Question

The rigid bar AC is supported by two axial bars (1) and (2). Both axial bars are made of bronze [E = 100 GPa; a = 18 x 10-6 mm/mm/°C). The cross-sectional area of bar (1) is A1 = 226 mm- and the cross-sectional area of bar (2) is Az = 362 mm. After load P has been applied and the temperature of the entire assembly has increased by 22°C, the total strain in bar (2) is measured as 1020 ue (elongation). Assume L1 = 1160 mm, a = 400 mm, b = 840 mm, and L2 = 2000 mm. Determine: (a) the magnitude of load P. (b) the vertical displacement of pin A. L2 Q

Answer 1

Remove the bar cet A&C To 4=1160 mm A = 226mm? A TB || L2=2000mm I A2= 362 mm? Tato b JP equilibrium equation EMAJO PXA-P2 x (atb)=0 P = Px 100 = P2 = 0.322P) . Tout Buo - For bar L2 elongation due to P2= Azp = P22 B2p= 01322 P X 2000 -1.78X165 p 362X100056X 103 elongation due to temperature D2y=6207 $27= lexjö 6 x2000 X 22=0.792 mm A2 = 12 P+ D2 T = 1178X165 P+0.792 AE

b strain ' in our in bax 2 = D2 = 1.78x105P +0.792, 1020 xót Ii - 2000 1178x105P +0.792 = 1020x17642000 1178x105 P = 2104-0.792 P= 70112:36 N D P-70.12 KN Pi = P_P2 = 70.12 - 0.322x70.12 Pi= 47.54 KN elongation of ball due to P,= PIXL= 47.54X18X1160 " A, E 226X105 Dip= 2.44 mm elongation of bur 0 due to Temperature At=LADJ Ant= 1160X 18 X176x22=046 mm elongation of bar = Alptat = 2144 toile =2igum

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