Question

Question 3 In Figure Q3, the plane truss ABCDEHGFA forms part of the supports of a crane on an offshore oil platform. The crane exerts two forces, each of magnitude 122.5-kN, and acting vertically downwards on truss joints B and D. Determine the magnitudes of the axial forces in members AB, BC, EH and GH of the truss, and state whether they are in equilibrium or not. 1.8m 2.2 m F G H 3.4 m 3.4 m Figure Q3

Answer 1

122.5kn 122.5KN Jo B miny 4 14 piano k 3.um 3.um 3.um. 3.um Due to Symmetry cu axial forle=0 4906 E AB=ED = 33 Fu = CH. HE= AF = 27.8 0 NA THE - 2x122.5kel HAINE (symmetry) NA = NE = 122-5kn NA+ AB samo, + AF Sino2=0 AB A Blaso, & AF Cos=0 0.944 122.5+ A BxO. 761+ AF Xo66 = 0 ABX 0.648 + AFXO.838=0. AB=-359.93 KNG AF = 278.32KN. u ATE" IF BF = AF Sindz = 151-58 KN F 4 - AF COSO2 I 233.G1KN FY. AFE

At "B' BC AB By. BF > BL+ Bucose + ABLoso, = 0 BF + Busind + AB Sino, = 0. =) ABsind, t BF Bu- - 262.7RN sing V BC=-(AB Coso, & Bucosa) 0.89 KN =) AB= -359.93KN = DE & compression - tenile AF = 278.32KN = HE B = 151.58KN = DH = CH. Fu= 233-41kn B4 = 262.7KH = GD. BC = 0.89 KN

Yes , they are in equilibrium as no motion is observed .