0
1.6kviews
For rigid jointed frame subjected to temperature variation in fig.Determine the Horizontal deflection at A. Assume α=12×106/oc,depth of member as 200mm.Neglect effect arial force

enter image description here

Subject: Structural Analysis II

Topic: Deflection of Statically Determinate Structures

Difficulty: Medium / High

1 Answer
0
8views

To find the horizontal deflection at A, apply fictitious or Dummy force P=1kN horizontal towards left.

(i)Axial force¯(N) and Bending moment ¯(M)diagram: enter image description here

Applying C.O.E:

mD=0 enter image description here

1×3MD=0

MD=3kN.m

Fy=0enter image description here

vD=0

FX=0enter image description here

1+HD=0

HD=1kN

Consider part 'A B':

enter image description here

Consider part BC:-

enter image description here

Consider part CD:-

enter image description here

BMc=1kNm_

BMD=3kNm_

(ii)Deflection at A:-[considering effect of axial forces]

(a)member AB_:-(10c30c) . tc=enter image description here

Δt=30c10c=20c

Δth=200.2=100

ˉA=12×1×1=0.5m2

ˉN=0

b)member BC_:(10c40c)

tc=10+(40102)=25c

Δt=4010=30c

Δth=300.2=150

ˉA=1×4=4m2

ˉN=1kN

C)member Cd:_(10c30c)

tc=10+(30102)=20c

Δt=3010=20c

Δth=200.2=100

ˉA=(12×3×3+12×1×1)=4m2

ˉN=0

Using Mohr's Equation

¯Pjj=αt[Δt.ˉAh+tcˉNL]formula

1.A=12×106[(100×0.5+20×0×1)AB+(150×4+25×1×4)BC+(100×4+20×0×4)CD]

A=12×106[(50)+(700)+(400)]

A=12×106[350]

A=4.2×103m

A=4.2mm()

(iii)Deflcetion at A(Neglecting axial Forces)_:

ˉPjj=αt[Δth.ˉA]

1.A=12×106[(100×0.5)+(150×4)+(100×(4))]

A=12×106(250)

A=3×103m

A=3mm()

Please log in to add an answer.