written 6.6 years ago by | • modified 6.6 years ago |
Subject: Structural Analysis II
Topic: Deflection of Statically Determinate Structures
Difficulty: Medium / High
written 6.6 years ago by | • modified 6.6 years ago |
Subject: Structural Analysis II
Topic: Deflection of Statically Determinate Structures
Difficulty: Medium / High
written 6.6 years ago by | • modified 6.6 years ago |
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:
Applying C.O.E:
∑mD=0
−1×3−MD=0
MD=3kN.m
∑Fy=0
vD=0
∑FX=0
−1+HD=0
HD=1kN
Consider part 'A B':
Consider part BC:-
Consider part CD:-
BMc=1kNm_
BMD=−3kNm_
(ii)Deflection at A:-[considering effect of axial forces]
(a)member AB_:-(10∘c→30∘c)
.
tc=
Δt=30∘c−10∘c=20∘c
Δth=200.2=100
ˉA=12×1×1=0.5m2
ˉN=0
b)member BC_:(10∘c→40∘c)
tc=10+(40−102)=25∘c
Δt=40−10=30∘c
Δth=300.2=150
ˉA=1×4=4m2
ˉN=1kN
C)member Cd:_(10∘c→30∘c)
tc=10+(30−102)=20∘c
Δt=30−10=20∘c
Δth=200.2=100
ˉA=(−12×3×3+12×1×1)=−4m2
ˉN=0
Using Mohr's Equation
∑¯Pj∫j=αt∑[Δt.ˉAh+tcˉNL]←formula
1.∫A=12×10−6[(100×0.5+20×0×1)AB+(150×4+25×1×4)BC+(−100×4+20×0×4)CD]
∫A=12×10−6[(50)+(700)+(−400)]
∫A=12×10−6[350]
∫A=4.2×10−3m
∫A=4.2mm(←)
(iii)Deflcetion at A(Neglecting axial Forces)_:
∑ˉPj∫j=αt∑[Δth.ˉA]
1.∫A=12×10−6[(100×0.5)+(150×4)+(100×(−4))]
∫A=12×106(250)
∫A=3×10−3m
∫A=3mm(←)