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Determine the degree of static and kinematic indeterminacy of the following structure

Subject*: Structural Analysis II

Topic: Flexibility Method

Difficulty: Medium / High

1 Answer
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63views

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DS

Ds=Dse+Ds;

enter image description here

=(53)(27)

=21

=1

Dk

Dk=4

Dsi=0[For beam D_{si}=0]

Ds=Dse+Dsd

=1+0=1

Ds=1

enter image description here

Ds

Ds=Dse+Dsi

Dse=r3(m1)(m1)

=63(21)(21)

=311=21=1

Dsi=0[For beam D_{si}=0]

Ds=1+0=1

Ds=1

Dk

Dk=6

enter image description here

Ds

Ds=Dse+Dsi

Dse=r3(m1)

53(21)

21

=1

Dsi=0

Ds=1+0=1

Ds=1

Dk

Dk=5

enter image description here

Ds

Ds=Dse+Dsi

Dse=r3

=73

=4

Dsi=0

Ds=4+0

Ds=4

Dk

Dk=1

enter image description here

Ds

Ds=Dse+Dsi

Dse=r3(m1)

=63(21)

=31

=2 Dsi=0

Ds=2+0

=2

Ds=2

Dk

Dk=5

enter image description here

Ds

Ds=Dse+Dsi

Dse=r3(m1)

=63(21)

=31

=2

Dsi=0

Ds=2+0

Ds=2

Dk

enter image description here

Ds

Ds=Dse+Dsi

Dse=r3

=53=2

Dsi=3×c[c=closed loop]

=3×3

=9

Ds=9+2=11

Ds=11

Dk

Dk=13

enter image description here

Dse=r3=63=3

Dsi=3×c=3×4=12

Ds=3+12=5

Ds=15

Dk

Dk=15

enter image description here

Ds

Ds=Dse+Dsi

Dse=r3=63=3

Dsi=3×c

=3×2=6

Ds=3+6=9

Ds=9

Dk

Dk=9

enter image description here

Ds=Dse+Dsi

Dse=r3=83=5

Dsi=3×c=3×2=6

Ds=5+6=11

Ds=11

Dk

Dk=9

enter image description here

Ds

Ds=Dse+Dsi

Dse=r3=30

Dsi=3×c=3×1=3

Ds=0+3

Ds=3

Dk

Dk=9

enter image description here

Ds

Ds=Dse+Dsi

Dse=r3(m1)

=63(31)

=32

=1

Dsi=3×c

=3×6=18

=32

=1

Dsi=3×c

=3×6=18

Ds=1+18=19

Ds=19

Dk

Dk=20

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Ds

Ds=Dse+Dsi

Dse=r3=43=1

Dsi=m2j3 (formula)

=102(6)3

=10123

=109

=1

Ds=2

Ds=1+1=2

Dk=2jr

=2×64

=124

=8

Dk=8

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Ds

Ds=Dse+Dsi

Dse=r3=33=0

Dsi=m2j3

=112(6)3

=11123

=119

=2

Ds=2

Dk

Dk=2jr

=2×63

=123

Dk=9

enter image description here

Ds=Dse+Dsi

Dse=r3=53=2

Dsi=M2j3

=8(2×5)3

=8103

=87

=1

Ds=2+1=3

Ds=3

Dk

Dk=2jr

=2×55

=105

=5

Dk=5

enter image description here

Ds

Dse=r3=431

Dsi=m2j3

=5(2×4)3

=583

=55=0

Ds=1+0

Ds=1

Dk

Dk=2jr

=2×44

=84

Dk=4

enter image description here

Dse=r3=43=1

Dsi=m2j3

=152×83

=15163

=1513

=2

Ds=1+2=3

Ds=3

Dk=2jr

=2×84

=164

=12

Dk=12

enter image description here

Ds

Ds=Dse+Dsi

Dse=r3

=73=4

Dsi=3×c=3×0=0

Ds=4+0=4

Ds=4

Dk

Dk=2

enter image description here

Ds

Ds=Dse+Dsi

Dse=r3=43=1

Dsi3×c=0

Ds=1+0

Ds=1

Dk

Dk=4

enter image description here

Ds

Ds=Dse+Dsi

Dse=r3=33=0

Dsi=3×c=3×0=0

Ds=0+0=0

Ds=0

Dk

Dk=3

enter image description here

Ds

Ds=Dse+Dsi

Dse=r3=93=6

Dsi=3×c=0

Ds=6

Dk

Dk=4

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