CE120_HW4Solutions - UNIVERSITY OF CALIFORNIA BERKELEY Department of Civil and Environmental Engineering Instructor J P Moehle Spring 2015 CE 120

CE120_HW4Solutions - UNIVERSITY OF CALIFORNIA BERKELEY...

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UNIVERSITY OF CALIFORNIA, BERKELEY Spring 201 5 Department of Civil and Environmental Engineering Instructor: J. P. Moehle CE 120 - Structural Engineering Solutions of Assignment No. 4 Due: 2 0 February 2013 Problem-1 Solution: Determine (a) the reactions at the supports, (b) the cable sag at joints B and E, (c) the tension force in each segment of the cable, and (d) the total length of the cable shown to the right. At the end of the problem solution, draw a free body diagram showing the results of (a), (b), and (c) clearly on the diagram, with the cable length written beneath the diagram he 75k T BC 30k a) Find Reactions: + M a =0; 30*20+30*40+30*60+30*80-R3*100 =0 R3=60k + ∑Fy=0; R2+R3 -30-30-30-30=0 R1=60k Taking a cut at C (Fig 1) + M c =0; R1*40+R2*24-30*20=0 R2=-75k=75k + ∑Fx=0; R2+R4 =0 R4=75k R1 R2 T CD b)Sag at B and E: Taking a cut at B (Fig2) + M B =0; 60*20-75*hb=0 hb =16ft Taking a cut at E (Fig3) + M E =0; -60*20+75*he =0 he =16ft hb 60k 75k T DE 60k 75k 60k 75k T CD C)Tension Forces T AB =sqrt(60 2 +75 2 )=96k T BC =sqrt(30 2 +75 2 )=80.78k (fig 2) T CD =sqrt(0 2 +75 2 )=75k (fig 4) T DE
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