Question

Question 1 (25 points) Determine the horizontal displacement of point C. Assume the members are pin connected at their ends. Take A = 400 mm? and E = 200 GPa for each member. 5 kN C 2 m 1.5 m 10 kN Member Foron N: Member forces due to external force P and external applied forces are shown on the figurt. Castigliano's Second Theorem : Applying Eq. 9-27, we have

Answer 1

Draw the F.B.D RB₂ d the support reactions, Z M O RA (2) = 10x1.5 RA = 7.5 KN {FR=0 > RB, = P+ RA = P+7.5 Sty=0 → RB2 = 10 KN of 1.5m ARA to kn Consider Joint D find the internal forces in members K > Fap {Fa=0 { Fy zo consider → FAD TO → Foc=10 kn Joint a On pre o foc { fy=0 fact Fac sino to Foca 0 -12.5 kn {Fa=0 = foc =P-FAC Coso - P+12.5% Sin (53-13) o = tan " (i) = 53.139 = 7.5+ P consider Joint A Emre q FAB - {fy=0 = FAB = - Fac sino = 10 KN FAD A

Make the table as shown below along with ON where n is internal forces in members ap Member ber ONN ap (P=5) L NCAN oso har 2 0 18.75 AB BC AC De AD o P+75 -12.5 10 0 -12.5 o o o i 0 Bus ris -12.5 2.5 1215 12.5 10 0 1.5 21.5 Ris Email = 18.75 using casting los theorem A= ENONAL AE 18.75 (4007106) (2008166) = 0.234 mm

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