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Find the Horizontal and Vertical deflection at Point E in the given Truss

Find the vertical and horizontal deflections of the joint E of the truss shown in figure.truss Area of each horizontal member = 1200 mm^2; Area of other members = 1500 mm². Modulus of elasticity= 200KN/mm^2

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Given Data:-

  • A_horizontal =1200 mm2
  • Aother member =1500 mm2
  • Modulus of Elasticity, E=200 kN/mm2
  • V=0

RA+RD=180kN

  • MA=0

(RD×6)+(120×1.5)+(60×4.5)=0

  • RD=75KN
  • RA=105KN
  • FAB=RAcosec60=105×23=121.24kN (C)
  • FAE=RAcot60=105×13=60.62KN(T)
  • FCD=RDcosec60=75×23=86.60KN(C)
  • FED=RDcot60=75×13=43.30KN(T)

Joint E

  • FBEsin60+FEsin60=0

  • FBE=FEC

  • FBEcos60FCEcos60+FEDFAE=0

2FBEcos60+43.3060.62=0 FBE=17.32KN (C)

  • FCE=17.32kN(T),

Joint B ΣH=0FBAcos60+FBEcos60+FBC=0FBC=51.95kN (C) 

  • K-Value(Vertical)

Vertical image

  • K-Value (Horizontal)

Horizontal

 Member P(KN)KVKHLAE×107δV=PKVLAEδH=PKHLAEAB121.240.58303300.7060BC51.950.603240.3900CD86.600.58303300.5050AE60.620.313240.2270.7ED43.300.303240.1620BE17.320.58303300.10CE17.320.5830330+0.10 Hence,

  • Vertical Deflection = 1.99mm
  • Horizontal Deflection = 0.76mm
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