Subproject Name

f4f0dfef-c158-4a95-ac32-acd89c363b0f 39 Subproject Name GFDIntano Philipps Technical Consultants Corporation 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

REFERENCES:

1. ...

SEISMIC PARAMETER

seismic zone coefficient

Project Title...

Z 0.40 :

(Reference or Note to the Reader)

near-source factor

N.a 1.50 :

(Reference or Note to the Reader)

\[TITLE]\

N.v 2.00 :

(Reference or Note to the Reader)

seismic coefficient, Soil Profile D

C.a 0.40 N.a * :

(Reference or Note to the Reader)

C.a 0.6

\[AUTHOR]\

\[DATE[YYYY\002D\MM\002D\DD]]\

C.v 0.56 N.v * :

(Reference or Note to the Reader)

C.v 1.12

DESIGN SPECTRAL RESPONSE ACCELERATION

T.s C.v 2.5 C.a * / :

T.o 0.20 T.s * :

T.s 0.7467

T.o 0.1493

T 03 0.01 range :

T s.A T T.o ≤ 2.50 C.a * 0.40 0.60 T T.o / * + (* while T.o T ≤ (T.o T.s ≤ (& 2.5 C.a * while T.s T ≤ C.v T / while 31 line :

T 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 231 mat

T.o 0.149333333333333

T 0 6.149333333333333 T.o range :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

T s.A 2.50 C.a * 0.40 0.60 T T.o / * + (* T T.o ≤ 2.5 C.a * T.o T ≤ (T T.s ≤ (* C.v T / cases :

T s.A vectorize 0.6 1.5 1.5 1.5 1.5 1.5 1.25 1.0714 0.9375 0.8333 0.75 0.6818 0.625 0.5769 0.5357 0.5 0.4688 0.4412 0.4167 0.3947 0.375 0.3571 0.3409 231 mat

T.o T ≤ (T T.s ≤ (& T.o T ≤ (T T.s ≤ (* 21 mat

Spectrum T T s.A vectorize augment :

spectrum Spectrum . 14 red plot :

Spectrum T.s 2 T.s 0.5 - 2 2 mat spectrum 0.75 1.875 ◄ Ts ... 12 black 1 5 mat 0 1.5 + 200 green 1 5 mat 5 1 sys

data Spectrum :

data Σ Finite differences Cumul Integration Y 0 : vx data 1 col : vy data 2 col : Y 1 el 0 : i 2 vx rows range Δx i el vx i el vx i 1 - el - : Y i el Y i 1 - el 12 / vy i 1 - el vy i el + (Δx i el * (* + : 21 line for vx Y augment 71 line :

Σ data Σ :

Σ

Σ Σ rows row 6.1227 3.4131 12 mat

Adapt 'backsubstitution' data data 5 data rows range 12 range el :

data 0 0.6 0.1493 1.5 0.2987 1.5 0.448 1.5 0.5973 1.5 0.7467 1.5 0.896 1.25 1.0453 1.0714 1.1947 0.9375 1.344 0.8333 1.4933 0.75 1.6427 0.6818 1.792 0.625 1.9413 0.5769 2.0907 0.5357 2.24 0.5 2.3893 0.4688 2.5387 0.4412 2.688 0.4167 2.8373 0.3947 2.9867 0.375 3.136 0.3571 3.2853 0.3409 3.4347 0.3261 3.584 0.3125 3.7333 0.3 3.8827 0.2885 4.032 0.2778 4.1813 0.2679 4.3307 0.2586 4.48 0.25 4.6293 0.2419 4.7787 0.2344 4.928 0.2273 5.0773 0.2206 5.2267 0.2143 5.376 0.2083 5.5253 0.2027 5.6747 0.1974 5.824 0.1923 5.9733 0.1875 6.1227 0.1829 422 mat :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

data Deriv data Derivative BackSubstitution X data 1 col : Y data 2 col : n X rows : deriv 1 el 0 : deriv n el 0 : i 2 n 1 - (range deriv i el 0.5 Y i 1 + el Y i el - X i 1 + el X i el - / Y i el Y i 1 - el - X i el X i 1 - el - / + (* : for deriv 1 el deriv 2 el : deriv n el deriv deriv rows el : X 1 deriv * augment 101 line :

D data Deriv :

Deriv D o 6 black plot :

Deriv D 2 1 sys

Hermite smooth derivative ...

New 0 0.6 0.1493 1.5 0.2987 1.5 0.448 1.5 0.5973 1.5 0.7467 1.5 0.896 1.25 1.0453 1.0714 1.1947 0.9375 1.344 0.8333 1.4933 0.75 1.6427 0.6818 1.792 0.625 1.9413 0.5769 2.0907 0.5357 2.24 0.5 2.3893 0.4688 2.5387 0.4412 2.688 0.4167 2.8373 0.3947 2.9867 0.375 3.136 0.3571 3.2853 0.3409 3.4347 0.3261 3.584 0.3125 3.7333 0.3 3.8827 0.2885 4.032 0.2778 4.1813 0.2679 4.3307 0.2586 4.48 0.25 4.6293 0.2419 4.7787 0.2344 4.928 0.2273 5.0773 0.2206 5.2267 0.2143 5.376 0.2083 5.5253 0.2027 5.6747 0.1974 5.824 0.1923 5.9733 0.1875 6.1227 0.1829 422 mat :

New New 110 range 12 range el :

support New :

<p>plotG(vx,vy,char,size,color) ... Hermite Polyline modules </p>

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

z n RepEnd m z rows : i 1 n range w i el z 1 el : for i n 1 + (m n + (range w i el z i n - el : for i m n + 1 + (m 2 n * + (range w i el z m el : for w 51 line :

data Strip nest stripped in 'R' u data 1 col : v data 2 col : k 0 : i 1 data rows 1 - range v i 1 + el v i el ≤ (v i 1 + el v i el ≥ (¤ R k k 1 + : el u i el v i el 12 mat : 11 line Undefined if 11 line for 21 line Un-nest R v R 1 el : j 2 R rows range v v R j el stack : for v 81 line :

M Unwrap V M 1 col : i 2 M cols range V V M i col stack : for V 31 line :

data sub subspace j 1 data rows 1 - (range Vsub j el i 1 sub range vx i el data j el i sub / data 1 j + el data j el - (* + : for vx 21 line eval : 11 line for v Vsub 1 el : j 2 Vsub rows range v v Vsub j el stack : for v 31 line 21 line :

Round OFF Matrix/Vector M n Round i 1 M rows range m i el M i el n round : for m 21 line :

X New 1 col : Y New 2 col : 12 mat

subspace to close Hermite fillet to data sub 1 :

<=  populate for more points at will t 01 0.1 range :

XY X Y augment : origin X Y + 15 blue plotG : Xo X : Yo Y : 12 mat 31 line

New Xo sub subspace Yo sub subspace augment : New Xo 1 el Yo 1 el 12 mat New stack : 21 line

isolate New New :

X New 1 col : Y New 2 col : SUB X Y . 12 black plotG : 31 line

Export data X Y augment :

data rows 10

<p> Polyline Construct </p>

r 2 : X X r RepEnd : Y Y r RepEnd : 31 sys

x c 10 x ≤ (x 1 ≤ (& cases :

Hermite PolyLine t P 16 / t 3^- 3 t 2^* + 3 t * - 1 + (3 t 3^* 6 t 2^* - 4 + (3 t 3^* - 3 t 2^* + 3 t * + 1 + (t 3^41 mat * :

Hermite basis cubics 0...1

x P 1 el x c * x P 2 el x c * x P 3 el x c * x P 4 el x c * 4 1 sys

t j XP μ j 11 line : t P 1 el X μ el * t P 2 el X μ 1 + el * + t P 3 el X μ 2 + el * + t P 4 el X μ 3 + el * + 21 line :

t j YP μ j 11 line : t P 1 el Y μ el * t P 2 el Y μ 1 + el * + t P 3 el Y μ 2 + el * + t P 4 el Y μ 3 + el * + 21 line :

t 01 0.05 range :

<= populate for more points at will

j runs 1..rows(X)-(r+1)

U j 1 X rows r 1 + (- (range : ct 1 : j j i 1 t rows range Hx i ct el t i el j XP eval : for ct ct 1 + : 21 line for Hx 41 line :

V j 1 X rows r 1 + (- (range : ct 1 : j j i 1 t rows range Hy i ct el t i el j YP eval : for ct ct 1 + : 21 line for Hy 41 line :

X rows r 1 + (- 11

collect the project xy U Unwrap V Unwrap augment : xy xy Strip : 21 sys

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

xy rows 90

pts support o 6 red plot :

xy pts 2 1 sys

data xy :

data Deriv data Derivative BackSubstitution X data 1 col : Y data 2 col : 12 mat n X rows : deriv 1 el 0 : deriv n el 0 : 12 mat i 2 n 1 - (range deriv i el 0.5 Y i 1 + el Y i el - X i 1 + el X i el - / Y i el Y i 1 - el - X i el X i 1 - el - / + (* : for deriv 1 el deriv 2 el : deriv n el deriv deriv rows el : X 1 deriv * augment 81 line :

D data Deriv :

D D 2 D rows 1 - (range 12 range el :

Deriv D o 6 black plot :

Deriv D 2 1 sys