100%(4)4 out of 4 people found this document helpful
This preview shows page 1 - 2 out of 4 pages.
UNIVERSITY OF CALIFORNIA, BERKELEYSpring 2015Department of Civil and Environmental EngineeringInstructor: J. P. MoehleCE 120 - Structural EngineeringSolutions of Assignment No. 4Due: 20February 2013Problem-1Solution:Determine (a) the reactions at the supports, (b) the cable sag at joints B and E, (c) the tension force in each segment ofthe cable, and (d) the total length of the cable shown to the right. At the end of the problem solution, draw a free bodydiagram showing the results of (a), (b), and (c) clearly on the diagram, with the cable length written beneath thediagramhe75kTBC30ka)Find Reactions:+∑Ma=0;30*20+30*40+30*60+30*80-R3*100 =0R3=60k+∑Fy=0;R2+R3-30-30-30-30=0R1=60kTaking a cut at C (Fig 1)+∑Mc=0;R1*40+R2*24-30*20=0R2=-75k=75k+∑Fx=0;R2+R4=0R4=75kR1R2TCDb)Sag at B and E: Taking a cut at B (Fig2)+∑MB=0;60*20-75*hb=0hb =16ftTaking a cut at E (Fig3)+∑ME=0;-60*20+75*he =0he =16fthb60k75kTDE60k75k60k75kTCDC)Tension ForcesTAB=sqrt(602+752)=96kTBC=sqrt(302+752)=80.78k (fig 2)TCD=sqrt(02+752)=75k (fig 4)TDE