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Find the vertical deflecttions of the Joint C of the loaded truss shown in fig. The cls area of members CD & DE are each 250mm2 & those of the other members are each 1250mm2.TakeE=200 kN/mm2

Subject: Structural Analysis 1

Topic: Deflection of Beams using Energy Method

Difficulty: High

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1 Answer
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Analysis of truss due to given loading:

We have,

AC=2cos(30)=23 mMA=0 gives(+ve)He×2=40×23He=403 kNVA=40 kNHa=403 kN


P-Analysis

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1. Joint C:

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FY=0(+ve)40PCDsin30=0PCD=80 kNPCD=80 kN (C)FX=0(+ve)PCDcos30PCB=0(80cos30)PCB=0PCB=403 kN (T)


2. Joint B:

PBD=0; PBA=403 kN (T)


3. Joint D:

PDA=0; PDE=80 kN (C)


4. Joint E

Resolving vertically

PCA=80sin30PCA=40 kN (T)

To find the vertical deflection at C

  • Remove the given load system & apply a vertical load of 1 kN at C


K-Analysis:

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Solve directly.

Member P(kN) K(kN) l(kN) A(mm2) PklA
AB 403 3 10003 1250 166.3
BC 403 3 10003 1250 166.3
CD 80 2 2000 2500 128
DE 80 2 2000 2500 128
AE -40 -1 2000 1250 64
AD 0 0 2000 1250 0
BD 0 0 1000 1250 0
= 652.6

Vertical deflection of C=y=PklAE=652.6200=3.263 mm_ Ans._

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