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APPENDIX A COMPUTER PRINTOUT OF AN ELASTIC ANALYSIS This section gives an example of a computer printout of an analysis for a frame with the extreme columns on one end substantially stiffer than the rest of the columns (see Figure A-13. This example corresponds to analysis M-1 presented in Table 2. The frame was analyzed for a 100 OF uniform tem- perature increase and for a coefficient of thermal expansion equal to 6 per million degrees Fahrenheit. 200 ft 20 21 1 1 2 2 3 O _ 1 O 1 B 1 Cal 28 -~ ~ 3 4 4 5 5 6 6 7 7 8 8 9 1 22 1 23 o ~ 39 40 P7; 32 ~ 33 24 25 18 Do 35 36 (D 37 Cal 38 39 41 1 42 27 o ~ 35 ma; ~71 F77 29 Ln f7: 30 a, 25 ft ~ Column Size = 24 24 in. Area {A} = 576 jn.2 Moment of I nertia I/) = 27648 in.4 m CD _ 34 /] t7 36 Beam Size = 14 20 in. Area {A) = 280 jn.2 Moment of Inertia I/) = 4667 in.4 FIGURE A-1 Elastic analysis of a frame with columns at one end stiffer than the rest of the columns. 33
Analys ~s M- 1 INPUT DATA PLANE fRAME BY STIFFNESS EQTS M.SOTERIADES 1969 ~TRUCiURL I 0. . LOADING NO. 1 STRUCTURE PARAMETERS* M NJ NR NRJ E _ 51 36 27 9 3000000. - JOI NT COORDI NATES AND RESTRA I NTS ~ JOINTX Y X - RESTR. Y - RESTR. Z - RESTR. 1 0.00 396.00 0 0 0 - 2 300.~O 396.00 - ~O 3 600.00 396.00 0 0 0 _ ~ ~ 4_ 900.00 396.00 Q_ _ _ . Q__ .Q 5 1200.00 396.00 o o o 6 1500.00 396600 0 O O _ _ 7 1800,00 396.00 - O __ o ~- _ _ 8 2100.00 396.00 0 0 0 9 2400.00 396.00 0 0 0 1U 0.~0 ~ /~.~0 ~o 11 12 13 14 -- - 1 5 16 17 ~ ~ ~ V ~ 1800,00396.00 - O -- 2100.00396.00 0 2400.00396.00 0 0.~o~ /~.~e 300.00276~00 0 ~on.oo 77~.0(3 ~- 900.00 276600 ~ 1200.00 276600 0 1500.00 276.00 o --- o_ 1800600 276.00 . 2100600 276.00 - i8 z400.00 ~76~D 19 0.00 156600 ~n son.no 1 s~.()o o o - 0 o o o o _Q o o o Q_ 21600.00156600 0 22900.00156.00 0 ?3l^.OQ.00156~00 0 241500600156.00 0 251800600156900 Q Z~7lUUe00155eVV ~ 272400.00156600 0 ?80.000.00 29300.000.00 30600.000.00 31 -900.Q00.00 321200.00o.oo 3315QQ~QQQ~QQ o Q . . _ o o O0 0 00 0 00 0 0 0 _ __Q .__ . ~ O 0 0 0 0 ~- O 0 ~0 u 0 0 0 1 _ . 1 _ . _ ~ . . 1 1 1 1 1 1 1 l---. _. __ _ ~..... 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ~.1 ~ - i'OQ~-UV u evu 35 2100.00 0600 36 2400.00 0 . 00 *Legend: Notes: M = No. of members in the frame NJ = No. of joints in the frame NR = No. of support restraints NRJ = No. of restrained supports E = Modulus of elasticity (lb/in.2) JJ = Left end of member JK = Right end of member CX = Directional cosine (x) CY = Directional cosine (y) R = End restraint index (zero = fixed at both ends) W = Dead load 1. Coordinates x and y are entered in system positioned on joint 28. 2. Member cross-sectional areas A are entered in in.2 3. Moments of inertia of members I are entered in in.4 4. Member lengths are given in inches 5. In general, all dimensions used in exclusively in inches and pounds 34 inches and-relate to a Cartesian input and output are
MEMBER PROPERT I ES * I JJ JO 1 1 2 2 3 ~. 4 4 ~ 6 6 7 7 7 8 - 8 8 9 1 10 2 11 ~_ :) 1C 4 13 ~ 14 AREAINERT IA LENGTH- -mu--- ~_ _~ 280600 4667600 300600 l eu00 O.uOO ~U.~O 280.00 4667.~O 300.~O l.u00 Q.~0 V u.~O 280.00 4667600 300.00 l.oUo u.~d ~.~e 280·00 4667. OO 300. OU 1. JuO u.uvo ~v.U0~ 2 80.00 4667.00 300.00 1. You _ ~ . O00__ ~_ ~ . OUO 280900 4667~00 300.00 1.~O U.~U ~U.~0 280.00 4667.00 300.00 1. O.~0 ~Ue00 280.00 4667600 300.~0 1.~0 ~.~0 ~-~U 576.00 0.00 120. OO ~ . 0UV-1 .~O ~ · U00 5 76.00 27648 .00 ~ 20.00 0. 000-1 .000 0 ~ · OOU 576 ~ 00 27648 .00 1 20.00 0 · 000-1 · 000 0 ~ · 000 576-00 27648600 120.~O 0.COO-1.OVO O O.00 576~00 27648~00 120 00 06000-1~000_ 0 _ ~ 000 576~00 27648~00 12() 0~) ()~00~)-1evO() O ()e`)~0 576 · 00 27648 · 00 1 20 ~ t)0 0 ~ 000-1 · Ot)v ~v ~ OL)U 576~0C) 27648600 120~00 06~)CJ0-1~000 O- t)~ 576~00 0~00 120.00 O.GO0-1.000 0 O.000 280~00 4667~00 3vO.00 1 -~)QV veOuv ~vaij 1 9 1 1 1 Z ~ Q ~t~ n r~ ~% ~r ~r x r x 20 12 13 2 2 1 4 1 5 23 15 16 24 16 17 2C' 17 18 26 10 19 27 11 20 ~ -~ ?8 17 21 29 1 ~22 31 15 24 32--16 25 33 17 26 34 18 ?7 35 19 20 36 '?O 21 37 21 22 38 22 7 - 3Q 23 24 40 24 25 41 25 26 42 26 27 43 1Q ?8------ 44 20 29 45 21. 30 .. ..*~. _~._ ._= 47 ?3 32 48 24 33 49 ? 5 34 50 26 35 51 27 ~¢ ~ v v _ ~ 280.00 280.00 280.00 280.00 280.00 280.00 576.00 _ _ ~ ~ - - - ~ C ~ _ _ ~ _ ~ ~ 0-00 120eOO OeGOO~leOOO O 4667~00 3vO.00 1 et)OV v.Vuv ~ 4667 ~ O() ^ - 4667~)0 46f,7 ~ 00 v ~ vv~ t) e U 4667 ~ 00 3CJO e ()`J 1 ~ OU;J ~ ~ U~U () 3 e (J~ 4667 ~ 00 3(~0 ~ 00 1 ~ 0~)U ~ o'`)0~) ~t) ~ ()00 4 6 6 7 ~ O () 3 () V ~ O () 1 e i~ ~ 0 _ () _ ~ ~ ~ ~ 4667 ~ 00 3vO ~ 00 1 ~ v()v~ t) ~ `)Ou O `) ~ vvO O · 00 1 2() ~ 0~) () ~ wL)v~1 ~ (3U t) U ;1 ~ t)uU 27648~00 120~0~) 0~()~)-1~000 ~J-~35) - 27648 ~ 00 12() ~ (;)() O ~ ()UO - 1 ~ ()~) (3 t) ~ t)ut) 27648.00_120. OO .0. OU0- 1. UO ~ _ ~ uCO 0.000 ...... u.uuo U · U ~ U · U U ~ · ~U~ U . ~ ~ ~ V · U0V - ~U~ · UQ · UU U ouo U · OU ~ · V - u-.-uu~ ~ . v~ U-~O · ~ V U · ~ U ~-~ ~vv~v 1 · vv~ v~vvv 300 ~ OO 1. OUO ~ .000 300.00 1. ~00 0. OUO v o O _ , . v ~ _ 576.00 576600 576. OU 576.00 576 ~ f~i 576.00 576.00 80 ~ OO 283.00 280.00 2fSi 280.~o 280.00 280.00 280.00 5-76. OO 576.00 576.00 576.0J 576.00 57.6..00 576.00 576.00 ~7t _nr~ 27648. OU r2-O ~ J-~- 27648.00 120.00 27645~(~ --12~).~d 27648.00 O.00 - 4667.00 4667 - OU 4667.00 =~67 - 00- 4667 ~ 00 46.67.e 00 4667.~u 4667~00 ... . ~ . oU 27648.00 7 764R .00 u.-~-r~~--~~~ ~ . 000-1 . 00, ~ ~,~_l.u~ O.~00-1 .000 u. OUO-1 ~ ouv C., 1. oUG ~ ~ OuO 1 ~ U~O u . ~uv l . OuO u .'uCo 1 . i~ ui' '0 . O'JV ~ ~ l.uJO u.Ovu u 1. uCO ~ . OUO O 1 e ~)~J~ ~J ~ O;)0 t 1. v`)o U . ()~() (, 0.OvO-l.~U v .000-1 ~ 000 O.~-1.000 ~ 27648. ~- - t55-.~d -v . ~u - -~-.~-- --~-- 27648.~O 156.JU ...276.~.00 156.~O 27648.~0 156.~O 27648.00 156. ~ ~ ~ ~ ~-> f +~V - _ _ _ ~ ~ 00 120.00 120 · O 3~O . ~ ~ 3Uu. JO 3uu .0u 36C . i30 30~.~u 300.00 300. Ou 300.00 156.~O 156.00 156.OV _ . Uuo-1 · ~d J. uu0-1 · U00 . u ~ ~-1 · Uo ~ . ~ou-1 · ~U ~ 56 ~ OO - -~.-~O-1 ~ OU ~ u U . . ... . . ... . . _.. _ .. LOAD DATA -~-3ADED -JO I NFSC_- o - - - -- -- ---- --- ---- - - - - LOAD~D MEMBS. = 0 ( Dl STR. L- O CONCEN. L= UNIFORM TEMP. CHANGE=lOO DEGREES COEFF._OF_THERMAL EXPANSION= 6.000_PER MILLION' DEGREES _ _ _ *See Legend, p . 34 . O OTHER L= 0 J 35
OUTPUT DATA -~-- DISPLACEMENTS J O I N TD I R EC T I ON- X 270.6006209E 00 26^ ^ ~ 250~2678654E 00 0.9373797E - 01 24_0.1304534F, 00 0.9374416E - 01 23-0.1678797E - 07 ~r.9374802E - 01 22- 0.1304534E 00 0.9374417F - 01 ? 1 _n o~7~aF nQ 20 19 . _ D I R EC T I ON-Y 0.9349361E-01 ~_ ~ ~ ~. D I R E C T I ON - Z 0.1217476E - 02 u . ~ ~ u ~ ~ u'¢ · ~ ~-~->7m¢T~-~r ~~r-=~ 18 E-O-~ -0.1 ~ 78297E-02 -0.7919014E-03 J.14~58-81 E_09 0.7919017E - 03 ~O .9373797 E-01 0.1578~-~- -0 *4206209E 00 -0 ~ 6006209E 00 0.9335021E-O1 069349361E-O1 ~_ ~ _ . ~A ~ ~ 0~2433519E-02 -0.1217476E-02 1 ~U. t~1 IO~C VU U-lO~OC UU 0.1052131E-03 17 0.5517835E 00 0.1653390E 00 -0~2089101E-03 _ 16 0.3677876E 00 0.1657378E 00 - 0.2370321E - 03 15 14 ~ _ O · 1836831 E 00 0.1657527E 00 ~0 ~ 13797~=E-~3 -0~3231054E - 07 0.1657592E 00 0.1037993£ - 09 _ 1-~ _ - 0.1836831E QO 0.1657527E 00 _0.131975aF 0^~ -0 ~ 3677877 E 00 -0 ~ 5517,836E 00 _.. ~.~_ ~2 11 - 10 9 8 _ 7 6 0.1657378E 00 Q.1653390E 00 ~.,,, ~, _ ^ ~_ 0 ~ 2320323E-03 0 ~ 2089104E-03 -V · 1 ~ ~ _ ~ 0 ~ 7292213 E 00 0.2374945 E 00 -0.5875955 E-04 0~5492213E 00 0.2373495E 00 0.1189688E-03 u.~e /~4iE u~ ~.2377333FOO 0.~726945E~-4 0~1842663E 00 0.2377463E 00 0~5139868E - 04 _n ,. ~ ~ 0 ~ m~ r_~ 7 ~ _ ~ ~ 77~ ^, ~ F ~n _ n~5QQ1 ~QF_ ~ n ~r ~ r c_ ~ ~., _ v ~r ., ~ ~ I ,~ ~ J 1_ V V - --~V~ ,t, V - - 4 - 0 ~ 1842664E 000.2377463 E OQ - 0.5139855E-04 3 -0 ~ 3675841 E QO0.2377333 E 00 -0.9926933E-04 ~_ ~ ~ ~ ~ ~ ~ ~ ~ ~ _ ~ A 1 -u ~ ~~c'i - ~ -0 · 7292214E 00 0. 2374945E 00 0. 5875952E-04 36
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