rela.+ive. noing spc7,, d,i.i a.re. vu Schuro:bk . Spi 1ci,tL li n ko.v., AUq, feus., /ihii F,4 or 6. n. ~ uowii,9 Shiihng af Legii, .,f G ;TL,,,, ?> e. : n Uo.de? /-}ain Auf/&ahel 6 - LJAe.n soll Stiff'i:ecs Fe El.d.+:,I di,d,ak 1:?.;..,z is Assin nr.i

z z. ~ STRUCTURAL

  • san M cv Jos n2

" } $ mECHRn\\CS 2H M DAre 1 l15'\\ 61 couunnis ~Talv/ 4 M o n .s v """"""" A S,S,OC, I,A T E S ,,,j /,, 4,,) l rr" Dart EliI Et. CHKD.BY y T A I E m b ed d e<l Sp eir..> Oifire v: i}b Ar. :<. h,'A..I /kr.e b.si< r >Ja > h NLab 4 l' ( c s' Y ln ' bic a.f,'o n Eeund dee,) L.8. _; 5-u Tran 0,1610' %t c.1s.to*f+

2. B l N-6 kn c.it.:cH/H. c.n sio' Alt 3.40 t/crt b n 0,12.// SNf o,tr /oN.

3.N h Li< bodF:J 3.67 10" $ I.83 100 #$d 1,'l9 kk.1bvfth 0-c. Txacn c. c. l 1

2.3 'nri.e PAC 8 D *~ e g STRUCTURAL ,y agN oxy,1 i z t 4 x ~ ^ mECHR0lCS couwenTs 'N#4 'k A ss CHMD.SY W -* DATe DI'I O = RSSOCIRTES j'. L f,# f., W"

  • c*"'**'*-

'~ NcJc. ie "ba, f,c M:: ,:<..Ha,, .e.~Ic /Ja' ~< +.6 Me w.u acdi.mle: L eetinI mdeI. (i.e.. x;= ei. & b Ys = .z. z !> .a r = csv.ec ). For Me Acb.ap aralya1, wdei,<w nede is i.: ellffe) due !~ lr-ak 6, &cisl rib bt;; wi,y sfrEq cu! sul , A e;q &,,, ai:2,. M e..Jec7,ic.,,/,n : L.kc,, :uin.,e, &:a ~u . ken. Fo r />o de. is s:ud de m.-dr: / TAe pvere:~e d N& . M /J e. n.,/c / 1M/1eAa e ne r a d d,c a s, is le er:wra ta,,, a. a. e wAan.J ePcio : n,d.,: sue: inc e /ccahd.dne/ca. u 4A ma,= + kow, e ki we %. i) TA a. =ar.,s. owa.Il a hL.I m<ss and d;IL,an a me, eeche r s$ relrhihn

1) Tle $a

% fc. <,,,e d' usiq Lp,w&./ s.<a %eir,. tkss is .A -- A i wah,hectra. al + 1l. edohedal o.<is eY a. 1 + A Y '- n e d :~.d, J u is ea I -= ag For-mass Ice.aIeJ se ard d we Je =,, e +>

k..e a

n,ac+:n e F .? ,J ~, : M. La;,,,: I ' =. f - A y 1 I ' f h ' =f .Tg g = f,,.;,,,, l ce r f, ~i b.l, w s e'.E Uge ."r,1::. ! #u r. < l o rr16..: ro .a s

,,,. J h,. !

%L,.,c f ,... a I

255. '4 4-g^ STRUCTURAL PAGE__bO CF Ju o N 2-787'E af

  • SON 212 16 1 mECHAnlCS couuanTs /dass DAT G 14 ASSOCIATES CNKD. BY D DATE D l l I $ 1-wm a c.ne. c....

% a Fa r M ',.. Lewee d und ,% u Oriq, Alalc / S / % c,s Or:a (corc/. <-s,e' X /b = lc 37 ~ fr X =s/.44ff 3 Y /%s /c29 $'[' 'f g, = -2. 3/ [f CACO f f ~g( 2g, 140 & /4 ass = = So} sx ll w -= 0.16 ? 4 /CY X -see '--{ f AcY 'l /1 ass = 0,113) lo K -sec * -[-f b 0d ~& s' fuss = 0* 12PC !?'I K -see.' H, y' )(= 9], ?0 Nem G rcl, e h flede. ) 6 < 't' -2 f s 2 p -I, S.z e - 2 6==m c2 - sec u-y., _2 /g X

  • /0 37 7-t dX - 8/. 64 - 7/,70 = 9. Tf #

18 g& y - s e e.2 g,( c -2. 3 / - 2 42 = d,2 / Yn,e _- % ~ 10 3 s e, x-ve '- a2= ~4 : - s f f..z : = 6 r ? C, =e N') t+ g b ;g bY WN N l t,by Y l y 2 /4 pfg = @3 - /f,3 A v ' - /f,, 4 2 3 y Sim;isr17 {ce e.lbr +~~ </,, e J,'o,a : Mq, = IQ,S -~ /4 x,, L s * - i*/ y,, s x '- y M,,, = / Q., / %,, L v = - /1, a x 9 y 1Alue : Fee b,v a, Ec d f-l,, = ^ <1& M /O- (9+0'(' 21 Y - /0 3 9 (c.15)

  • f

.o //ff,g = 0.'7 9 8 3 </0 'd 7 lipy,g = 0,1121 Irf - Ao : 1Yo rtsY - 9 +c (9.44 ) *

  • /Cg 5 - Lee 2

/A}'y,, ~ 0, //L L ~ ~}y fl g,g ~ l', 2 ^ 8:*

  • 10

- /C 31(c,;;) * - (.n5[1,11) f h'j. C.3 '/F L V' l

25 l PACE 3 o7 J:b Na . N 2 g STRUCTURAL f sY ' AM A oars 212 IN mECHAnlCS couwsNTs /',y K,,, [,,., '., i CHKO.mY Dd DATE SII l% W umummmmmusum .e, c.,,, Uppe r bec /4 a Aiw ida is tcco),m 1,e,. l \\ X = 42.9 6 V = -3.I4 1 = S42.o 9 A x = 28.s?' Osia,3 Me,, ra v, a s pg e. AY-o,SB' 42' 2.1/ fo Uger-J3eu,o dage* r M ep,,, = 0.198 +.to - t r o (c.s e ) * ~ to 3 g(2. 91)

  • 0 # ~ Yf t.

l

lif,

= 0,987+ /0 li p y ;p, = 0, /12/.168 - /0 31(2.9f)* ~ 1+ c (38,C.8)

  • Y A~*" b

/4p 0.969 C */C = y /4 hip = c '. & G C It ~ /c 29 (c. PN * - to ?(2e. <N ', 7 "' YH f}7,,, = c. 2 3 3 o to k,,s k /:<,., / />,m 'A s j q u,,. ei,,rei,nx y c n: u. s s ._}}

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