Question

Using the concept learned in the two activities above, formulate the slope deflection equations for each case CD = 4m, AD=BE=5m, DE = 7m. El is constant. P=40 kN inclined at 40° and it is being applied 3m from D. ep во ਦੇ Op (b) Frame with Sidesway (a) Frame without Sidesway What are the joint conditions needed for both cases? Determine the end moments for case a and draw SD and MD.

Answer 1

Solue р 4 Bay 40. 54 51. PSin 40° Py 0.642 P Pos40° 0.766 P. fixed and moments (KNM) o HEB MBE 0 McD = Moe 0 HOA E MAD =-0.642x40384 (7² MDE 0.642 Px 3 x 42 (7) 2 -a62 12 MDE --25.156 KNN 18.867 kny HED - Pya? b. il? 0.642x40x3²A4 (732

Slope de llection_quatione HGI Hig 00; + Og - 20 lig Lij NID = Men & BE LED (a be a PD cas D=0 og NICO oo BET (d Oct 08) : 1.50001 +0.150DET 4 Home - Mont BER MDC + BED (200 Dc-0) Loc 0 - gel (d On + Bc) 1.5ODEL 10.45 0.61. 4 NEDA NDA + BEL (200 & OA - 20 LDA LOA cas A= 0 , OA=0) 0 4 BEL (200 & 0-0 0-0) = 1.200€1. 5. HEAD HAD & BEL (20A & OD-2A "LAD LAD í OA = 0 ,D=0) + Belt = 0.6 DDEL.

Hroe HDE 4 361 LDE (200+ 0€ - 20 LOE (as D = o) Hipe = -25.156 + 385 (000+ 0c) 7 + -25.156 of 0.857 0DET # 0.428 0€ € I. MED TO HED of Ben (Qoe + On - 20 LED LED 18.869 + BET (DOE +00) 18.867 4 0.857 0[ [ + 0.428 OD EL, 7 HIEB HEB t BEI LEB LEB ( 204 + 08-94_ (as 0g = 0,0=0) 0 + See (206) 1.20€ ET HEEB HABE MBE & BEI (20Bf OE-2A Loe L BE AFO ( OB=0 =0) O + 3€ DE 0.6 DE ET equilibrium equation - using E HD=0 MADE & Mfpe & MEDA = 0

1.200 €1 of 1.500 61 +0.750 F1. - 25.156 + 0.854 ODET + 0.428 05 ES 0 3,557 ODÉS + 0.75 OCEL + 0.4280€ ES = 25.156 LO { He ao of HFEB HEED ro 18.867 + 0.857 0€ ET + 0.4280DT + 1.20€ ES = 0 2.067 DEES + 0.428 OD 1 = -18.867 0.428 EDET 18.867 -2.067 OE EI OD -18.867 -2.0570€ ET 0.428 EI, OD - 44.081 -4,806 0€ El - de ODER + 441.081 Erozo 4.806 ES HECD o 1.5 DCES + 0.75 ODES - 0 1.5 Oct 5-0.95 ODEM - OD value of Oc and OE in 20c Pus Porting

3.554 Spt Г + (- 0.335 0pЕГ) - 0-428 вт (- Врел - уч. ч.gobt 4.dot ef - 25. J50 25. J56 9.564 opti 0.315 QoE 1 О.o89 Opel - 4 9.099 9pe = 09. 156 90 - 39.15% 3.o93 ЕГ 4,426 Е. doc 00 , 0. Со 2 9. Ч2 6 Е1 м2 - 4.413 ЕТ О. ODES ! 14.08 21, 80 60 21.doc - | 1.42, 3, Г. 4.J12. ЕГ » 4 gott 1.464. EI 9.12 1. 192

Hoor 1.50€ +0.75 ODES ! .5 ml - 19.02 ) ME! Mie! t 0.759.426 HEY = -7.0615 + 1.0695 O KNM. 1.500 € + 0.75 0 ET, >> 1.579.426 1958-4.713 % El ES EI 14.139 - 3.534 10.605 KNN. MEI + (0.16520-4 NEDA 1.2001 1.2 % 9.426 X = 11.911 Knal. HEAD 0.6 OD EI = 0.675.4264 Ef = 0.6*1.41264 Ef = 5.655 kWM. HEDE -25.156 + 0.857 Ones of 0.428 DE EI. = -25.56 4 (0.862294125.281) +(0-1987-11-193. -25.156 +8.078 -4.764--21.842 kwn. HEED 18.867 + 0.867 DE EL + 0.428 ODEL. 18.867 of 13.360 KNN.

Hrea 19.859 KR1M MORE Hen Hoc G Member DA HIDA 12 Dec 1.9 - 11.199. 0.601 0.6 xr11.133 x - 6 - 613 6N+ {, sfy 0 Rotro Taking Rey - HD + Moe : 0 Rooh 0 - 10.605 : 0 Rce 19.605.-2.65110N, u Ro 2.651 KNM. Ho Monont about Doo z fx En Taking HA HOS O та Momond about D. 50 HANE Alfon & HEAD = 0 Hans 5 + 5.655 4 11.81 16.966 5 3.393 KNI Но - 3.393 KNS HA MERA

Member DE MADE 25.68 HEED G 3M 4M RO O sfy Ro + RE = 25.68. Taking moment about en f Rox? 25.6804 - NFDE TUFED = 0 Root 102.72 -21.842 + 13,860 =0 RD - 111.202 15.886. Kne 7 RE a 25.68 - 15.886 9.999 KN Member EB HEB HE co ON. Ha most recente More f E fx HE THB EO Tak moment about e HB *54 HABE & MFEB= 0 HB 45 -13.859 – 6.679 50 HB - 20.038 – 4.00 KN. 5 HE HB MEBE -14.00 kn,

Bineid (vosot) 444.94 PASH 13.360 Jo.bo5 121.842 A B 9999 6.679 TAL C.F.D 18.537 9.794 न © 4.00 E 3.893 2.651 fo 4.00 (A 3,893

(6) Py = 26.68 De di &N 5M 501 th, Px 0.766 2.0.7666410 30.64 KN fixed and woment KNM MAD HEB . 0 NBE MOA +25.684 92204,- + 10.769 KNN. MED = + Pa2b cl2 72 NDE = Pab? -25.156 KNM, - 25.60 x 39042 I 2 92 Slope deflection equation 3ER ( 2 @it On Mais Mig t (20; 09-21 29 Lig ;) HEAD MAD BET LAD (don + Op-20) COA=0) O of 30 5 0.6 0.65 COD -0.) HEAD =

HEDE NDE & Ben of BEL (2.0D & OE - 2. LDE LDE .-25.356 +994 (80p + 0€ - 29.) HIDE -25.166 of 0.85700ES +0.428 0ťET -0.867 NEDE -15.156 + 0.85100€! +0.428 OEET -2051 DES NEED MED I BEL ( 2 OF & On - 2A LED LED 6 ) 19.867 + (00€ + os -29) 7 NEED 18.867 + 0.857 0fff +0.428 Ones - 0.851 DET MEDA HDA d BES LDA (200 of OA - a LDA ->> O BET (200 to - 2A 5 5 > Lil ODEO 1.2 ODER - 0.24 DET ) MFEB MEB + BEL (20€ E OB - 20 LEB LEB ( 20€ + 0 are HEEB 1.20€ ET 0.24 DEL

HIBE LBE o "BE & BEL (20B & QE - 20 LBE + SEL ( De - ) ME BE =) O.GDE EL - O BEI ( 0.6EEL -0.24 DET Toint equilibrium equations Shoo HEDE of NFDA O -25.156+0.867 ODER + 0.4280€ ES -0.867DET. + 1.200ES - 0.24 DES o 2.057 001 +0.4280€ ES - 1.0974C1 = 95.156 ENE O HED of HFEB 0 18.867 +0.869 85 € + 0.42800€ - 0.85DEI. + 1.20€ FC -0.24 DEL = 0 2.057 0ę ES + 0.428 ODES - 1.097 DET = -18.869 Efx HATHB = Px