Question

Question 2 Using virtual work, determine the vertical displacement at joint E. Assume D is aroller and is a pin. A= 2in² E=2940 )usi с 2'0 tan o 2'0" Efy-o Dyr Fy-6 1.3 0 - 36.86 12 SME=0 40 -(Dy x 48 +(6x2) = 0 Ay 3x Px

Answer 1

duen Ginu= A= 2 in? 29403 ksi from ex-0 [RE = 3k E = B b> forces ou each number: с 1 li Joint D FAA 2' V6K 2 fot Ro=2k Sofa ay Reactie forces : Etro Efy FDA = 2K HERO B 8.99 с 2.24 1:24 15 X8.99 5,99 ci) soint A 74 tano = 1.5 30 36.86 E 2:24 6K Rp 2' FAECOS O FAB Efy Faesina AFAE 6 3K Rot Rp = 6 EMA Efx=0 FAE sind = PAB - -Rex 4 + 6X2 = TRO = 3k Efy FAE loro 3

FAE 3 los 36.86 3.74K Efx=0 from eq -0 FBC FBF sind + 2.24 - ③ Efy = 0 374xsin 36-86 = FAB FAB for los 36.86 = 8.99 = 2.24k FBF =11623k Joint E from eq - FEB FBC 11:23 sin 36186 +2124 3.74 3.74 sind FBC Poi FEF 8.99k 6. 3.74050 Joint fi Efx = 0 11.24 ffc FER +3irusino -O >.11.2ysi'nde 2.24 FER - - 2.24K RE=3 1112uloso FEB - 6 - 3.74609 36.86 = 0 Ety=0 I FEB - 8.99K Rift ffc = 11124 los o FBrcoso Joint B ffc - lli2 los 36.86 – 3 FBC ffc = = 5.99k. for sino 2124 FBF 18.99

Joint Di Now, Abbly virtual load , remoue real loads & calculate support reactions & member forus. FAD 7 FDE B Ef=0 Efy = 0 is fDE=0 Ro=FAD=0.5k. 1 Cabi Joint A. FAEcono 2' ---- FAB IK FAESIMO e 0 Sol OIS FAE ay Reaction at support : A 0:37 0.74 B C Efy=0 FAE 10$ 36,86 = 0.5 10.62 VO yo.5 FAE Xo.so horor =0.62k . 컁 F 0137 Efx=0 FAR = 0.62 x Sin36,26 RE IFAB= 0.37K Ety=0 Rot Rf = 1k 0 Due to symmetry. Ro=RA = 0.5k

Joint : E a Joint FEARGO FEAR PIEB offre FEASINO FED FEF -0.62 Sino 0137 RE 0.62 .0.626030 Efy FEA OSO + FEB= IK FEB = 0.50 Efx= Efy.= 0 ffc = "01626050-0.5 frc = 0.50 -0.50 = 0 FER 0.6 2 sin 3686 01374) I HEF Actual load 6 kips- Virtual load Ikibs Joint Bi Foraso Gross sections are = 2 2 in. 0 0.37 FBC Young Modules = 29403 Ksi forsing XFOF Voiso Efy = for 0.62 k. 0.5o Cos 36,86 Efx = 0 0:37 +0.62 Sin36.86 FBC FBC 0.74K

Member Nck) N(K) Lebt ) DA 0.5 3 1.5' AB MNL (K?ft) 2.25 1065 5.79 0.37 2.24 2' AE 0.623 2.51 BE 3.74 8.99 0.50 1:51 6.74 0.74 8.99 Вс BE 2' 13.30 -0.62 • 11.24 2.51 7. 42 EF 0:37 2:24 2' 1.65 ЕС. 5.99 1051 0 DE 0 2' 0 EnNL = 48.80 using virtual Work equ: TA - En NL AE 8.8 x 121m/b+) xlk?!) (2 in) (29403) ksi) A Ev = 0.0099 0.olin. DEN ² oool in.